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ISBN print: 978-3-0364-0991-7
ISBN eBook: 978-3-0364-1991-6
DOI book: 10.4028/b-Sr819d
© 2026 Trans Tech Publications Ltd, All Rights Reserved

Incremental and Sheet Metal Forming

Edited by
Dr. Giuseppina Ambrogio
Prof. Mihaela Banu

Incremental and Sheet Metal Forming

Special topic volume with invited peer-reviewed papers only

Edited by
Dr. Giuseppina Ambrogio and Prof. Mihaela Banu

Scientific.Net

Copyright © 2026 Trans Tech Publications Ltd, Switzerland

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp -1-0

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Accepted:
2026-04-09

Online:
2026-04-16

Preface

The original version of this paper is available on https://www.scientific.net/SSP.389.-1.pdf

This issue focuses on contributions that detail new developments and enhance the understanding of incremental and sheet material forming processes. The topics of interest include (but are not limited to) novel process designs, in-process measurement techniques, innovative tooling, methods for the analysis and modelling of friction phenomena and methods for the optimization, robust design and control of incremental and sheet forming processes. It is expected to address the following topics related to incremental forming and sheet material forming:

Development of novel incremental forming strategies

Hybrid processes combining sheet forming with additive or subtractive manufacturing

Advanced forming techniques for lightweight alloys, composites, and high-strength steels

Flexible forming systems for customized or low-volume production

Adaptive, modular, and reconfigurable tooling for flexible forming

Design and materials for forming tools to improve life and surface finish

Multi-axis machine kinematics and robotic forming platforms

Cooling, lubrication, and surface engineering for tooling performance

Finite element models for incremental and sheet forming processes

Multi-physics simulations including thermo-mechanical and tribological effects

Use of AI/ML in predictive modeling and defect detection

Digital twins and virtual commissioning of forming lines

Multi-objective optimization for formability, accuracy, and cost

Statistical and machine learning approaches for robust process design

Real-time feedback control and adaptive process adjustment

Editors

The original version of this paper is available on https://www.scientific.net/SSP.389.-1.pdf

Giuseppina Ambrogio
Mihaela Banu

University of Calabria
University of Michigan

Co-editors

The original version of this paper is available on https://www.scientific.net/SSP.389.-1.pdf

Joost Duflou
Carpoforo Vallelano
Torgeir Wello
Beatriz Silva
Ihab Ragai

Katholieke University of Leuven
Universidad de Sevilla
Norwegian University of Science and Technology
Universy of Lisbon
Penn State University

Table of Contents

Preface

Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges

Jan Erik Rath, Doran Nettig, Thorsten Schüppstuhl

Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Doran Nettig, Jan Erik Rath, Johann Kipping, Thorsten Schüppstuhl

Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

Richard Walther, Linda Fleischer, Maik Linnemann, Verena Psyk, V. Kräusel

Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Elizabeth Mamros, Austin Clark, Philip Barnett, Ihab Ragai, Shaffer Derek, Kristofer Laser Jr

Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Donghoon Han, Donghyuk Cho, Seik An, Jeong Whan Yoon

Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Romina Conte, Stefano Trimarchi, Francesco Gagliardi, Luigi De Napoli, Giuseppina Ambrogio

Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Franz Reuther, Verena Psyk, Verena Kräusel

On the Surface Quality of Incrementally Formed Niobium Sheets

Antonio Formisano, Antonello Astarita, Marco Garlaschè, Umberto Prisco, Fabio Scherillo, Massimo Durante

Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Mattia Dal Maso, Enrico Simonetto, Andrea Ghiotti, Stefania Bruschi, Stefano Filippi, Lukas Hauser, Mathias Liewald

Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Jan Sommer, Lars Uhlmann, Max Meerkamp, Tim Herrig, Thomas Bergs

Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Lasse Langstädtler, Andreas Tausendfreund, Christian Schenck

Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

Francesco Borda, Serafino Caruso, Luigino Filice

Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

Jiyoung Moon, Alexander Frigge, Philipp Niemietz, Tim Herrig, Thomas Bergs

Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment

João P.G. Magrinho, Angela Cusanno, Miguel Jesus, Antonio Piccininni, Gianfranco Palumbo, Maria Beatriz Silva

Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets

Karl J. Tilly, Emad Scharifi, Junhe Lian

Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Angela Cusanno, João P.G. Magrinho, Antonio Piccininni, Pasquale Guglielmi, Donato Sorgente, Gianfranco Palumbo, Maria Beatriz Silva

Influence of Process Parameter Variations on Stamping-Bending Component Quality

Maximilian Buchner, M. Damaškovič, L. Koller, Wolfram Volk, M. Althoff, Christoph Hartmann

Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Max Gröbel, Karl J. Tilly, Emad Scharifi, Junhe Lian

Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Zixuan Mu, Youngrok Lee, Jeffrey Abell, Alan Taub, Mihaela Banu

Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Maziar Khademi, Peng Neo Zhang, Michael P. Pereira, Matthias Weiss

Experimental and Numerical Investigation of AA6061 Tube Flowformability

Katia Mocellin, Nagasai Meghana Rani Kauta, Pierre Olivier Bouchard

Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Bernd Arno Behrens, Sven Hübner, Ulrich Holländer, André Langohr, Alexander Schnettger, Henrik Depke, Lorenz Albracht

Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Bernd Arno Behrens, Sven Hübner, Simon Pauli, Henner Rüschkamp, Simon Kimmina, Denis Fink, Behdad Yaaalimadad

Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Elizabeth Mamros, Derek Shaffer, Ihab Ragai, Austin Clark

Reducing the Uncertainty in Flow Forming of Metastable Austenites

Lukas Kersting, Mustafa Koyuncu, Bahman Arian, Julian Rozo Vasquez, Ansgar Trächtler, Werner Homberg, Frank Walther

Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Ali Beigzadeh, Enrico Simonetto, Andrea Ghiotti, Stefania Bruschi

Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

Mehmet Okan Görtan, Ümit Türkmen, İlker Kuzucu, Elif Çivisöker, Rahman Ervan

Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Viktor Böhm, Thomas Spörer, Michael Ott, Georg Fuchs, Paul Richter, Jeremias Tschannerl, Linghao Kong, Ahmed Ismail, Sebastian Münstermann, Boris Lohmann, Wolfram Volk

Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Ecem Ozden, Oleksandr Kurtov, Hans Vanhove, Joost R. Duflou

Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Daria Gelbich, Frank Schweinshaupt, Thomas Stoel, Philipp Niemietz, Tim Herrig, Thomas Bergs

Keywords Index

Authors Index

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 1-9

doi: 10.4028/p-u5oc0K

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-19

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-16

Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

Jan-Erik Rath 1,a*, Doran Nettig 1, b and Thorsten Schüppstuhl 1,c

1 Hamburg University of Technology, Institute of Aircraft Production Technology, Denickestr. 17, 21073 Hamburg, Germany

a*jan-erik.rath@tuhh.de, b  doran.nettig@tuhh.de, c  schueppstuhl@tuhh.de

*corresponding author

Keywords: incremental sheet forming, composite, fiber reinforced plastic, free forming, robot.

Abstract

Fiber-reinforced thermoplastics (FRTP) offer high strength-to-weight ratios as well as weldability and recyclability, making them attractive for lightweight applications. Conventional thermoforming of continuous FRTP, however, requires part-specific molds, limiting economic viability for prototypes, individual parts, and small series. This study investigates a robotic hot double-sided incremental forming (DSIF) process developed for dieless, flexible forming of continuous FRTP sheets together with metal dummy sheets. Five different generic demonstrator parts with varying wall angles, degrees of symmetry, forming depths, and sizes were formed to assess process capability. Results demonstrate that typical defects such as fabric wrinkling and deconsolidation can be successfully avoided, and that the geometric accuracy achievable is comparable to that of metal DSIF. Challenges exist in forming larger parts due to the failure of the employed metal dummy sheets.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

The utilization of fiber-reinforced plastics (FRPs) in high-performance applications across aerospace, automotive, sports, and medical sectors continues to show significant growth [1]. Among the various reinforcement architectures, woven fabrics made from glass and carbon fiber are common as they offer a good compromise of mechanical reinforcement, handling properties, and drapability, alongside broad availability [2]. Compared to traditional thermosets, thermoplastic matrices are increasingly preferred, attributed to their enhanced ductility, damage tolerance, and inherent capabilities for welding, reshaping, and recycling [1,3]. The high viscosity of thermoplastics favors the use of fully impregnated and consolidated organosheets as semi-finished products. These are formed using thermoforming techniques that require part-specific molds, which are associated with significant tooling costs and long lead times until the first part is produced. Thus, prototype, individual part, and small-scale production are, in many cases, uneconomical [4,5].

Incremental sheet forming (ISF) could be a flexible, dieless manufacturing alternative. In this process, a simple standard tool traverses a numerically controlled trajectory, locally deforming a clamped sheet material [6]. Variants of ISF include single-point (SPIF), two-point (TPIF), and double-sided incremental forming (DSIF), with DSIF emerging as the most promising configuration in terms of achievable formability, flexibility, and geometric accuracy [7,8]. While ISF is wellestablished for metals and partially adapted for thermoplastics [9,10], its transfer to continuous fiberreinforced thermoplastic (FRTP) composites is associated with some unique challenges and is still at an early stage of research [5,11].

The anisotropic, inextensible nature of continuous woven fibers in FRTPs requires fabric draping governed by bending, in-plane shear, and intra-ply sliding as deformation mechanisms, rather than the stretch-dominated modes prevalent in metals and polymers [12,13]. Consequently, rigid clamping of the organosheet is not possible without fiber breakage [11]. Therefore, researchers such as Al Obaidi et al. [5] adopted a "floating" clamping configuration, in which the organosheet is interposed between two metallic dummy sheets, separated by PTFE sheets, allowing relative movement during SPIF. During the process, the thermoplastic matrix must be heated to above its glass-transition or
melting temperature to allow formability, which was realized by clamping the sheet layup on top of an isolated chamber heated by hot air blowers [5,14], a thermal radiation plate [11], or an infrared lamp [15,16]. Also, the utilization of a heated and pressurized fluid was proposed [17]. Most of those SPIF approaches employed elementary z-level or spiral toolpath strategies known from metal ISF, not considering the draping behavior of FRTP. Consequently, defects such as wrinkling, cracking, and delamination occurred, and forming depth and wall angles were limited [5,11,15,16]. Drapeaware SPIF toolpaths proposed by Rath and Schüppstuhl [14] have shown promise in suppressing wrinkling and enhancing dimensional accuracy. However, the separation of the metal dummy sheets due to unwanted global deformation remained problematic when the distance between the clamped edge and the formed geometry was high in the SPIF process [14].

Therefore, the authors developed and successfully implemented the first DSIF system tailored to the forming of FRTP, offering a force-controlled flexible local support on the back side of the layup [18]. This setup, employing two synchronized industrial robots, is briefly described in the next section. Forming experiments are conducted with woven fiber reinforced organosheets, producing five different demonstrator parts, one of which in three different sizes. Results are analyzed qualitatively for wrinkling and deconsolidation defects, and geometric accuracy is quantified.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

Hot DSIF Setup.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

The setup for hot DSIF of FRTPs is depicted in Fig. 1 and described in detail in [18]. It relies on two KUKA KR 300 industrial robots with handling capacities of 300 kg , mounted on a steel platform on opposing sides of a modular clamping frame. The frame carries a stainless-steel base plate which is designed to secure either sheet layups of 695×695 mm2 or a reduction module for sheet layups of 350×350 mm2 with toggle clamps. The layups, in which the FRTP is quasi-floatingly interposed between two metal dummy sheets, are prepared on a separate layup table and clamped via peripheral clamping strips with screws. After securing a clamped layup on the base plate or the reduction module, the sheets are heated globally by a PID-controlled closed convective oven system. While the layup and base plate constitute one side of the oven, the other is comprised of a flexible insulation material suspended between the base plate and the flange of the support robot, allowing the necessary tool movement within the enclosed hot area. A water-cooled cooling coupler decouples the six-axis force-torque measurement cell (Schunk FTN-Omega 160) mounted on the robot flange from the hot side of the support tool. Tools with hemispherical tips and different diameters can be attached via a collet system. The main forming tool is designed similarly but employs a Schunk FTN-Omega 191 force-torque cell for higher loads and does not require cooling.

[picture]

Fig. 1. Hot DSIF Setup for FRTP forming - a) front view with reduction module and clamped sheet layup, b) back view with flexible insulation material (right), c) illustration of sheet layup.

Fig. 1. Hot DSIF Setup for FRTP forming - a) front view with reduction module and clamped sheet layup, b) back view with flexible insulation material (right), c) illustration of sheet layup.

In operation, the robot carrying the main (guiding) forming tool is position-controlled and follows the programmed toolpath. The motion of the support robot is geometrically coupled to that of the guiding robot via KUKA RoboTeam. The time-synchronized relative-motion commands of the support robot are calculated as offsets from the center point of the main tool along the normal of the formed surface. To maintain the target normal force, an implicit PD-force controller continually adjusts the tool separation based on load-cell feedback [18].

Materials.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

Styrene-acrylonitrile (SAN) organosheets with two layers of twill-woven carbon fibers with a basis weight of 245 g/m2 and a resulting fiber-volume-content of 47% at 0.6 mm thickness were cut to three different sizes: 200×200 mm2, denoted as S,300×300 mm2(M), and 615×615 mm2( L). Layups were prepared using DC04 steel sheets with a thickness of 0.7 mm on the front side and aluminum EN AW-1050A H111 sheets with a thickness of 1 mm on the back (supporting tool) side. Organosheet sizes S and M were interposed between metal sheets of 350×350 mm2, and L between metal sheets of 695×695 mm2. Fiber orientations were aligned with the sheet edges. PTFE sheets of 0.05 mm thickness and the same sizes as the metal dummy sheets were used to separate metal and organosheets and to allow the relative movement with a low coefficient of friction. To keep the organosheet in its central position, it was attached to the underlying PTFE sheet with polyimide tape in its corners. Graphite spray was applied to the outside faces of the metal dummy sheets to reduce friction with the tooltips. The layup is illustrated in Fig. 1 c ).

Forming Experiments.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

To investigate the capabilities of the process, five different demonstrator geometries, D1-D5, described in Table 1, were produced. In addition to a cone, which is a standard geometry commonly used in the ISF state of the art, four more complex geometries were designed to address various process challenges. These were multi-curved surface geometries that varied in terms of degree of symmetry, maximum wall angle, and minimum corner radius. In addition, one of the geometries was produced in three different sizes, S-L, to investigate the scalability of the process. The development of the applied processing strategy will be described in detail in a separate publication.

Table 1. Demonstrator geometries with geometric data.

Name | Description | Size | Depth | Wall Angle | Forming Strategy
D1-S | Cone | Ø 160 mm | 40 mm | 40° | S12-S12-S9-D3-S3-S0
D2-S | Cone with varying | Ø 160 mm | 40 mm | max 60° | S12-S12-S9-D3-S3-S0
D2-M | wall angle | Ø 220 mm | 50 mm | max 60° | S12-S12-S9-S9-D3-S3-S0
D2-L |  | Ø 500 mm | 70 mm | max 60° | S33-S30-D3-S3-S0
D3-S | Cone with eccentric tip | Ø 160 mm | 25 mm | max 28.4° | S9-S9-D3-S3-S0
D4-S | Square pyramid with twisted circular tip | 180 × 180 mm² | 44 mm | 35° | S12-S12-S12-D3-S3-S0
D5-S | Square pyramid with varying wall angle | 160 × 160 mm² | 50 mm | 40-60° | S12-S15-S15-D3-S3-S0

After preparing, clamping, and securing the layup, the air inside the oven chamber was heated to the target temperature of 180∘C, measured with a type K thermocouple at mid-height next to the sheet layup. During heating, the clamping force was kept low to allow the thermal expansion of the metal sheets. After reaching the target temperature, the clamping force was increased. Forming was then conducted with hemispherical hardened steel 1.2210 tooltips with 20 mm diameter, while the temperature was maintained. The support force was set to 200 N and the tool speed to 20 mm/s.

Based on stl meshes of the target geometries, toolpaths were generated by a custom path planning digital process chain, which will be thoroughly described in another publication. In the first step, the target geometry is divided into multiple intermediate shapes using linear height interpolation to improve formability. The approximate maximum depth increase in each intermediate shape is noted next to the utilized toolpath strategy designation in Table 1. For each shape, toolpaths can be
generated according to two different strategies. The first is a spiral contour toolpath strategy, commonly used for metal ISF, with a constant scallop height of 2 mm . This toolpath strategy is denoted S in Table 1 and is depicted in Fig. 2 b). The second strategy is a refinement of the fiberfollowing draping strategy that showed promising results in suppressing wrinkles in the SPIF experiments in [14]. It builds upon an approximation of the fiber orientations in the target shape. Starting with two central orthogonal paths following the initial 0/90∘ fiber orientations, the shape is covered inside outwards in parallel lines with the same path distance of 2 mm , which are connected to a continuous path. This strategy, denoted D in Table 1, is depicted in Fig. 2 c).

[picture]

Fig. 2. a) Geometry D5 with b) spiral toolpaths " S " and c) draping toolpaths " D ".

Fig. 2. a) Geometry D5 with b) spiral toolpaths " S " and c) draping toolpaths " D ".

As the draping toolpaths are associated with high forming forces, especially in the deepest points of the shape, the step depth is limited, and a large number of intermediate shapes would be required. Therefore, as visible in Table 1, the draping toolpath strategy D was used only for the second-to-last intermediate shape, while all other intermediate shapes were formed with the spiral toolpath S. The toolpath of the last intermediate shape was repeated after deactivating the heating, so that a certain consolidation force was applied during cooling of the FRTP. After forming was finished and the oven temperature was below 40∘C, the layup was removed from the setup, declamped, and the formed part was separated from the metal and PTFE sheets.

Results

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

All geometries were successfully processed by the digital process chain, generating toolpaths for each intermediate shape and post-processing them to executable code for both robots. The forming process could be finished for all parts but D2-L, the cone with varying wall angle scaled to the biggest possible size in the current setup. In this case, the front steel sheet failed by tearing at a depth of 60 mm , towards the end of forming the second intermediate shape, as shown in Fig. 5 b).

The times for preparing the layup, heating, forming, cooling, and dismantling accumulated to approximately 3 hours for size S geometries, 4.5 hours for the size M geometry, and would have been approximately 10 hours for the size L geometry. The formed parts were analyzed qualitatively regarding possible wrinkling, tearing, or surface defects in the organosheets. Furthermore, a GOM ATOS 3D scanner was used to capture 3D scans of the formed parts, which were then compared to the target geometry by calculating maximum deviations after iterative closest point matching. Finally, a cross-section of part D1-S was prepared and analyzed under an optical microscope, comparing it to virgin material.

Qualitative Analysis.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

The results of the demonstrator parts are shown in Fig. 3 and Fig. 5. It can be seen that all small and medium-sized geometries were successfully manufactured, including the non-rotationally symmetrical (D3, D4, D5) and off-center (D3) geometries, the comparably high wall angles up to 60∘ (D2, D5), and small corner radii of 12 mm (D5). No wrinkling can be observed in the woven fabric in the formed areas, indicating successful fabric draping with visible shear introduced. The coverage of the surface with matrix appears relatively uniform, also in flat areas such as the tips of the cone D1, see Fig. 4, and the pyramid D5. The typical forming defects matrix migration and accumulation, as well as exposed fibers or dry spots, indicating deconsolidation, could largely be avoided. In contrast, the remaining areas of the organosheets surrounding the formed geometry, which would be
trimmed in a postprocessing step, show slight fabric wrinkling, uneven matrix distribution, matrix flaking, and possible dry spots, highlighted as C in Fig. 4. This is due to the fact that they did not experience any tool passes and therefore also no consolidation force from the tool pressure. However, local surface defects can also be observed in the formed areas due to wrinkling of the PTFE foils, which led to imprints in the matrix of the composite, see detail B in Fig. 4. Moreover, particularly the flat tips of the cones D1-S and D2-M show slight grooves of a characteristic spiral shape, corresponding to the tool paths, see detail A in Fig. 4.

In the largest part, D2-L, which could not be formed to the final shape, significant fabric wrinkling can be observed in Fig. 5 a). This is particularly visible in the diagonals of the sheet, where most shear would be necessary. These wrinkles are likely to be attributed to the absence of a drape-aware toolpath, as the experiment had to be terminated before the third intermediate shape, which would have been formed with the draping strategy. Moreover, the comparably large deformations necessary in each intermediate shape, combined with the larger size of the metal sheets, led to a high global deformation and a separation of the metal sheets, leaving room for wrinkles.

[picture]

Fig. 3. Successfully formed demonstrator parts D1-D5 in sizes S and M.

Fig. 3. Successfully formed demonstrator parts D1-D5 in sizes S and M.

[picture]

Fig. 4. Formed cone D1-S with generally satisfactory surface quality, but grooves of the tool in the tip (detail A), and imprints of wrinkles of PTFE foil in the matrix (detail B). The surrounding area, which was not formed, shows signs of deconsolidation and wrinkles (C).

Fig. 4. Formed cone D1-S with generally satisfactory surface quality, but grooves of the tool in the tip (detail A), and imprints of wrinkles of PTFE foil in the matrix (detail B). The surrounding area, which was not formed, shows signs of deconsolidation and wrinkles (C).

[picture]

Fig. 5. a) Part D2 in size L, not successfully formed to completion, b) tears in the steel sheet leading to the abortion of the forming process during forming D2-L.

Fig. 5. a) Part D2 in size L, not successfully formed to completion, b) tears in the steel sheet leading to the abortion of the forming process during forming D2-L.

Geometric Accuracy.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

The 3D-scanned surfaces of the successfully formed geometries are shown in Fig. 6, with the color scale indicating the signed distance to the target surfaces. The majority of the surface areas lie within a tolerance of ±1 mm. Underforming, indicated by negative values and blue color, appears mostly around the tips of the geometries and along the edges at the transitions between different wall angles in geometries D2 and D5. The corresponding maximum deviation is in a range of 1.55 to 1.82 mm for all geometries except the cones with varying wall angles D2, standing out with a maximum deviation of 2.71 and 2.84 mm at the tip. Meanwhile, a global bending-induced deformation of the sheet layup caused bulging around the base region, leading to overforming near the flange-wall transition, which is indicated by positive values and red color. It is particularly prominent in parts D5 and D2-M, with maximum deviations of 3.35 mm and 2.49 mm , respectively. In the asymmetrical part D3, this effect is pronounced on the side with a higher wall angle. Comparing the two D2 sizes, size M shows slightly larger inaccuracies than size S, with the extent of overforming particularly pronounced in the larger part.

[picture]

Fig. 6. 3D Scans of the formed geometries, colors indicating the signed distance to the target shapes; a) cone, b) cone with varying wall angle in size S and c) size M,d ) cone with eccentric tip, e) square pyramid with twisted circular tip, f) square pyramid with varying wall angle.

Fig. 6. 3D Scans of the formed geometries, colors indicating the signed distance to the target shapes; a) cone, b) cone with varying wall angle in size S and c) size M , d ) cone with eccentric tip, e) square pyramid with twisted circular tip, f) square pyramid with varying wall angle.

Overall, with maximum absolute geometric deviations between 1.6 and 3.35 mm , the geometric accuracy is comparable to that of typical metal DSIF [19-21]. For example, in a recent benchmark study, underforming in critical areas of a complex part was in the range of 1.7 to 3.2 mm , and overforming in the base-wall transition at a maximum of 4 mm [21]. It should be noted that no compensation strategies for machine stiffness or springback have been employed to date. As reported by Konka et al. [20], maximum deviations of a cone could be reduced from 2.2 mm to 1 mm by employing sheet springback and machine stiffness compensation.

Internal Part Quality.

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

To evaluate the internal part quality and consolidation state, a micrograph of the cross-section of part D1-S was compared with the virgin, pre-consolidated starting material. As visible in Fig. 7, the virgin material shows a homogenous and flat surface covered by matrix material, but internal cracks and voids. As a result of the forming process, the consolidation state of the material was increased, and a reduction in void content was observed. However, as also explained in the qualitative analysis, the surface smoothness was reduced.

[picture]

Fig. 7. Micrographs of cross-sections of the virgin material (left) and the formed part D1-S (right).

Fig. 7. Micrographs of cross-sections of the virgin material (left) and the formed part D1-S (right).

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

The experimental results demonstrate the capability of the previously developed hot DSIF setup, digital process chain, and processing strategy to manufacture geometrically diverse parts. Five distinct geometries with individual challenges, including asymmetries, varying wall angles up to 60∘, depths up to 50 mm , and corner radii as low as 12 mm , were successfully produced. Most importantly, sufficient shear could be introduced in the fabric to enable wrinkle-free results. Therefore, the forming strategy relying on multiple intermediate shapes, combining classical spiraling and drape-aware toolpaths, proved effective in all of these cases. The pressure applied by the tools during the cooling of the part aided in achieving satisfactory consolidation of the composite material, as evidenced by comparing the formed and peripheral areas of the parts. To further increase the surface quality of the final part, a smaller path distance could be used in the last intermediate shapes. Furthermore, using a separator material with higher strain and a reduced tendency to crease could avoid the matrix imprints currently caused by wrinkles in the PTFE sheets.

3D scans show satisfactory overall geometric accuracy, with maximum deviations arising from underforming at the tip edges and from global deformation at the transition from the base plane to the wall. A higher wall angle and a larger geometry increase this effect. Toolpath compensation algorithms taking into account the elastic springback of the metal sheets as well as the machine stiffness could aid in increasing the geometric accuracy further.

While the process is already somewhat scalable, there are currently still limitations regarding the maximum component size that can be manufactured. The failure of the metal dummy sheet during the forming of the largest part highlights the need for a forming strategy that accounts for both metal and organosheet deformation mechanisms. Further investigations are necessary to enable process optimizations to manufacture parts of larger scale successfully. In addition, forming sheets with higher thicknesses should be investigated to determine process boundaries in this dimension.

Overall, the foundation for a thorough, systematic analysis of relevant process and material parameters is laid by demonstrating the capability of the newly developed DSIF system to produce various parts of different complexity. The experimental results prove the high potential of the novel technology for the flexible manufacturing of FRTP components in prototype, individual part, and
small series production. Further research potential lies in continued optimization of process parameters and in further leveraging the ability to steer the shape evolution by optimizing intermediate shapes and toolpath strategies to achieve even greater process flexibility and part quality.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

This research was funded by the German Federal Ministry for Economic Affairs and Climate Action under the program LuFo VI-1 iFish, grant number 20Q1917C. We thank the project partners Björn Riecken, Benedikt Kötter, and Christian Keun of CompriseTec GmbH.

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The original version of this paper is available on https://www.scientific.net/SSP.389.1.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 11-25

doi: 10.4028/p-8f1QUK

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-05

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

Doran Nettig 1,a*, Jan-Erik Rath 1, b, Johann Kipping 1,c and Thorsten Schüppstuhl 1, d

1 Hamburg University of Technology, Institute of Aircraft Production Technology, Denickestr. 17, 21073 Hamburg, Germany

a* doran.nettig@tuhh.de, b  jan-erik.rath@tuhh.de, cjohann.kipping@tuhh.de, d  schueppstuhl@tuhh.de

*corresponding author

Keywords: incremental sheet forming, composite, fiber reinforced plastic.

Abstract

Incremental Sheet Forming (ISF) enables the flexible creation of shell-shaped structures. Unlike conventional forming, ISF does not require a bespoke forming tool, greatly reducing upfront costs and lead times, especially for small lot sizes. Several parameter classifications for the ISF of metals and polymers have been proposed in the past. Such classifications increase awareness of possible levers for process optimization, guide experimental analysis, and enable a holistic understanding. Lately, fiber-reinforced polymers (FRP) are of increasing interest in ISF. In previous studies, ISF systems for various kinds of FRP have been developed, and several parameters and target variables have been investigated. However, there is currently no classification that addresses the specific parameters and target variables relevant to this material class. Therefore, the goal of this work is to develop such a classification to create a comprehensive foundation for future FRP ISF investigations. This effort is undertaken by building upon existing classifications and reviews independent of the material class and synthesizing these with a systematic literature review of FRP ISF investigations. The resulting classifications cover a broad range of parameters and target variables and reveal a structure that guides a systematic understanding and ensures future expandability.

Introduction

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Incremental sheet forming (ISF) has been extensively studied as a flexible alternative to conventional forming processes relying on molds [1]. The dieless manufacturing process uses part-agnostic, often hemispherical tools to incrementally generate the desired target shape [2]. This greatly reduces upfront investment costs and lead-times, making it particularly interesting for small series, prototypes, and highly individualized parts. Most ISF investigations up to this point have addressed metals and later polymers. Research in these domains has identified a vast space of relevant parameters to understand and optimize the process. Multiple classifications have been developed to structure this space and to capture and compare process variants and parameters [3-5].

In recent years, ISF has also been applied to the material class of fiber-reinforced polymers (FRP). These high-performance lightweight materials are common in industries like aerospace, performance sports, and orthopedics [6]. In these industries, the need for flexible production processes is widespread, making ISF a promising pathway. The first study on the ISF of FRP was published more than a decade ago [7]. In recent years, reviews on the broader material class of composites, with a focus on structural metal, polymer, and metal-polymer composites, have also included works on FRP [8, 9]. However, there currently exists no structured classification of the space of parameters and target variables that could provide a comprehensive foundation for the analysis of this process. Classifications exist especially for metal ISF, but key differences in the material behavior cast doubt on the transferability of knowledge to FRP. To establish a classification that is suited for the ISF of FRP, this work starts with an analysis of the content and structure of existing classifications and reviews. This basis is combined with a quantitative and qualitative systematic literature analysis of FRP ISF.

Based on structural observations in existing classifications, the content of previous reviews, and the parameters and target variables found in the FRP ISF literature, a classification of parameters and target variables is developed, specifically tailored to this material class.

Methods

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Following the analysis of existing overviews on composites as well as other material classes, the landscape of individual studies on FRP ISF is systematically reviewed. The goal of this review is to identify the structure, parameters, and targets relevant to past research efforts on this topic. The review is performed on the databases Scopus and Google Scholar. The search string logic is provided below, with the search strings for Scopus and Scholar being only adjusted in syntax.

The title includes at least one of: SPIF, DSIF, ISF, Incremental Forming, Incremental Sheet Forming, Pin Forming, Shell Shaping, Dieless, MouldFree AND at least one of: composite, fibre*, fiber*, cfr*, textile*, fabric, organo AND the document is either a paper or an article.

Literature is included for further analysis if the following criteria are met: Fiber-reinforced material is used, parts are directly manufactured in an ISF process in a narrow sense (i.e. not multistep forming, modular molds or in-situ consolidation), and the papers are written in the English language. Of the works meeting these inclusion criteria, only those performing some real-world experiments are included in the subsequent quantitative analysis. Works that are solely conceptual, designs, or numerical studies are still included in the qualitative analysis to identify characteristics that might emerge from the overall solution space.

Following execution of the search strategy, 66 sources on Scopus and 89 results on Google Scholar match the search string. The last search was performed on November 7, 2025. After screening titles and abstracts based on the defined inclusion criteria, 29 unique sources are retained for further analysis. Of these, 25 are included in the quantitative analysis, while four are considered only in the qualitative assessment because they reported no real-world experiments. For the quantitative analysis, the factors studied in each work, the target variables, the materials used, and the type of experiment performed are extracted manually, along with the year of publication. The subsequent categorization and evaluation of parameters and targets are supported by custom Python scripts.

Based on the analysis, the initial lists of targets and parameters obtained from the ISF overviews are expanded by those found in the FRP literature. Based on ideas found in metal ISF classifications and the previous analysis, a unifying taxonomy is created that captures the parameter and target spaces of FRP ISF, and insights derived from this structure are discussed.

Analysis of Existing Overviews

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Parameters.

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

Seven existing ISF overviews are selected to be representative of a variety of perspectives to cover both a wide range of relevant parameters as well as different classification structures. Two are recent and application-driven works that present very elaborated classifications: In Vanhulst et al. [5] the classification is presented as part of a large benchmark study and the one found in Bremen et al. [10] serves to set up an experimental data base. These two works present comprehensive classifications, but are mainly concerned with the ISF of metals. Two additional works presenting classifications are analyzed that in addition to metals also consider the ISF of polymers [3,4]. While the works mainly concerned with metal ISF provide the most elaborated classifications in both structure and content, they are also the furthest from FRP in regards to its material behavior. For this reason, further reviews are included: One which specifically addresses ISF for thermoplastics [11] and two which address ISF of composites (including metal-metal and metal-polymer composites) [8, 9]. These reviews do not provide complex classification structures and cover a limited number of parameters, yet provide valuable insights into the material-specific parameter spaces.

In the following, these seven overview publications will be analyzed regarding their structure to identify commonalities that might inform the structuring of an FRP ISF classification. Following the
structural analysis, the content of the classifications is extracted and synthesized to form a unified parameter list that will serve as a basis for the parameter list created for the FRP ISF classification.

Aside from the content, an important aspect of any classification is its structure. The classifications found in the existing literature vary in both structural complexity and specificity. Some only list a number of classes or parameters [3], some show more complex taxonomies [4, 5, 10]. The most elaborate structure is found in Vanhulst et al. [5] and Bremen et al. [10], who describe three similar top-level classifications or domains. These are Platform, Workpiece, and Process (Vanhulst), and Process, Product, and Tool & Parameters (Bremen). The majority of the parameters in the Platform domain in Vanhulst et al. and in the Process domain in Bremen et al. consist of the machine description. Product and Workpiece domains of the two different studies can be directly identified with each other. Lastly, the Process parameter domain in Valhulst et al. has a large overlap with the Tool & Parameter domain in Bremen et al., including tool path and movement parameters. Kumar et al. [4] take a different approach of differentiating between classifications for the general process, warm forming techniques, the toolpath, and process parameters. McAnulty et al. [3] do not include any subclassifications in their framework but provide a list of important parameters. Similarly, the reviews addressing thermoplastic and composite materials do not propose any specific classification at all but include parameter lists [8, 9].

Regarding the content of the classifications, Table 1 will be used as a guide throughout this work. First, the parameters from existing overviews are collected in columns one to three. Later, the parameters from the FRP ISF literature are collected in columns four and five. Finally, the remaining columns document the additions and modifications to the list collected from the overviews that transform it into the final list of parameters included in the developed classification.

Table 1. Parameters from overviews (col. 1-3) and FRP ISF literature ( 4+5 ) with number of publications (NoP); Modifications made to form the content of the classification (right side).

Existing Frameworks NoP>1 | NoP | Existing Frameworks NoP=1 | FRP ISF Works | NoP | Added Parameters | Removed Parameters
Step Size | 7 | Anisotropy | Temperature | 9 | Area Weight | Layer Arrangement
Initial Sheet Thickness | 6 | Application Frequency | Step Size | 7 | Back Sheet Material | Forming Side
Spindle Speed | 6 | Application Method | Maximum Wall Angle | 7 | Back Sheet Thickness | Material Type
Tool Size | 6 | Axis Config | Fiberorientation | 5 | Back Side Pressure | Sheet Material
Feed Rate | 5 | Backing Plate Details | Fiber Volume Fraction | 3 | Clamping Force |
Forming Temperature | 5 | Deepest Cavity | Path Type | 3 | Components being Clamped | Replaced Parameters
Maximum Wall Angle | 4 | Forming Orientation | Layup | 3 | Cooling Ramps | Reinf. Weight Fraction
Forming Method | 3 | Forming Side | Tool Size | 3 | Fiber Geometry | Forming Temperature
Forming Strategy | 3 | Geometry Features | Temperature Distribution | 2 | Fiber Material | Forming Force
Tool Shape | 3 | Input Sheet Geometry | Initial Sheet Thickness | 2 | Fiberorientation | Heat Source
Toolpath Type | 3 | Material State | Spindle Speed | 2 | Front Sheet Material | Material State
Type of Heating | 3 | Material Type | Temperature Ramps | 1 | Front Sheet Thickness |
Clamping Geometry | 2 | Reinforcement Weight Fraction | Fixture | 1 | Front Side Pressure |
Forming Force | 2 | Superimposed Shape | Cooling | 1 | Heating Ramps |
Layer Arrangement | 2 | Symmetry | Feed Rate | 1 | Matrix Material |
Load Capacity | 2 | Temperature Distribution | Oilbath | 1 | Reinforcement Struct. Details |
Lubrication Type | 2 | Tensile Strength |  |  | Reinforcement Struct. Type |
Machine Stiffness | 2 | Tightest Radius |  |  | Seperator Material |
Machine Type | 2 | Tool Coating |  |  | Seperator Thickness |
Part Dimensions | 2 | Toolpath Direction |  |  | Storage Condition |
Part Shape | 2 | Type of Preform Fabrication |  |  | Support Angle |
Positioning Accuracy | 2 | Youngs Modulus |  |  |  |
Sheet Material | 2 |  |  |  |  |
Spindle Rotation Direction | 2 |  |  |  |  |
Tool Material | 2 |  |  |  |  |
Tool Type | 2 |  |  |  |  |
Work Space Size | 2 |  |  |  |  |

For now, a total of 102 uniquely named parameters is extracted from the overviews. After unifying the naming conventions and dissolving and summing to specific or general parameters, 49 unique parameters remain. These are listed in the first and third columns of Table 1. Only the 27 parameters shown in the first column of Table 1 occur in more than one classification, with the number of publications (NoP) covering each parameter shown in the second column. Only seven appear in more than half of the overviews, which are Step Size ( 100\% ), Initial Sheet Thickness ( 85.7\% ), Spindle Speed ( 85.7\% ), Tool Size ( 85.7\% ), Feed Rate ( 71.4\% ), Forming Temperature ( 71.4\% ), and Maximum Wall Angle (57.1 1% ). It is also apparent that none of the overview publications is exhaustive. The highest number of leaves is found in Bremen et al. [10], who cover 30 of the total 49 parameters synthesized from all overviews.

Target Variables.

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In the analysis of target variables in the existing overviews, there is no classification to be found that would warrant a structural analysis comparable to that of the parameters. Still, an important distinction can be found between target variables and failure criteria. While the former are similar across the different material types, the latter differ greatly between them. The goal of the following section is to collect the target variables and failure criteria found in the overviews to later combine these with the systematic analysis of the FRP ISF literature to develop a FRP ISF suited classification. Similar to the parameters, the targets are collected within Table 2, with the first three columns regarding the overview publication and the last being reserved for the later analysis of the FRP ISF literature.

In metal ISF, McAnulty et al. [3] focused their review on part formability, represented by the formable wall angle. As a side note, they also mention surface quality, geometric accuracy, resulting material properties, and the forming force as further possible targets, though they are not further investigated. Kumar et al. [4] concerned their analysis particularly with the forming force. Bremen et al. [10] and Vanhulst et al. [5] address five major outcomes or challenges in ISF, that, although using slightly differing names, describe very similar targets. One is the forming limit or producibility of the part, which is associated with the wall angle. Another is the thinning of the sheet, which precedes its failure. The geometric accuracy is also addressed in both works, which is further differentiated into elastic and plastic deformation. The surface quality or finish is the last part-related target. Process time, or more generally, productivity, is the last overall target mentioned in both works. Aside from these, Vanhulst et al. also address specific effects impairing the process outcome, namely the tent and pillow effects, as well as the occurrence of corner folds.

Table 2. Target Variables from overviews and FRP ISF literature.

Targets in the existing overview literature | Targets in FRP ISF
Metal | Thermoplastics | Composites |
Formability | Formability | Formability | Wall Angle
Wall Angle | Wall Angle | Wall Angle | Forming Depth
Surface Finish | Surface Finish | Forming Depth | Surface Finish
Geometric Accuracy | Geometric Accuracy | Surface Finish | Geometric Accuracy
Material Properties | Void Content | Geometric Accuracy | Thickness Distribution
Forming Force | Chain Orientation | Spring Back | Shrinkage
Thinning | Force | Mechanical Strength | Pull-In
Process Time | Energy | Fatigue Properties | Mechanical Strength
| Cost | Force | Voids
|  |  | Force
Failure Modes / Criteria
Necking after Thinning | Oblique Cracks | Oblique Cracks | Tearing
(Pillowing) | Circumferential Cracks | Circumferential Cracks | Wrinkling
(Corner Folds) | Wrinkling through Twisting | Wrinkling | Bulging
|  | Bulging | Deconsolidation
|  | Excessive Void Formation | Delamination
|  | Delamination |

In thermoplastic ISF, Zhu et al. [11] name similar target variables, namely formability, accuracy, surface finish, force, energy, and cost. Yet, the mechanisms influencing some of these targets differ: Regarding formability, although they also name wall angle as a primary metric, they identify two failure modes that are not present in metal ISF. These are the wrinkling as a result of a twist in the part, resulting from the tool movement, as well as an oblique fracture in the wall area. They also point out that in-plane fracture occurs, but without the preceding necking observed in metals. They also address the microstructure of the material, particularly the void content and chain orientation. While the quality targets are otherwise similar, they additionally name economic cost and energy consumption as target variables.

Liu et al. [8] describe similar material-dependent failure criteria for composites as for neat polymer, namely, circumferential and oblique cracks. In addition to these failure criteria, they point
out the importance of wrinkles not just through global twisting, but also caused during the forming of woven reinforcements. Voids and delamination are added to the list of possible failure criteria. Still, maximum drawing angle and depth are mentioned as the main formability metrics. Forming quality is differentiated into accuracy, surface quality, mechanical strength, and fatigue properties. The forming force is also designated as a target.

Hussain et al. [9] classify wrinkling, rupture, and bulging as the main failure modes in reinforced composites. Aside from formability, they looked at force, springback, geometrical accuracy, and surface quality.

Review of Investigations on FRP ISF

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

The goal of this section is to systematically review the FRP ISF literature to identify the parameters and target variables currently investigated and varying between investigations. These will then be used to judge the applicability of findings from the overview literature to this material class and to identify necessary adjustments and additions. Special attention is given to the materials investigated within the scope of FRP ISF, as these differ significantly between investigations.

The 25 studies selected for the quantitative analysis are listed in Table 3, together with key contents, which shall serve as a reference for the following analysis. It is to be noted that the materials, parameters, and target variables listed and analyzed are already terminologically unified and might differ from the wording used within individual publications. Additionally, only those aspects of the listed publications that directly address the incremental sheet forming process are analyzed. Any auxiliary experiments, material testing, and so forth are therefore excluded.

Table 3. Studies on FRP ISF and the materials, parameters, and targets investigated in each.

Ref. | Author | Year | Matrix | Fiber | Structure | Parameter | Targets
[7] | Fiorotto | 2010 | Epoxy | Glass | Woven | Layup | Tear
[12] | Ikari | 2016 | PA6 | Carbon | Short | Path Type, Cooling | Tear, Surface Quality (Meltdown)
[1] | Conte | 2017 | PA6 | Glass | Short | Temperature, Step Size, Wall Angle | Shrinkage, Thickness
[13] | Okada | 2017 | PA6 | Carbon | Short |  | Geometry
[14] | Okada | 2018 | PA6 | Carbon | Short | Initial Sheet Thickness, Tool Size | Geometry
[15] | Ambrogio | 2018 | PA6 | Glass | Short | Wall Angle, Step Size, Temperature, T-Ramp | Tear, Geometry, Shrinkage, Thickness
[16] | Al-Obaidi | 2019 | PA6 | Basalt | Woven | Layup, Wall Angle | Delamination, Voids
[17] | Al-Obaidi | 2019 | PA6 | Glass | Woven | Temperature Distribution | Wall Angle, Tear, Voids, Pull-in
[18] | Kubit | 2019 | Epoxy | Glass | Woven |  | Strength
[19] | Torres | 2020 | Solanyl | Glass | Short | Step Size, FVF, Temperature, Wall Angle | Depth
[20] | Hou | 2020 | PLA | Natural | Woven | Path Type, Fixture, Step Size, Initial Sheet Thickness | Depth, Surface, Bulge
[21] | Xiao | 2021 | Epoxy | Carbon | Woven | Fiber Orientation | Wrinkles
[22] | Emami | 2023 | PA6 | Glass | Layup | FVF, Temperature, Fiber Orientation | Thickness, Geometry, Depth
[23] | Bagheri | 2023 | PA6 | Glass | Short | Temperature, Spindle Speed, Step Size, Wall Angle | Depth, Shrinkage
[24] | Xu | 2023 | Epoxy | Carbon | Woven |  | Tear, Shear, Pull-in
[25] | Tanaka | 2023 | TP | Carbon | Short | Temperature | Geometry, Tear
[26] | Kalaei | 2024 | PA6 | Glass | Woven | FVF, Temperature, Step Size, Fiber Orient. | Depth
[27] | Rath | 2024 | SAN | Carbon | Woven | Path Type | Wrinkles, Tear
[28] | Nettig | 2024 | PA6 | Carbon | Nonwoven | Tool Size, Temperature, Temperature Distribution | Depth, Deconsolidation
[29] | Sun | 2024 | PP | Carbon | Layup | Temperature, Fiber Orientation | Geometry, Wall Angle, Depth
[30] | Ikari | 2024 | PA6 | Carbon | Short | Spindle Speed, Wall Angle, Feed Rate, Step Size, Oil Bath | Geometry, Surface
[31] | Rath | 2025 | Vitrimer | Carbon | Layup |  | Tear
[32] | Xu | 2025 | Epoxy | Carbon | Woven | Layup, Tool Size | Wrinkles, Tear
[33] | Formisano | 2025 | PP | Natural | Woven | Fiber Orientation, Wall Angle | Force, Depth
[34] | Kallai | 2025 | PA12 | Carbon | Woven |  | Geometry, Deconsolidation

Materials.

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The materials used in FRP ISF must be distinguished into the FRP itself and, possibly, multiple other layup constituents. The FRP can be described by its matrix material, its reinforcement material, and the reinforcement structure. Four main structures have been investigated in FRP ISF so far. As seen in Fig. 1 a), the most prevalent is the use of woven reinforcements, which were investigated in
49\% of studies. The next most studied are short fiber reinforcements with 36\%. Laminates composed of unidirectional layers and nonwoven long-fiber reinforcements have been investigated in only a few studies ( 12\% and 4\%, respectively). Details of the reinforcement structure are, notably, often not stated in the literature. For example, the weave type or the method of preform fabrication could affect the process, but are not always included in its description.

The type of fiber is also crucial for the material behavior. Fig. 1 shows carbon and glass fibers to be the dominant materials used, with 52% and 36% of works, respectively. Only a few investigations so far address natural or inorganic fibers. While the fiber material is defined in all studies, the fiber geometry is rarely described. For discontinuous reinforcements, the fiber length has a significant influence on the material properties [35], yet it is almost never recorded in the publications.

[picture]

Fig. 1. Reinforcement structures a) and fiber materials b) by percentage of publications.

Fig. 1. Reinforcement structures a) and fiber materials b) by percentage of publications.

The studies on thermoset matrix materials usually just mention using epoxy resin-based systems. In studies on thermoplastics, the polymer used is reported in all but one investigation [25]. As illustrated in Fig. 2, thermoplastic matrix materials have been studied in 76% of works, with Polyamide 6 being the most prominent, accounting for over 60% of thermoplastic studies. Other polymers used are Polypropylene [29, 33], Styrene Acrylonitrile [27], Solanyl [19], Polylactic Acid [20], and Polyamide 12 [34]. To date, one study has investigated the incremental forming of vitrimers [31]. A parameter often not mentioned in the studies is the description of the storage condition before the forming procedure. Especially for hydrophilic polymers such as polyamides and non-shelf-stable thermosets, this information can be crucial for interpreting results and ensuring reproducibility.

[picture]

Fig. 2. Matrix materials by percentage of publications.

Fig. 2. Matrix materials by percentage of publications.

In addition to the composite material itself, some of the processes employ additional metal sheets. This is most common with continuous fibers, where all but one publication [33] used metal dummy sheets, most often with a quasi-floating clamping of the composite to allow the pull-in required for its deformation. Although less commonly, metal sheets have also been used with short fiber reinforcements [1]. The materials used for the dummy sheets may differ between the sides of the composite sheet [32]. When the composite and metal are not meant to be bonded together, a separator, like thin Polytetrafluoroethylene foil, has been used [17, 20, 27].

Parameters.

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

Although FRP ISF is a comparatively new field with a total of just 25 works being included in this quantitative assessment, a surprisingly large number of 16 unique parameters has been investigated so far (see Table 1). There is some overlap between the parameters studied in the FRP ISF literature and the parameters synthesized from the overviews. However, a wider variety of workpiece and temperature-related parameters has been studied: Aside from the forming temperature, there are also investigations on the temperature distribution, temperature ramps, and active cooling methods. The initial sheet thickness and maximum wall angle are mentioned in a large number of publications, just as in the overview literature. However, the influence of other workpiece properties, such as fiber orientation, fiber volume fraction, and layup configuration, is also frequently investigated. In comparison, only relatively few and standard process and platform-related parameters have been studied so far, namely step size, spindle speed, feed rate, tool size, path type, and fixture type. Except for the fixture type, these are all part of the 27 parameters listed before. Without the tool path type and including sheet thickness, wall angle, and temperature, they make up the seven most prevalent parameters in the existing overview literature. In conclusion, the parameters from the existing ISF literature remain relevant to FRP ISF, and, in particular, process- and platform-related parameters are largely covered by at least some existing frameworks. However, especially for workpiece- and temperature-related parameters, the parameter space should be expanded to include the already studied parameters.

From a qualitative review of the literature, it is evident that a wide range of process configurations, including SPIF [27], TPIF [21], and DSIF [32], have been employed in single- [20] and multi-step processes [22] (i.e., multi-stage toolpaths where the final geometry is approached through several successive forming passes). While heating is always used in some form, a wide range of application methods has been explored in global [17] and local [14] heating schemes. The works omitted from the quantitative analysis indicate that the solution space continues to grow. A Hot-DSIF system with force-controlled support has been developed [36], as well as concepts to use hydrostatic pressure as a back-pressure support [37]. While only studied numerically, the initial blank outline has also been varied in one publication [38].

Based on this analysis, combined with the previous section on the materials used in FRP ISF, a list of 20 parameters not found in the overview literature is derived and listed in column six of Table 1. In the following, it will further serve as the foundation for the development of an FRP ISF suited parameter framework.

Target Variables.

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The FRP ISF literature also shows a wide variety of investigated target variables, with a total of 15 unique targets being investigated in the 25 works. While there is some overlap among targets, such as geometric accuracy and shrinkage, or deconsolidation and void content, the variety still shows the many different perspectives and considerations necessary to assess FRP ISF results. The broader number of failure criteria seen in the reviews of Liu et al. [8] and Hussain et al. [9] is confirmed by the quantitative analysis. Tearing, maximum forming depth, maximum wall angle, wrinkling, deconsolidation, delamination, and bulging have all been studied to assess formability. Other targets studied are also found in conventional ISF, such as the geometric accuracy, surface quality, thickness distribution, forming force, and mechanical strength. However, there are also targets such as edge pull-in, shear, shrinkage, and void content that are less commonly investigated in other material classes.

Classification for FRP ISF

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

Parameters.

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

Table 1 serves as a reference for the synthesis of the final parameter list. To generate a unified parameter classification for FRP ISF, the 49 unique parameters synthesized from the overview analysis serve as the basis. Next, the total of 20 new parameters derived from the FRP ISF literature
are unified with the previous 49. In doing so, the terms Reinforcement Weight Fraction, Forming Temperature, Forming Force, Heat Source, and Material State are replaced by wording better suited in the context of FRP ISF and the rest of the parameter space. Furthermore, Layer Arrangement, Forming Side, Material Type, and Sheet Material are removed by dissolving them into more complex parameter combinations, e.g., by explicitly describing each layer and its side. The unification results in a total of 66 parameters. The new parameters reflect the insights that temperature-related parameters have a crucial influence on the process. They therefore require a more nuanced description in FRP ISF. Due to the more complex material systems employed, product-related parameters become more diverse. The listing of these is often incomplete in existing literature, making interpretation and reproduction difficult. The fiber structure becomes another decisive factor influencing the entire process setup. To emphasize this, it is represented with the parameters Reinforcement Structure Type and Reinforcement Structure Details within the developed classification. The latter is intentionally kept quite general, as there is not yet enough literature to gauge all possibly important parameters of the fiber structure. However, it should be expanded in practice to include as many characteristics of the specific fiber structure under investigation as possible. Examples might be the weave pattern or the initial fabric thickness before blank consolidation.

To sort the parameters into a meaningful classification, an approach with three main categories, similar to those discussed with the classifications of Bremen et al. [10] and Vanhulst et al. [5], is adopted. However, to enable simple expandability and to ensure that all leaves share the same specificity, a consistent three-level system is introduced, structuring the taxonomy into domains, classes, and parameters. The final classification is illustrated in Table 4. The 66 parameters are grouped into eight classes, organized into three domains. The three domains are Platform, Product, and Process.

Table 4. Parameter classification for FRP ISF (added parameters underscored, renamed once italic).

The platform domain groups the mostly constant physical properties of the solution. It contains anything that can be observed without a process running. Its parameters are the most difficult to standardize because changing them requires fundamental physical adjustments of the solution, though to varying degrees. For example, changing tooling might be more feasible than changing the machine type or stiffness. As a consequence, they stay mostly constant within individual research but differ heavily between research groups. The product domain addresses the input and output of the process. Both the initial and target properties of the workpiece are grouped here. With its parameters, the generalizability and possible process variance can be investigated. The process domain is the realm of transient properties. It is the leverage that remains once a platform is set up and a product is chosen. The adjustment of these properties, therefore, also does not require material investment, making it easier to reproduce a given parameter set. However, possible strong correlations with parameters of the platform and product still have to be considered in comparative analysis.

The classes of each domain serve as a semantic clustering of the subordinate parameters. They could be viewed as subcomponents of the process or as classes in its solution space. For the Platform domain, the classes Machine, Tool, and a combined class Fixture & Heating System are chosen. The Process domain is subdivided into the three combined classes Path & Motion, Temperature & Lubrication, and Force & Pressure. The Product domain is described by Material and Geometry Parameters. These classes are not necessarily exhaustive, and further sub-classification might be possible, as is already insinuated by the use of combined classes. Still, to ensure an easy-to-expand framework and distinct structure, a class should always cluster parameters that have a high degree of conceptual or effective interconnectedness.

Lastly, the parameters are the leaves of the taxonomy. They describe both quantitative and categorical properties. To avoid bloating of the framework and to keep it sufficiently general, some parameters in the current formulation might require multiple values to describe them. E.g., the Tool Size of a flat-head tool would require both its major and minor radii. The Part Dimensions parameter might even include three values, one for each spatial dimension. In this regard, this "value components" layer could be considered a fourth level of the taxonomy. Alternatively, each value component could be treated as a separate parameter, thereby dissolving the more general parameters into their subcomponents.

The significant shift in the importance of the domains and classes between conventional and FRP ISF is now also evident in the final framework. In particular, temperature and material parameters are less prevalent in the existing overviews, with only six Product-related parameters occurring in more than one framework and only two belonging to the Temperature & Lubrication class in the Process domain. Their strong influence in the incremental forming of FRP and the more complex material compositions requires a much more nuanced description of these parameters. The final framework contains 7 Temperature and Lubrication parameters and a total of 27 parameters in the Product domain, reflecting this shift.

Target Variables.

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The target variable space has only been systematized to a limited extent in the existing overview literature. To structure this space, three main categories are chosen based on the targets discussed in the previous sections. The categories chosen here are Primary / Formability targets, Secondary / Quality targets, and Tertiary / Process targets. These three categories group target variables to answer the questions:

Was the process able to produce the part,

What part quality could be reached,

What is the process performance aside from the resulting part and in turn to achieve the following three goals,

Enable the process,

Improve the outcome,

Improve and understand the process.

The final target classification is shown in Table 5. It contains all targets identified in the overviews and in the FRP ISF literature, and includes further targets derived from the questions and goals associated with the three categories. Its structure and contents are described in the following.

Concluding from the previous discussion of formability, it is clear that a single formability measure is not a feasible target variable in FRP ISF. In metal ISF, the approach to measure formability through the maximum wall angle is valid due to the assumption of a single dominant failure mode, fracture after necking through material thinning, and a clear relation of the wall angle to the material thinning. However, severe deviations, such as pillowing or corner folds, could also be considered a "failure" of the process. In thermoplastics, where multiple fracture modes and wrinkling are present, a single formability measure becomes less viable. In FRP ISF, this is exacerbated even further.

That is why formability becomes a category rather than a single target. The wall angle is no longer a target either, but instead, it has to be treated as a parameter affecting possibly multiple underlying mechanisms, as can already be seen in multiple FRP ISF studies. The same also applies to other
geometric properties currently used as formability measures, like the forming depth. While this viewpoint may merit debate in the conventional ISF context, it is crucial in FRP ISF. Here, formability is not mainly determined by thinning, but rather a combination of multiple failure scenarios, depending heavily on the initial product configuration. The failure criteria most important in FRP ISF can be structured as shown in Fig. 3. While all formability aspects are relevant to all products to some extent, the product characteristics determine which aspect dominates the formability. Short fiber reinforced polymers seem dominated by tearing and fracture. With continuous fiber reinforced polymers, especially using a quasi-floating fixture, wrinkling dominates the formability limits. With long fiber or non-woven reinforcements, the expansion or deconsolidation becomes increasingly important. Delamination is an additional failure mode that is relevant only in multi-layer structures, particularly in fiber metal laminates.

Table 5. The developed target variable framework for FRP ISF.

Primary / Formability | Secondary / Quality | Tertiary / Process
Tear | Global Geometric Accuracy | Energy Consumption
Wrinkling | Strength | Forming Forces
Deconsolidation | Stiffness | Processing Time
Delamination | Surface Roughness | Material Waste
| Surface Quality | Particle Emissions
Metal Tear | Thickness Distribution | Noise Emissions
Metal Bulging | Local Geometric Deviations |
Metal Corner Folds | Edge Pull In |
Seperator Tear | Shrinkage |
Seperator Wrinkling | Spring Back |
| Shear Distribution |
| Fiber Ondulation |
| Void Area Fraction |
| Boundary Void Area Fraction |
| Fiber Geometry |
| Void Geometry |
| Constituent Distribution |
| Filament Failure |
| Matrix Cracks |

When using dummy sheets and/or separators, the situation is further complicated by the fact that their failure criteria are combined with those of the composite. This adds tearing, pillowing (bulging), corner folds, and separator wrinkling to the list of failure criteria.

All of these combined criteria might be independently affected by different parameters. While certain geometric features will certainly worsen the effects, limiting the assessment to these features as targets obscures the underlying mechanisms and hinders interpretations, comparisons, and optimization. With the more complex failure criteria, formability targets can to an extent be transferred to their associated quality criteria, e.g., the thickness distribution.

While the exact mechanisms are less investigated than for metals and thermoplastics, a possible attempt to view their transition is shown in Fig. 4. Material tearing could be preceded by a certain thickness distribution, individual filament failure, or matrix cracks. Deconsolidation up to the point at which it is considered a failed part can be assessed from the part's thickness distribution and void area fraction. Parameters affecting wrinkling could be assessed by examining the shear distribution and local geometric deviations. Delamination could be preceded by an increase in the interfacial void area fraction. This is not intended to provide explanations but rather to emphasize that the boundary between a failed part and a bad part, i.e., between assessing formability and assessing quality, is not necessarily precise. This can also be used to assess the effects of parameters on a formability metric by measuring a related quality metric.

[picture]

Fig. 3. Failure criteria in FRP ISF and their relation to the reinforcement structure type.

Fig. 3. Failure criteria in FRP ISF and their relation to the reinforcement structure type.

Especially by examining the microstructure of the material, further targets like Fiber Undulation, Fiber- and Void Geometry, and Constituent Distribution can be made available for analysis that may underlay other formability and quality targets. Of course, it is essential to also consider more performance-related quality criteria to assess the process outcome. These are, for example, the Global Geometric Accuracy, Surface Roughness, and Mechanical Strength. They are all collected in the Quality category for now. Further subgroups could be introduced here, such as Mechanical Performance, Geometric Properties, and (Meso)- and Microstructure. Lastly, to further understand the process and, more importantly, to assess and optimize its non-technical performance, the last set of target variables is that which cannot be investigated on the end product. Examples of these targets include Energy Consumption, Forming Forces, Processing Time, Material Waste, and Particle- and Noise Emissions.

As the target space has less existing structure to rely on and differs even more significantly from more common materials, the targets discussed here and listed in Table 5 should even less be assumed to be a complete coverage of the FRP ISF target space. Still, it should serve as a valid starting point for future expansion.

[picture]

Fig. 4. Possible transition from formability criteria to their related quality metrics.

Fig. 4. Possible transition from formability criteria to their related quality metrics.

Notes on Transferability

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

The taxonomical and structural analysis of the parameter and target spaces is crucial for experiment design and analysis, and can, on its own, already give insights into the transferability and understanding of previous results. For example, using a cone test on a metal sheet and a CFRP layup and measuring the maximum formable wall angle for certain parameter combinations might seem comparable or transferable. Yet explicitly stating the underlying targets reveals a different insight. In the first case, it is the thinning-dependent tear of the sheet, something that occurs in the CFRP only to a very limited extent. In the second case, it might be dominated by shear-dependent wrinkling of the CFRP, which, in contrast, does not typically occur in a metal sheet. Parameters having an identical influence on the thinning of a metal sheet and the wrinkling of a CFRP might exist, but would be a mere coincidence. What appears to measure the same target variable at first glance is, in fact, not.

Examining the relationship between formability and quality criteria also enables more efficient experiment design. It is not necessary to form to failure if it is clear which quality criteria indicate it.

Basic material testing may be important when the translation of material properties into process properties is known.

Lastly, given the vast number of parameters and the absence of standards, it is even more critical to have a comprehensive framework for the documentation of all parameters and factors in any given experiment and a broad recording of target variables to enable transfer between experiments and research groups.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

By combining existing classifications with reviews of metal, thermoplastic and composite materials and a systematic review of the FRP ISF literature, comprehensive classifications for the parameter and target spaces of FRP ISF were developed. The parameter classification was structured into three domains and eight subsequent classes that currently cover 65 parameters. The target classification structures 34 corresponding variables into the categories of formability, quality and process.

Large parts of the platform parameter domain were directly derived from existing classifications, whereas the parameter space was significantly expanded in the Temperature & Lubrication and Force & Pressure classes of the Process domain and across the Product domain. Regarding the target variables, it was found that a unified measure of formability is not feasible in FRP ISF. Instead, formability represents a category of separate target variables including multiple failure modes, strongly dependent on reinforcement type and layup configuration. Formability targets can be linked to quality targets, which enables improved experimental design and analysis. To guide a holistic process understanding, the classification also includes performance-related, macroscopic, and microscopic properties. Process related targets complement the formability and quality assessment by facilitating process understanding and assessing its economic and ecological performance.

The classifications are designed to be expandable by additional structure and content as further insights emerge. They can guide the conceptualization and design of experiments as well as the comparative analysis of past and future FRP ISF research and may serve as a starting point for investigations in related material classes.

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The original version of this paper is available on https://www.scientific.net/SSP.389.11.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 27-35

doi: 10.4028/p-2QfLSa

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-18

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

The original version of this paper is available on https://www.scientific.net/SSP.389.27.pdf

R. Walther 1,a*, L. Fleischer 1,b, M. Linnemann 1,c, V. Psyk 1,d, V. Kräusel 1,e

1 Fraunhofer Institute for Machine Tools and Forming Technology, Reichenhainer Straße 88, 09126

Chemnitz, Germany

a*richard.walther@iwu.fraunhofer.de, b  linda.fleischer@iwu.fraunhofer.de, c  maik.linnemann@iwu.fraunhofer.de, d  verena.psyk@iwu.fraunhofer.de, e  verena.kraeusel@iwu.fraunhofer.de

Keywords: electromagnetic forming, drop tower, die material.

Abstract

The rebound-effect that frequently occurs during electromagnetic sheet metal forming is one of the main causes of deviations in the shape and dimensional accuracy of flat surfaces. The selection of the die material and its corresponding energy absorption capabilities has a critical impact on this effect. This article analyses materials with different physical properties in terms of their energy absorption behavior under dynamic impact load. A variety of model tests are being conducted to examine a wide range of impact velocities and energies. The experimental setups comprise two variations of a drop tower test, which can be used to determine the percentage of impact energy absorbed at high and low momentum. To achieve higher impact velocities, a third experiment involving an electromagnetically accelerated impact body was conducted for the material that demonstrated the best result in the preceding tests.

Introduction

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Electromagnetic forming (EMF) is an impulse-based, high-velocity forming process for electrically conductive materials that uses Lorentz forces for plastic forming. As shown in figure 1, during electromagnetic forming, a tool coil is subjected to a damped sinusoidal current, which generates a magnetic field around the coil and induces an oppositely directed current in the workpiece. The interaction between these currents and magnetic fields creates Lorentz forces that deform the workpiece. Due to the high forming velocity, this process results in significantly higher formability and reduced spring back when forming aluminum sheet alloys compared to conventional processes. However, the high forming velocity means that the workpiece has a correspondingly high level of kinetic energy when it encounters the die. If this kinetic energy is not dissipated sufficiently, the remaining energy can cause the workpiece to bounce back. This is called the rebound-effect [1].

[picture]

Fig. 1. Principle electromagnetic forming.

Fig. 1. Principle electromagnetic forming.

One way to reduce the rebound-effect is to vary the die material [2,3]. Upon contact with the die, high localized loads and sudden stresses can occur under certain boundary conditions. To achieve good forming results, the die material must be able to absorb high energy during the short contact period without sustaining damage.

One of the first studies on how the die properties influence the forming results was conducted by Risch et al. [2]. In a simulation of the EMF process, a spring-damper-system was substituted for the die instead of a completely meshed FE-model. The spring stiffness represents the geometrical and material stiffness. The damping coefficient represents the materials damping properties. Both parameters were varied while using the same input energy for the coil. The results show that there is an optimal damping coefficient for each of the spring stiffnesses investigated. Too little or too much damping has a negative effect on the forming result. On the other hand, the workpiece geometry achieved the best possible flatness with a relatively low spring stiffness. In fact, it was so low that the bottom of the die was moved by the workpiece at the time of impact. In [5], Liu et al. have conducted similar simulation studies with the addition of experimental tests. The outcomes are almost identical. These studies show that dissipating impact energy is a difficult task, as the mechanisms in materials with good energy absorption may involve deformation. While rebound can be reduced, the deformation of the die can also lead to deviations from the target geometry of the workpiece. In addition, a severely deformed die is no longer usable. In both studies, no specific materials were examined.

When searching for studies regarding the energy absorption of materials, in most cases the tests are destructive [7,8,9] as the corresponding use cases may allow damage in exchange for better energy absorption, like a crash scenario. For sheet metal forming, this is not desirable as the die will be used to produce up to thousands of parts, while delivering accurate forming results repeatedly.

The only paper investigating the energy absorption of die materials under dynamic impact conditions directly is [3]. The materials researched were steel, elastopal and wood. In a test, an impact body was accelerated in a pipe at 10 m/s and 25 m/s. Given that the impact body weights 377 g , the impact energy can be calculated as 19 J and 118 J respectively. Elastopal stores energy in form of elastic deformation, returning some part of it to the impact body. With impact absorption rates of 6070%, elastopal showed the worst results. With 92%, wood may have absorbed the most energy, but it gets damaged due to the impact stress. While the results with steel showed good absorption rates at low impact energies, the values dropped from 91% to around 60% at high impact energies. In summary, no suitable material for the die was identified. Until now, little research has been conducted on this topic.

Investigated Materials

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In this paper, potential die materials with different physical properties and certain material combinations are analyzed regarding their energy absorption under impulsive load and damaging behavior. It is also of interest whether there is a correlation between energy absorption and characteristic material properties, such as density, hardness and Young's modulus.

Steel, compressed laminated wood and a polyurethane (PUR) modelling block were chosen as references, as they were used in [3,5]. The new materials to be examined are agglomerated cork, a rubber granulate mat, vulcanized fibre, viscoelastic PUR and sand. According to [9], agglomerated cork can dissipate energy under dynamic loads effectively because of its cellular microstructure. At low loads, the material shows elastic behavior. With increasing loads, the stress-strain curve plateaus. The cell walls bend elastically and the air inside the cells is compressed, increasing stiffness. Under this load, the restoring forces of the elastic cell walls are high enough that the agglomerated cork returns to its original state when slightly dented. At higher loads, the cell walls of cork collapse progressively and the damage gets irreversible.

Rubber on the other hand is commonly used for impact absorption in footwear [11] and playground safety mats [12], which is why it may be of interest for the given use case. Rubber and other elastomers, such as elastopal, absorb energy through elastic deformation upon impact. Part of the
energy is converted into heat through internal friction, but a significant amount of impact energy may be returned to the impact body.

In contrast, viscoelastic PUR behaves differently under dynamic loads. First, the impact also causes elastic deformation, with part of the energy being turned into heat. The difference lies in the energy return behavior. Compared to the contact time of the impact body, the viscoelastic PUR takes significantly longer to regain its original shape after the initial deformation. In conclusion, a substantial amount of energy is stored instead of returning it to the impact body. This effect reduces rebound significantly [10].

A material whose energy absorption properties have not yet been investigated is vulcanized fibre. It is a highly sustainable, cellulose-based material which consists of multiple paper layers laminated over a chemical reaction [13].

The last material examined is sand. It is used in roadside barriers or rock sheds to mitigate impact forces. In general, the main mechanism for dissipating impact energy in sand is grain friction. If the sand has air between the grains and enough room for deformation, the energy absorption is at its highest. But for the use in dies, the impact behavior must be repeatable. The loose grain structure results in sand changing its shape when impacted. Thus, a container with a rigid top layer is required. For the top layer, steel appears to be suitable. As explained in [6], the impact energy traverses steel in form of an elastic deformation wave. This enables steel to transfer a great amount of impact energy to a larger area of the underlying material while maintaining its shape. To prevent the volume of sand from changing, a sufficient pre-compaction is needed. Compacted sand tends to expand under shear forces, causing the particles to rearrange themselves, but due to the confined space, the grains are pushed on top of each other. Besides grain friction, this effect also contributes to the dissipation of energy [14]. All the materials investigated are listed in table 1.

Table 1. Overview of the examined materials.

Die material | Density in kg/m³ | Young's-modulus in N/mm² | Hardness | Compressive strength in N/mm² | Thickness of sheet/stacked material in mm
Steel (S355JR) | 7850 | 210000 | 180 HB | 355 | 10/40
Compressed laminated wood | 800 | 14000 | Shore D 70-80 | 55 | 40/40
PUR modelling block | 1350 | 3400 | Shore D 83 | 95 | 40/40
Agglomerated cork granulate | 200 | <10 | Shore A 50 | <2 | 10/40
Rubber granulate mat | 800 | <10 | Shore A 40 | <2 | 20/40
Vulcanized fibre | 1300 | 4500 | Shore D 70-80 | 150 | 6/36
Viscoelastic PUR | 800 | 10 | - | - | 12,5/37,5
Sand (+ Steel Plate) | 1500 | - | - | - | 30 (+10)

As indicated in [2,3], depending on the mechanisms at work in the material to dissipate energy, higher thickness can have a positive effect on energy absorption. The material thickness was set to approximately 40 mm to keep the variable parameters of the tests manageable. Materials that were only available in smaller sheet thicknesses were stacked.

Experimental Setup and Implementation

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The energy absorption is characterized by three different model tests. All three test setups are based on the rebound hardness test by Leeb [15]. In these tests an impact body with a defined mass, velocity and resulting energy strikes the surface of the material sample. Figure 2a shows the principle test setup, which is the same for all three implementation variants. The front of the impact body has a hemispherical shape with a radius of 25 mm . To prevent damage to the hemispherical impact body,
it was made of steel instead of aluminum, which is usually used as workpiece material. The material samples are placed in a material holder and secured with a fixing plate.

[picture]

Fig. 2. Measuring setup (a) and data (b) for calculation of impact and rebound energy.

Fig. 2. Measuring setup (a) and data (b) for calculation of impact and rebound energy.

To determine the impact and rebound energies, the corresponding velocities are needed [6]. Optoelectronic sensors were used to determine the time which the impact body needs to overcome a defined distance s directly before and after the impact. In all tests, they were placed as low as possible to ensure accurate measurements. The sensors send a signal when there is no object in front of them. Using the distance s between the two optoelectronic sensors (fig. 2a) and the difference in trigger times Δtimpact  and Δtrebound , the impact velocity vimpact  and the rebound velocity vrebound  are calculated as shown in equation (1) and (2). Δtimpact  is the difference between the trigger times t1_on  and t2 _on  during impact, as shown in figure 2 b.Δtrebound  is the difference between the trigger times t2_off  and t1_off  during rebound.

vimpact =sΔtimpact vrebound =sΔtrebound 

(1)(2)

The impact energy Eimpact  and rebound energy Erebound  can be calculated using the following equations, given the known mass m of the impact body.

Eimpact =m2·vimpact 22Erebound =m2·vrebound 2

(3)(4)

The relative energy absorption η is calculated by dividing the absorbed energy Eabsorbed  by the impact energy.

η=Eimpact −Erebound Eimpact =Eabsorbed Eimpact (5)

The initial investigations of the die materials were carried out using a drop pipe, as shown in figure 3a. It consists of a drop pipe, under which the material holder is placed. The die materials were analyzed using the already mentioned hemispherical impact body. The drop pipe tests are conducted with an impact body weight of 0.5 kg at heights of 1,2 and 3 meters. This corresponds to impact velocities of 4.2, 5.3 and 6.5 m/s as well as impact energies of 4.5, 6.5 and 10.3 J . To investigate the influence of higher impact energies, a second test setup shown in figure 3b was created. The drop tower comprises a drop weight and the material holder positioned under it. The hemispherical impact body is attached to the drop weight. This results in a combined drop body mass of 10.75 kg . The drop height can be varied from 0.4 to 1.8 m , generating impact velocities from 2.6 to 6 m/s and impact
energies from 37 up to 192 J . The material that demonstrated the highest energy absorption in the initial two test setups was then analyzed in a third setup. The goal was to investigate the dependence of impact velocity on energy absorption. The test setup is shown in figure 3c. By adding an aluminum body, the hemispherical steel body was electromagnetically accelerated using a tool coil. This results in an overall impact body weight of 0.77 kg . To guide the impact body, a polyoxymethylene (POM) tube was used. The tube material was chosen because of good sliding properties. The drop height was set to be 0.35 m . The material holder used in the first two test setups is located under the POM tube. By gradually increasing the charging energy of the tool coil and thus the impact body velocity, a curve is generated showing the dynamic energy absorption behavior of the material. Several tests were conducted at impact energies ranging from 3.6 to 31.2 J and velocities of 3 to 9 m/s, respectively.

[picture]

Fig. 3. Drop pipe (a), drop tower (b) and electromagnetically accelerated impact body (c) test setups: (1) optoelectronic sensors, (2) fixing plate, (3) material holder, (4) material sample, (5) drop pipe, (6) drop weight, (7) hemispherical impact body, (8) POM tube, (9) tool coil.

Fig. 3. Drop pipe (a), drop tower (b) and electromagnetically accelerated impact body (c) test setups: (1) optoelectronic sensors, (2) fixing plate, (3) material holder, (4) material sample, (5) drop pipe, (6) drop weight, (7) hemispherical impact body, (8) POM tube, (9) tool coil.

Results and Conclusion

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First, the drop pipe tests were carried out. The results are summarized in figure 4. The red error indicator shows the range in which the results fluctuate. It must be mentioned beforehand that there was no clear correlation between the energy absorption rate and the impact energy for this test series. In the following discussion, the results from the three drop heights are averaged. For all drop heights, the PUR modelling block showed the worst results with an average energy absorption of 50%. With around 57%, the vulcanized fibre was only slightly better. The rubber mat achieved an absorption rate of 67%, which is similar to the elastopal investigated in [3]. While agglomerated cork is slightly better at 70%, a dent is formed at 2 m drop height. It regains shape after a short period of time. At 3 m , the damage gets irreversible. The compressed laminated wood achieved an absorption rate of 72%. What should be noted is that the material was damaged at all drop heights. By comparing the hardness, density and E-modulus with the wood used in [3] and [4], the selected material variant may have been too soft for a valid comparison. On the other hand, it is already known that even harder compressed laminated woods are damaged when used in an EMF process. In summary, none of the materials mentioned up to this point can be recommended for making dies.

[picture]

Fig. 4. Drop pipe test results at 4.5, 6.5 and 10.3 J impact energy with error indicator (red).

Fig. 4. Drop pipe test results at 4.5, 6.5 and 10.3 J impact energy with error indicator (red).

The first material that seems promising is the viscoelastic PUR at 81% energy absorption. It is important to mention that there was no indentation after the impact. In conclusion, the impact energy in these tests was too low to engage the viscoelastic material behavior, which limits the materials ability to absorb energy. With an absorption rate of 90%, steel was the second best material tested, followed only by the sand-steel combination at 91%.

To test the materials under higher impact loads, the drop tower test with a drop height of 0.4 m was conducted, which corresponds to an impact energy of 37 J . Besides the already mentioned agglomerated cork and compressed laminated wood, which were not tested again, vulcanized fibre and the PUR modeling block were also damaged. The only useful measurements were taken for the viscoelastic PUR, steel and the sand-steel combination. As expected, the energy absorption of viscoelastic PUR increased to around 85%. The impact body caused a temporary indentation, which means energy is stored in the material after the impact. The indentation left behind disappears after a finite period and the same amount of energy can be absorbed again. At 91%, the sand-steel combination remains the best, independent of impact energy.

By further increasing the drop height to 1.8 m , which corresponds to an impact energy of 192 J , only the viscoelastic PUR stays undamaged. Its absorption rate further increases to 88%. With 6 m/s, the impact velocity is similar to 6.5 m/s in the drop pipe test. The material shows a clear correlation between impact energy and energy absorption but is independent of impact velocity.

With a direct impact of the hemispherical impact body, the load is concentrated on a spot. By adding a steel plate, the load is distributed more evenly on the material below. Some of the materials damaged in the previous tests might benefit from this. In another drop tower test, all materials were reduced to 30 mm in thickness and covered by a 10 mm thick steel plate. Figure 5 shows the results of the drop tower tests of the materials in combination with a steel plate. As drop height, 0.4 m was chosen. The test setup for steel and the sand-steel combination remained the same, as steel was already used for the top layer.

As desired, none of the tested materials were damaged. Starting with the rubber mat, the energy absorption stays at 72%, which is similar to the previous tests without the steel plate. The absorption rates of vulcanized fibre, the PUR modelling block, the compressed laminated wood and agglomerated cork all increased to 83%,85%,85.5% and 86.5% respectively. As stated in [3], the impact absorption of steel decreases with increasing impact energy. The value dropped to 83%. In conclusion, steel can be used as a die material, provided that the impact energies are low. Lastly, the energy absorption of viscoelastic PUR increased to 90%, which makes this combination almost as good as sand and steel. As shapeless sand is difficult to handle, the combination of viscoelastic PUR and steel may be more attractive for the application in dies.

[picture]

Fig. 5. Drop tower test results at 37 J impact energy and indirect impact on steel plate with error indicator (red).

Fig. 5. Drop tower test results at 37 J impact energy and indirect impact on steel plate with error indicator (red).

Since sand with a steel cover plate had the best overall results, a series of tests was carried out with an electromagnetically accelerated impact body for investigating the absorption behavior at higher velocities.

One factor also investigated in this test is the influence of momentum on energy absorption. The same impact energy can be generated with different combinations of speed and mass, as shown in equations (3) and (4). In [7], Artero-Guerrero et al. summarized many previous studies on this topic. The results showed that the momentum had no significant influence. In [8], different standardized drop weight test systems produce slight differences in results. Mathe et al. found that a longer contact time at high momentums, particularly with softer materials, results in larger indentations and potentially small differences in the energy absorption rate compared to a low momentum impact at the same energy level. The momentum can be calculated using the following equation [8].

p=m·v(6)

That results in a momentum of 30 kg· m/s for the drop tower test and 6.8 kg· m/s for the accelerated impact body test at impact energies of 37 and 31 J respectively. To take the momentum into account, the velocity of the impact body was increased steadily. Figure 6 shows the results of the electromagnetically accelerated impact body tests.

[picture]

Fig. 6. Relation between energy absorption, momentum and impact velocity for the sand-steel combination.

Fig. 6. Relation between energy absorption, momentum and impact velocity for the sand-steel combination.

First, no significant influence of impact velocity could be determined, as the energy absorption stays consistent. The lower average energy absorption values of approx. 83% instead of 91%
determined in the earlier experiments (see fig. 4,5) are due to the test setup. To fix the POM tube in place during the tests, the top of the machine table is lowered until the tube can no longer move. This exerts additional pressure on the metal plate, which limits the movement of the sand grains. To verify whether the properties of the sand-steel combination changed during this test series, the impact body was dropped in the POM tube without additional acceleration or pressure exerted on the steel plate. This was done before and after the test. The results were an energy absorption of 91% for both cases. In conclusion, the energy absorption properties of the sand-steel combination are independent of impact velocity. By comparing the results of the drop pipe, drop tube and accelerated impact body tests, no influence of momentum was shown, as the results are 91% throughout. For all examined velocities, momentums and impact energies, the energy absorption of sand and steel remains consistent.

Lastly, it was of interest if there were correlations between the energy absorption and material properties, like density, E-modulus and hardness. With its lose grain structure, only the density could be determined for sand at approx. 1500 kg/m3. When comparing steel and the viscoelastic PUR, which show comparable energy absorption rates depending on the impact energy, the densities differ significantly at 7850 kg/m3 and 800 kg/m3 respectively. While the E-modulus for steel is at 210000 N/mm2, the value for viscoelastic PUR is at 10 N/mm2. Consequently, no correlation between the material properties and the energy absorption could be established for the examined materials. The main reason is the difference in mechanisms at work to dissipate energy in the materials.

Summary and Outlook

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In this paper, materials with different physical properties were investigated in three impact body tests. The goal was to determine the material with the best energy absorption to reduce rebound for EMF. Especially compared to previously used materials like compressed laminated wood or the PUR modelling block, alternatives with significantly better energy absorption and no signs of damage were found. The combination of sand with a form-stable steel cover plate as well as the viscoelastic polyurethane both seem promising as potential die materials to reduce rebound in the EMF forming process. The energy absorption of the sand-steel combination is independent of the impact energy in the range of values examined. In contrast, the energy absorption of viscoelastic PUR improves as the impact energy increases, while that of steel decreases. For all Materials, no dependence of impact velocity or momentum on energy absorption was found. In the future, the results must be validated by using the materials as dies in a real EMF process. If the absorption rates are different compared to the model tests, the material of the impact body may influence energy absorption. This has yet to be investigated. As the results for steel showed good absorption rates at low impact energies, comparative tests should be carried out. Further tests are also required to verify the optimal material thickness or depth of the sand container for maximum energy absorption.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.27.pdf

V. Psyk, D. Risch, B. L. Kinsey, A. Tekkaya, M. Kleiner, Electromagnetic forming - a review, Journal of Materials Processing Technology, Bd. 211, pp. 787-829, 2011. https://doi.org/10.1016/j.jmatprotec.2010.12.012.

D. Risch, C. Beerwald, A. Brosius, M. Kleiner, On the Significance of the Die Design for Electromagnetic Sheet Metal Forming, TU Dortmund, 2004. .

D. Risch, A. Brosius, E. Tekkaya: Analysis of Different Die Materials for the Electromagnetic Sheet Metal Forming Process, 9th International Conference on Technology of Plasticity, ICTP 2008. ISBN 978-89-5708-152-5.

M. Linnemann, Analyse und Automatisierung von inkrementellen elektromagnetischen Umformprozessen, Dissertation, TU Chemnitz (2022).

X. Liu, L. Huang, J. Li, An experiment and simulation study of the rebound effect in electromagnetic forming process, 6th International Conference on High Speed Forming (2014) .

D. Risch, Energietransfer und Analyse der Einflussparameter der formgebundenen elektromagnetischen Blechumformung, Dissertation TU Dortmund (2009).

J.A. Artero-Guerrero, J. Pernas-Sánchez, J. López-Puente, D. Varas, Experimental study of the impactor mass effect on the low velocity impact of carbon/epoxy woven laminates, Composite Structures (2015), .

S. A. Mathe, A. Juarez, S. F. Peralta, Energy and Momentum in Mechanical Impact Testing, Jacobs Technology Inc. (2024).

M. R. Sheikhi, S. Gürgen, O. Altuntas, Energy-Absorbing and Eco-Friendly Perspectives for Cork and WKSF Based Composites under Drop-Weight Impact Machine, Machines 2022, 10, 1050. https:// .

M. Heim, M. Seidl-Nigsch, H. Loy, Hochdämpfende Polyurethan-Elastomere, PU Magazin (2021).

R.M. Silva, J.L. Rodrigues, V.V. Pinto, M.J. Ferreira, R. Russo, C.M. Pereira, Evaluation of shock absorption properties of rubber materials regarding footwear applications, Polymer Testing 28 (2009) 642-647, doi:10.1016/j.polymertesting.2009.05.007.

P. L. Davidson, S. J. Wilson, D. J. Chalmers, B. D. Wilson, D. Eager, A. S. McIntosh, Analysis of Energy Flow During Playground Surface Impacts, Journal of Applied Biomechanics, 29 (2013) 28-633.

R. Scholz, A. Delp, F. Walther, In Situ Characterization of Damage Development in Cottonid Due to Quasi-Static Tensile Loading, Materials, 13 (2020) 2180. .

S. Kahraman, I. Keskin, H. I. Yumrutas, I. Esen, An Experimental Method to Determine the Impact Energy Absorption Capacity of Soils: Factors Affecting the Impact Energy Absorption of Sandy Soils, Buildings 2025, 15, 1570. https:// .

K. Kovler, F. Wang, B. Muravin, Testing of concrete by rebound method: Leeb versus Schmidt hammers, Materials And Structures, 51 (2018). .

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 37-49

doi: 10.4028/p-CeZQ53

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Accepted:
2026-02-16

Online:
2026-04-16

Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

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Mamros Elizabeth 1,a, Clark Austin 2,3,b, Barnett Philip 4,c, Ragai Ihab 2,d*, Shaffer Derek 5,e and Laser Kristofer Jr. 2,f

¹Bucknell University, Lewisburg, PA 17837, USA

2 The Pennsylvania State University, Erie, PA 16563, USA

3 GROB Systems Inc., Bluffton, OH 45817, USA

4 University of Tennessee, Knoxville, TN 37996, USA

5 Phoenix Laser Solutions, Meadville, PA 16335, USA

a  elizabeth.mamros@bucknell.edu, b  aclark@grobsystems.com, c  pbarnet3@utk.edu,

d * ihab.ragai@psu.edu, e  derek.shaffer@phoenixlaser.com, f  kwl5440@psu.edu

*corresponding author

Keywords: incremental forming, PEEK, UHMWPE, cranioplasty, implants, biocompatible, impact testing.

Abstract

The human skull can become fractured or injured through impact and often requires repair through a craniectomy and subsequent cranioplasty, surgery performed to repair defects or damage to the cranium. Challenges related to material choice, which must be biocompatible, and customization for each patient's anatomy remain. One possible solution is fabrication of patientspecific cranial implants, out of biocompatible polymers, using single point incremental forming (SPIF). In this paper, polyetheretherketone (PEEK) and ultra-high molecular weight polyethylene (UHMWPE) are formed using SPIF at room temperature to manufacture a cranial implant. The SPIF process is used to produce formed parts from which test specimens were extracted to evaluate the tensile performance and thermal properties. Formed cranial implants were impacted using a drop weight to evaluate their suitability under relevant conditions. The geometric conformance of the SPIF process was studied to compare the material behavior for the specified polymers after forming. The results validate that SPIF can be conducted at room temperature with PEEK and UHMWPE biocompatible polymers to enable custom implant manufacturing. However, PEEK exhibited superior performance in terms of tensile strength, geometric conformance, energy absorption, and melting temperature, and is recommended over UHMWPE for future implant applications.

Introduction

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After sustaining a significant impact to the human head, the brain often swells as part of the body's inflammatory response. In emergency situations, a craniectomy, a surgery that removes a section of the skull to relieve pressure on the brain, may be performed. Later, cranioplasty, a second surgery that repairs the skull by replacing the bone, is performed. The bone is typically replaced by an implant or the patient's own bone. These implants require specific properties and biocompatibility for this application and are often made of commercially-pure titanium. However, challenges, including surface modification required for osteointegration, casting, radiologic incompatibility, and allergy risks [1], have sparked an interest in alternative material options such as polymers.

The use of polymers in biomedical implants offers several advantages, especially in terms of biocompatibility [2], mechanical properties, and design flexibility. Polymers are typically lighter than metals and offer lower heat conductivity. Many polymers, such as polyetheretherketone (PEEK) [3] and ultra-high molecular weight polyethylene (UHMWPE) [4] are bioinert, non-magnetic, radiolucent, and easier to process than metals. More specifically, PEEK is often used due to its similarity to bone in terms of strength and energy absorption properties, which are more similar than titanium. UHMWPE is known for its high wear resistance, high toughness, and low coefficient of
friction. However, it can cause osteolysis, disintegration of bone tissue caused by the introduction of wear particles from an implant.

In recent years, SPIF has increasingly been explored for biomedical applications due to its unique capabilities in forming complex, customized components from sheet materials without the need for dedicated dies. Bagudanch et al. compared forming a cranial implant using UHMWPE and SPIF to a SPIF variant, two point incremental forming (TPIF), which uses a negative die on the non-toolside of the sheet to provide additional support during forming [5]. Chen et al. investigated the temperaturedependent formability of PEEK when fabricating a cranial plate using heat-assisted SPIF [6]. RosaSainz et al. formed cranio-maxillofacial implants using PEEK and SPIF at room temperature to investigate formability [7]. PPS-based composites have been studied for applications of skull repair [8] and orthopedic implants [9], but SPIF of these materials remains unexplored.

In this work, a double dome geometry and a cranial implant were fabricated using SPIF at room temperature and two biocompatible polymers. PEEK and UHMWPE are investigated as potential replacements for titanium in implant manufacturing. Although these materials have been studied separately, a direct comparison is needed to identify the advantages and disadvantages of each of these polymers when fabricating custom cranial implants utilizing SPIF. Material and impact properties, thickness measurements, and geometrical accuracy results are presented.

Materials and Methodology

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Materials.

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PEEK and UHMWPE were the polymeric materials selected for this investigation. Table 1 shows the associated manufacturing methods.

Table 1. Selected polymeric materials and corresponding manufacturing methods.

Material | Manufacturing Method(s)
PEEK | Injection Molded (IM), Extruded
UHMWPE | Extruded

PEEK.

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PEEK samples were injection molded from Victrex 450 G pellets at Penn State Behrend. An Arburg 470E 1000-290 was used to make the 152.4 mm×152.4 mm plaques with a thickness of 3.175 mm . The material was melted in the injection molding barrel set at 416∘C. They were formed at a volumetric fill rate of 111.1cc/sec. The mold was maintained at 71∘C with the use of a Regloplas P160M steam temperature controller. Prior to molding the material, raw pellets were dried at 149∘C for a minimum of 8 hours. Samples were molded at a 47 second cycle. Additionally, extruded sheets of PEEK, with a thickness of 3.175 mm , were purchased from an industrial supplier.

UHMWPE.

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UHMWPE extruded sheets were purchased directly from another industrial supplier with a nominal thickness of 3.175 mm . Sheets were purchased as squares with an initial size of 609.6 mm and were then cut to 152.4 mm squares for the forming process.

Single Point Incremental Forming.

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SPIF experiments were conducted using a HAAS vertical 3-axis CNC milling center with consistent parameters for all samples. A hemispherical tool with an 8 mm diameter and free rotation, a feed rate of 2000 mm/min, and a step down size of 0.5 mm were selected based on previous works of the authors [10,11]. An example of the tool is shown in Fig. 1a. All formed sheets had initial dimensions of 152.4 mm×152.4 mm, and the clamping fixture consisted of two aluminum plates, with a 115 mm(4.5in) forming area in the center, that were bolted together and held in a Kurt Vice shown in

Fig. 1b. Mastercam [12] was used to generate the toolpath. Experiments that resulted in sample failure were aborted at the first sign of failure. The experimental setup utilized an AMTI MC12-6-4000 dynamometer and Optris 640 i infrared (IR) camera for force and temperature measurements, respectively. A thermal image during forming of IM PEEK double dome is shown in Fig. 1c.

[picture]

Fig. 1. (a) Tool geometry, (b) Kurt Vise with fixture setup, and (c) forming set up as seen by the thermal camera.

Fig. 1. (a) Tool geometry, (b) Kurt Vise with fixture setup, and (c) forming set up as seen by the thermal camera.

The geometries of interest were a double dome and a cranial implant as shown in Fig. 2. The double dome geometry, developed for benchmarking a composites formability [13], was intentionally selected to allow for the extraction of tensile specimens from the side walls and flat region. This version represents a modification of the original geometry to account for geometric limitations of the SPIF process. The cranial implant was chosen as a proof of application to the biomedical industry.

[picture]

Fig. 2. Target geometries: double dome (left) and cranial implant (right). Units in mm.

Fig. 2. Target geometries: double dome (left) and cranial implant (right). Units in mm.

Thickness Distribution.

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The thickness of the double dome parts was measured using a Magna-Mike 8600 to analyze the material distribution after forming along both principal axes. A total of 15 and 17 thickness measurement points were taken along the major and minor axes, respectively. A magnetic probe is aligned with the desired measurement location on the surface of the specimen, and a metal ball, connected to the probe by a strong magnetic current, is in contact with the opposite surface of the specimen [14]. The distance between the probe and the steel ball constitutes the material thickness at that point. The values were recorded for each specimen at the locations shown in Fig. 3.

[picture]

Fig. 3. Double dome measurement locations.

Fig. 3. Double dome measurement locations.

Geometrical Accuracy.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Geometrical accuracy was measured using laser scanning with a Creaform HandySCAN Black Elite as depicted in Fig. 4 which offers up to 0.025 mm of accuracy and is capable of measuring parts from 0.05 m to 4 m in size. The scans were captured using the Creaform OS2 software packaged with mesh resolution settings of 0.5 mm , a shutter speed of 1.55 ms , and a high-resolution scan mode. This provides a high level of dimensional accuracy in the scan while developing a mesh size on the output surface file that is manageable. The three-dimensional models output from these scans were then compared in the Creaform OS2 software to the input CAD models used to generate the SPIF tool paths. In order to do this consistently and align the parts as accurately as possible, the bottom, undeformed regions of the double-domes are used to align the scanned features to the input computeraided design (CAD) model features. Two-dimensional, cross-sectional overlays are used to visually understand and interpret the data through the center section of the parts. Since the parts are not axisymmetric, two sections are taken perpendicular to each other to fully capture the deviation of the parts. The geometrical accuracy was measured at the same locations as the material thickness for consistency.

[picture]

Fig. 4. Handheld scanner experimental setup with scanning targets on the turntable and fixture.

Fig. 4. Handheld scanner experimental setup with scanning targets on the turntable and fixture.

Tensile Testing.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Tensile test specimens were prepared in accordance with ASTM D638 Type V specimens [15]. Waterjet cutting was utilized to extract samples from the modified double-dome geometry in the recessed cavity (representing an unformed region) and the flat portion of the formed walls. Experiments were conducted using an MTS Criterion 43 load frame with a 5 kN cell. The displacement rate was set at 10.0 mm/min(100%/ minute strain rate ) until specimen failure for each material and manufacturing method. A minimum of three samples were tested for each condition except for the extruded PEEK formed region, for which only one sample was recovered. The tensile modulus, peak stress, and failure engineering strain (i.e., strain at peak stress) are reported in accordance with the test standard.

Falling Dart Impact Testing.

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Formed cranial samples were impacted with 278 J of energy from a 20 mm diameter hemispherical indenter with 6.08 kg mass at 9.56 m/s velocity from a 4663 mm drop height (Model 9450, Instron). The force and displacement were measured using a striker instrumented with an internal accelerometer. Specimens were clamped on both sides in a thermostatic chamber as shown in Fig. 5. The temperature was maintained at 37∘C to emulate human body temperature. The system was equipped with an anti-rebound system, which prevents the striker from making multiple impacts with the sample. The impact velocity and energy were chosen to emulate the proposed US National Highway Traffic Safety Administration Federal Motor Vehicle Safety Standard (FMVSS) no. 228 [16], which prescribes a 4.5 kg mass crash dummy head striking a hood or fender at 11.1 m/s (a total of 278 J of energy). It was not possible to achieve the FMVSS recommended mass and velocity combination with the equipment available, so the mass and velocity were matched as closely as possible while maintaining the same total energy.

[picture]

Fig. 5. Inside of thermostatic chamber for impact testing showing the sample clamping mechanism and location of striker impact.

Fig. 5. Inside of thermostatic chamber for impact testing showing the sample clamping mechanism and location of striker impact.

Differential Scanning Calorimetry (DSC).

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Samples were extracted from the double-dome formed parts in both the wall and flat regions for thermal analysis. as shown in Samples of 4 mg to 9 mg mass were heated at a ramp rate of 20∘C/min for two cycles (DSC 8500, Perkin Elmer) based on the material: PEEK, 20∘C to 400∘C and UHMWPE, 20∘C to 200∘C. Samples were run in triplicate. The onset and peak melting temperatures were identified from the second cycle, whereas the melting enthalpy was measured from the first to capture the thermal history of the material. The degree of crystallinity, XC, was determined following equation (1):

XC=ΔHmΔHf0(1)

where ΔHm is the heat of melting identified from the DSC data and ΔHf0 is the enthalpy of fusion for a completely crystalline material (taken as 130 J/g from PEEK and 289.3 J/g for UHMWPE).

Results

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Forming Force and Temperature.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Thermal and axial force measurements were collected during the forming process. An example timetemperature distribution plot is shown in Fig. 6a. Temperature data for all tests is shown in Table 2, where Q1 and Q3 represent the first and third quartile measurement values, respectively. In general, PEEK exhibited higher temperatures than UHMWPE in both cranial and double-dome forming while double dome forms yielded higher temperatures than cranial implants due to prolonged forming time. Forming double domes with PEEK exhibited higher temperatures than forming cranial implants with PEEK. However, for UHMWPE, the temperatures during forming double-dome remained comparable to cranial form levels. Additionally, higher axial force on the spindle, that is downward force in the direction of forming ( Z -axis), was found in PEEK than in UHMWPE. The X and Y data show oscillations between approximately ±170 N as the tool changes directions during each segment of the toolpath, as show in Fig. 6b. It is hypothesized that the slightly higher negative values indicate that the material exhibits mild anisotropy, which could be addressed in future work. Force data in the direction of forming ( Z -axis) is listed in Table 3 and examples of formed implant samples are presented in Fig. 7.

[picture]

Fig. 6. (a) IM PEEK Double Dome (a) Time-Temperature distribution and (b) Time-Force distribution.

Fig. 6. (a) IM PEEK Double Dome (a) Time-Temperature distribution and (b) Time-Force distribution.

Table 2. Temperature measurements during forming.

Geometry | Material | Processing | Q1 [°C] | Median [°C] | Q3 [°C] | Maximum [°C] | Std Dev σ [°C]
Cranial | PEEK | Extruded | 23.5 | 27.7 | 35.2 | 49.9 | 7.3
Cranial | PEEK | IM | 26.6 | 35.7 | 45.5 | 54.4 | 10.0
Cranial | UHMWPE | Extruded | 23.3 | 27.8 | 30.7 | 34.4 | 3.9
Double Dome | PEEK | Extruded | 51.8 | 78.1 | 92.7 | 112.2 | 24.3
Double Dome | PEEK | IM | 48.9 | 70.9 | 85.7 | 108.3 | 22.6
Double Dome | UHMWPE | Extruded | 29.3 | 38.4 | 49.3 | 56.0 | 10.5

The force measurements shown in Table 3 represent the first, Q1, and third, Q3, quartile measurement values. The maximum force value recorded occurred during the forming of the cranial implant for the extruded PEEK material. The injection molded PEEK cranial implant required slightly lower ( ~245 N less) force during forming. In general, the double-dome geometry required lower forming forces than the cranial implant for all three material combinations, with UHMWPE requiring significantly lower forces than PEEK.

Table 3. Axial force measurements (Z-axis) during forming.

Geometry | Material | Processing | Q1 [N] | Median [N] | Q3 [N] | Maximum [N] | Std Dev σ [N]
Cranial | PEEK | Extruded | 902.54 | 1089.81 | 1253.73 | 1758.38 | 387.88
Cranial | PEEK | IM | 764.20 | 945.69 | 1099.16 | 1509.73 | 351.41
Cranial | UHMWPE | Extruded | 1117.39 | 1201.46 | 1274.42 | 1592.46 | 337.18
Double Dome | PEEK | Extruded | 1033.32 | 1115.61 | 1165.88 | 1368.27 | 237.98
Double Dome | PEEK | IM | 387.00 | 541.35 | 629.87 | 758.42 | 189.49

[picture]

Fig. 7. Examples of formed cranial implant samples.

Fig. 7. Examples of formed cranial implant samples.

Thickness Distribution.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Fig. 8 shows that all three materials, formed using the double-dome geometry, exhibit a nonuniform thickness distribution along the distance from the edge of the sheet. Each of these materials exhibits two distinct regions of thinning along the formed walls. In the middle, the thickness distribution represents the undeformed region. The difference in thickness distribution between the three materials can be attributed to the fact that both PEEK and UHMWPE respond differently to temperature. Frictional heat can lead to greater polymer chain lability, especially when near the glass transition temperature, where it thins more readily.

In general, the samples show consistent thinning at high-strain regions (deformed) for all materials. UHMWPE demonstrates superior thickness retention and reduced thinning severity compared to both the extruded PEEK, and IM PEEK. The two PEEK variants exhibit similar forming results, which show that the type of polymer has a stronger influence on thickness distribution than the manufacturing method.

[picture]

Fig. 8. Thickness distribution along (a) major axis and (b) minor axis.

Fig. 8. Thickness distribution along (a) major axis and (b) minor axis.

Geometrical Accuracy.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

Fig. 9 shows the average geometric deviations, with respect to the target geometry CAD model, for two double dome specimens of each material and manufacturing method combination. The geometric deviations were measured at the same locations as the thickness distribution in the previous
subsection. The largest geometric deviations are observed in the flange region for all specimens due to the elastic recovery after removal from the clamping fixture (springback). Towards the center of the geometry, IM PEEK showed the largest geometrical inaccuracy, with the largest positive deviations ( ~0.11 mm ). Contrastingly, extruded PEEK and UHMWPE showed very minimal deviation (~±0.03 mm) in the same region. This indicates that the processing method has a stronger influence on the geometrical accuracy of the formed part than the type of polymer, possibly due to flow-induced anisotropy or residual stress differences due to changing in the cooling rate between the two processing conditions.

[picture]

Fig. 9. Geometric deviation from CAD model along (a) major axis and (b) minor axis.

Fig. 9. Geometric deviation from CAD model along (a) major axis and (b) minor axis.

Mechanical Properties.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

The tensile properties of the materials in the formed and unformed regions are reported in Table 4. Specimens extracted from the unformed regions of the PEEK specimens exhibited the same performance for both injection molded and extruded materials. The numbers in parenthesis for the formed regions indicate the p -value in a two-sample student's t -test to identify the statistical significance of the observed changes. This analysis could not be applied to the extruded PEEK samples due to limited sampling; however, the resulting properties were quite similar to the injection molded material. For p -values <0.05, the properties are statistically indistinguishable between the undeformed and deformed states. The strength and modulus of the PEEK specimens were reduced by 34.8% and 9.4%, respectively. The failure strain had a strong correlation but did not meet the threshold to indicate a statistically significant decrease. This change in performance may be due in part to surface roughness of the formed surface but is also likely the result of molecular chain reorientation during forming. For UHMWPE, the formed and unformed samples were statistically indistinguishable, indicating the forming process had less of an effect on the local mechanical performance.

Table 4. Tensile testing results for specimens extracted from deformed and undeformed regions.

Material | Processing | Region | Strength (MPa) | Modulus (GPa) | Failure Strain (%)
PEEK | IM | Unformed | 92.1 ± 0.9 | 3.2 ± 0.1 | 6.0 ± 0.2
|  | Formed | 60.1 ± 2.2 (1.41E-9) | 2.9 ± 0.2 (0.01) | 5.1 ± 1.0 (0.09)
| Extruded | Unformed | 94.4 ± 1.8 | 3.3 ± 0.04 | 6.0 ± 0.3
|  | Formed | 53.2 | 2.8 | 3.6
UHMWPE | Extruded | Unformed | 35.3 ± 1.7 | 1.0 ± 0.05 | 166.8 ± 5.5
|  | Formed | 35.7 ± 2.9 (0.86) | 1.0 ± 0.04 (0.71) | 173.4 ± 14.0 (0.48)

During impact testing, the anti-rebound system engaged during the deformation process. This was apparent in the data as a negative force, indicating that the accelerometer had begun accelerating
upward with the engaged system. As such, the energy absorbed was calculated by integrating the force-displacement curve from the point of contact to the first negative force value (Fig. 10). The subsequent data, while still showing an increasing displacement, is no longer physically meaningful (the displacement is simply calculated by double integrating the force signal [17]). Prior to impact, there was a small amount of displacement during the freefall of the impactor, with the force near zero. This region is also excluded from impact energy calculations.

[picture]

Fig. 10. Example data showing the region of the test data that is integrated to calculate the impact energy absorption of the cranial implants.

Fig. 10. Example data showing the region of the test data that is integrated to calculate the impact energy absorption of the cranial implants.

Fig. 11 shows the formed cranial implants after the impact. The impact performance of the formed implants is reported in Table 5. For the PEEK specimens, the injection molded material absorbed slightly more energy than the extruded. This is in good agreement with the tensile strength measurements, which showed a slightly higher tensile strength for the extruded PEEK. The reason for these differences requires further study but could be attributed to polymer chain alignment induced during the extrusion process. The UHMWPE absorbed substantially less energy than the PEEK. This is in the range of energy noted to result in skull fracture (14 to 68.5 J [18]). As such, UHMWPE may not be a suitable choice of material for cranial implants, whereas PEEK absorbed substantially more energy than typically required for skull fracture. None of the specimens of either type fractured, instead plastically deforming around the impactor, as shown in Fig. 11.

Table 5. Impact testing results.

Material | Processing | Energy Absorbed (J)
PEEK | Injection Molding | 112.2 ± 3.7
| Extruded | 126.7 ± 1.9
UHMWPE | Extruded | 25.9 ± 0.5

[picture]

Fig. 11. Typical failure modes for the three materials tested showing no apparent fracture.

Fig. 11. Typical failure modes for the three materials tested showing no apparent fracture.

Thermal Properties.

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

The thermal properties of the materials in the formed and unformed regions of the double-dome are reported in Table 6. The injection molded and extruded PEEK were not distinguished in this analysis, but all samples were extracted from the same specimen to ensure repeatability. For the PEEK specimens, the melting onset and peak temperatures did not change substantially due to forming. However, there was an increase in the crystalline percentage, indicating that strain-induced crystallization likely occurred. Several authors have reported evidence of strain-induced crystallization in PEEK, particularly at high strain rates [19,20]. Evaluating the strain rate during the SPIF process is a topic of future work. Alternatively, the increased crystallization may also be due to cold crystallization. During the SPIF process, the temperature rises at the forming locations due to friction between the tool surface and the part, as shown in the IR data.

Table 6. Thermal properties measured using DSC for specimens extracted from formed and unformed regions.

Material | Region | Melting Onset Temperature (°C) | Melting Peak Temperature (°C) | XC (%)
PEEK | Unformed | 327.8 ± 0.9 | 342.7 ± 1.8 | 21.9 ± 3.6
| Formed | 321.6 ± 6.4 | 342.7 ± 2.7 | 25.6 ± 3.4
UHMWPE | Unformed | 127.5 ± 0.9 | 138.8 ± 1.0 | 48.2 ± 0.2
| Formed | 128.8 ± 1.7 | 139.1 ± 0.9 | 46.9 ± 1.3

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

This study investigated the thermal, mechanical, and structural responses of PEEK and UHMWPE during single-point incremental forming (SPIF) of cranial and double-dome geometries. The following points represent the major findings:

Thermal measurements demonstrated that PEEK consistently reached higher temperatures than UHMWPE, with the highest values observed during double-dome forming due to longer tool-material interaction and increased frictional heating. Force measurements also revealed that PEEK required substantially higher forming forces than UHMWPE, and that cranial geometries imposed greater resistance than double-dome forms.

Thickness distribution analysis showed that all three materials exhibited non-uniform wall thinning, with characteristic regions of high strain along the formed walls. UHMWPE demonstrated superior thickness retention and reduced thinning severity compared to both extruded and injection-molded PEEK, indicating greater ductility and resistance to localized strain accumulation.

The geometric deviations measured in the flange region were the largest with respect to the CAD model. Extruded PEEK and UHMWPE showed much greater geometrical accuracy in the center of the double dome geometry along both axes compared to IM PEEK. This indicates that the material processing likely affected the amount of residual stress in the material, which affected the amount of relaxation following forming and unclamping from the fixture.

The similarity in thickness profiles between extruded and injection-molded PEEK suggests that the polymer type had a greater influence on deformation behavior than initial processing route. Mechanical testing further highlighted that forming significantly reduced the tensile strength and modulus of PEEK, likely due to molecular chain reorientation and surface roughening during deformation, whereas UHMWPE showed no statistically significant change in tensile performance between formed and unformed regions.

Impact and thermal analyses provided additional insight into the suitability of these materials for cranial implant applications. PEEK exhibited substantially higher impact energy absorption than UHMWPE, exceeding typical skull fracture energy thresholds while retaining structural integrity through plastic deformation rather than fracture.

Although minor differences were observed between injection-molded and extruded PEEK, both outperformed UHMWPE in terms of energy absorption, which can be critical in preventing reinjury at the implant site.

Differential scanning calorimetry revealed increased crystallinity in formed PEEK regions, suggesting strain-induced and/or cold crystallization during SPIF, while UHMWPE showed minimal thermal modification.

Collectively, these results indicate that PEEK offers superior mechanical robustness and impact resistance for cranial implant forming via SPIF, whereas UHMWPE, despite favorable thickness retention, may be less suitable for load-bearing cranial applications due to its lower impact energy absorption capacity.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

The authors would like to thank James Hart at Phoenix Laser for performing the 3D scans. The authors would also like to thank Mr. Brian Young for injection molding the PEEK specimens, and undergraduate researcher assistants Arame Cisse, Broc Dawson, Senudin Mehinovic, Velia Minerbi, and Mason Sheeley along with Andrew and Christopher Bartlett of Penn State Behrend for their assistance with the experimental work. The authors would like to thank José L. Martínez Collado at the University of Tennessee Knoxville for his assistance in impact testing. We acknowledge the partial support of the US National Science Foundation in the form of a Travel Support Grant [CMMI 2511050], which enabled the authors to attend and present at this conference.

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The original version of this paper is available on https://www.scientific.net/SSP.389.37.pdf

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Rosa-Sainz, A., García-Romeu, M. L., Ferrer, I., Silva, M. B., and Centeno, G., 2023, "On the Effective Peek Application for Customized Cranio-Maxillofacial Prostheses: An Experimental Formability Analysis," Journal of Manufacturing Processes, 86, pp. 66-84. .

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Mamros, E., Ragai, I., and Young, B., 2025, "Effect of Manufacturing Process on Mechanical Properties of Polyetheretherketone (PEEK) Cranial Implants Produced by Single-Point Incremental Forming (SPIF)," Materials Research Proceedings, 54, pp. 1191-1200. .

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This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 51-58

doi: 10.4028/p-L8oWxo

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-16

Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

Donghoon Han 1,a, Donghyuk Cho 1, b, Seik An2,c and Jeong Whan Yoon 1,3, d*

1 KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea

2 KIA, 95, Kiajadongcha-ro, Ujeong-eup, Hwaseong-si, Gyeonggi-do, Republic of Korea

3 School of Engineering, Deakin University, Waurn Ponds, VIC 3216, Australia

a  dhhan218@kaist.ac.kr, b  d.cho@kaist.ac.kr, c  asik@kia.com, d * j.yoon@kaist.ac.kr 

Keywords: electric motor, hairpin, finite element modeling, twisting process.

Abstract

This study presents an integrated finite element-based framework for analyzing the final protrusion length of enameled copper hairpins during stator manufacturing. Protrusion uniformity is essential for reliable laser welding, yet it is often degraded by layer-dependent deformation during expanding and twisting. To clarify the mechanisms governing protrusion variation, a bilayer material model for the copper-enamel system was developed and validated using tensile tests, indentationbased inverse characterization, and three-point bending experiments. Mechanically consistent boundary conditions for expanding and twisting were reconstructed from manufacturing observations and incorporated into FE simulations. The results indicate that twisting governs protrusion length through axial material redistribution, whereas expanding mainly serves as a feasibility-enabling step that establishes stable tool engagement. Based on these insights, a physics-guided regression formulation was introduced to relate key twisting kinematics to protrusion length. The proposed framework provides a mechanistic basis for understanding protrusion variability and supports further development toward rapid prediction and variability control.

Introduction

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Hairpin stator technology has become a key enabler for high-efficiency electric motors due to its high slot fill factor and favorable thermal performance [1,2]. In hairpin stator manufacturing, the uniformity of the final protrusion length of hairpin legs is critical for reliable laser welding and overall assembly quality [3,4]. However, significant layer-to-layer protrusion variation is frequently observed after the expanding and twisting processes, leading to excessive post-cutting and increased copper waste.

Despite its practical importance, the origin of protrusion variability remains insufficiently understood. Protrusion length is influenced by multiple interacting factors, including the initial geometry of the hairpin leg, the mechanical response of the enamel-coated copper wire, and the complex kinematics of expanding and twisting [5,10,11]. In production environments, direct measurement of internal deformation and tool-hairpin interaction is not available, making it difficult to isolate dominant mechanisms through experiments alone.

To address this challenge, the present study adopts a finite element-based framework to investigate protrusion behavior during hairpin forming. A bilayer material model is developed to represent the mechanical contribution of the enamel coating [6-9], and realistic boundary conditions for expanding and twisting are reconstructed from process observations. Using FE-generated datasets from representative forming conditions, a physics-guided regression formulation is developed to provide a reduced-order description of the twisting-driven protrusion mechanism. The proposed framework aims to clarify the mechanistic origin of protrusion variability and establish a basis for further quantitative development.

This paper contributes a mechanically consistent FE framework capable of reproducing protrusion evolution under realistic forming conditions, and a mechanistic clarification that twisting governs protrusion through axial feed redistribution, whereas expanding primarily ensures stable engagement and feasible initial conditions. The framework further demonstrates that, under identical production
settings across layers, final protrusion scatter is predominantly inherited from layer-dependent initial geometric offsets. These findings establish a quantitative basis for reduced-order protrusion prediction and geometry-based variability control.

Material Modeling

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Accurate representation of the mechanical behavior of enameled copper hairpins is essential for predicting deformation and springback during the expanding and twisting processes. Although the enamel coating is thin, prior studies have shown that it contributes non-negligibly to bending stiffness and elastic recovery, particularly under small-radius deformation. Accordingly, a bilayer material modeling strategy-consisting of a copper core and an outer enamel coating-was adopted, following established approaches for coated conductors and hairpin components [5-9].

Uniaxial tensile tests were conducted to characterize the mechanical behavior of the copper core. To exclude the influence of the enamel coating, a 20−mm gauge section was machined from an 80−mm wire segment by locally removing the enamel, as illustrated in Fig. 1a. Because drawn copper wires can exhibit within-spool mechanical variability due to drawing history and microstructural gradients [13,14], specimens were extracted from the head, middle, and tail regions of the same spool.

Fig. 1b compares the true stress-strain responses obtained from the three locations. Only minor differences in yield stress and hardening rate were observed, indicating that the mechanical heterogeneity along the spool length is negligible for the present application. Consistent with previous observations for hairpin conductors [5], a single representative stress-strain curve was therefore adopted to define the isotropic hardening behavior of the copper core in the FE simulations. The calibrated material coefficients are summarized in Table 1.

[picture]

Fig. 1. (a) Uniaxial tensile test specimens. (b) Tensile test results of each sections.

Fig. 1. (a) Uniaxial tensile test specimens. (b) Tensile test results of each sections.

Table 1. Material coefficients of hairpin copper.

386.2 | 241 | 4.74

Indentation-Based Inverse Characterization of the Enamel Layer.

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

Direct tensile testing of the enamel coating is impractical due to its extremely small thickness. Therefore, the enamel properties were identified using an indentation-based inverse finite element approach, following methodologies established for thin coatings and layered materials [5-7,15]. An axisymmetric indentation model was employed to efficiently reproduce the experimental nano-indentation force-depth response while retaining sufficient accuracy for coating characterization.

Fig. 2 shows the axisymmetric indentation FE model and the effective indenter geometry. Prior to introducing the enamel layer, indentation simulations were first performed on bare copper to calibrate
the effective indenter tip radius. As demonstrated in Fig. 3a, simulated force-depth curves obtained with different assumed tip radii were compared with experimental measurements, and the best agreement was achieved for an effective tip radius of approximately 1200 nm , consistent with values reported in the literature for calibrated or partially blunted indentation tips [5,15].

With the indenter geometry fixed, the enamel layer was reintroduced into the model for inverse material identification. Based on prior reports indicating negligible strain-hardening behavior in thin polymer-based coatings [6,7], the enamel was modeled as an elastic-perfectly plastic material. The Young's modulus was obtained directly from the unloading stiffness of the indentation experiments, while the yield strength was calibrated by matching the simulated and experimental indentation responses on the coated region. Fig. 3b illustrates the sensitivity of the simulated force-depth curves to the assumed enamel yield strength, from which a value of approximately 75 MPa was identified.

[picture]

Fig. 2. Schematic of (a) nano-indentation test FE model and (b) the indenter tip radius.

Fig. 2. Schematic of (a) nano-indentation test FE model and (b) the indenter tip radius.

[picture]

Fig. 3. (a) Reverse-engineering result of the copper indentation force-depth response for various indenter tip radii. (b)Enamel indentation force-depth response for various assumed yield stress.

Fig. 3. (a) Reverse-engineering result of the copper indentation force-depth response for various indenter tip radii. (b)Enamel indentation force-depth response for various assumed yield stress.

Bilayer Material Model Construction.

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

The calibrated copper and enamel properties were combined into a three-dimensional bilayer FE model, with layer thicknesses assigned based on microscopy measurements. Eight-node reduced-integration brick elements were used for both layers, enabling explicit representation of the stiffness contribution and springback effect of the enamel coating during forming simulations.
To validate the bilayer material model under bending-dominated deformation, three-point bending tests were performed on hairpin segments. Digital Image Correlation (DIC) was used to track deformation during loading and unloading, as shown in Fig. 4, allowing direct measurement of bending and springback angles. Table 2 compares the experimentally measured angles with FE predictions. The agreement within approximately 0.2∘ confirms that the proposed bilayer material model reliably captures the mechanical response relevant to the expanding and twisting processes, consistent with previous validation studies on hairpin and coated-conductor components [5].

[picture]

Fig. 4. DIC snapshots from the three-point bending test at the moments corresponding to (a) the bending angle and (b) the bent angle.

Fig. 4. DIC snapshots from the three-point bending test at the moments corresponding to (a) the bending angle and (b) the bent angle.

Table 2. Experimental and simulation comparison of three point bending test of hairpin.

Test | Bending angle[°] | Bent angle[°] | Spring-back[°]
1 | 60.0 | 54.5 | 5.5
2 | 60.2 | 54.7 | 5.5
3 | 59.9 | 54.7 | 5.2
Simulation | 59.78 | 54.08 | 5.7

Finite Element Modeling of the Expanding and Twisting Processes

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

Because the production equipment does not provide direct measurements of tool positions or core motion, the boundary conditions for expanding and twisting were reconstructed from manufacturing observations and geometric measurements. To improve computational efficiency while preserving relative tool-hairpin kinematics, the reconstructed core motion was represented by equivalent prescribed tool motions in the FE model. The expanding stage was modeled only to ensure physically realistic initial conditions for twisting, as its influence on the final protrusion length was found to be weak within the feasible process window. In contrast, the twisting stage governs axial material feeding from the straight segment into the curved region and thus dominates protrusion variation; accordingly, twisting was implemented using coupled axial displacement and tool rotation reconstructed from the servo-motor logs, with a small reverse rotation applied at the end to relax torsional constraint prior to unloading.

The reconstructed expanding and twisting sequences were implemented in a rigid-tool/deformablehairpin FE framework. To reduce numerical complexity associated with large rigid-body motion of the stator core, the core motion was kinematically replaced by equivalent prescribed tool displacements while preserving the relative tool-hairpin kinematics. The resulting deformation characteristics are illustrated in Fig. 5 and 6. During expanding, layer-dependent opening shapes appear due to differences in tool engagement depth, whereas twisting induces progressive axial feeding of the straight segment into the curved region through coupled axial-rotational motion, producing the characteristic S-shaped deformation. This mechanism directly governs the final axial protrusion length and provides the physical basis for the reduced-order predictor developed in the following section.

[picture]

Fig. 5. FEM-based visualization of expanding processes (a) initial position of hairpins and tools (b) initial partial insertion (c) initial radial expansion (d) axial insertion (e) reverse widening and (f) final expanding.

Fig. 5. FEM-based visualization of expanding processes (a) initial position of hairpins and tools (b) initial partial insertion (c) initial radial expansion (d) axial insertion (e) reverse widening and (f) final expanding.

[picture]

Fig. 6. FEM-based visualization of twisting processes (a) initial position of hairpins and tools (b) initial axial insertion into the twisting tool (c) further axial descent and tool rotation (d) reverse rotation.

Fig. 6. FEM-based visualization of twisting processes (a) initial position of hairpins and tools (b) initial axial insertion into the twisting tool (c) further axial descent and tool rotation (d) reverse rotation.

Initial Protrusion Length Control of Hairpin Leg

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

Because identical twisting conditions are applied across all hairpin layers in the actual production line, twisting-related parameters cannot explain the observed layer-to-layer scatter in the final
protrusion length. Instead, the dominant source of variation is the large and non-uniform initial protrusion length among layers prior to forming. Finite element simulations using the original layerspecific initial leg lengths reproduce pronounced deviations in the final protrusion, indicating that initial geometric offsets are transmitted almost directly through the expanding and twisting stages. This trend suggests an approximately one-to-one correspondence between the initial and final protrusion lengths, highlighting the role of axial material feeding during twisting as the primary mechanism governing protrusion transfer. Overall, these findings emphasize that controlling the initial protrusion length is essential for reducing layer-dependent scatter, and systematic strategies for initial-length control will be investigated in future work.

Regression Model for Predicting Final Protrusion Length

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To provide a compact mathematical description of the protrusion mechanism observed in the FE simulations, a physics-guided regression formulation was introduced. The aim of this model is not to construct a fully calibrated predictor for all manufacturing conditions, but to formalize the dominant geometric relationship governing protrusion length during twisting.

FEM results consistently show that the final protrusion length is primarily controlled by axial material feeding from the straight hairpin segment into the curved region during twisting. This feeding process is driven mainly by the twisting angle and the initial insertion length into the twisting tool, as illustrated by the deformation characteristics in Fig. 6. Based on this observation, the protrusion length Lp is expressed as a function of twisting-related kinematic variables as

Lp=a0+a1θ+a2lins+a3θlins(1)

where θ denotes the twisting angle and lins  represents the initial insertion length into the twisting tool. The coefficients ai are regression parameters reflecting the effective geometric contribution of each term.

Eq. 1 is constructed to reflect the observed deformation mechanism rather than to maximize statistical fitting accuracy. The inclusion of the interaction term θlins  accounts for the coupled effect of rotation and axial engagement, which governs the amount of material redistributed into the curved region during twisting. Other process variables were omitted because their direct effect on protrusion length was found to be limited within the feasible forming window.

Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

The FE results clarify the distinct roles of the expanding and twisting stages in determining the final protrusion length. Twisting governs the axial redistribution of material, where the straight segment is progressively fed into the curved region through coupled rotation and axial motion (Fig. 6). Consequently, the final protrusion is highly sensitive to the effective axial feed generated during twisting, making this stage the primary deformation-driving mechanism. In contrast, expanding mainly influences the local opening geometry and the stability of tool engagement. Once stable engagement is achieved, the direct impact of expanding on the final protrusion remains limited, and expanding can be regarded primarily as a feasibility-enabling step that provides physically realistic initial conditions for twisting.

Importantly, the observed layer-to-layer scatter in protrusion length cannot be explained by differences in twisting conditions, since identical forming settings are applied to all layers in production. Instead, simulations indicate that non-uniform initial protrusion lengths among layers are largely transmitted through the forming sequence, leading to a near one-to-one correspondence between the initial and final protrusion lengths. These findings suggest that protrusion variability arises from the combination of twisting-driven material redistribution and layer-dependent initial geometric offsets. The mechanistic understanding obtained here supports the development of reduced-order predictors for rapid estimation and motivates further investigation into geometry-based strategies for mitigating layer-to-layer variation.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

This study presented an integrated FE framework to analyze protrusion variation in twisted hairpin legs by combining bilayer material modeling with mechanically consistent boundary conditions reconstructed from manufacturing observations. The framework enables systematic evaluation of the expanding and twisting stages while maintaining fidelity to the practical forming sequence.

The results indicate that twisting governs the final protrusion length through axial material redistribution from the straight segment into the curved region, whereas expanding mainly serves as a feasibility-enabling step that establishes stable tool engagement and provides physically realistic initial conditions for twisting. Furthermore, under production conditions where identical forming settings are applied across layers, the analysis demonstrates that layer-to-layer protrusion scatter is primarily driven by non-uniform initial protrusion geometry.

By clarifying the respective contributions of deformation-driven mechanisms and initial geometric offsets, this work provides a mechanistic basis for reduced-order prediction of protrusion behavior and motivates further development toward geometry-based variability control.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.51.pdf

W. Maddumage, S. Ouenzerfi, S. Harmand, A. Cairns, A. Paykani, Thermal management of hairpin winding traction motors in electric vehicles: Parametric evaluation of impinging oil jet cooling using CFD simulations, Appl. Therm. Eng. 273 (2025) 126414.

A. Dannier, F. Di Bruno, F. Fiume, E. Fedele, G. Brando, Hairpin Winding Technology for Electric Traction Motors: Design, Prototyping, and Connection Rules, Proc. 2022 International Conference on Electrical Machines (ICEM), IEEE, pp. 1170-1175.

H. Yu, L. Li, J. Wu, Laser welding method and quality analysis of hairpin windings in electric drive motors, Opt. Laser Technol. 174 (2024) 110452.

T. Will, A. Olowinsky, M. Gillner, Prediction of electrical resistance of laser-welded copper pin-pairs with surface topographical information from inline post-process observation by optical coherence tomography, Int. J. Adv. Manuf. Technol. 127 (2023) 2947-2961.

H. Choi, P. Fazily, J. Park, Y. Kim, J.H. Cho, J. Kim, J.W. Yoon, Artificial intelligence for springback compensation with electric vehicle motor component, Int. J. Mater. Form. 15 (3) (2022) 22.

X. Long, X. Liu, H. Zhang, Indentation reverse algorithm of mechanical response for metallic coatings based on neural network and finite element method, Materials 16 (7) (2023) 2617.

A.R. Hosseinzadeh, F. Berto, G. Meneghetti, Determination of mechanical properties using sharp macro-indentation test and inverse analysis, Theor. Appl. Fract. Mech. 89 (2017) 1-10.

B.B. An, R.R. Wang, D.S. Zhang, Region-dependent micro damage of enamel under indentation, Acta Mech. Sin. 28 (6) (2012) 1651-1658.

Z. Wang, K. Wang, W. Xu, X. Gong, F. Zhang, Mapping the mechanical gradient of human dentin-enamel junction at different intratooth locations, Dent. Mater. 34 (3) (2018) 376-388.

I.N. Chou, S.C. Wang, Finite element analysis and optimization of springback reduction in Uchannel bending, J. Mater. Process. Technol. 89-90 (1999) 340-347.

N.A. Maske, J.K. Sawale, Taguchi approach for investigation of springback effect in aluminum sheet, Int. J. Mech. Eng. Rob. Res. 2 (3) (2013) 322-329.

D.T. Nguyen, J.E. Park, D.H. Kim, Optimization of influential process parameters on the deep drawing of aluminium 6061 sheet using Taguchi method and finite element analysis, in: Proc. KSME Spring Conf., 2009, pp. 1045-1050.

C. Depoorter, K. Faes, J. Penning, Mechanical heterogeneity in drawn copper wires due to microstructural gradients, Mater. Sci. Eng. A 666 (2016) 229-238.

S.H. Choi, Y.S. Kim, J.W. Lee, Effect of drawing sequences on mechanical inconsistency in copper conductors, J. Mater. Process. Technol. 265 (2019) 1-10.

N.V. Nguyen, J.J. Kim, S.E. Kim, Methodology to extract constitutive equation at a strain rate level from indentation curves, Int. J. Mech. Sci. 152 (2019) 363-377.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 59-64

doi: 10.4028/p-5nnEHa

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-20

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-16

Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

The original version of this paper is available on https://www.scientific.net/SSP.389.59.pdf

Conte Romina 1,a*, Trimarchi Stefano 1, b, Gagliardi Francesco 1,c, De Napoli Luigi 1, d, Ambrogio Giuseppina 1,e

1 University of Calabria, via P. Bucci, 87036 Rende (CS), Italy

a* romina.conte@unical.it, b stefano.trimarchi@unical.it, c francesco.gagliardi@unical.it, duigi.denapoli@unical.it, e  giuseppina.ambrogio@unical.it 

Keywords: thermoplastic, single point incremental forming, hot forming, PMMA.

Abstract

Thermoplastic-based sheets (TBSs) are increasingly adopted in the automotive and aerospace sectors due to their potential for producing lightweight and durable structures. However, conventional manufacturing techniques, such as compression molding, offer limited process flexibility, as they rely on costly, dedicated molds. Single Point Incremental Forming (SPIF) represents a promising die-less alternative. Nevertheless, its application to thermoplastics requires strict control of the process conditions to avoid material failure. This study focuses on the validation of a novel experimental apparatus for pressure-assisted hot SPIF. The developed equipment enables precise, real-time control and regulation of both the working temperature and the hydrostatic support pressure, which are critical parameters for enhancing polymer formability. A key aspect of the experimental procedure is the use of an aluminum sacrificial sheet placed between the forming tool and the polymeric blank. This intermediate layer fulfills a dual role by ensuring a hermetic hydraulic seal to prevent fluid leakage and by promoting uniform pressure distribution during the forming process. The experimental results demonstrate the effectiveness of the proposed setup, achieving successful deformation of TBSs with high geometric accuracy. Overall, this research confirms the feasibility and robustness of the designed equipment for processing unconventional materials, offering a flexible and efficient alternative to traditional rigid tooling technologies.

Introduction

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The manufacturing industry is increasingly driven by the demand for highly customized, lightweight, and high-performance components. In this context, Single Point Incremental Forming (SPIF) has emerged as a promising technology due to its extreme flexibility and the absence of dedicated dies, which significantly reduces lead times and costs for small-batch production. While SPIF has been extensively characterized for metallic sheets, the necessity to extend this dieless forming capability to thermoplastic based sheets (TBSs) is becoming crucial. These materials offer superior strength-to-weight ratios and chemical resistance, yet their shaping via traditional methods often lacks the versatility required for rapid prototyping and customized applications.

However, the transition from metals to polymers introduces significant challenges. Unlike metals, polymeric materials exhibit complex viscoelastic and viscoplastic behaviors that are heavily dependent on process parameters, particularly temperature. Early research by Martins et al. [1] demonstrated the feasibility of SPIF for commercial polymers at room temperature, identifying key failure modes and the critical role of tool-sheet interaction. More recently, the focus has shifted towards assisted forming strategies to overcome the limitations of cold forming, such as significant springback and limited formability. For instance, Almadani et al. [2] investigated a novel contactless hot air SPIF approach, highlighting how thermal management can reduce tool wear and improve geometric accuracy in polycarbonate sheets. These studies underscore the growing scientific interest in deforming polymers through non-conventional, incremental strategies to unlock new design possibilities.

Building on this background, the authors of the present work have conducted extensive research to define the process window for TBSs. Previous studies by Conte et al. [3] focused on the formability
of fiberglass-reinforced Polyamide 6 (PA6), developing specific setups to control the working temperature above the glass transition point. Further investigations [4, 5] explored the influence of process parameters on material failure and the potential for re-manufacturing thermoplastic composite structures, proving that SPIF can effectively process short-fiber reinforced matrices when thermal conditions are optimized. Indeed, SPIF could address the challenges of manufacturing TBSs preserving, at the same time their structural integrity and avoiding weak points due to uneven strain distribution [4,5].

Despite these advances, the processing of long-fiber reinforced plastics remains a critical frontier due to the risk of fiber breakage and the higher forces involved. In a very recent preliminary study [6], the authors proposed a customized process solution specifically designed to handle the complexities of long-fiber composites. The current study aims to validate and commission the specifically designed equipment, by experimental tests. Indeed, while the previous work introduced the concept, this paper focuses on the testing phase, providing experimental evidence of the process feasibility and the reliability of the new setup. For this preliminary experimental phase, polymeric sheets were used. The following sections will describe the equipment in detail, the employed material, and discuss the results of the validation trials, demonstrating how this novel approach can successfully plastically deform polymer panels.

The Designed Equipment

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The full experimental equipment is illustrated in Fig. 1.

[picture]

Fig. 1. Developed experimental equipment.

Fig. 1. Developed experimental equipment.

The equipment is designed to control temperature and pressure during the working phase [6]. A polymeric seal is located at the bottom of the processing tank, with glass wool positioned laterally. These materials act as thermal insulators to maintain a uniform temperature throughout the forming phase.
Specifically, the processing tank chamber is filled with a mixture of water and glycol. At the top, a seal, a polymer sheet, and a metallic sheet are stacked in that order, with the metallic sheet in contact with the rigid tool [4]. Once the upper edge of the metal sheet is clamped, the heating element is activated to reach the working fluid temperature. The fluid is then pressurized to generate a hydrostatic force, ensuring contact between the polymer and metallic sheets until both the forming and cooling phases are complete.

During the forming phase, the sheets deform into the processing tank chamber, causing volumetric displacement of the fluid. To maintain constant hydrostatic pressure, the system employs an
expansion vessel coupled with a pneumatic regulator. This regulator modulates the inlet air pressure to align with the required working pressure, ensuring stable system operation in conjunction with a vent valve.

Consequently, the pressure within the working zone is regulated via a control panel, which establishes the specific pressure profile required within the expansion vessel. A stratified thermal separator (cooling tank) is positioned at the exit of the processing tank to reduce the fluid temperature before its entry into the expansion vessel. A remote probe thermometer monitors the temperature within the processing tank. For safety reasons, a secondary thermometer measures the temperature in the cooling tank to preclude the return of high temperature and pressurized fluid into the expansion vessel.

The Process Feasibility

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Materials.

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SPIF was performed using 1 mm thick Al 2024 sheets and 2 mm thick Poly(methyl methacrylate) (PMMA) sheets [7]. The choice of aluminum was driven by its thickness and mechanical properties, which act to maintain dimensional stability and restrict upward yielding during the deformation of the underlying polymer.
Differential Scanning Calorimetry (DSC) was conducted to characterize the thermal properties of the PMMA, according to the ISO 11357 standard [8]. Analyses were performed using a DSC25 (TA Instruments). Three samples weighing between 2 and 6 mg were prepared and subjected to one cycle of a heating ramp at a constant rate of 10∘C/min. The resulting heat flow curve is presented in Fig. 2, from which a glass transition temperature ( Tg ) of 108∘C was determined.

[picture]

Fig. 2. PMMA heat flow curve.

Fig. 2. PMMA heat flow curve.

Experimental phase.

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During the process, a truncated cone specimen was fabricated, characterized by an upper diameter of 150 mm , a final height of 30 mm , and a wall angle of 30∘. Three experimental tests were conducted by varying the hydrostatic pressure, which was set to 0.1,0.2, and 0.4 bar, respectively.

For all tests, the working temperature was maintained at 115∘C. This temperature was selected based on the glass transition temperature of the polymeric material. The polymer was in contact with a water-glycol mixture, selected specifically to ensure controlled and safe boiling conditions throughout the experiments. To maintain a constant working temperature, the system was continuously monitored and heated using a thermocouple-regulated heating element. To ensure thermal equilibrium, the forming process was initiated only after a stabilization period of approximately 10 minutes; this duration was established by measuring the temperature on the upper face of the sheet during the start-up phase.

A rigid forming tool with a diameter of 10 mm was employed. The tool path followed a counterclockwise spiral trajectory with a vertical step-down of 1 mm per revolution, a spindle speed of 1000 rpm , and a feed rate of 400 mm/min. The upper and lower surfaces of the polymeric sheet, after completion of the forming process and subsequent unclamping, are shown in Fig. 3.

[picture]

Fig. 3. a) Upper surface and b) lower surface of the PMMA SPIFed sheet.

Fig. 3. a) Upper surface and b) lower surface of the PMMA SPIFed sheet.

After unclamping, the PMMA sheets were 3D-scanned using an Artec Eva system (accuracy: 0.1 mm , resolution up to 0.2 mm ). The acquired scans were subsequently imported into GOM Inspect software, where the measured geometries were superimposed onto the nominal model. Geometric deviations were quantified by evaluating the distance between the scanned surfaces and the nominal geometry over the entire formed area. This analysis enabled the assessment of shape accuracy and the identification of localized deviations associated with different hydrostatic pressure conditions. The resulting deviation maps were used to investigate the influence of process parameters on the dimensional accuracy of the formed PMMA components.

Discussion of Results

The original version of this paper is available on https://www.scientific.net/SSP.389.59.pdf

The results shown in Fig. 4 demonstrate how pressure variation significantly affects the final geometry, with the three samples exhibiting seemingly contradictory trends. Specifically, the deviation maps on the left side of Fig. 4 illustrate the global 3D geometric deviations of the entire scanned specimens relative to the nominal geometry. To provide a more detailed local analysis, the graphs on the right side display the 2D deviation profiles extracted along a representative planar crosssection. These superimposed curves are included to explicitly highlight the point-by-point discrepancy between the manufactured shape and the target profile.
The specimen formed at 0.1 bar showed relatively low deviation metrics (Mean Absolute Deviation: 1.77 mm ; SD: 2.42 mm ), yet it presented visually consistent geometrical discrepancies, such as curved walls and a pronounced radius at the upper diameter. This behavior suggests that the pressure was insufficient to generate the necessary hydrostatic force, failing to ensure complete adhesion between the polymeric blank and the sacrificial Al sheet.
Conversely, the specimen formed at 0.2 bar appeared to replicate the target geometry more accurately at first glance. However, quantitative analysis revealed higher deviation metrics (Mean: 2.43 mm ; Min: -7.44 mm ) compared to the 0.1 bar case. This indicates that while the pressure increase effectively resolved the inter-sheet adhesion issue, the hydrostatic force may have been excessive relative to the structural stiffness of the Al sheet. Consequently, the Al layer likely yielded or deflected beyond the nominal tool path, introducing a discrepancy between the target shape and the final polymeric geometry.

Finally, the specimen formed at 0.4 bar experienced excessive deformation and thinning at the base diameter. Although it exhibits the lowest mean absolute deviation ( 1.59 mm ), it also shows the largest deviation range ( +5.29 mm to -10.99 mm ), confirming that excessive pressure leads to process instability.

Overall, these findings clearly highlight that hydrostatic pressure plays a pivotal role in the process and must be carefully tailored according to the specific polymer type, the working temperature, and the structural resistance of the sacrificial metallic sheet.

[picture]

Fig. 4. Deviation maps showing differences between measured and nominal geometries for the three operating conditions: a) 0.1 bar, b) 0.2 bar, and c) 0.4 bar. For each condition, the global 3D deviation map is shown on the left, and the corresponding 2D deviation profile along a representative cross-section is displayed on the right.

Fig. 4. Deviation maps showing differences between measured and nominal geometries for the three operating conditions: a) 0.1 bar, b) 0.2 bar, and c) 0.4 bar. For each condition, the global 3D deviation map is shown on the left, and the corresponding 2D deviation profile along a representative cross-section is displayed on the right.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.59.pdf

The study successfully validated a novel experimental apparatus designed for the pressure-assisted hot SPIF of thermoplastic sheets. The proposed system demonstrated precise control of both the working temperature and the hydrostatic support pressure, effectively overcoming key limitations typically encountered in the forming of polymeric materials.

The experimental campaign conducted on PMMA sheets at a constant temperature of 115∘C highlighted the complex role of hydrostatic pressure in determining final part quality. Specifically, the results indicated that insufficient pressure ( 0.1 bar) fails to ensure complete adhesion between the polymer and the metallic sheet, leading to geometric defects such as curved walls. Conversely, while
increasing the pressure to 0.2 bar improved the visual replication of the shape by resolving the adhesion issue, it also revealed a critical trade-off: the hydrostatic force exceeded the structural stiffness of the sacrificial aluminum sheet, causing it to yield beyond the nominal tool path and introducing quantitative deviations. Excessive pressure ( 0.4 bar) proved detrimental, resulting in unstable and excessive deformation. Furthermore, the use of a sacrificial aluminum sheet proved effective in ensuring a hermetic hydraulic seal and promoting uniform pressure distribution throughout the forming process.

Overall, the findings confirm the reliability and versatility of the proposed equipment as a flexible solution for processing unconventional materials. Future work will focus on extending this approach to long-fiber-reinforced thermoplastics, exploring the controlled thermal and hydrostatic conditions to mitigate fiber damage and enhance material formability.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.59.pdf

P.A.F. Martins, L. Kwiatkowski, V. Franzen, A.E. Tekkaya, M. Kleiner, Single point incremental forming of polymers, CIRP Ann., 58 (2009) 229-232.

M. Almadani, A. Guner, H. Hassanin, K. Essa, Optimisation of a novel hot air contactless single incremental point forming of polymers, J. Manuf. Process., 117 (2024) 302-314.

R. Conte, G. Ambrogio, F. Gagliardi, P. Russo, L. Filice, Preliminary Experimental Analysis on Incremental Forming of Fiberglass Reinforced Polyamide 6, in: AITeM 2017, 2017.

R. Conte, G. Ambrogio, D. Pulice, F. Gagliardi, L. Filice, Incremental Sheet Forming of a Composite Made of Thermoplastic Matrix and Glass-Fiber Reinforcement, Procedia Eng., 207 (2017) 819-824.

G. Ambrogio, R. Conte, F. Gagliardi, L. De Napoli, L. Filice, P. Russo, A new approach for forming polymeric composite structures, Compos. Struct., 204 (2018) 445-453.

G. Ambrogio, F. Borda, R. Conte, L. Filice, F. Gagliardi, Processing of sheets made of long fibers reinforced plastics by SPIF, Mater. Res. Proc., 41 (2024) 1536-1543.

G. Ambrogio, F. Gagliardi, R. Conte, P. Russo, Feasibility analysis of hot incremental sheet forming process on thermoplastics, Int. J. Adv. Manuf. Technol., 102 (2019) 937-947.

International Organization for Standardization, ISO 11357-1:2016 Plastics - Differential scanning calorimetry (DSC) - Part 1: General principles, (2023).

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 65-74

doi: 10.4028/p-P58jF8

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-04

Revised:
2026-02-20

Accepted:
2026-02-24

Online:
2026-04-16

Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

The original version of this paper is available on https://www.scientific.net/SSP.389.65.pdf

Franz Reuther 1,a*, Verena Psyk 1, b and Verena Kräusel 1,c

1 Fraunhofer Institute for Machine Tools and Forming Technology, Reichenhainer Strasse 88, 09126 Chemnitz, Germany

a*  franz.reuther@iwu.fraunhofer.de, b  verena.psyk@iwu.fraunhofer.de, c  verena.kraeusel@iwu.fraunhofer.de

*corresponding author

Keywords: simulation, bipolar plates, hollow embossing rolling, disturbances.

Abstract

Hollow embossing rolling (HER) is a promising continuous forming technology for producing thin metallic bipolar half plates (BPHP) with micro-channel structures used in fuel cells and electrolyzers. This study presents a simulation-based analysis of process-specific disturbances influencing the forming accuracy and quality of HER-formed BPHP. Using a validated LS-DYNA shell-based model, the effects of six disturbance variables, roller misalignments (axial, tangential, angular), roller gap variation, initial sheet thickness deviation, and changes in friction coefficient, were systematically investigated. Results show that even small roller misalignments of ±10μ m or manufacturing related roller gap deviations of +5μ m lead to significant changes in rolling force, strip draw-in, and sheet thinning behavior. Variations in friction coefficient notably affect draw-in and wrinkling tendencies. Overall, the study highlights the high sensitivity of the HER process to geometric and frictional disturbances and provides quantitative tolerance limits crucial for precision manufacturing and robust continuous BPHP forming.

Introduction

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Hollow embossing rolling (HER) is a promising technology for continuous high rate forming of bipolar half plates - BPHP, i. e. thin metallic plates used as media distributors in fuel cell stacks [1] or electrolyzers [2]. Based on several preliminary studies with different approaches to the continuous rolling of complex channel geometries [3,4], this process approach has been significantly enhanced over the past five years. The starting point for this development was a series of numerical studies for designing, validating, and optimizing a basic virtual model approach [5]. This enabled not only the transfer of the validated models to full-scale plates [6], but also the experimental verification of the process [7] on specially developed rolling machines at the Fraunhofer Institute for Machine Tools and Forming Technology IWU [8]. The advantages of the HER process over conventional technologies such as hydroforming or stamping include significantly higher production rates due to continuous strip movement and in general lower forming forces, which enable a much more compact and cost-effective machine design [9]. However, forming ultra-thin metallic strips with thicknesses of 0.05−0.10 mm and micro-channel structures in the sub-millimeter range is still highly challenging. These boundary conditions require exceptionally high precision in the manufacturing of the embossing rollers, their alignment and their synchronous rotation. The aim of this study is the simulation-based evaluation of process-specific disturbances related to these process conditions in order to analyze their influence on the resulting quality of BPHP formed by HER and the derivation of tolerance requirements.

Simulation Set Up for Investigation of Disturbance Variables

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A miniaturized BPHP geometry measuring 45×30 mm is used for the following investigations for which experimental and numerical investigations have already been published in Reuther et al. [5].

The testing geometry combines different flow field zones with trapezoidal channel cross-sections and geometric elements representing typical BPHP for PEM fuel cells (Fig. 1 a). The initial sheet thickness is t0=0.1 mm.

[picture]

Fig. 1. Forming demonstrator BPHP: (a) experimental results of HER and geometry, (b) validated and optimized simulation model of hollow embossing rolling [5].

Fig. 1. Forming demonstrator BPHP: (a) experimental results of HER and geometry, (b) validated and optimized simulation model of hollow embossing rolling [5].

With the aim of a simulation-based investigation of disturbances in hollow embossing rolling on this BPHP geometry, a corresponding shell-based model was set up in LS-DYNA R12.1 (Fig. 1 b) using the already validated modelling approach presented in [5]. The rigid surface meshes of the forming rollers rotate synchronously with each other and gradually form the channel geometry into the sheet metal strip. This is fed under strip tension on the inlet side σx,i=100 N/mm2 in order to prevent uncontrolled strip draw-in and therefore excessive wrinkling. Another key feature is the flexible definition of the rotation axes, which is implemented for each roller mesh using springdamper elements. By defining a sufficiently large constant clamping force Fz,c at the axis suspension of the upper roll, the strip can be carried along by the contacts in accordance with the experimental boundary conditions. Due to this flexible axis modelling, the effective rolling gap sw does not remain constant at the initially specified value of sw=t0, but can change as a result of the current rolling force Fz caused by different local BPHP cross-sections (load-dependent rolling gap change Δsw ). Both aspects have been identified as important features for accuracy during model validation and are therefore also taken into account in this study. Based on the previous investigations [5], a static friction coefficient of μs=0.25 is defined as first assumption. Further boundary conditions for modeling with regard to strip and roller meshing, as well as other setting parameters for explicit computation, are based on previously developed standards for shell-based simulation of HER with LS-DYNA [10]. Elastic-plastic material modelling of the strip material (austenitic stainless steel 1.4404) was implemented using an anisotropic material law with strain rate dependency based on uniaxial tensile tests at different strain rates and rolling direction orientations as well as bulge tests according to [5].

Definition of Disturbances and Evaluation Criteria

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Based on this reference simulation setup, different disturbance variables are implemented separately in the reference model and the changes in the result variables are analyzed in order to systematically identify correlations. As shown in Fig. 2, a selection of six different disturbance variables is investigated: Misalignments of the upper roller mesh relative to the lower roller leading to changes in the rolling gaps between the rollers especially at the trapezoidal oriented channel flanks. A distinction is made here between axial δy, tangential δx, and angular misalignment δα. While axial misalignment primarily affects the existing rolling gap of channels oriented longitudinally to the rolling direction (RD), tangential and angular misalignment affects the rolling gap in channels
oriented transversely to the RD. Generally, no change is visible in the case of horizontally oriented cross-section areas (channel head and foot areas) as the roller meshes are only shifted horizontally to each other. In contrast, the roller gap variation δsw symbolizes a geometrical change in the die roller due to assumed manufacturing inaccuracies. This change is defined in simple terms as homogeneous oversize, which is represented equally in the flat areas of the channel cross-sections and in the channel flanks. Positive values lead to a smaller effective rolling gap and vice versa. A similar effect is caused by a variation in the initial sheet thickness δt0. With t=t0+δt0 clamping effects in the rolling gap increase for δt0>0, because the thicker strip is formed into the initial roller meshes of the reference simulation. Variations in the static friction coefficient δμs are also investigated as a final disturbance variable. Since the contact and friction situation generally has major influence on the forming result in the microforming of BPHP-typical channel structures, it can be assumed that corresponding variations also significantly affect the results. Varying friction coefficients can be caused, for example, by different surface roughnesses of the rollers or strip materials or by an inhomogeneous lubricant supply, whereby these fluctuations cannot be sufficiently limited due to manufacturing or process-related factors.

[picture]

Fig. 2. Investigated disturbance variables: misalignments, variation of roller gap and initial thickness as well as coefficient of friction variation.

Fig. 2. Investigated disturbance variables: misalignments, variation of roller gap and initial thickness as well as coefficient of friction variation.

For the systematic analysis of the result changes, a range of process-specific evaluation variables are used, which are summarized in Table 1. A change in the stretching behavior during channel forming is represented by the resulting sheet thickness variation Δt. Effects on strip draw-in and the associated wrinkling tendency are analyzed by transversal and longitudinal strip draw-in changes (Δye,Δxe) as well as a wrinkle criterion ΔεWT according to [6]. In addition, there are possible changes in the rolling force ΔFz during continuous channel forming. Geometric changes of the forming demonstrator are considered here as changes of the channel height Δh and the resulting flatness deviation ΔδE. The evaluation is carried out in accordance with the specifications in Table 1 and the listed threshold levels each defining the transition from a minor to a significant change in results. Usually, the results are analyzed by average values (e.g., ΔFz― ) and the corresponding standard deviations. In order to highlight individual effects, some results are summarized by calculating the mean value only for individual sections ( A,B,C,D ), specific areas ( x1,x2,x3,x4 ), or time periods ( t1, t2,t3,t4 ), at which certain areas are to be formed (Fig. 3).

Table 1. Evaluation criteria with corresponding methods, reference and thresholds values.

result variable change | evaluation method | reference value | threshold level
strip thickness Δt in µm | section-based (A-D), separate evaluation of channel flanks, heads and foots [6] | 25 µm (t₀ - tmin) | ±1µm (~5 %)
draw-in (transversal) Δye in mm | transversal draw-in of the strip edge (y-dir.), zone-based evaluation (x1–3) | 0.4 mm (ye,max) | ±0.02 mm (~5 %)
draw-in (longitudinal) Δxe in mm | longitudinal draw-in of the strip end (x-dir.), evaluation at different time periods (t1–3) | 2.0 mm (xe,max) | ±0.10 mm (~5 %)
rolling force ΔFz in kN | evaluation at different time periods (t1–3) | 5 kN (Fz,max) | ±0.25 kN (~5 %)
channel height Δh in µm | section-based (A-D) | 0.5 mm (hmax) | ±5 µm (~ 1 %)
flatness deviation ΔδE in mm according to [6] | deviation to target-geometry, separate evaluation for clamped an unclamped state | - | 0.1 mm

[picture]

Fig. 3. Evaluation for BPHP testing geometry: section definition, zones and time periods.

Fig. 3. Evaluation for BPHP testing geometry: section definition, zones and time periods.

Effects of Disturbance Variables on Evaluation Criteria and Discussion

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Axial misalignment.

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Assuming an axial misalignment δy of the upper roller of max. ±30μ m, several significant result changes can be observed compared to the reference simulation, which exceed the defined threshold level. The axial misalignment is first evident in the form of increasing rolling forces (Fig. 4 a). For δy>+20μ m and <−10μ m, significant rolling force changes occur throughout the entire channel forming period compared to the reference due to the locally reduced rolling gap in all areas with longitudinal channels (Fig. 4 b , time period t2 ). The average transversal edge draw-in Δye is even more sensitive, being significantly lower for the middle part section x2 even at an axial misalignment of δy~−5μ m. Changes in the edge draw-in are therefore a suitable evaluation criterion for identifying axial misalignment of the forming rollers experimentally. Due to the increased rolling forces (Fig. 4 c), axial misalignment is also accompanied by increasing rolling gap changes (on average +0.7μ m at δy=−20μ m ). The average sheet thickness change in the channel flanks is small according to Fig. 4 a, but the large standard deviations also indirectly indicate a significant influence here. The alternating decrease and increase in the rolling gap in the successive channel flanks of longitudinal channels results in alternating larger and smaller thinning effects. Even at δy=−5μ m, changes in the maximum thinning in the channel flanks of ±5μ m(~±5%) can be detected on average, which is a relevant order of magnitude, particularly regarding forming limits and crack formation in the channel flanks. The thinning of adjacent flanks of longitudinal channel structures with identical cross-sections can therefore also be used as an evaluation criterion to quantify axial misalignments of the forming rollers experimentally.

[picture]

Fig. 4. Effects of axial misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of transversal draw-in, (c) exemplary change of rolling force.

Fig. 4. Effects of axial misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of transversal draw-in, (c) exemplary change of rolling force.

Tangential misalignment.

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With a tangential misalignment δx of the forming rollers the locally smaller rolling gaps at transversal channels lead to increased rolling forces, which can be seen, for example, for δx=±30μ m, for time periods t1 and t3 (Fig. 5 b).

[picture]

Fig. 5. Effects of tangential misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of rolling force, (c) exemplary change of thickness in longitudinal section D .

Fig. 5. Effects of tangential misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of rolling force, (c) exemplary change of thickness in longitudinal section D .

For these evaluation areas, the threshold values are also exceeded at δx>+10μ m and <−20μ m (Fig. 5 a). A tangential misalignment of the forming rollers is also characterized by larger average channel heights of transversal channels (section D) when δx=±10μ m is exceeded. Similar to the explanations for axial misalignment, the locally changed rolling gaps also lead to alternating larger and smaller thicknesses in the channel flanks (Fig. 5 c ).

Angular misalignment.

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The influence of an angular misalignment δα of the forming rollers was evaluated analogously by several simulations with different angular positions of the upper roller. To ensure comparability with the misalignment types, δx was changed in radian increments of 10μ m for the roller diameter of 105 mm , which corresponds to an angular value of 0.011∘. As expected, the resulting sensitivities are comparable to those of tangential misalignment (Fig. 6 a).

[picture]

Fig. 6. Effects of angular misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of rolling force, (c) exemplary change of longitudinal draw-in.

Fig. 6. Effects of angular misalignment: (a) significant changes of evaluation criteria, (b) exemplary change of rolling force, (c) exemplary change of longitudinal draw-in.

Again, significantly higher rolling forces (Fig. 6 b) and channel heights in transverse channel areas for δα<−10μ m and >+20μ m can be observed. The difference between positive and negative angular misalignment also arises here due to the different situation in the rolling gap. With a negative angular misalignment δα and a positive tangential misalignment δx, the rolling gap of the firstly formed transversal channel flank is reduced, resulting in a higher increase in rolling force than an equivalent rolling gap reduction of the subsequent transversal channel flank. A tangential misalignment of δα<−10μ m and >+20μ m is also associated with significant changes in longitudinal draw-in (Fig. 6 c ). Due to the narrower rolling gap, a lower longitudinal draw-in is observed at the beginning of channel forming (t1) with a negative angular misalignment.

Initial sheet thickness variation.

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For a comprehensive evaluation of process robustness, the effect of an initial thickness change δt0 in the range of ±15μ m was also analyzed as a further possible process-specific disturbance variable. As expected, this results in significant rolling gap changes equivalent to the change in sheet thickness (Δsw~δt0). Even at only δt0=+5μ m, a significant increase in rolling forces can be observed (Fig. 7 a). On the one hand, the force required to form an identical channel geometry generally increases with higher initial sheet thickness; on the other hand, a clamping effect increasingly occurs in the flanks (Fig. 7 b). Since the meshes of the roller segments are identical, there are no changes in the predicted channel heights. Further significant changes in the results can already be observed for δt0<−10μ m and >+5μ m for the transversal edge draw-in ye. This edge draw-in reduces with increasing initial sheet thickness, as more resistance is caused by the thicker strip drawing into the outer channel of the surrounding sealing bead. Significant changes in results due to a sheet thickness change of δt0>±5μ m can also be observed for the longitudinal draw-in xe. This is mainly caused by a generally reduced longitudinal draw-in of the strip when the first transversal channel is formed with a higher initial sheet thickness. Furthermore, higher plastic strains in longitudinal direction already occur in the middle plate area decreasing longitudinal draw-in as well. The significantly affected draw-in behavior in the transversal and longitudinal directions also correlates with the changed results of wrinkling criterion ΔεWT according to [6]. For δt0=+15μ m, wrinkling critical areas are much smaller than for δt0=−15μ m (Fig. 7 c ).

[picture]

Fig. 7. Effects of initial thickness variation: (a) significant changes of evaluation criteria, (b) exemplary change of cross-sectional situation, (c) exemplary change of wrinkling tendency.

Fig. 7. Effects of initial thickness variation: (a) significant changes of evaluation criteria, (b) exemplary change of cross-sectional situation, (c) exemplary change of wrinkling tendency.

Roller gap variation due to manufacturing inaccuracies.

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As the machining of such fine channel cross-sections is usually associated with tolerances in the range of ±10μ m, the variation in the rolling gap due to manufacturing inaccuracies is another potential disturbance variable for HER. The changes in the results compared to the reference simulation are therefore analyzed when the upper die roller is provided with a uniform offset δsw of ±15μ m. The resulting rolling gap in the channel area with an identical lower punch roller is thus sw=t0−δsw (Fig. 8 b). In general, similar result sensitivities can be observed as in the influence analysis of a sheet thickness change (Fig. 8 a). Firstly, the significant increase in rolling forces at δsw>0 resulting from the reduction in the effective rolling gap is remarkable. The corresponding threshold value ( ~5% of the reference value) is already reached at δsw=+5μ m, meaning that a manufacturing-related rolling gap decrease of 5μ m already results in significant rolling force increase. As expected, the loaddependent rolling gap change also increases with higher offset δsw. The narrower rolling gap tends to result in lower sheet thicknesses in the channel flanks and head and foot areas. The threshold value for the change in results is reached here on average at δsw=±15μ m, whereby standard deviations already indicate significant local changes in results at lower values of δsw. Both the transversal edge draw-in and the longitudinal strip draw-in are also reduced as a result of a decreasing rolling gap and reach the corresponding threshold values at δsw=+5μ m. While flatness deviation remains almost unchanged in the clamped state, there is also a significant increase in flatness deviation in the unclamped state for δsw>5μ m. Fig. 8 a also shows that negative values for δsw, resulting in a larger rolling gap between the rollers due to manufacturing inaccuracies, generally do not lead to any significant changes in the simulation results.

[picture]

Fig. 8. Effects of roller gap variation: (a) significant changes of evaluation criteria, (b) exemplary change of cross-sectional situation.

Fig. 8. Effects of roller gap variation: (a) significant changes of evaluation criteria, (b) exemplary change of cross-sectional situation.

Coefficient of friction variation.

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Experimental studies on model validation have already shown that static friction coefficients of μs= 0.25 occur due to scaling effects of microforming in the HER of BPHP and have a major influence on the forming results [5]. For this reason, possible process-related variations in the static friction coefficient δμs=±0.15 are finally analyzed, which can arise, for example, due to varying surface roughness or inhomogeneous lubricant supply. The resulting friction coefficient is μs=0.25+δμs, covering a range from 0.1 to 0.4 . Unlike previous results, such parameter variation causes only a slight change in the rolling forces below the threshold value. However, the influence on the thinning behavior of the strip in the channel cross-sections is much more significant. As expected, a higher coefficient of friction leads to more pronounced thinning in the channel flanks and less thinning in the channel head and foot areas, as the higher frictional forces inhibit flow from these flat areas (Fig. 9 a). The threshold value for the change in results is exceeded on average from δμs=±0.1, although standard deviations already indicate significant changes in the sheet thickness results even with minor changes in the friction coefficient. As a result of a changed coefficient of friction, significant changes in the results also occur with regard to transversal (Fig. 9 b) and longitudinal strip draw-in. Even at δμs=±0.05, the corresponding threshold value for the change in results is exceeded. Higher coefficients of friction and the associated higher frictional forces reduce the resulting transversal and longitudinal strip draw-in, which also reduce wrinkling-critical areas in the surrounding flange area (Fig. 9 c). Particularly at lower coefficients of friction ( δμs<0 ), a clear increase in the predicted flatness deviation can also be observed, which can primarily be attributed to generally reduced stretching effects in the longitudinal and transverse directions of the strip. In contrast, no significant changes in flatness deviations occur at higher friction coefficients ( δμs>0 ).

[picture]

Fig. 9. Effects of coefficient of friction variation: (a) significant changes of evaluation criteria, (b) exemplary change transversal draw-in, (c) exemplary change of wrinkling tendency.

Fig. 9. Effects of coefficient of friction variation: (a) significant changes of evaluation criteria, (b) exemplary change transversal draw-in, (c) exemplary change of wrinkling tendency.

Limitations.

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It is important to note that the idealized conditions of FE models, particularly in shell-based meshing and contact modeling, are typically associated with limitations and model errors. Although the qualitative correlations are entirely plausible, quantitative values should be further validated through extended experimental studies.

Summary

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In this study, the effects of process-specific disturbances in hollow embossing rolling (HER) were investigated for continuous production of bipolar half plates (BPHP) with complex channel geometries. Using previously optimized and validated FE models, the effects of roller misalignments, roller gap and sheet thickness variations as well as changing friction coefficients were analyzed on process-relevant evaluation criteria of HER. In summary, it was demonstrated that a forming roller misalignment of ±10μ m leads to significant changes in results above the defined threshold values for the ideal reference state. This is mainly caused by increasing rolling forces as a result of locally narrower rolling gaps. Depending on the type of misalignment, channels oriented either longitudinally or transversely to the rolling direction will exhibit changes in the rolling gaps of the channel flanks. Significant changes in the results compared to the reference case can then be observed both in terms of thinning effects of the channel flanks and in terms of the transversal and longitudinal strip drawin. The influence of roller misalignment should not only be evaluated as a possible quality-impairing disturbance variable in BPHP forming, but also in terms of minimizing tool load and wear effects. Similar effects were caused by changes in initial sheet thicknesses and reduced rolling gaps due to manufacturing inaccuracies, also leading to a change in rolling force due to the changed situation in the rolling gaps. From a technological point of view, reduced rolling gaps due to manufacturing inaccuracies are particularly critical. Even an oversize of only δsw=+5μ m already affects the evaluation criteria significantly. In this case, the required rolling force increases by 5% compared to the ideal reference simulation. Accordingly, very tight manufacturing tolerances of ±5μ m are recommended for the forming rollers in order to provide ideal conditions for the HER process. Further investigations on the influence of the coefficient of friction also confirm significant effects on the evaluation criteria of thinning, strip draw-in, and the resulting flatness deviation. From a technological point of view, smaller coefficients of friction, for example caused via additional lubrication, are generally associated with negative effects, as the increased longitudinal and transverse draw-in results in a smaller locally strip stretching, which then becomes visible in the form of more pronounced wrinkling tendencies and flatness deviations.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.65.pdf

Porstmann, S., Wannemacher, T., Drossel, W.-G., 2020. A comprehensive comparison of state-of-the-art manufacturing methods for fuel cell bipolar plates including anticipated future industry trends. J. Manuf. Process. 60, 366-383.

Reuther, F., Melzer, S., Geist, A., Polster, S., Psyk, V., 2024. Iterativer Designprozess für hohlprägegewalzte Elektrolyseurplatten am Beispiel von "HyVentus". FC FUEL CELL CONFERENCE 2024, 12 November 2024, Chemnitz.

Abeyrathna, B., Zhang, P., Pereira, M.P., Wilkosz, D., Weiss, M., 2019. Micro-roll forming of stainless steel bipolar plates for fuel cells. Int. J. Hydrogen Energy 44 (7), 3861-3875.

Bauer, A., Härtel, S., Awiszus, B., 2019. Manufacturing of Metallic Bipolar Plate Channels by Rolling. JMMP 3 (2), 48.

Reuther, F., Dix, M., Kräusel, V., Psyk, V., Porstmann, S., 2024. Model validation of hollow embossing rolling for bipolar plate forming. Int J Mater Form 17 (2).

Reuther, F., 2025. Simulation of hollow embossing rolling for full-scale bipolar plates, in: Material Forming: ESAFORM 2025. Material Forming. 05/07/2025. Materials Research Forum LLC, pp. 1972-1981.

Heidrich, S., Wagner, M., Kurth, R., Reuther, F., Ihlenfeldt, S., 2025. Key Parameters in Hollow Embossing Rolling of Metallic Bipolar Plates, in: International Rolling Conference (IRC 2025) Conference Proceedings. International Rolling Conference 2025. 2025. Association for Iron & Steel Technology.

Wagner, M., Alaluss, M., Langheinrich, J., Reuther, F., Kurth, R., Ihlenfeldt, S., 2024. Prozessüberwachung mittels maschineninhärenter Sensoren/Transparency improvement in hollow embossing rolling of metallic bipolar plates - Process monitoring by using machineinherent sensors. wt 114 (01-02), 15-20.

Porstmann, S., Polster, S., Reuther, F., Melzer, S., Nagel, M., Psyk, V., Dix, M., 2021. Objectives and fields of tension in the comparison of manufacturing processes for metallic bipolar plates. Fuel Cell Conference FC³, 2021, Chemnitz.

Reuther, F., Psyk, V., Kräusel, V., Dix, M., 2023. Simulation of Hollow Embossing Rolling for Bipolar Plate Forming using LS-DYNA©. 14th European LS-DYNA Conference, 2023, Baden-Baden.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 75-81

doi: 10.4028/p-BKD4Wl

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-11

Revised:
2026-02-25

Accepted:
2026-02-27

Online:
2026-04-16

On the Surface Quality of Incrementally Formed Niobium Sheets

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Antonio Formisano 1,a, Antonello Astarita 1, b*, Marco Garlasché 2,c, Umberto Prisco 1, d, Fabio Scherillo 1,e and Massimo Durante 1,f

¹Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le V. Tecchio 80, 80125 Napoli, Italy

2 CERN - European Centre for Nuclear Research, Geneva, Switzerland

a aformisa@unina.it, b antonello.astarita@unina.it, c marco.garlasche@cern.ch, d umprisco@unina.it, efabio.scherillo@unina.it, f  mdurante@unina.it 

Keywords: Incremental Sheet Forming, Niobium, Surface Quality, Hardness.

Abstract

Incremental sheet forming is a viable method for manufacturing highly customized components from non-conventional materials. Among these, niobium is a metal of growing interest due to its potential in various technological applications. In this experimental study, the incremental forming of high-purity annealed niobium sheets was investigated, with particular attention given to the surface finish of the formed parts. To this end, the surface morphology of the components, specifically fixed wall conical frusta, and the forming forces were analyzed. The results indicate that, despite the material's notable formability, the incrementally formed niobium surfaces exhibit poor quality. This is attributed to the unique properties of niobium, suggesting that the development of surface treatment strategies is advisable to improve this aspect.

Introduction

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Niobium ( Nb ) is a ductile transition metal that exhibits several distinctive properties, making it suitable for a wide range of technological applications. One of the most demanding and compelling uses is in the fabrication of superconducting radiofrequency (SCRF) accelerating cavities [1] because among superconducting materials, Nb exhibits the highest lower critical magnetic field and superconducting transition temperature and a high normal state thermal conductivity [2-4].

However, this non-conventional material is subject to complex and unusual surface phenomena that can compromise the quality of the finished surfaces (an aspect of primary importance for SCRF cavities in service [5]). For instance, predicting the surface finish after a metal forming process can be challenging [6], and the resulting surfaces may exhibit an orange peel effect and high roughness due to the non-uniform deformation of large grains with varying crystalline orientations [7]. Moreover, the sheets may be affected by galling, a type of adhesive wear characterized by the macroscopic transfer of material between metal surfaces due to their relative sliding motion [8].

Incremental sheet forming is a manufacturing technique originally developed for common metal alloys as an alternative to conventional forming methods, particularly for shaping flat metal sheets into complex three-dimensional profiles [9]. The core principle of this technique involves the progressive deformation of a clamped sheet of material by a forming tool, which is controlled by a computerized numerical control (CNC) machine. The tool follows a programmed path, gradually shaping the sheet into its final geometry [10]. More recently, this process has been applied to metals that are traditionally difficult to form, such as magnesium, titanium, and their alloys [11-13], with the goal of improving both formability and surface quality.

A previous study by the authors [14] examined key aspects of the incremental forming of thin rolled Nb sheets, including formability limits, forming forces, surface roughness, and other relevant parameters. The study revealed that, despite the brittle nature of the material, the sheets exhibited remarkably high formability during incremental forming. A maximum formability angle of approximately 75∘ was achieved through varying wall angle conical frusta tests. Furthermore, fixed wall angle tests resulted in very low surface roughness values under different tool/sheet contact conditions, although scratches caused by galling were still observed.

This work presents an experimental investigation into cold incremental forming of high-purity annealed RRR300 Nb sheets. By analyzing the forming forces and the morphology of the worked surface, the study aims to correlate the surface quality of incrementally formed Nb components with their mechanical properties, while proposing strategies to enhance the understanding of incremental forming applied to Nb sheets.

Materials and Methods

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Fixed wall angle conical frusta were fabricated using cold incremental sheet forming, starting from high-purity annealed RRR300 Nb sheets (supplied by Ningxia Orient Tantalum Industry Co., LTD) with a thickness of 1.0 mm . The main geometrical features of the conical frusta are listed below (see Fig. 1):

wall angle α=60∘;

height h=35 mm;

radius of the major base R=35 mm.

[picture]

Fig.1. Geometrical features of the conical frusta

Fig.1. Geometrical features of the conical frusta

A C.B. Ferrari high-speed four-axis vertical machining center operated at a feed rate of 1000 mm/min, driving a non-rotating stainless-steel stylus with a hemispherical head, 10 mm in diameter. The stylus acted as the forming tool for the sheet, which was clamped along its periphery by a blocking system with a square area measuring 100 mm per side. These process parameters have been chosen by considering both the available literature and previous papers of the authors where the incremental forming of niobium sheets has been investigated.

A unidirectional spiral-based strategy was adopted as the toolpath, with a vertical step depth of 1 mm . Furthermore, the process was carried out under lubricated conditions using Boelube 70104 (100 A) lubricant (supplied by Orelube) to minimize the risk of failure and defects [15].

An image of the experimental setup is shown in Fig. 2.
The formed parts were inspected for failures and/or defects, including twisting, which was quantified by measuring the twist angle (it corresponds to the rotation angle after the forming process of a cross, marked on the bottom of the plane sheets, with respect to its initial position), to assess the formability of the incrementally formed Nb sheets.

Additional insights were obtained through the evaluation and interpretation of the forming forces ( FXY,FZ and FTOT, representing the in-plane, vertical and total forming forces, respectively) as well as the moment around the vertical axis ( Mz ). These parameters were recorded at a sampling rate of 50 Hz using a K-MCS10 multicomponent sensor, integrated with the QuantumX MX840B data acquisition system and Catman Easy AP software.

Finally, the surface quality was assessed through visual inspection and roughness measurements (five repetitions) taken along the cross-section of the formed surfaces using a Mitutoyo Surftest SJ301 tester. The evaluation adopted differential inductance and Gaussian filters as the detecting method, with the cut-off value selected in accordance with ISO 4288-1996 standards.

[picture]

Fig. 2. Experimental setup of the incremental sheet forming process

Fig. 2. Experimental setup of the incremental sheet forming process

Results and Discussion

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The process was carried out successfully (Fig. 3 shows a conical frustum), without any tearing or wrinkling. However, the frustum exhibited a twisting angle of 2.4∘, which is attributed to in-plane forming forces generating a torque ( Mz ). Compared to incrementally formed polycarbonate sheets under similar working conditions [16], where this phenomenon also led to instabilities, the observed twisting was minimal.

[picture]

Fig. 3. Conical frustum produced via incremental sheet forming

Fig. 3. Conical frustum produced via incremental sheet forming

Fig. 4 shows the trends of the forming forces and the moment Mz. After an initial transition phase, the forces (Fig. 4a) reached a quasi-steady state condition, corresponding to the plastic deformation of the sheet. This condition was associated with a decrease in MZ (Fig. 4b), due to the progressive reduction in the diameter of the conical frusta as vertical displacement increased.

[picture]

Fig.4. Trends of forces (a) and moment (b) during the incremental forming process of Nb sheets

Fig.4. Trends of forces (a) and moment (b) during the incremental forming process of Nb sheets

Quantitatively, the forming forces remained low (one of the distinctive characteristics of the incremental forming process; FTOT did not exceed 1400 N ). However, Fig. 4a reveals that the in-plane forces were comparable to the vertical ones, which is an uncommon outcome. It is worth noting that three components contribute to the in-plane forces, i.e. the thrust exerted on the cone wall, the friction resulting from the relative motion between the tool and the sheet and the flattening effect caused by vertical displacement [17]. While the first component was predictably low, being dependent solely on the combined shapes of the tool and the conical frusta, the other two components were relatively high. Fig. 5 illustrates the morphology of the worked surfaces. Despite the presence of lubricant, which reduces friction, the figure reveals scratches caused by galling. Additionally, the worked surfaces show technological imprints left by the forming tool. These signatures are particularly significant, also due to the considerable vertical indentation (surveyed by a mechanical feeler pin) left on the sheet, measuring 0.24 mm .

[picture]

Fig. 5. Morphology of the worked surfaces

Fig. 5. Morphology of the worked surfaces

Concerning surface roughness, measurements yielded a mean roughness Ra=4.03μ m and a root mean square roughness Rq=5.20μ m. These values are significantly higher than those obtained from square frusta from fixed wall angle tests using pure Nb rolled sheets under similar working conditions, for which Ra=1.78μ m and Rq=2.26μ m [14].

As observed with incrementally formed grade 1 titanium thin sheets, where thermal oxidation treatments ensured high surface quality [13], the work hardening induced by rolling similarly benefits Nb sheets. This suggests the need to develop appropriate surface treatments. Indeed, according to the material datasheet, undeformed Nb sheets employed in this study exhibit a Vickers hardness of 51.5 HV, whereas hardness tests on the rolled sheets reported in [13] revealed increased hardness, ranging from 100.2 HV (after rolling) to 112.0 HV (after incremental forming).

Conclusions and Future Work

The original version of this paper is available on https://www.scientific.net/SSP.389.75.pdf

This study presents an experimental investigation into the cold incremental forming of high-purity annealed RRR300 niobium sheets. The principal findings are as follows:

Niobium sheets exhibit excellent workability under incremental forming conditions, demonstrating high formability and minimal defect generation;

The total forming forces are low, although the in-plane and vertical components are comparable;

The surface quality of the formed components is significantly affected by the inherently low hardness of niobium, showing technological imprint and scratches.

Developing surface treatment strategies to enhance the surface quality of incrementally formed niobium components represents a promising direction. Furthermore, future research could focus on simulating the forming process to enable a more comprehensive analysis of the process parameters.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.75.pdf

This work was supported by the "Programma per il Finanziamento della Ricerca di Ateneo (FRA) 2022" of the University of Naples Federico II.

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The original version of this paper is available on https://www.scientific.net/SSP.389.75.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 83-94

doi: 10.4028/p-g9Pcig

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-18

Revised:
2026-02-21

Accepted:
2026-02-25

Online:
2026-04-16

Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

The original version of this paper is available on https://www.scientific.net/SSP.389.83.pdf

Mattia Dal Maso 1,a*, Enrico Simonetto 1, b, Andrea Ghiotti 1,c, Stefania Bruschi 1, d, Stefano Filippi 2,e, Lukas Hauser 3,f and Mathias Liewald 3, g

1 Department of Mechanical Engineering, Università degli Studi di Padova, 35131 Padua, Italy

2 Rheonex Srl, Vicolo d'Arcano 8, Udine, 33100, Italy

3 University of Stuttgart, Institute for Metal Forming Technology (IFU), 70174 Stuttgart, Germany

a  mattia.dalmaso@phd.unipd.it, b  enrico.simonetto.1@unipd.it, c  andrea.ghiotti@unipd.it, d stefania.bruschi@unipd.it, e info@rheonex.com, f lukas.hauser@ifu.uni-stuttgart.de, ¹ mathias.liewald@ifu.uni-stuttgart.de 

Keywords: Deep drawing, Blank-holder, Pressure distribution, Numerical simulations, Sheet metal forming, Magnetorheologic actuator, Ferrofluid.

Abstract

This study investigates the structural response of blank-holders (BHs) equipped with spatially distributed magnetorheological (MR) actuators for adaptive deep drawing. While MR actuators provide fast, independent, and high-resolution force modulation, their effectiveness depends critically on the BH's ability to transmit spatially differentiated loads without excessive diffusion or unrealistic stress localization. The relationships between BH stiffness, actuator spacing, and pressure localization at the sheet interface remain only partially understood, limiting the implementation of distributed blank-holding strategies. To address this gap, a comprehensive finite element (FE) framework is developed, combining a full closed-cup deep-drawing model with a complementary simplified configuration that isolates local deformation mechanisms under single-actuator loading. Parametric analyses examine the influence of BH thickness, local actuator force, and actuator spacing on stress distribution, localization radius, and overlap between adjacent load paths. Results show that BH thickness is the dominant factor governing spatial resolution: thinner BHs enable sharp pressure localization, whereas thicker ones diffuse local loads and suppress stress peaks. The spacing between actuators must therefore be selected as a function of BH stiffness to avoid stress-free regions while preserving distinct pressure footprints. For the reference industrial configuration ( 60 mm BH thickness), an actuator spacing of approximately 150 mm achieves the optimal compromise between localization capability and continuous sheet support. The proposed framework establishes quantitative design criteria for BH geometries compatible with MR-based adaptive forming and supports the development of next-generation blank-holding systems offering enhanced process stability, reduced scrap, and improved material-flow control.

Introduction

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Deep drawing is a widely used sheet-metal forming process whose robustness depends on the controlled flow of material under variable friction, geometry, and mechanical properties [1]. The blank-holder (BH) plays a central role by stabilizing the flange, preventing defects, and regulating inplane strain distribution. Conventional BH systems apply a global, uniformly distributed blank retracting force, which ensures process simplicity but offers limited capability to address local variations on blank draw-in arising from anisotropic material behaviour, uneven lubrication, or complex part geometries.

Recent high-dynamic actuation technologies, particularly magnetorheological (MR) actuators [2], enable pressure profiles that vary around the BH circumference both spatially and temporally. Despite this progress, the interaction between BH stiffness, actuator spacing, and the level of pressure localization achievable at the sheet interface remains insufficiently understood [3], therefore the full capability of MR actuators is limited. This study addresses these gaps through a systematic finite
element (FE) investigation [4] of deep-drawing processes equipped with spatially distributed MR actuation.

Traditional BHs, typically designed as thick and rigid plates, ensure structural stability [5] but inherently suppress local adjustments of pressure, an increasingly important capability in adaptive forming, damage mitigation, and scrap reduction. Existing BH solutions provide only partial spatial control. Segmented BHs [6] introduce local actuation but require complex assemblies and may create contact discontinuities [7]. Shaped BHs compensate pressure profiles through geometry but lack adaptability [8]. Mechanical spring-based [9] and nitrogen gas spring-based [10] systems add compliance but offer poor controllability [11], while hydraulic units generally operate with limited spatial resolution [12]. As a result, current industrial BHs cannot fully exploit modern actuation strategies requiring fast, high-resolution adjustments [13].

MR actuators overcome many of these limitations [14]. As shown by Simonetto et al. [2], they use MR fluids [15] whose rheological properties change under a magnetic field, enabling compact, fastresponding devices capable of independently modulating force across dense arrays [16]. These characteristics make them promising for distributed blank-holding, provided that the BH structure itself supports the transmission of spatially distinct loads [17]. Excessively rigid BHs diffuse local actuation effects, while overly compliant ones compromise global stiffness and can generate excessive pressure peaks. Effective distributed forming therefore requires a carefully balanced BH design.

The present study examines how BH thickness influences pressure localization, how actuator spacing affects interaction between adjacent load paths, and how these mechanisms can guide the design of BH geometries suited for MR-based distributed forming. Through detailed FE simulations, a unified framework is developed linking BH stiffness, actuator layout, and applied forces to the resulting pressure distribution on the sheet, supporting next-generation adaptive blank-holding strategies.

Magnetorheologic Actuator

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Magnetorheological actuators enable precise control of force-stroke curves, including configurations in which the available force decreases monotonically with increasing stroke. This response is tuned by regulating the magnetic field applied to the MR fluid, which is achieved by modulating the current in the internal coils through a dedicated power transformer. When activated, ferromagnetic particles within the fluid align with the magnetic field, increasing both viscosity and yield stress. By adjusting the field intensity, the actuator can rapidly transition between low-resistance and high-resistance states, enabling highly responsive, real-time force control suitable for distributed blank-holding applications.

Fig. 1a shows a longitudinal section of the actuator, illustrating its internal components and pressure zones, while Fig. 1b presents an example of a decreasing force-stroke curve and the corresponding current profile required to generate it. By knowing the pressures values and their application surfaces, it is possible to evaluate the damping force of the actuator:

F=PinA1+Ppr(A1+A3−A2)(1)

Where Pin is the MR-fluid pressure, consisting of the magnetic-resistance component activated by the applied current and the viscous component associated with fluid motion, Ppr instead, is the preload pressure of the nitrogen gas, needed for compensate the volume of the piston rod entering the cylinder during the stroke.

[picture]

Fig. 1. a) Section of the MR actuator; b) Example of force and current curve of the MR actuator along the stroke of the piston.

Fig. 1. a) Section of the MR actuator; b) Example of force and current curve of the MR actuator along the stroke of the piston.

Therefore, the effectiveness of MR-based local actuation depends on the BH's ability to maintain spatially distinct load paths. When the BH is too rigid, localized forces are spread over a wide contact region, suppressing pressure peaks and reducing spatial resolution. Conversely, a BH that is too compliant may produce excessive localization, leading to unrealistic stress concentrations and reduced global support.

Numerical Framework

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A comprehensive FE simulation campaign was carried out to study the blank-holder plate structural elastic behaviour under localized loading. The numerical model reproduces the deep drawing of a closed-cup geometry (Fig. 2a) made of DC04 steel using an industrial tooling configuration. A complementary simplified model (Fig. 2c), involving only a single actuator, is included to isolate local deformation mechanisms.

The 0.7 mm thick sheet is modeled using shell elements with an elastic-plastic constitutive law calibrated for DC04 steel (Fig. 2b). The material parameters adopted are: Young's modulus E=210, Poisson's ratio v=0.3, initial yield stress σy0≈170MPa, and an isotropic hardening law described by a Hollomon-type relationship σ=Kεn with K=525MPa and n=0.22. The blank-holder plate is represented by three-dimensional solid elements, enabling evaluation of through-thickness stress gradients and the influence of BH thickness on compliance, i.e., its tendency to deform elastically under applied loads. The blank-holder and tools are modeled as made of tool steel with linear-elastic behavior, using a Young's modulus E=210GPa as stiffness is primarily governed by their elastic properties. Actuators are implemented as independent vertical solid elements applying controlled normal loads to the BH surface according to Fig. 2, replicating the action of MR units. Contact interactions between sheet, BH , and die include frictional effects, ensuring realistic draw-in and pressure development. Boundary conditions reflect the industrial die-BH-punch configuration.

Two key structural parameters were systematically varied: the blank-holder (BH) thickness, which determines its elastic stiffness (or, inversely, its structural compliance) under loading; and the actuator spacing.

[picture]

Fig. 2. a) Numerical model of a closed-cup geometry; b) Closed-cup blank before and after the forming process; c) Simplified model of one single MR actuator.

Fig. 2. a) Numerical model of a closed-cup geometry; b) Closed-cup blank before and after the forming process; c) Simplified model of one single MR actuator.

The latter controls the spatial density of force application, ranging from closely spaced, highdensity layouts to widely spaced, low-density configurations. Furthermore, multiple force levels were applied to evaluate their effects on the resulting stress distributions and contact pressure fields.

Performed numerical valuation focuses on both local and global indicators of BH behaviour. Stress distributions through the blank-holder thickness, modeled as a thick plate, are used to assess whether the structural response is dominated by bending or transverse shear deformation. The contact pressure distribution at the BH -sheet interface characterizes the magnitude and spatial extent of load transfer. The degree of superposition between pressure distributions generated by adjacent actuators provides a measure of actuator interaction and the effective spatial resolution of force control. Peak contact pressures and the depth of stress penetration into the blank-holder thickness offer further insight into the structural sensitivity to localized loading.

Summarizing, these metrics describe how BH geometry and actuator arrangement influence the transmission and redistribution of localized loads. The modeling framework captures the interplay between local elastic deformability and overall structural stiffness, offering a valid design for blankholders compatible with MR-based distributed forming systems.

Single cylinder model: local effects

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Force variation. Before examining the influence of blank-holder thickness and actuator spacing, it is necessary to first assess the effect of the applied actuator force itself and to evaluate how variations in this force modify the stress state within the system.

[picture]

Fig. 3. a) Stress distribution σzz in the middle section of the single cylinder model with a cylinder force of 12.5 kN ; b) σzz peak stress vs. Actuator force measured at point P .

Fig. 3. a) Stress distribution σ z z in the middle section of the single cylinder model with a cylinder force of 12.5 kN ; b) σzz peak stress vs. Actuator force measured at point P .

[picture]

Fig. 4. σzz component at the base of the blank-holder for different force values applied to the cylinder; BH thickness of 60 mm .

Fig. 4. σzz component at the base of the blank-holder for different force values applied to the cylinder; BH thickness of 60 mm .

To isolate this phenomenon, the simplified numerical model containing a single actuator is particularly useful, as it allows direct observation of the stress response under different applied force levels. Fig. 3a shows the stress distribution on a representative section of the simplified model for a cylinder force of 12.5 kN , in which the blank-holder plate thickness corresponds to that of the industrial closed-geometry tool (60 mm). Fig. 3b reports the peak stress component in the direction normal to the blank-holder surface ( σ zz) for the various applied force levels. As expected, the peak stress at point P increases linearly with the amount of the force applied by the actuator, confirming the proportional relationship between local loading and the resulting stress concentration.

Another relevant aspect in evaluating the effect of varying actuator force is determining the spatial extent of the stress field at the base of the blank-holder. Understanding how far the stress propagates laterally is essential, as it provides insight into whether the applied force influences the minimum spacing required between adjacent actuators. Fig. 4 presents the σ zz component measured at the lower surface of the blank-holder. The results show that the extent of the stress distribution remains essentially unchanged as the applied actuator force increases. Although the magnitude of the stress scales with the imposed load, its lateral spread is largely unaffected. This behaviour indicates that the force level does not govern the spatial reach of the stress field and therefore does not influence the criteria for actuator spacing in the BH design.

From these observations, it can be concluded that the applied force affects only the intensity of the local stress but not its distribution radius. Consequently, actuator spacing must be defined primarily by geometric and stiffness-related parameters rather than by the magnitude of the force delivered by each actuator.

Thickness variation. Another key parameter that can be effectively examined through the simplified numerical model is the blank-holder thickness. This parameter is particularly influential because it governs the degree of stress localization beneath the actuators, independently of the applied force, as demonstrated in the previous section. Within this framework, five different blank-holder thicknesses were investigated, all defined as multiples or fractions of the reference industrial thickness of 60 mm : (i) 15 mm ; (ii) 30 mm ; (iii) 60 mm ; (iv) 90 mm and (v) 120 mm . Fig. 5 reports the σ zz stress profiles at the lower surface of the blank-holder for the various thickness configurations. Calculated results clearly illustrate that reducing the blank-holder thickness increases the peak stress transmitted to the sheet while simultaneously narrowing the lateral spread of the stress field. In other words, a thinner blank-holder exhibits higher local elastic deformability, allowing the applied load to concentrate more strongly beneath the actuator and confining its influence to a smaller region.

Conversely, increasing the blank-holder thickness leads to a more uniform distribution of stress over a wider area and a reduction in the peak stress value. A thicker plate behaves as a stiffer structural component, diffusing localized loads more effectively and thereby attenuating the degree of pressure localization. This behaviour is consistent with classical plate theory, where bending stiffness scales with the cube of the thickness; even modest increases in thickness therefore produce substantial reductions in local deformation. These observations confirm that BH thickness is the dominant structural parameter controlling stress localization and, consequently, the achievable spatial resolution in distributed blank-holding systems. Understanding this relationship is essential for designing blank-holder plates capable of transmitting spatially differentiated pressures without compromising global stiffness or formability robustness.

To clarify the influence of blank-holder thickness on the appropriate spacing between adjacent actuators, which will be examined in detail in the following section, Fig. 6 presents the distribution diameters D of the σzz stress distribution extention at the lower surface of the blank-holder for the various thickness configurations. The results reveal an approximately linear increase of D with increasing blank-holder thickness, although the trend gradually approaches an asymptotic upper limit of roughly 250 mm (even with a BH thickness of 150 mm the D value is ≈250 mm ). This saturation indicates that beyond a certain stiffness level, further increases in blank-holder thickness provide diminishing contributions to the lateral spread of the transmitted load.

From these observations, when temporarily disregarding the more complex interactions occurring during forming, namely those between the blank-holder and the blank, the blank and the die, and the blank and the punch, a first approximation of the ideal actuator spacing can be established. For a given blank-holder thickness, the recommended spacing between two consecutive actuators should match the corresponding stress-distribution diameter D at the BH base. Such spacing ensures that no regions of zero stress arise at the sheet-BH interface (which would occur if spacing exceeded D, making local control of material flow impossible in that areas), while also preventing excessive overlap of adjacent pressure fields (which would occur if actuator spacing are chosen smaller than D and would negate the benefits of spatially differentiated pressure control). This relationship provides a preliminary geometric criterion for designing actuator arrays capable of maintaining effective spatial resolution in MR-based distributed blank-holding systems.

[picture]

Fig. 5. σzz distribution at the BH base for different plate thicknesses.

Fig. 5. σ z z distribution at the BH base for different plate thicknesses.

[picture]

Fig. 6. a) Stress field diameter D vs. BH thickness in the single cylinder numerical model; b) σzz distribution at the BH base for a 12.5 kN load and 30 mm BH -thickness.

Fig. 6. a) Stress field diameter D vs. BH thickness in the single cylinder numerical model; b) σ z z distribution at the BH base for a 12.5 kN load and 30 mm BH -thickness.

A more comprehensive discussion of thickness and spacing effects, considering the full closedcup geometry and therefore the complete numerical model, follows in the next section. There, the influence of blank-tool interactions on optimal actuator placement and blank-holder design is addressed, offering a more realistic basis for industrial implementation.

Closed Geometry Global Effects

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Thickness variation. As in the previous section, several blank-holder thickness configurations were examined, this time applied to the full deep drawing process of the closed-cup geometry illustrated in Fig. 2a. Unlike the simplified model, by which the sheet is merely compressed between the BH and the die, in the full geometry of the drawing die, the sheet undergoes significant deformation as it is drawn into the cavity by the punch. The evolving motion of the sheet during forming alters the characteristics of the sheet-BH interface, introducing effects that were not present in the simplified configuration. These differences lead to results that deviate slightly from the conclusions previously obtained, and therefore warrant a dedicated discussion.

Fig. 7 shows the distributions of interface stresses between the sheet and the blank-holder for the various thicknesses with the load on cylinders equal to 12.5 kN . The overall trend remains consistent with the findings from the simplified model: thinner blank-holder plates do promote stronger localization of the applied load, whereas increasing thickness spreads the pressure more uniformly across the contact surface.

[picture]

Fig. 7. σzz distribution at the interface between blank and BH for three different BH plate thicknesses; applied force: 12.5 kN each.

Fig. 7. σ z z distribution at the interface between blank and BH for three different BH plate thicknesses; applied force: 12.5 kN each.

[picture]

Fig. 8. σzz vs. actuator location for three different BH thickness

Fig. 8. σ z z vs. actuator location for three different BH thickness

However, the additional motion of the sheet introduces new gradients and interactions that modify the shape and symmetry of the resulting pressure fields.

Fig. 8 reports the σzz stress component along a line passing through three consecutive actuators. Again, a highly localized stress field with pronounced peaks is observed for a thickness of 30 mm , while a nearly homogeneous stress distribution characterizes the 120 mm configuration. For the reference thickness of 60 mm , the stress fields of adjacent actuators exhibit a mild overlap in the regions midway between two cylinders, confirming that the original spacing of 150 mm provides an adequate level of localization without generating stress-free zones. This indicates that the original structural layout already meets the criteria for spatially resolved actuation. A closer inspection of the 60 mm pressure distribution reveals that the stress peaks beneath the three actuators are not perfectly uniform. Owing to the blank's motion and deformation during the drawing process, the outer actuators generate slightly higher stress peaks than the central one, introducing a measurable asymmetry in the stress distribution. This effect highlights the influence of the evolving sheet geometry on load transmission and underscores the importance of accounting for forming-induced kinematics when defining design guidelines based on simplified models. The observed asymmetry originates from the fact that the sheet does not undergo a uniform displacement during the drawing process. As the material flows toward the die cavity, different zones do experience more pronounced draw-in, increased local bending, and locally higher frictional resistance. These effects increase the reaction forces transmitted to the outer actuators, leading them to develop slightly higher stress peaks than the central one and ultimately producing the measured imbalance in the pressure field.

Inter-cylinder space variation. Building on the considerations developed in the previous sections, it is now possible to define the ideal actuator spacing for an efficient blank-holder design. The analyses presented here do refer to the reference blank-holder thickness of 60 mm ; for other plate thicknesses, the same reasoning can be directly extended by adopting the corresponding ideal spacing value D shown in Fig. 6a.

To investigate the influence of actuator spacing, three distances were examined: 120 mm,150 mm, and 180 mm . The value of 150 mm represents the nominally optimal spacing (the simplified-model prediction was approximately 157 mm , but a slightly smaller value was chosen here to avoid the formation of stress-free zones during the actual forming process, in fact, the material in those areas cannot be actively controlled by the actuators, making the local sheet flow ungovernable and significantly increasing the risk of wrinkling).

[picture]

Fig. 9. σzz distribution at the BH base for three different cylinders spacing; cylinder force of 12.5 kN each.

Fig. 9. σzz distribution at the BH base for three different cylinders spacing; cylinder force of 12.5 kN each.

Fig. 9 illustrates the σ zz-distributions at the sheet- BH interface for the three spacing configurations. When the spacing is reduced to 120 mm , the pressure fields generated by adjacent actuators overlap extensively, leading to an almost uniform stress distribution across the interface. From Fig. 10 it is possible to observe that the contributions from adjacent actuators, in the 120 mm spacing-case, accumulate in the intermediate regions, effectively producing a summed response. While such homogenization eliminates low-stress zones, it also suppresses the distinct pressure peaks needed for localized control of the material flow. One of the potential benefits of a reduced actuator spacing is the increased control in the bending region, as the actuators are necessarily positioned closer to the die's curvature, but losing all the advantages of spatial differentiation.

At the opposite extreme, a spacing of 180 mm produces a markedly localized response as evident in Fig. 9: the stress peaks beneath each actuator are well separated, and wide regions of low or nearzero stress appear between them. This configuration reduces the effectiveness of distributed blankholding, since large portions of the flange are left uncontrolled. However, the actual extent of these low-stress areas depends on the blank size. In the early stages of forming, the entire flange still lies under the influence of all eight actuators, meaning that the sheet remains globally supported (but with zero stress zones). Only when the material is drawn inward and portions of the blank move beyond the effective spatial extent of the actuator-induced stress distribution does the risk of insufficient blank-holding increase, leaving segments of the blank edge less controlled and more susceptible to wrinkling or uncontrolled draw-in.

The intermediate spacing of 150 mm offers a balanced condition: individual actuators retain their ability to generate localized pressure peaks, yet the overlap between adjacent stress distribution extensions remains sufficient to avoid unregulated regions; in fact, in this case, the stress profile remains strictly positive along the entire outline, ensuring continuous regulation of the sheet flow. At the same time, the localized peaks directly beneath the actuators remain clearly identifiable, confirming that the system preserves the spatial differentiation required for effective distributed blank-holding. This spacing therefore achieves an optimal balance between maintaining localized actuation effects and preventing uncontrolled regions along the flange.

Moreover, numerical simulations have shown that maintaining a 150 mm spacing and a blankholder thickness of 60 mm , while differentiating the forces applied by the individual actuators, enables a significantly higher minimum thickness in the formed component (≈0.62 mm) compared with the current configuration ( ≈0.57 mm ). These results and their implications on advanced actuator positioning strategies will be discussed in detail in future publications.

[picture]

Fig. 10. σzz vs. inter-cylinder distance for three different spacing values

Fig. 10. σ z z vs. inter-cylinder distance for three different spacing values

Conclusions

The original version of this paper is available on https://www.scientific.net/SSP.389.83.pdf

This work provides a systematic investigation of how blank-holder geometry and actuator arrangement influence the transmission of spatially differentiated loads in deep drawing processes employing magnetorheological actuators. Through a combination of simplified and full-geometry FE models, three key findings were elaborated in this contribution: (i) Blank-holder thickness is the primary determinant of stress localization. Thinner BHs exhibit high local elastic deformation, producing strong, narrow pressure peaks beneath each actuator. Increasing thickness diffuses these peaks and reduces their amplitude. The diameter of the stress-affected zone increases approximately linearly with plate thickness of BH and tends toward an upper bound, indicating diminishing benefits for very stiff BHs. (ii) Local actuator force affects peak stress intensity but not the spatial reach of the stress field. The radius of the stress-distribution extension remains essentially unchanged across the examined force range, meaning that actuator spacing should be defined by geometric and stiffness-related parameters rather than by load levels. This decoupling simplifies the design of actuator arrays for MR-based systems. (iii) Actuator spacing governs the balance between spatial resolution and global process control. When spacing is too small, adjacent pressure fields overlap excessively, homogenizing the interface stress and suppressing local actuation effects. When spacing is chosen too large, extensive low-stress regions arise between actuators, reducing control authority and increasing susceptibility to wrinkling. For the reference of 60 mm BH plate thickness, a spacing of 150 mm ensures continuous sheet support while maintaining distinct localized pressure peaks.

Overall, the study establishes a unified framework linking BH stiffness, actuator spacing, and localized loading behavior, offering practical guidelines for designing blank-holders that fully exploit the capabilities of MR actuators. The results demonstrate that effective distributed blank-holding requires an intermediate level of BH stiffness and an actuator pitch tailored to the thickness-dependent stress-distribution diameter. These findings provide the structural foundations for advanced adaptive forming technologies, enabling improved robustness, reduced material waste, and enhanced control of in-plane deformation during deep drawing.

Future work will extend the present structural analysis toward fully coupled process simulations including material plasticity, contact evolution, and real-time control strategies. Experimental validation under industrially representative conditions will be essential to quantify the robustness of the findings against parameter variability and to assess long-term reliability of MR actuators.

In industrial application a key advantage of MR actuators is their capability to dynamically adapt the applied force in response to process variability (e.g., changes in lubrication), thereby enhancing
robustness under real production conditions. Future developments may involve the integration of AIbased control systems, such as neural networks trained on real-time process parameters (e.g., sheet draw-in), which represents both a promising opportunity and a technological challenge for industrial implementation.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/SSP.389.83.pdf

This study was carried out within the PNRR research activities of the consortium iNEST (Interconnected North-Est Innovation Ecosystem) funded by the European Union NextGenerationEU (Piano Nazionale di Ripresa e Resilienza (PNRR) - Missione 4 Componente 2, Investimento 1.5 - D.D. 1058 23/06/2022, ECS_00000043). This manuscript reflects only the Authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.83.pdf

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Huang, H., Lv, Q., Li, L., Xu, Y., Liu, C., Zhang, T., & Liu, Z. (2023). Individually segmented blank holding system driven by electromagnetics for stamping: modeling, validation, and prototype. Journal of Materials Processing Technology, 313, 117883.

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Hishida, Y. Wagoner, R.H. Analysis of Blank Holding Force Control Forming Using Hydraulic Forming Simulator; Advanced Technology of Plasticity (1993), pp. 1740-1745

Brun, M., Ghiotti, A., Bruschi, S., & Filippi, S. (2021). Active control of blankholder in sheet metal stamping. Procedia CIRP, 100, 151-156.

De Vicente, J., Klingenberg, D. J., & Hidalgo-Alvarez, R. (2011). Magnetorheological fluids: A review. Soft matter, 7(8), 3701-3710.

Goncalves, F. D., Koo, J. H., & Ahmadian, M. (2006). A review of the state of the art in magnetorheological fluid technologies--Part I: MR fluid and MR fluid models. The Shock and Vibration Digest, 38(3), 203-220.

Liu, Y., Li, M., & Ju, F. (2017). Research on the process of flexible blank holder in multi-point forming for spherical surface parts. The International Journal of Advanced Manufacturing Technology, 89(5), 2315-2322.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 95-106

doi: 10.4028/p-CZkoq7

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-21

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-16

Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

The original version of this paper is available on https://www.scientific.net/SSP.389.95.pdf

Jan Sommer 1,a*, Lars Uhlmann 1, b, Max Meerkamp 1,c, Tim Herrig 1, d and Thomas Bergs 1,2,e

1 Manufacturing Technology Institute - MTI of RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen

2 Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen

a*j.sommer@mti.rwth-aachen.de, bl.uhlmann@mti.rwth-aachen.de, c m.meerkamp@mti.rwth−aachen.de, d  t.herrig@mti.rwth-aachen.de, et.bergs@mti.rwth-aachen.de 

*corresponding author

Keywords: bipolar plates, forming, titanium, thinning, geometry.

Abstract

. Background. Bipolar plates are key components of fuel cell systems, as they significantly determine efficiency, power density, and service life. In aerospace applications, their importance is further emphasized due to the dual requirement of corrosion resistance and strict weight reduction. Titanium Grade 1 combines low density and excellent corrosion resistance. However, its industrial application is limited by restricted formability. The aim of this paper is a systematic investigation of the forming behavior of Titanium Grade 1 foil material in order to define forming limits and derive manufacturing-oriented design recommendations for bipolar plates in aviation.

Procedure

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Sixteen distinct geometry features were developed to represent characteristic forming conditions. In addition to cross-section variations, the flow field angle was systematically altered to assess its influence on local stress and strain distribution. Furthermore, the key process parameters forming speed, forming force, and lubricant amount were varied to evaluate their impact on the forming quality. The assessment focused on form filling and material thinning. For this purpose, metallographic cross-sections were prepared, and optical 3D measurements were conducted using a Keyence system to precisely capture local wall thickness variations.

Key findings

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Process parameters: The forming behavior of Titanium Grade 1 is strongly influenced by the applied forming force and lubrication. Form filling becomes sufficient only above 350 MPa (3.000kN), while the lubricant amount is decisive for achievable forming depths due to the hydrostatic oil cushion effect. In contrast, forming speed shows no significant influence. Anisotropy remains a critical factor, particularly in 0∘ rolling direction, where premature thinning leads to fracture.

Geometry parameters: Small radii are highly critical, while feature depth leads to expectedly higher thinning. Steeper flank angles improve form filling but at the cost of increased thinning. Pitch shows limited influence, although it may become relevant at very small values. Channel design is challenging, as sharp flow field angles consistently result in severe thinning and pose difficulties in tool manufacturing.

Introduction

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The aviation sector is undergoing a major transition driven by the need for sustainable mobility and the European "Flightpath 2050" targets, which call for reductions of 75% in CO2 and 90% in NOx
emissions compared to the year 2000 [1]. To meet these objectives, alternative propulsion systems with zero or near-zero emissions are being pursued, with hydrogen-powered fuel cells emerging as a promising option. Fuel cells combine high specific energy density, low noise and zero local emissions making them particularly suitable for aircraft [2,3].
For aviation, fuel cell systems must be not only efficient but also extremely lightweight and compact. Up to 30 fuel cell stacks may be integrated into a single aircraft depending on power requirements and density of the fuel cell, making power density a decisive factor [4]. Bipolar plates (BPPs) dominate both stack mass and manufacturing cost, contributing roughly 80% and 40% respectively [5,6,7]. Their design therefore has a direct impact on overall system performance.
BPPs separate reactants, distribute gases via a flow field, provide electrical conduction between cells and support thermal and water management. Their micro-structured flow fields must be optimized to reduce pressure losses and maximize electrochemical performance [8]. However, component manufacturability is limited by the formability of the sheet material. High geometric precision must therefore be achieved without excessive thinning or cracking during forming.
Automotive applications widely use corrosion-resistant stainless steels such as AISI 316L (1.4404) or AISI 304 (1.4301) due to their good formability and low cost [9]. For aerospace, however, their high density represents a drawback. Titanium, especially Titanium Grade 1, offers low density, good electrical conductivity and excellent corrosion resistance, making it an attractive lightweight material for fuel cell stacks [10]. Yet its forming behaviour is considerably more challenging. Compared to stainless steels with fracture elongations around 50%, Titanium grade 1 shows only around 30% elongation [11,12]. Its hexagonal close-packed (HCP) crystal structure produces strong anisotropy, and its low elastic modulus ( ~110GPa ) results in pronounced springback, making dimensional accuracy and repeatability difficult [13].
Previous investigations on stainless steels indicate that flank angle and fillet radius strongly affect thinning during forming [14]. Steeper flanks improve form filling but intensify local strains, while small radii promote early necking. However, there is little empirical data on whether these relationships persist for titanium foils and how forming force, forming speed, lubrication and rollingdirection orientation interact with geometric constraints.
To close this research gap, the present study systematically analyses the forming behaviour of Titanium Grade 1 foils for aerospace BPP applications. The influence of key process parameters (forming force, punch speed, lubricant quantity and material orientation) and geometric features (fillet radius, pitch, flank angle and channel depth) on material thinning and form filling is investigated using surface measurements and metallographic cross-sections. The objective is to determine forming limits and derive manufacturing-oriented design recommendations for titanium bipolar plates, supporting future lightweight and emission-free aviation.

Materials and Methods

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Tool Design and Feature Geometries

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The forming tools used in this study were designed to investigate the influence of geometric design features on the forming behavior of Titanium grade 1 bipolar half-plates (BPHP). Both punch and die were modelled using SolidWorks 2024. The design process was based on literature findings and previous experimental results on sheet forming of titanium foils. The forming gap between punch and die was defined as 100μ m, corresponding to the nominal sheet thickness. The active forming area of each tool measured 350 mm×150 mm, with sixteen isolated feature zones of 20 mm×20 mm distributed symmetrically across the surface. Fig. 1 shows the schematic tool design of the forming punch.

[picture]

Fig. 1. Schematic tool design.

Fig. 1. Schematic tool design.

The 16 forming features were used in further investigations to determine the interactions between the bipolar plate thinning and form filling, as well as the characteristic geometric features of the forming tools. To do so, five geometric characteristics of a bipolar plate tool were defined. Namely, the flank angle α, top bottom radius r1, top fillet radius r2, pitch distance d, and channel depth h. Additionally, the flow field angle β was introduced to represent the channel orientation within the flow field. Each feature was implemented in three discrete levels to enable factorial evaluation of non-linear effects. To reduce the number of features to fit on the punch, one reference geometry was defined with α=55∘,r1=0.25 mm,r2=0.35 mm,d=1.6 mm,h=0.35 mm and β=0∘ from which each geometric feature was varied in two levels. The cross section of the reference geometry is shown in Fig. 2.

[picture]

Fig. 2. Schematic BPHP cross section with its geometric features.

Fig. 2. Schematic BPHP cross section with its geometric features.

The features were chosen to represent realistic design limits of PEM fuel cell flow fields while maintaining manufacturability under precision micro-milling. Each variant was integrated into both punch and die geometries, resulting in a modular tool concept allowing simultaneous forming of multiple feature configurations under identical process conditions. Table 1 shows each feature with its modification compared to the reference geometry in Fig. 2.

Table 1. Overview of features modified compared to the reference geometry.

Pos. | Feature | Pos. | Feature | Pos. | Feature | Pos. | Feature | Pos. | Feature
1 | α = 45° | 4 | r₁ = 0.35 mm | 7 | h = 0.4 mm | 10 | d = 1.7 mm | 13 | β = 90°
2 | α = 65° | 5 | r₂ = 0.25 mm | 8 | h = 0.45 mm | 11 | β = 45° | 14 | β = 135°
3 | r₁ = 0.15 mm | 6 | r₂ = 0.45 mm | 9 | d = 1.5 mm | 12 | β = 30° | 15 | β = 150°

Tool Manufacturing

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The tools were fabricated from hardened tool steel 1.2379 (X155CrVMo12-1) with a hardness of 55 HRC using a Makino iQ500 micro-milling machine. The machine operates with sub-micrometer positioning accuracy and was selected to achieve the required surface quality and dimensional precision. Machining was conducted in several finishing stages with reduced spindle speed and feed rate to avoid tool deflection and thermal distortion. After machining, both tools, die and punch, were inspected using a tactile profilometer (MahrSurf XC 20) to verify contour accuracy and detect potential deviations. Since the tactile profilometer only enables line measurements, the flow field angles β weren't measured regarding their accuracy. In the following Fig. 3, the tactile measurement of the punch (Fig. 3 a)) as well as of the die (Fig. 3 b)) are shown. The measurement was done from position 7 (pos. 7) to position 1 (pos. 1) comparing to Fig. 1. As can be seen in the graphs, all channel heights were met. However, a closer look at the individual channels reveals that there is a height
difference Δh of up to 10μ m across all channels of each feature. This could lead to an insufficient form filling while forming. All other feature geometries show an analogous behavior in terms of channel height distribution.

[picture]

Fig. 3. Tactile measurement of a) tool punch b) tool die.

Fig. 3. Tactile measurement of a) tool punch b) tool die.

When taking a closer look at each channel of the die or punch, you can see further manufacturing defects additionally to the height distribution. As can be seen in Fig. 4, the punch shows a bead in the middle of each channel with a height of h=26μ m. In the forming of foil material with thicknesses t of t≤100μ m, this could lead to fracture during forming. On the other hand, the die shows small deviations from the target geometry in the radii. However, compared to the punch, these errors don't show a critical size.

[picture]

Fig. 4. Manufacturing defects of the punch (left) and the die (right) after milling.

Fig. 4. Manufacturing defects of the punch (left) and the die (right) after milling.

Experimental setup

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After the tool evaluation, the empirical experiments were conducted. For the investigation of the forming behavior Titanium grade 1 with a thickness of t=100μ m was used and cut into blanks measuring 350 mm×150 mm as is shown in Fig. 5 b). Additionally, the tools were aligned to each other, using dial gauges. This is particularly important to prevent unwanted contact with the tool punch and die which could lead to fractures during forming or in the worst case to high wear or a failure of the tools. Due to confidentiality feature designs, the complete BPHP geometry cannot be shown in Fig. 5 a).

[picture]

Fig. 5. Experimental setup a) alignment of the tools and b) cutting of the metal foil.

Fig. 5. Experimental setup a) alignment of the tools and b) cutting of the metal foil.

After the experimental setup was finished, the experimental forming began. To not only evaluate the influence of the tool geometries on the forming behavior of the BPHP, the process setup was also investigated using a partial factorial experimental design. Therefore, a reference process setup was installed using four different process parameters, namely the forming force Ff, the forming speed vf, the lubricant amount ml as well as the rolling direction γ. The setup of the reference process is shown in Table 2.

Table 2. Process setup of reference process.

Process parameter | Value
Forming force Ff | 4,000 kN
Forming speed vf | 5 mm/s
Lubricant amount ml | 0 g/m²
Rolling direction γ | 90° to rolling direction

Differing from this setup, each process parameter was varied minimum two times, except the rolling direction, where only rolling directions of γ=0∘ and γ=90∘ were investigated. The partial factorial experimental design can be seen in Table 3. Each of the process setups was used three times in terms of statistical validation. In total 27 forming operations where performed.

Table 3. Partial factorial experimental design.

Process parameter | Value |  |
Forming force Ff | 1,000 kN | 2,000 kN | 3,000 kN
Forming speed vf | 10 mm/s | 20 mm/s |
Lubricant amount ml | 3 g/m² | 10 g/m² |
Rolling direction γ | 0° to rolling direction |  |

Sample preparation

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After forming, the BPHP were first measured geometrically using the optical measurement system Keyence VR 6200. For this purpose, a line measurement was performed along the geometric features, analogous to the tactile measurements of the tools. The optical measurement serves to compare the tool and the resulting BPHP contour. In addition, the BPHPs were separated along the geometric features and embedded afterwards. After grinding and polishing the samples, they could then be evaluated regarding thinning. An attempt was made to separate the geometric features with flow field angles β along the angle. As can be seen in Fig. 6 b), this did not always result in evaluable micrographs due to the imprecise separation method, which is why the evaluation was based on the straight geometric features.

[picture]

Fig. 6. Metallographic preparation of the BPHP a) embedded b) cross section of flow field angle β.

Fig. 6. Metallographic preparation of the BPHP a) embedded b) cross section of flow field angle β .

Results

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The following chapter presents, discusses, and analyzes the results of the experimental forming tests. To reduce the number of micrographs, the influence of the geometric features on thinning and form filling of the BPHP was evaluated using one process setup, the reference process setup from Table 2. For the evaluation of the material thinning, seven different positions were determined across one flow
field channel pitch. In Fig. 7 the micrograph of the reference geometry formed using the reference setup can be seen.

[picture]

Fig. 7. Micrograph of the reference feature geometry formed using the reference process setup.

Fig. 7. Micrograph of the reference feature geometry formed using the reference process setup.

The material thinning Δt is shown along the channel pitch. As can be seen, the maximum material thinning Δtmax  occurs in the bottom fillet radii r1 with Δt~26μ m. The next highest material thinning can be found in the top fillet radii r2 with Δt~18μ m. The flow field flanks as well as the channel top and bottom show nearly no material thinning with the bottom even thickening up. It is also noticeable that there is an indentation on the surface of the channel top. This can be attributed to manufacturing defects in the stamp, as the depth of the indentation corresponds exactly to the height of the manufacturing defect on the stamp side.
The depth of the flow field channel h is 326.7μ m, which is nearly 25μ m less than the constructed tools. This can also be seen in Fig. 8 where the form filling of the BPHPs was evaluated, comparing the BPHP contour with its regarding die. The form filling of the BPHP is not sufficient, especially in the bottom fillet radii. This could be attributed to the closed tool geometry, which can lead to premature contact between the punch and die in the event of small deviations from the target geometry. This prevents further penetration of the punch, resulting in incomplete form filling. This phenomenon would transfer to all other feature geometries, as they would also be unable to penetrate further into the die in the z-direction.

[picture]

Fig. 8. Form filling of the reference feature with reference setup.

Fig. 8. Form filling of the reference feature with reference setup.

In the following, the influence of the different geometry features as well as process parameters is shown. To reduce the complexity of the analysis, the following section will focus on the design and process variables that show the greatest influence on the material thinning Δt and form filling Δh of the BPHP.

Influence of geometry features

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Flank angleα.

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One of the geometric features evaluated is the flank angle α. Among other things, this determines the volume flow and the minimum achievable pitch distance during operation. The aim of the design is often to select a particularly steep flank angle. On the forming side, however, a steeper flank angle leads to increased thinning of the material across the individual geometric features, as can be seen in Fig. 9.

[picture]

Fig. 9. Micrographs of flank angles α a) 45∘ b) 65∘.

Fig. 9. Micrographs of flank angles α a) 45 ∘ b) 65 ∘ .

The maximum thinning Δtmax occurs at the bottom fillet radii r1 for all flank angles. However, due to the assumption of contact between the tool punch and die on bottom radius rl, the evaluation of the maximum thinning is insufficient. Therefore, the average thinning Δt∅ will be discussed for the upcoming results in this paper. In Fig. 10 these correlations are shown. As can be seen, the average material thinning Δt∅ shows a nearly linear progression increasing with an increasing flank angle α. Additionally, the form filling seems strongly dependent on the α as well. While the difference in the tool die depth and BPHP channel depth Δh is 12.6μ m for α=45∘, the difference in form filling nearly doubles with α=55∘/65∘.

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Fig. 10. Correlation between flank angle α, the material thinning Δt and the form filling Δh.

Fig. 10. Correlation between flank angle α , the material thinning Δ t and the form filling Δ h .

Bottom fillet radiusr1.

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Another geometric feature showing great impact on Δtø and Δh is the top bottom radius r1. Compared to the top fillet radius r2 the bottom fillet radius r1 shows a stronger influence on both the form filling Δh as well as the material thinning Δt. This is mainly due to the fact that the bottom fillet radius r1 was chosen smaller than the top fillet radius r2, so therefore the stronger material thinning occurs in the sharper radii as can be seen in Fig. 11. While the material thinning in correlation with α was distributed along the full cross section of the BPHP, the change in material thinning Δt occurs mainly in the changed bottom radius r1.

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Fig. 11. Micrographs of the bottom fillet radius a) r1=0.15 mm b ) r1=0.25 mm.

Fig. 11. Micrographs of the bottom fillet radius a) r 1 = 0.15 m m b ) r 1 = 0.25 m m .

Taking into account Fig. 12, the correlation between bottom fillet radius r1 and Δt∅ as well as Δtmax  shows a linear decrease with increasing radii, showing the biggest differences in r1 itself. The difference in form filling however does not seem to correlate with the radii in any way.

[picture]

Fig. 12. Correlation between bottom radius r1, the material thinning Δt and the form filling Δh.

Fig. 12. Correlation between bottom radius r 1 , the material thinning Δ t and the form filling Δ h .

Channel depthh.

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The last geometric feature analysed is the channel depth h. To evaluate the maximum forming limits for the Titanium grade 1, the channel depth was increased to h=400μ m and h=450μ m compared to the reference geometry with a channel depth of h=350μ m. As anticipated, the material thinning Δt increases with increasing channel depth, since the elongation increases as well. However, it is interesting to note that the maximum material thinning occurs in the bottom radius r1 while all other geometric features seem to keep a constant thickness. Furthermore, when comparing the geometric feature of the bottom fillet radius with r1=0.15 mm in Fig. 11 a ) with the material thinning Δt of the channel depth h=0.45 mm in Fig. 13 b ), the influence of r1 on the maximum material thinning Δtmax  is greater than the one of the channel depth h even considering the higher elongation across the whole cross section.

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Fig. 13. Micrographs of different channel depths h a) h=0.4 mm b)h=0.45 mm.

Fig. 13. Micrographs of different channel depths h a) h = 0.4 m m b ) h = 0.45 m m .

When looking at the correlations between the channel depth h the material thinning Δt and the form filling Δh in Fig. 14, the trends appear as expected. As the channel depth h increases, so does the material thinning, both maximum Δtmax  and average Δt. The form filling, on the other hand, shows no clear trend and lies between 21.5μ m and 23.3μ m for all channel depths. Compared to the influence of α and r1, the influence of an increasing in depth h on the material thinning Δt is smaller, which is shown by a flatter curve in Figure 14.

[picture]

Fig. 14. Correlation between channel depth h, the material thinning Δt and the form filling Δh.

Fig. 14. Correlation between channel depth h , the material thinning Δ t and the form filling Δ h .

Influence of process parameters

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After the influence of the geometric features was evaluated, the influence of the process parameters on Δt and Δh needs to be investigated. While the forming speed vf between 5 mm/s and 20 mm/s did not show any significant influence on the material thinning or form filling, the increase in forming force Ff led to greater forming depths, as expected. No greater form filling was achieved above a force of 3,000kN. However, this is strongly related to the formed reference surface, which is why a press force of 3,000kN is not necessarily sufficient for forming all BPHP geometries.
In the following, only the influences of the rolling direction y and the Lubricant amount m/ on the target variables Δt and Δh will be discussed.

Rolling directionγ.

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One of the most important material properties for forming is the anisotropy which leads to different formability in dependency of the rolling direction γ. This is especially relevant for titanium materials, since titanium only possess three gliding systems and is therefore prone for anisotropic material behavior. This is validated when analysing the micrograph of the feature geometry with h=450μ m with the sheet in γ=0∘. The material thinning Δt is greater at γ=0∘ to the rolling direction than at γ=90∘, both in terms of Δtmax  and Δt∅. At higher forming degrees, the material thinning leads to a necking in the bottom fillet radius r1 resulting in cracks at thicknesses of t~50μ m. Since the crack only appears on one side of the cross section, this indicates a small displacement of punch and die. The forming depth h, on the other hand, shows no dependence on the rolling direction and differs by only Δh=0.6μ m between γ=0∘ and 90∘.

[picture]

Fig. 15. Micrograph of feature geometry h=0,45 mm with a) a rolling direction γ of 0∘ b) a rolling direction γ of 90∘ and c) the correlation between rolling direction γ, the material thinning Δt and the form filling Δh.

Fig. 15. Micrograph of feature geometry h = 0 , 45 m m with a) a rolling direction γ of 0 ∘ b) a rolling direction γ of 90 ∘ and c) the correlation between rolling direction γ , the material thinning Δ t and the form filling Δ h .

Lubricant amountm1.

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The last process parameter discussed in this paper is the amount of lubrication m1. Lubricants can optimize the friction between the metal sheet and the tools, however, they also need to be removed after forming, so without any sufficient improvement in material thinning, the use of lubricants in BPHP forming is not recommended. In Fig. 16 the micrographs of a forming feature with the usage of lubricants are shown. As can be seen, the material thinning is lower when using lubricants. However, the usage of lubricants hinders the form filling Δh of the flow field channels due to the formation of a hydrostatic oil cushion. The lower form filling on the other hand could lead to decreased material thinning Δt due to a smaller elongation of the material.

[picture]

Fig. 16. Micrographs of the feature h=0.45 mm with a) m1=3 g/m2 mm b)m1=10 g/m2.

Fig. 16. Micrographs of the feature h = 0.45 m m with a) m 1 = 3 g / m 2 m m b ) m 1 = 10 g / m 2 .

When comparing the curves of the material thinning in Fig. 17, the maximum material thinning as well as the average material thinning show similar progressions. With higher usage of lubricants, the material thinning decreases. Especially the difference from the dry process to the low amount of lubricants m1=3 g/m2 shows a strong impact on the material thinning which is implied by the steep slopes between m1=0 g/m2 and m1=3 g/m2 compared to the slopes between m1=3 g/m2 and m1=0g/m2. However, the curve of the form filling progresses opposed to the material thinning, which means that no reliable statement can be made about the relationship between material thinning and lubricant quantity, as the elongation is lower when lubricants are used due to the lower form filling.

[picture]

Fig. 17. Correlation between the lubrication amount m1, the material thinning Δt and the form filling Δh.

Fig. 17. Correlation between the lubrication amount m 1 , the material thinning Δ t and the form filling Δ h .

Discussion and Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.95.pdf

The present investigation aimed to evaluate the formability of Titanium Grade 1 foil under the geometric and process constraints associated with bipolar plate manufacturing. The results clearly demonstrate that both geometry-related and process-related parameters strongly influence the thinning and form filling of bipolar half-plates. Among all geometric features, the bottom fillet radius r1 was found to be the most critical parameter. Across all feature variations, maximum thinning consistently occurred in this region, confirming that sharp curvature transitions generate the highest local strain accumulation. Although an increase in channel depth h naturally raises the overall material elongation, the pronounced sensitivity to r1 indicates that geometric stress concentration dominates over global deformation in determining thinning severity. The flank angle α also showed a strong influence: steeper angles resulted in decreased cavity penetration and simultaneously induced higher thinning. In contrast, pitch variations had only a minor effect under the conditions investigated,
although trends suggest that significantly smaller pitch distances may become relevant when geometric spacing approaches the forming limit of the material.
Regarding process parameters, the forming force exhibited the strongest effect on form filling. Sufficient replication of the tool geometry was achieved only at forces of 3,000kN and above. However, increasing the force beyond this threshold intensified thinning, particularly at the bottom fillet radius. Consequently, the usable forming window is limited by the simultaneous requirement of adequate form filling and acceptable wall-thickness reduction. A further influential process parameter was lubrication. The use of lubricants substantially reduced thinning, especially when transitioning from dry forming to low-level lubrication. At the same time, lubrication reduced form filling due to the formation of a hydrostatic oil cushion that counteracts punch penetration. Forming speed showed no measurable impact within the tested range, indicating that strain-rate sensitivity is negligible under quasi-static conditions. Finally, the rolling direction study confirmed the expected anisotropic behaviour of Titanium Grade 1: forming at 0∘ to the rolling direction resulted in earlier onset of critical thinning and even fracture in stamping geometries, whereas the achievable form filling was not direction dependent.
From a manufacturing standpoint, this emphasizes that flow-field layouts cannot be optimized solely on the basis of fluid dynamics or electrochemical performance. Instead, their manufacturability must be considered as an integral design constraint. The results generated in this study provide quantitative evidence and enable the formulation of initial design guidelines for titanium-based bipolar plates, including the prioritization of larger radii, moderate flank angles, and alignment of geometric features with respect to material anisotropy.
Future work should build on the findings of this study to further expand the process window for titanium foil forming. First, adaptive tool concepts like modified die radii or multi-stage forming could reduce localized thinning while maintaining acceptable form filling. Second, the introduction of controlled tribological conditions may enable a reduction of required forming forces and mitigate lubricant induced incomplete form filling. Third, an improved tool-manufacturing strategy is expected to be beneficial, particularly regarding the elimination of machining defects that influence thinning and indentation. Furthermore, future tools should not be designed as closed units but should incorporate a small drawing gap to prevent premature contact between the punch and the die. Finally, additional analysis of geometries with inclined flow field angles β is necessary, since the separation of cross sections proved experimentally challenging and prevented systematic evaluation of angled features in this study. Overall, by linking geometric design and process setup to predictable forming outcomes, the presented methodology supports the development of manufacturability oriented bipolar plate designs and offers a foundation for future large-scale industrialization of titanium bipolar plates.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.95.pdf

This research was funded by Bundesministerium für Wirtschaft und Klimaschutz (BMWK, Federal Ministry for Economic Affairs and Climate Action; project number 20N2204D KeyTech2GreenPower).

References

The original version of this paper is available on https://www.scientific.net/SSP.389.95.pdf

European Commission, 2011. Flightplan 2050: Europe's vision for aviation; maintaining global leadership and serving society's needs; report of the high-level group on aviation research. Publ. Off. of the Europ. Union, Luxembourg.

Barbir, F., 2006. PEM Fuel Cells, in Fuel Cell Technology, Springer London.

Sperling, P, Horstkotte, R, Sommer, J, Gierlings, S, Janssen, H, Herrig, T, Bergs, T, & Brecher, C. "Challenges in the Production of Fuel Cells for Aviation." Proceedings of the ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. London, United Kingdom. June 24-28, 2024. V009T17A012. ASME.

Liu, Q., Lan, F., Zeng, C., Chen, J. et al., 2022. A review of proton exchange membrane fuel cell's bipolar plate design and fabrication process 538, p. 231543.

NOW GmbH Nationale Organisation Wasserstoff- und Brennstoffzellentechnologie, 2022. Wertschöpfungskette Brennstoffzelle: Metastudie.

Jayakumar, K., Pandiyan, S., Rajalakshmi, N., Dhathathreyan, K.S., 2006. Cost-benefit analysis of commercial bipolar plates for PEMFC's 161, p. 454.

Hwang, W., Sung, Y.-E., 2023. Recent Developments of Polymer Electrolyte Membrane Fuel Cell Design 14, p. 120.

Leng, Y., Ming, P., Yang, D., Zhang, C., 2020. Stainless steel bipolar plates for proton exchange membrane fuel cells: Materials, flow channel design and forming processes 451, p. 227783.

Alo, O.A., Otunniyi, I.O., Pienaar, H., Iyuke, S.E., 2017. Materials for Bipolar Plates in Polymer Electrolyte Membrane Fuel Cell: Performance Criteria and Current Benchmarks 7, p. 395.

Xu, Z., Li, Z., Zhang, R., Jiang, T. et al., 2021. Fabrication of micro channels for titanium PEMFC bipolar plates by multistage forming process 46, p. 11092.

METALCOR GmbH, 2023. Datenblatt: 1.4404 (AISI 316 L), S31603 | METALCOR.

METALCOR GmbH, 2023. Datenblatt: Titan-Grade 1 (3.7025), R50250 | METALCOR.

Gottstein, G., 2014. Materialwissenschaft und Werkstofftechnik: Physikalische Grundlagen, 4th edn. Springer Berlin Heidelberg, Berlin, Heidelberg.

Beck, M., Riedmüller, K.R., Liewald, M., Bertz, A., Aslan, M.J., Carl, D. (2023). Investigation on the Influence of Geometric Parameters on the Dimensional Accuracy of High-Precision Embossed Metallic Bipolar Plates. In: Liewald, M., Verl, A., Bauernhansl, T., Möhring, HC. (eds) Production at the Leading Edge of Technology. WGP 2022. Lecture Notes in Production Engineering. Springer, Cham. .

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 107-114

doi: 10.4028/p-Odegn2

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-22

Revised:
2026-02-18

Accepted:
2026-02-24

Online:
2026-04-16

Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

Lasse LANGSTÄDTLER 1,2,3,a*, Andreas TAUSENDFREUND 1,2,4,c and Christian SCHENCK 1,2,3,b

1 University of Bremen, Bibliothekstraße 1, 28359 Bremen, Germany

2 MAPEX - Center for Materials and Processes, 28334 Bremen, Germany

3 Bremen Institute for Mechanical Engineering, Badgasteiner Straße 1, 28359 Bremen, Germany

4 Bremen Institute for Metrology, Automation and Quality Science, Linzer Strasse 13, 28359 Bremen, Germany

a*lasse.langstaedtler@uni-bremen.de, b  cschenck@uni-bremen.de, c  a.tausendfreund@bimaq.de 

Keywords: Electrohydraulic forming, pressure wave, shockwave, schlieren imaging

Abstract

Electrohydraulic forming involves a complex energy transfer from the initial plasma explosion through the fluid to the sheet metal, where the pressure wave propagation critically determines the amplitude, distribution, and timing of the resulting acceleration forces. These dynamics can be influenced not only by the explosion itself but also by fluid properties and the geometry and volume of the pressure vessel. To enable systematic process optimization, this study introduced a multi-sensor methodology that captured the transient behavior of the forming process. The approach integrated piezoelectric pressure sensor measurement and high-speed backgroundoriented schlieren imaging to analyze the pressure wave propagation, as well as in-situ two-point laser triangulation to monitor the sheet metal displacement. Experiments using different exploding wires varying discharge energies demonstrate the method's effectiveness. The results reveal different pressure wave velocities from 800 m/s to 1700 m/s and link displacement data to wave-induced impulses. Additional phenomena such as process-related light emissions and cavitation bubble formation were temporally resolved. The study further introduced that, after an initial learning phase with full sensor integration, selected sensors can be omitted in specific scenarios without loss of essential information, highlighting the efficiency and adaptability of the proposed diagnostic approach.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

In the manufacturing of parts with complex channel structures, media-based high-velocity forming processes such as wire based electrohydraulic forming offer significant advantages in terms of contactless force transmission and reduced spring back.
Impulse forming processes have been introduced to thin sheet metal forming and micro production in recent years [1]. The investigations showed advantages regarding flexibility in tooling, material behavior like spring back calibration as well as energy efficiency [2]. When applied to bipolar plates, these benefits translate into higher efficiency and with reduced component weight. However, due to the complex interactions among multiple physical domains such as electromagnetics, structural mechanics, and fluid dynamics, as well as governing pressure generation, propagation within the fluid, and the forming of the component, an accurate description and design of media-based impulse forming processes is not yet feasible. [3]
Different investigations were conducted to analyze the multi physical aspects starting from the pressure wave generation. In the near-field, the plasma channel behavior showed a correlation to the discharge current and wire properties which finally influenced the effectiveness of the propagation pressure wave due to peak pressures [4]. The wave speed was determined to be lower in the nearfield than in the far-field [5]. In the far-field, the speed of sound is expected to be the wave velocity
in electrohydraulic forming. Thus, it can be assumed that the shockwave speed is influenced by the fluid pressure [6].
The mapping of pressure fields by forming results was shown by Eguia et al. [7]. They described gradients in the electrohydraulic forming results that were related to the transient pressure action which could be reduced using exploding wires. To generate a real insight into the process, in-situ two-point laser triangulation of the sheet metal displacement was introduced to electrohydraulic forming [8]. There are various publications on the simulation of pressure wave propagation in electrohydraulic forming [9]. However, there is no coherent analysis, and the pressure wave in the fluid as a mode of transmission has not yet been experimentally proven for electrohydraulic forming. The presented research focused on developing a multi-sensor approach for electrohydraulic forming. Consequently, the main aim was to prove this approach by a first fundamental analysis of the interactions between adjustable process parameters, the transient pressure field within the working fluid and the forming process for electrohydraulic forming. Therefore, in the first step the pressure wave was investigated. The aim was to detect the pressure wave based on the different sensors as it was assumed to be a main influencing factor to understand the energy transmission in the working media process. The pressure wave was then described by wave speed, amplitude and curvature within the pressure vessel. With a view toward potential application in bipolar plates, the investigations focused on 1.4404 sheet material with a thickness of 0.1 mm and wire based electrohydraulic forming.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

Testing set-up and procedure. A pulsed-power machine was used for electrohydraulic forming, Figure 1a. The pulsed-power machine consisted of a capacitor bank (8x E62.S24-503C60, electronicon GmbH , Gera, Germany) with a capacitance of C=100μ F which was loaded by a highvoltage power supply (HPP120656-CLD, iseg GmbH, Radeberg, Germany) to the loading voltage U0. The capacitor bank was short-circuited by a high current switch (ignitron NL8900, National Electronics, LaFox, Il, USA) over a wire with 20 mm length. Consequently, a peak current arose which vaporized the wire resulting in a wire plasma explosion. The wire was attached between two insulated electrodes placed in a pressure chamber stacked with further functional rings - pressure ring, inspection window ring - and the forming die. The resulting pressure vessel was filled with distilled water as a pressure transmitting working media, Figure 1b. This approach integrated piezoelectric pressure sensor measurement and high-speed background-oriented schlieren (BOS) imaging to analyze the pressure wave propagation as well as in-situ two-point laser triangulation to monitor the sheet metal displacement which also can be related to the energy transfer according to the pressure wave.

[picture]

Fig. 1. Testing set-up: (a) pulsed-power machine, (b) cross-sectional view of pressure chamber assembly

Fig. 1. Testing set-up: (a) pulsed-power machine, (b) cross-sectional view of pressure chamber assembly

Two different set-ups A and B with different heights s and same 70 mm diameter of the pressure vessel - with and without inspection window ring - were used in this work for different testing scenarios, table 1. The annealed stainless-steel sheet (EN 1.4404 / AISI 316L) with dimensions of 100×100 mm2 and a thickness s0 of 100μ m was placed on the forming die.

Table 1. Testing scenarios

scenario | set-up | pressure vessel height s [mm] | sensors | loading energy [J] | wires
1 | A | 210 | pressure, schlieren, displacement | 50, 68, 85 | Cu99: d = 0.28 mm, R = 1.63
2 | B | 100 | pressure, displacement | 85 | Al99.5: d = 0.35 mm, R = 1.49 Cu99: d = 0.28 mm, R = 1.63 W99: d = 0.18 mm, R = 1.93

A round blank holder with a diameter of 70 mm was used. O-rings were applied between pressure chamber and rings as well as face plate and sheet metal. The pressure waves of the wire explosion traveled through the water and caused pressure on the sheet metal. The sheet metal was consequently formed on a milled die made of EN 1.4301 / AISI 304. The whole forming package was mounted in a clamping frame.
In testing scenario 1, the loading energy Ec was varied from 50 J to 85 J . The tests were performed with 0.28 mm pure copper wire resulting in a quotient R (cp. Eq. 1 [8]) of the loading energy and the vaporization energy EV - according to the volume V , the density ρ and the vaporization enthalpy Δhv of the wire - from R≈1 to R=1.6. It was assumed that the wire evaporated differently by variation of the supplied energy which resulted in changes in the pressure wave propagation and forming. Here, it should be noted that the additional melting energy required was assumed to be negligible. In this scenario the distance between wire axis and sheet metal was 184 mm .

R=ECEV=0.5·C·U02 V·ρ·Δ hV(1)

In testing scenario 2, the wires were varied using pure aluminium (A199.5), pure copper (Cu99) and pure tungsten (W99) whereas the loading energy was kept constant with Ec=85 J. In this scenario the distance between wire axis and sheet metal was reduced to 74 mm .
A free-forming die was used which enabled two simultaneous bulging operations by rectangular cutouts of 8×16 mm2 with 3 mm edge radius. The workpiece was held down with a gap of 0 mm to the die. All tests were repeated three times.
Measurement set-up and procedure. The multi-sensor methodology was used to analyze the transient behavior of the forming process. The measuring equipment and USB oscilloscope used were operated using a separate potential-free power supply, and the measuring computer was used in battery mode. Based on the two different test scenarios, different sensors were considered in the wave analysis.
A piezo-electric pressure sensor ( 102 B03,PCB piezotronics GmbH , Hückelhoven, Germany) was used with a battery powered signal conditioner ( 480 C 02 , PCB piezotronics GmbH , Hückelhoven, Germany). The pressure sensor was mounted uninsulated in the pressure ring with sps=64 mm. Triggered by the discharge current which coupled into the measurement signal as interference, the pressure sensor time period Δtps to the first pressure peak could be determined which was in the range of around 100 microseconds, Fig. 2a. The peak was chosen since following peaks could be used for reflection analysis in future. The time was correlated to the distance from wire to pressure sensor and assumed to represent the formation of the pressure wave from near- to far-field to a certain mean value of pressure wave velocity vps.

[picture]

Fig.2. Measurement: (a) example pressure curves for different loading energies 100 J−400 J, (b) example measured displacement h as a function of time t [8]

Fig.2. Measurement: (a) example pressure curves for different loading energies 100 J − 400 J , (b) example measured displacement h as a function of time t [8]

The sapphire inspection window (diameter of ∅80 mm and thickness of 20 mm ) gave access to the fluid chamber for schlieren imaging. The high-speed camera (fastcam nova S12, photron, Reutingen, Germany) enabled recording rates of 200,000fps which resulted in shutter speeds of Δtbos =5μ s. To realize the background oriented schlieren method, a speckle pattern with speckle size of around 1 mm and distance of around 3 mm was placed on the backside of the fluid reservoir on a second inspection window. This second window enabled sufficient background lighting by a power LED. Triggering the collection of video frames by the process lightning, the pressure wave travels along the inspection window - with the center at sbos =122 mm to the wire axis. The pressure wave could be seen by differential imaging (Fig. 3a) and by BOS-imaging with cross-correlation code using matlab [9], Fig. 3b. The transient frame by frame information of speed vbos_f can be calculated by the quotient of travelled pixels and the distance Δsbos  and Δtbos . Furthermore, two kind of mean value velocities vbos_m were calculated. One value was based on the distance from wire to the center of the window and the time period starting from process lighting. The second value was calculated based on the local velocities from frame to frame.

[picture]

Fig. 3. Measurement: (a) raw view through inspection window and differential image, (b) crosscorrelated images and visualization of pressure wave

Fig. 3. Measurement: (a) raw view through inspection window and differential image, (b) crosscorrelated images and visualization of pressure wave

Two photoelectric sensors (LK-H157, Keyence, Osaka, Japan) were implemented for in-situ measuring the displacement h of the workpiece in the center (sensor 1) and 26 mm to the side (sensor
2) sampled every 2.55μ s, Fig. 2b. This arrangement enabled a two-point insight into the arising pressure field. The measurement set-up was operated with a separate electrical potential (hvdisconnected) to reduce electrical interferences. The distance between sheet metal and wire axis depended on the testing scenario sbos =184 mm and 74 mm . The time period Δtds was then determined by calculation for a 5% threshold value of the maximum sheet metal velocity. This time period was in the range of a few hundred microseconds.

Results

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

The pressure sensor data provided insight into the area between the wire and the pressure sensor. This area could also be described as the near-field. The time to maximum pressure decreased, resulting in a slight increase in wave velocity from 830 to 870 m/s for different loading energy values, Figure 4a. Furthermore, the choice of wire material at a constant charging energy of 85 J had a significant influence on the wave velocity calculated using pressure sensor data. The highest wave velocities in the near field were calculated for copper wire, followed by aluminum and tungsten, Figure 4b.
With increasing propagation, the wave became visible and measurable in the inspection window area. Here, the wave travelled into the far-field region. The BOS-data was collected in test scenario 1. The velocity of the wave was determined in different variants. Figure 5a shows the average velocity over five frames and the average over the time from the process lightning to detection in the inspection window. Here too, in both cases the wave velocity increased with the loading energy. At the same time, the two calculation variants led to slightly different values. What must be highlighted here is, the waves were identified as shock waves with velocities of 1650 m/s to 1720 m/s. For the energy variation the shock waves showed a comparable curvature.

[picture]

Fig. 4. Pressure sensor data: (a) calculated wave velocity as a function of the loading energy, (b) wave velocity for different wire materials

Fig. 4. Pressure sensor data: (a) calculated wave velocity as a function of the loading energy, (b) wave velocity for different wire materials

In all cases clear main wave fronts were detected and used for determination of the velocities, however, for higher energies an increase of reflection appeared. Regarding the wave velocity along the inspection window, it was determined to be constant for the lowest charging energy. With increasing charging energy, there was an increase in wave velocity up to 1800 m/s from frame to frame, Fig. 5b. Nevertheless, this transient wave velocity within a few microseconds could also be attributed to measurement uncertainties.

[picture]

Fig.5. BOS Method data: (a) average wave velocity as a function of the loading energy, (b) wave velocity as a function of time, (c) correlation of maximum pressure value and wave velocity

Fig.5. BOS Method data: (a) average wave velocity as a function of the loading energy, (b) wave velocity as a function of time, (c) correlation of maximum pressure value and wave velocity

As the wave continued to move forward, it reached the sheet metal and caused a free forming. The calculated wave velocity was determined to increase with the loading energy from 800 m/s and then reached a maximum value of around 1300 m/s, Fig. 6a. At the same time, there were differences in the values obtained when using sensors 1 and 2 of 10%, which can be attributed to the curvature of the wave. Compared to the pressure sensor and the BOS method, this variant led to higher fluctuations in the calculated velocities. In addition, lower velocities were determined for the set-up with smaller pressure vessel height s , whereas the difference between sensor 1 and 2 occurred again. Wave velocities for different wire materials were calculated to be constant, Fig. 6b.

[picture]

Fig. 6. Distance sensor data: (a) wave velocity as a function of the loading energy, (b) wave velocity at sensor 1 for different wire materials

Fig. 6. Distance sensor data: (a) wave velocity as a function of the loading energy, (b) wave velocity at sensor 1 for different wire materials

Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

The velocity of the pressure wave could be calculated based on different sensor data. However, differences in the velocities accrued that could be referred to physical effects and the pressure wave propagation as well as the determination of distances and time periods Δti.
For the pressure sensor there were two influencing factors to be critically discussed - the start trigger and stop trigger. As start trigger the current peak was used. However, it could be expected that there was a time difference between the electrical discharge, the wire explosion and the breaking away of the pressure wave. Hence, the velocity was underestimated. The pressure peak was used as end trigger. Here, the wave event theoretically begins shortly beforehand with the rising pressure value, which again leads to an underestimation of the velocity. Nevertheless, it was assumed that this error in the range of 10% does not change the fact that the pressure sensor-based velocities are the lowest. This was explained by the non-linearity of the explosion and wave propagation in the near-field.

Although it required more effort to use, the BOS-method provided a detailed view into the pressure vessel fluid. This allowed various phenomena to be observed directly - not only detecting the shockwaves presence and velocity, but also its geometry and process lighting as well as the occurrence of gas bubbles. The theoretical error that appeared when selecting the start trigger for calculating an average velocity could be prevented by evaluating the velocities within the inspection window. The only error that remained to be mentioned here was caused by the resolution of the camera which was reduced at high frame rates. However, this error was very low according to the resolution of 0.07 mm per pixel.
Considering the BOS- data - even though this observation was confirmed in the other data - an increase in velocity was observed by increasing loading energy. In the case of pressure and distance sensor data this could be again explained by an error in time period calculation. However, this behavior was confirmed as valid using the BOS-method and can be explained by the increasing pressure in the fluid which has an influence on the speed of sound, cp. Fig. 5c. Similarly, this explained why a value higher than theoretical velocity at atmosphere pressure was measured even at the lowest energy level.
The distance sensor data reacted more sensitively to variations in the charging energy. This could be attributed to errors in the start trigger regarding the discharge current and the calculation of the end trigger which may be affected by delay due to sheet metal inertia. Nevertheless, the two sensors provided further information about the process. The difference in speed between sensors 1 and 2 could be related to the longer path of the wave, if it travelled with a curved geometry as seen with BOS-method. However, the resulting error in velocity due to curvature was a factor ten smaller than the actual measured difference. This illustrated the assumption that the edge of the wave lagged behind the center. One effect that explains this behavior is the whip effect described in [8], caused by the sheet metal clamping used.

Summary and Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

In this paper a multi-sensor approach was introduced to electrohydraulic forming and proven as a concept for in-process pressure wave analysis. The following observations were summarized:

Different sensor data were usable to describe the pressure wave along the pressure vessel.

BOS-method directly delivered an insight to the pressure wave from curvature to velocity.

The pressure wave velocity varied along the pressure vessel with velocities up to 1800 m/s.

Pressure sensor data could be related to near-field behavior detecting the lowest velocities.

The change in shockwave velocity with loading energy and wire material was related to the change of sound velocity of compressed water.

As a conclusion, the energy transmission could be described by near-field effects like the wire explosion and resulting time delay and far-field effects like the transient pressure wave front with a pressure amplitude and geometry. The energy transmission ends in the impulse transfer and reaction of the sheet metal after been reached by the pressure wave.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

The authors gratefully acknowledge the support by the German Research Foundation DFG for the project "Wirkmedienbasierte Impulsumformung von Kanalstrukturen". This research was funded by the DFG (German Research Foundation), grant number 529030284.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.107.pdf

Q. J. Zhao et al.,,Study of micro electro-magnetic bulging on a stainless-steel foil", Manufacturing Review, 2, 2015.

E. Cantergiani et al., "Example of two industrial Electro-hydraulic forming applications highlighting the advantages of high strain rates", Conference: NEBU NEHY, 2018.

R. Han, "Electrical Explosion in a Medium: Plasmas, Shock Waves, and Applications", in: T. Shao and C. Zhang (eds.), Pulsed Discharge Plasmas, Springer Series in Plasma Sc. and Tech.

S. Efimov et al., "Addressing the efficiency of the energy transfer to the water flow by underwater electrical wire explosion". Journal of Applied Physics, 106 (7).

Y. Tagawa Y et al. "On pressure impulse of a laser-induced underwater shock wave", Journal of Fluid Mechanics. 2016.

H. Shu et al., "Measurement of the sound velocity of shock compressed water". Sci R. 11, 2021.

I. Eguia et al., „Pressure Field Stabilisation in High-Voltage Underwater Pulsed Metal Forming Using Wire-Initiated Discharges, Key Engineering Materials Vol. 473, 2011.

L. Langstädtler and C. Schenck, "Strain rates in electrohydraulic forming of thin stainless-steel sheet metals", International Conference on High-Speed Forming, Dortmund, 2025.

A.V. Mamutov et al., "Modeling of electrohydraulic forming of sheet metal parts", JMPT, 2015.

JoshtheEngineer (2021): BOS matlab script. online via

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 115-123

doi: 10.4028/p-0SlKmg

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2025-12-26

Revised:
2026-02-20

Accepted:
2026-02-24

Online:
2026-04-16

Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

The original version of this paper is available on https://www.scientific.net/SSP.389.115.pdf

BORDA Francesco 1,a, CARUSO Serafino 1, b* and FILICE Luigino 1,c

1 Department of Mechanical, Energy and Management Engineering, University of Calabria, 87036 Rende, CS, Italy

(*corresponding author)

Keywords: Plasma arc welding; controlled tube expansion; AISI 316 stainless steel; multi-step expansion; finite element modeling.

Abstract

The increasing demand for reliable and high-performance heat-transfer components has stimulated the development of robust joining and forming strategies for thin-walled stainless-steel tubes. In this work, the Controlled Tube Expansion of Plasma Arc Welded AISI 316 stainless-steel tubes was investigated through a combined experimental and numerical approach. Welded tubes with an initial diameter of 130 mm were expanded to 180 mm using a three-step mechanical expansion process, and six different expansion sequences were experimentally evaluated. Finite element simulations were performed using a coupled thermo-mechanical model incorporating a damage-based fracture criterion to predict material failure during expansion. Numerical predictions were in good agreement with experimental observations and allowed the identification of a critical cumulative damage threshold governing tube failure. Based on these results, a processability domain was defined, clearly distinguishing safe and unsafe expansion paths. The study demonstrates that tube expandability is strongly dependent on the deformation path and highlights the importance of progressive expansion strategies for maximizing material ductility while preventing fracture.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.115.pdf

The growth in demand for high-performance heat-transfer systems has intensified the demand for reliable and efficient joining techniques for stainless-steel tubes, especially those produced from AISI 316 [1-3]. Among the existing welding technologies, Plasma Arc Welding (PAW) has emerged as a key enabling process due to its superior stability, high energy density, and ability to produce narrow and deeply penetrating welds [4-6]. These characteristics are of paramount importance for applications involving Controlled Tube Expansion (CTE), where weld integrity plays a decisive role in ensuring both the quality of the expanded joint and the overall structural reliability of the system [7-9]. Minor imperfections in the PAW weld, such as lack of fusion, overheating, or microstructural inhomogeneities, can significantly reduce the ductility of the tube and compromise its response during mechanical expansion. Despite the broad industrial relevance of CTE processes, predicting the risk of tube failure during expansion remains of considerable challenge. The material is subjected to complex deformation paths and the failure process is dominated by interactions between weld geometry, thermally affected microstructures, and multiaxial stress states. To address these difficulties, numerical simulations based on the Finite Element Method (FEM) have become indispensable tools. FEM allows for detailed reproduction of the expansion mechanics and provides access to stress and strain fields that are difficult or impossible to measure experimentally [10-12]. A central aspect of such simulations involves an accurate fracture criterion capable of predicting the onset of damage and rupture under the specific loading path imposed by the expansion process [1315]. The proper prediction of this criterion is essential not only to determine optimal process steps for obtaining defect-free expanded tubes but also to define a robust processability domain. This domain delineates safe expansion conditions, where tube integrity is preserved, from unsafe regimes leading to failure. Ultimately, the integration of PAW process characterization with advanced FEM modeling provides a powerful framework for enhancing process reliability, reducing trial-and-error experimentation, and improving the design of next-generation mechanically expanded tube-sheet joints.

Experimental Procedure

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PAW experiments were carried out on AISI 316 stainless steel (Table 1) using an automated torch system (SITEC BSL 1000 LTC) equipped with a THERMAL ARC 4A DUAL FLOW TORCH. The welding was performed on 0.5 mm thick sheets, subsequently folded and joined to produce tubes with an initial diameter of 130 mm and a length of 200 mm , as shown in Fig. 1a.

Table 1. Nominal chemical composition of AISI 316 stainless steel (wt.%)

Elements | Cr | C | Mn | Si | Ni | P | S | Mo | Cu | Fe
Weight % | 16.8 | 0.016 | 1.44 | 0.218 | 10.1 | 0.031 | 0.023 | 2.01 | 0.418 | Balance

Welding parameters included a current of 115 A , a welding speed of 69.33 mm/s, and a plasma gas flow rate of 15 L/min, while Argon was supplied as shielding gas at 4 L/min.

[picture]

Fig. 1. Experimental procedure for tube expansion: a) initial welded tube; b) positioning of the tube on the first expansion station; c) tube at the end of the first expansion step; d) fully expanded tube after the third expansion step.

Fig. 1. Experimental procedure for tube expansion: a) initial welded tube; b) positioning of the tube on the first expansion station; c) tube at the end of the first expansion step; d) fully expanded tube after the third expansion step.

After fabrication, the tubes were expanded from 130 mm to 180 mm using a SITEC expansion machine (Figs. 1b-1c) to manufacture components intended for aeration systems (Fig. 1d). The expansion system consists of three sequential stations specifically designed to perform the diameter increase in three controlled steps, thereby reducing the risk of excessive deformation that would likely occur if the entire expansion were executed in a single pass. Each station includes eight identical Teflon dies (black elements in Figs. 1b-1c), which move at an expansion speed of 0.74 mm/s. Although identical in number, the die geometries vary from station to station to achieve a progressive deformation of the tube. Additionally, each station is equipped with an upper flat punch that prevents upward displacement of the tube during expansion, a phenomenon that may occur due to the process kinematics. To determine the optimal sequence of diameter increments for obtaining defect-free expanded tubes while defining a robust processability domain, six experimental cases with different expansion sequences were investigated, as summarized in Table 2.

Table 2. Experimental plan for the multi-step tube expansion process

Process procedure | Diameter expansion [mm]
| I Step | II Step | III Step
1 | 10 | 10 | 30
2 | 10 | 20 | 20
3 | 10 | 30 | 10
4 | 20 | 10 | 20
5 | 20 | 20 | 10
6 | 30 | 10 | 10

For statistical robustness and to ensure the reliability of the results, three replications were performed for each test condition, yielding a total of eighteen experiments conducted in randomized order. This approach also strengthens the subsequent numerical analysis of the fracture criterion and supports the definition of a reliable processability window.

Analysis of the six proposed procedures for expanding the tubes from 130 mm to 180 mm clearly indicates that only procedure 2 successfully achieves the target diameter in a technologically sound manner, Figure 2. Although all procedures reach the required 50 mm total expansion, several of them exhibit poorly balanced deformation increments, with excessively large initial or final steps that may induce material instability, ovalization, or surpass the operational limits of the equipment. Certain sequences focus the deformation at one step of 30 mm , while others introduce too large an increment during the initial stage, which hampers the smooth progression required for deformation. In contrast, procedure 2, which involves equal increments of 10, 20, and then 20 mm deformation, provides an equal and measured share of deformation at the three stations. Thus, this pattern avoids mechanical instabilities and promotes better control during the processes, as it is the only procedure that can successfully deform the sample from 130 mm to 180 mm . These experimental outcomes are particularly valuable for analyzing the fracture criterion employed in the numerical modelling. They provide reliable data on the material's deformation limits and on the conditions beyond which the tube can no longer withstand the imposed diameter increase. The subsequent FE simulations will enable detailed investigation of the material damage evolution at each expansion step, offering a scientific explanation for the observed failure modes and allowing for a more accurate definition of the feasible processing domain for the expansion operation.

[picture]

Fig. 2. Comparison of tube expansion outcomes for two experimental procedures: a) failure observed for the 10-10-30 mm sequence; b) successful expansion for the 10-20-20 mm sequence.

Fig. 2. Comparison of tube expansion outcomes for two experimental procedures: a) failure observed for the 10-10-30 mm sequence; b) successful expansion for the 10-20-20 mm sequence.

Finite Element Modeling of Tube Expansion

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The commercial FE software DEFORM-2D TM  SFTC was employed to simulate the CTE process through a coupled thermo-mechanical analysis performed in a two-dimensional axisymmetric framework reproducing the experimental expansion configuration. The workpiece was discretized into 12,000 elements and modeled as a plastic material with isotropic hardening. Each station's die was modeled as a rigid body consisting of 1,200 elements, as illustrated in Fig. 3. Regarding the kinematic boundary conditions, an expansion speed of 0.74 mm/s, consistent with the experimental procedure, was imposed on the die, allowing translation along the X direction while constraining motion in the Y direction.

[picture]

Fig. 3. Finite element model of the tube expansion process: axisymmetric mesh of the tube and dies and die-tube interaction setup.

Fig. 3. Finite element model of the tube expansion process: axisymmetric mesh of the tube and dies and die-tube interaction setup.

The tube was also constrained in the +Y direction movement, reflecting the experimental use of an upper flat punch that prevents upward displacement during the expansion process. The die-tube interaction was described using a sliding friction formulation based on the Coulomb law, τ=μσn, where σn is the normal stress at the die-tube interface, and μ=0.05 is the local friction coefficient, determined from available data between Teflon (die) and AISI 316 stainless steel (tube) and calibrated through consistency between numerical results and experiments. Tube failure during expansion was modeled using the Brozzo et al. [16] fracture criterion, which accounts for the influence of hydrostatic stress, as expressed in Eq. (1):

∫0ε¯f2σ13(σ1−σm)dε¯=D(1)

where εf is the effective strain at failure, σ1 the principal stress, σm the hydrostatic stress and D the material damage constant. The material flow stress was described using the tabular data format σ(ε,ε˙,T) available in DEFORM-2D TM  SFTC, which expresses flow stress as a function of effective strain, strain rate and temperature.

Results and Discussion

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By means of the FEM, it was possible to accurately reproduce the tube expansion process, predicting the evolution of the mechanical behavior of the workpiece and providing a sound mechanical interpretation of the corresponding experimental results. Figure 4 shows the good agreement between numerical predictions and experimental results for Procedure 1 (10-10-30). In particular, the model accurately identifies the critical zone, which coincides with the fracture location observed experimentally.

[picture]

Fig. 4. Numerical-experimental comparison of tube expansion results for the 10−10−30 mm loading sequence: a) predicted damage distribution and b) experimentally observed fracture location.

Fig. 4. Numerical-experimental comparison of tube expansion results for the 10 − 10 − 30 m m loading sequence: a) predicted damage distribution and b) experimentally observed fracture location.

Thanks to the numerical framework and to the implementation of the fracture criterion, the underlying mechanical mechanisms governing the success or failure of the expansion process could be investigated in greater depth. This approach enabled the identification of the fundamental factors controlling damage accumulation and, consequently, the definition of the optimal expansion steps required to obtain defect-free expanded tubes. In particular, the numerical analysis made it possible to start from the only experimentally identified safe process procedure (the No. 2 in Table 2) with diameter increments of 10-20-20 mm, which is the sole sequence capable of achieving complete tube expansion without fracture, and to systematically analyze all alternative procedures, providing a clear mechanical explanation for why they inevitably lead to failure.

Table 3 reports the evolution of cumulative damage predicted during the three-step tube expansion process, clearly demonstrating that the sequence of diameter increments plays a decisive role in determining the structural integrity of the tube.

Table 3. Numerical prediction of cumulative damage during the multi-step tube expansion process

Process procedure | Damage value
| I Step | II Step | III Step
1 (10-10-30) | 0.11 | 0.15 | 11.10
2 (10-20-20) | 0.11 | 1.98 | 2.75
3 (10-30-10) | 0.11 | 7.32 | 7.83
4 (20-10-20) | 1.10 | 1.92 | 4.91
5 (20-20-10) | 1.10 | 3.89 | 3.95
6 (30-10-10) | 1.80 | 2.85 | 2.89

Considering the experimental results, the finite element analysis indicates that only the 10-20-20 mm expansion procedure successfully completes the tube expansion without inducing material damage, whereas all other sequences lead to cumulative damage levels exceeding the material's integrity threshold. Notably, all failed procedures reach cumulative damage values above 2.75 , which defines the critical threshold for fracture. In contrast, the 10−20−20 mm sequence reaches a maximum cumulative damage of 2.75 at the end of the third step, indicating that the material is fully utilized without approaching its ductility limit. These findings confirm that failure is directly associated with exceeding a critical damage threshold rather than occurring randomly.

Mechanically, the first expansion step is crucial in defining the residual deformability of the tube. An initial diameter increase of 10 mm produces minimal damage, allowing for progressive and homogeneous plastic deformation in subsequent steps. In procedures with larger initial expansions of 20 or 30 mm , significant early-stage damage substantially reduces residual ductility, predisposing the tube to premature failure. In the 10−20−20 mm sequence, damage accumulates gradually and evenly
throughout the process, preventing excessive strain localization and enabling stable strain hardening. This controlled deformation delays the nucleation and coalescence of microvoids responsible for ductile fracture. Conversely, in alternative sequences, damage is highly concentrated in a single expansion step, rapidly exceeding the critical threshold. Excessive increments applied at intermediate or final stages impose deformation levels that the material cannot accommodate, even if earlier steps are mild.

Overall, the results demonstrate strong internal consistency and physical significance. All expansion strategies exceeding the critical damage value of 2.75 lead to tube failure, whereas the 10−20−20 mm sequence fully exploits the material's ductility without surpassing the fracture limit. Based on these findings, a robust processability domain was defined (Figure 4), clearly delineating safe expansion conditions, where tube integrity is preserved, from unsafe regimes leading to inevitable material failure.

[picture]

Fig. 4. Processability domain for multi-step tube expansion, showing safe (green) and unsafe (red) deformation regimes. The 10−20−20 mm expansion path lies entirely within the safe region, illustrating a progressive and damage-controlled deformation strategy.

Fig. 4. Processability domain for multi-step tube expansion, showing safe (green) and unsafe (red) deformation regimes. The 10 − 20 − 20 m m expansion path lies entirely within the safe region, illustrating a progressive and damage-controlled deformation strategy.

Figure 4 provides a concise representation of the processability domain obtained from the combined experimental and numerical investigation. The region of safe and unsafe expansion strategies has been pointed out in this diagram, showing not only the dependence of tube expandability on the total extent of expansion but also the pathway of deformation used. The region has been coloured differently to make it distinct, and this includes the region of safe expansion, which has been coloured green, while the other has been coloured light red. Inside the green safe region, deformation is increasingly and controlled, and this provides the material the opportunity to resist high plastic strain without embarking on unstable processes of failure. The 10−20−20 mm expansion path lies entirely within this region, confirming that an initially mild deformation step is critical to preserve sufficient residual ductility for subsequent expansions. From a micromechanical perspective, this behavior reflects the gradual evolution of void nucleation and growth, which remains stable as long as strain localization is avoided and the material's hardening capacity is not prematurely exhausted. In contrast, all other investigated procedures intersect the light red unsafe region, as they involve diameter increments that induce excessive damage at one or more stages. In these cases, localized plastic flow dominates the material response, accelerating void coalescence and resulting in ductile fracture. The processability domain also provides predictive capability. Instead of relying on trial-and-error experimentation, it offers a rational framework for designing expansion schedules that maximize formability while minimizing the risk of fracture. By constraining each expansion step within the green safe region, the material's ductility can be fully exploited in a repeatable and reliable
manner, which is particularly relevant for industrial applications requiring robust and defect-free processes. Finally, the fact that the safe and unsafe regions are clearly demarcated confirms the preeminent importance of damage-controlled fracture in the process. This confirms the appropriateness of the fracture criterion chosen, the importance of the finite element simulations, as well as the accuracy of the proposed methodological approach for modeling the process of tube expansion. Figure 4 thus summarizes the key findings of this work, presenting an intuitive processability map that identifies a unique safe expansion path and a well-defined damage threshold, offering both scientific insight and practical guidance for the design of multi-step tube expansion processes.

Conclusions

The original version of this paper is available on https://www.scientific.net/SSP.389.115.pdf

This work presents a comprehensive experimental-numerical investigation of the Controlled Tube Expansion of PAW-welded AISI 316 stainless-steel tubes, with the aim of identifying reliable expansion strategies and defining a robust processability domain. The main conclusions can be summarized as follows:

the results indicate that, in PAW-welded AISI 316 material tubes, the effect of the sequence of diametric expansion increments is significantly greater than that of total expansion. The weld path can appreciably influence damage and subsequent failure modes when different deformation processes, leading to identical final diameters, are considered;

among the analyzed procedures, only the 10−20−20 mm size increment pattern was successful in reaching the desired size without breakage. Such a method helps increase plastic deformation evenly;

finite element simulations incorporating a damage-based fracture criterion revealed the presence of a critical cumulative damage value of approximately 2.75 . All expansion routes exceeding this critical damage resulted in material failures that confirmed that material fracture is a function of damage rather than instability;

with the combined experimental-numerical approach, it has become possible to define the domain of processability, which distinguishes without ambiguity the areas of expansion conditions as being either safe or unsafe. This domain can be efficiently used in the design of processes involving multiple steps in tube expansion.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/SSP.389.115.pdf

The authors gratefully thank Dott. G. Mezzatesta of Profiltek s.r.l. (Italy) for its valuable contribution to the research.

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The original version of this paper is available on https://www.scientific.net/SSP.389.115.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 125-133

doi: 10.4028/p-8Tbjxt

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-07

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

The original version of this paper is available on https://www.scientific.net/SSP.389.125.pdf

MOON Jiyoung 1,a*, FRIGGE Alexander 1, b, NIEMIETZ Philipp 1,c, HERRIG Tim 1, d and BERGS Thomas 1,2,e

¹Manufacturing Technology Institute MTI of RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, Germany

2 Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen, Germany

aj.moon@mti.rwth-aachen.de, b  a.frigge@mti.rwth-aachen.de, c  p.niemietz@mti.rwth-aachen.de, d  t.herrig@mti.rwth-aachen.de, et.bergs@mti.rwth-aachen.de 

Keywords: Sheet-metal Forming, Punch Wear Assessment, Multivariate Analysis.

Abstract

In precise sheet-metal forming operations such as fine blanking, the closed tool design precludes direct observation during production, which makes indirect monitoring of punch wear necessary. Previous work has shown that the sheared surfaces of the scrap web can be used to infer the punch wear through spatial correlation analysis of areal roughness parameters. However, these correlations have so far each explained only a limited portion of the variance and have only been investigated for a single punch geometry, leaving their robustness and generalizability open to question. In this work, multivariate regression approaches and feature importance analysis are used to combine complementary areal roughness parameters and generate robust indicators of punch wear. The plausibility of these indicators is validated by linking the correlated scrap web sheared surface features to physically interpretable wear mechanisms, such as worn surface area or punch breakage. Furthermore, the approach is extended to multiple punch geometries to examine the extent to which the identified correlation patterns can be transferred to different tool designs and process conditions. The results demonstrate the generalizability of spatial correlation-based indicators across different geometries and process conditions.

Introduction

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Unplanned downtime in manufacturing causes substantial economic losses. The world's 500 largest manufacturing companies lose approximately $1.4 trillion annually through unplanned downtime, equivalent to 11% of their revenues [1]. As one of the manufacturing processes that are widely used across various industries, sheet-metal forming processes rely on tools that are subject to wear during operation. Among the various tool components, punches represent critical wear parts that require precise dimensional control throughout their lifetime. Particularly in processes such as fine blanking, the economic impact of punch wear intensifies. Since worn punches can no longer meet these tight tolerances, more frequent replacement is necessitated, and downtime costs increase. The closed tool design of fine blanking process prevents direct observation during production, making indirect monitoring of punch condition essential for preventing costly unplanned stops.

Indirect monitoring in sheet-metal forming processes commonly include process signals, such as force or acoustic emission (AE). Kubik et al. proposed a machine learning-based inline wear quantification workflow that relies on engineered process features and explicitly identifies which signal-derived descriptors are most relevant for wear-state discrimination [2]. Becker et al. applied explainable deep learning approach to fine blanking force time series to reveal which time regions drive the wear prediction [3]. To this extent, Niemietz et al. investigated representation learning methods for fine blanking force signals and demonstrated that the stability and variance of individual low-dimensional representation components can be interpreted as physically meaningful indicators of wear progression [4]. Most recently, Unterberg et al. demonstrated data-driven indirect punch wear monitoring where scrap web sheared surface roughness is treated as a proxy for punch condition and is linked to process signals such as acoustic emission features across shearing and stripping phase [5].

While these data-driven methods demonstrate the value of engineered features for wear monitoring, similar feature extraction principles have been applied to different process monitoring tasks as well. Frigge et al. employed sensor fusion techniques to combine statistical, temporal, and spatial features extracted from force and AE signals for crack prediction in fine blanking [6]. Similarly, Ortjohann et al. applied forward feature selection on eddy current measurements to identify the most informative frequency harmonics for predicting sheared surface tears [7]. Feature extraction methods have also been extended to spatial domain analysis. Recent research of Moon et al. revealed the spatial relationship between punch and scrap web sheared surface [8]. They demonstrated correlations between punch surface characteristics and scrap web sheared surface roughness, where individual parameters explained up to 60% of the variability. However, the previous analysis was limited to a single punch geometry from one experiment, leaving the transferability of these correlations unexplored. The goal of this work is to investigate influences of areal roughness parameters of scrap web sheared surfaces on those of the corresponding punches across different punch geometries and process setups, thereby establishing robust and generalizable indicators for punch wear monitoring in sheet-metal forming processes.

Methods

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To systematically study how punch wear manifests in the sheared surface of scrap webs across different tool and process configurations, a series of fine blanking experiments was performed on a Feintool XFT 2500 speed press. 12 punches with varying geometries, sheet materials, lubricants, and production lengths were investigated (see Table 1). The experiments covered three geometry families (Types A-C; see Figure 1) and four sheet materials ( 58CrV4,42CrMo4,100Cr6, and C75S) processed at thickness of 5−6 mm under varying industrial lubrication conditions. Among these, three experiment sets {P1,P2},{P3,P4}, and {P5,P6} were conducted with paired punches, producing two parts per stroke. All remaining experiments used a single punch configuration.

Table 1. Overview of punches and production conditions.

Punch index | Geometry type | Punch material | Coating | Sheet material | Sheet thickness | Lubricator | Number of production strokes
P1 | Type A | BOEHLER K490 | PLATIT FEINAL | 58CrV4 | 5 mm | WISURA FMO 5020 | 41,410
P2 | Type A | BOEHLER K490 | PLATIT FEINAL | 58CrV4 | 5 mm | WISURA FMO 5020 | 41,410
P3 | Type Ba | BOEHLER S390 | PLATIT FEINAL PLUS | 42CrMo4 | 5 mm | RAZIOL CLF 48 HL | 31,400
P4 | Type Bb | BOEHLER S290 | PLATIT FEINAL PLUS | 42CrMo4 | 5 mm | RAZIOL CLF 48 HL | 31,400
P5 | Type Bc | BOEHLER S390 | PLATIT FEINAL PLUS | 42CrMo4 | 5 mm | BERUFORM STO 121 ZF | 33,000
P6 | Type Bd | BOEHLER S290 | PLATIT FEINAL PLUS | 42CrMo4 | 5 mm | BERUFORM STO 121 ZF | 33,000
P7 | Type Ca | BOEHLER S390 | PLATIT FEINAL PLUS | 58CrV4 | 6 mm | BERUFORM XFO 2577 | 10,800
P8 | Type Ca | BOEHLER S390 | PLATIT FEINAL PLUS | 58CrV4 | 6 mm | RENOFORM FMO 5020 | 2,000
P9 | Type Ca | BOEHLER S390 | PLATIT FEINAL PLUS | 100Cr6 | 6 mm | RENOFORM FMO 5020 | 2,000
P10 | Type Cb | BOEHLER S390 | PLATIT FEINAL PLUS | 58CrV4 | 6 mm | RENOFORM FMO 5020 | 2,000
P11 | Type Cb | BOEHLER S390 | PLATIT FEINAL PLUS | C75S | 6 mm | RENOFORM FMO 5020 | 700
P12 | Type Cb | BOEHLER S390 | PLATIT FEINAL PLUS | C75S | 6 mm | RENOFORM FMO 5020 | 1,000

[picture]

Fig. 1. Part geometry families: (a) Type A dimensional specifications, (b) Type B variants showing structure symmetry and laser-structured area in top view as well as the schematic 3D punch model. The left/right sides of punches feature different laser textures, which are not examined in this study. (c) Type Ca dimensional specifications, (d) Type Cb dimensional specifications.

Fig. 1. Part geometry families: (a) Type A dimensional specifications, (b) Type B variants showing structure symmetry and laser-structured area in top view as well as the schematic 3D punch model. The left/right sides of punches feature different laser textures, which are not examined in this study. (c) Type Ca dimensional specifications, (d) Type Cb dimensional specifications.

Across all production runs, the last scrap web from each experiment was collected to represent the state of the shearing interface at the end of tool life or at the end of the experimental run. These scrap webs, together with the worn punches, were subsequently characterized using a Keyence VR-6000 3D optical profilometer to quantify wear morphology and to extract corresponding roughness parameters on both tool and sheared surfaces. Following rotation and leveling correction, the measurable flat regions along the shearing edges were segmented into uniformly distributed edge segments per punch, consistent with established procedures for spatially resolved wear characterization. Several segments exhibiting irregular production-induced artefacts, or severe mechanical damage that would bias the roughness statistics were excluded. Across all 12 punches, this yielded a total of 415 valid edge segments.

For each retained edge segment, surface regions were defined with punch surfaces extending 2 mm below the shearing edge as shown in Figure 2. For each edge segment, 21 areal roughness parameters from ISO 25178 were extracted, and proportion of the worn area (Eq. (1) and normalized removed volume (Eq. 2) were measured.

 Worn area proportion =∫0bW(x)dxb·2mm Normalized removed volume = Removed volume b·2mm

(1)(2)

[picture]

Fig. 2. Schematic representation of punch wear measurement methodology. Left: Cross-sectional view (A-A') showing segment width b , surface Region W(x), and 2 mm evaluation depth. Right: Longitudinal section illustrating the removed volume (hatched area).

Fig. 2. Schematic representation of punch wear measurement methodology. Left: Cross-sectional view (A-A') showing segment width b , surface Region W ( x ) , and 2 mm evaluation depth. Right: Longitudinal section illustrating the removed volume (hatched area).

To ensure one-to-one spatial correspondence between punch segments and scrap web segments, the corresponding scrap web sheared surface segments, representing the contact areas with the punch, were further subdivided into five equally spaced sub-areas along the shearing direction. Sub-area heights were 1 mm for 5 mm sheet thickness and 1.2 mm for 6 mm sheet thickness. 21 areal roughness parameters are extracted for each sub-area, yielded sequences of five values per roughness parameter for each segment, representing the spatial evolution of sheared surface features along the shearing direction. To characterize the shape and variability of these sequences, 27 statistical and temporal features were extracted using the Python TSFEL library, resulting in 567 sequence-derived features per scrap web segment.

Based on the spatially resolved measurements, the problem is formulated as two-step multivariate regression tasks in which a shared feature matrix 𝐗 is used to jointly predict two punch wear indices. Specifically, the input Matrix 𝐗∈ℝ415×p contains either p punch areal roughness parameters or p scrap web sequence-derived features for 415 edge segments, while the output matrix 𝐘∈ℝ415×2 comprises the worn area proportion and the normalized removed volume. The relationship is expressed as:

𝐘=𝐗𝐁+𝐄,(3)

where 𝐁∈ℝp×2 contains target-specific regression coefficients and 𝐄 represents residual errors. The objective of this study is therefore twofold. First, it aims to identify which punch surface areal roughness parameters most robustly describe the spatial manifestation of wear on the shearing edge. Second, it seeks to determine whether these wear-relevant punch-parameters can subsequently be inferred from scrap web sequence-derived features, enabling indirect punch wear assessment.

Before using the defined wear indices as supervision targets for indirect monitoring, it is first assessed whether they can be consistently explained by plausible punch surface roughness descriptors (Task T1). Next, whether the same wear indices can be inferred from scrap web sheared surface features, enabling indirect wear assessment (Task T2). Therefore, the modelling framework must satisfy two following requirements:

The shearing process is influenced by several interacting factors, such as lubrication, contact conditions, and complex wear mechanisms. These mechanisms can interact in ways that may introduce nonlinear relationships between the measured scrap web features and the punch roughness parameters. A regression model therefore needs the capacity to capture potential nonlinear relationships and feature interactions, without requiring strong assumptions about their exact structure. Gradient-boosted decision-tree models, such as CatBoost, are well suited for this purpose, as they can represent nonlinear feature interactions, handle heterogeneous feature scales, and remain robust under limited sample sizes [9].

The dataset is composed of segments originating from different punches, materials, lubricants, and production campaigns, resulting in heterogeneous operating conditions and clustered data structures. A suitable modelling framework must therefore provide a reliable estimate of how well the learned relationships generalize across different experimental contexts. To meet this requirement, the evaluation strategy must explicitly respect the grouping structure of the data and ensure balanced representation of wear states across training and test sets, which is achieved by employing 5-fold group-stratified cross-validation (CV). For both tasks, SHAP values were therefore computed exclusively on out-of-fold predictions within the CV procedure and aggregated across folds, ensuring that the resulting feature attributions reflect robust and generalizable relationships rather than artefacts of a single model fit.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.125.pdf

For the first task, all 21 punch areal roughness parameters were used as input features, while the proportion of worn area and the normalized removed volume served as target variables representing punch wear. Model training and evaluation were performed using a multitask CatBoost regression model, allowing both wear metrics to be learned jointly while exploiting shared structure between them. To ensure that the identifying wear-related punch parameters are not driven by a single traintest split, model evaluation was performed using 5 -fold group-stratified CV. Table 2 summarizes the fold-wise cross-validated R2 values for both wear metrics, demonstrating consistently high and stable predictive performance across all folds.

Table 2. Group-stratified cross-validated R2 for predicting punch wear indices from punch areal roughness parameters (Task T1).

Fold

Worn area

proportion

Normalized

removed volume

1 | 0.919 | 0.975
2 | 0.927 | 0.955
3 | 0.912 | 0.942
4 | 0.824 | 0.930
5 | 0.864 | 0.925

Subsequently, SHAP values were computed in an out-of-fold manner for each fold and aggregated across folds, yielding robust global importance estimates that reflect contributions under unseen experimental conditions. Figure 3 shows the global SHAP importance for worn area proportion and normalized removed volume. While several roughness parameters contribute to both targets, a small subset consistently dominates across wear metrics. In particular, parameters related to material volume and bearing ratio (mostly Vmc, Smr1, and Smr2) exhibit the highest and most stable SHAP contributions. This indicates that volumetric surface characteristics are most informative for describing the spatial manifestation of punch wear.

[picture]

Fig. 3. Global SHAP importance plots for multitask prediction of (a) worn area proportion and (b) normalized removed volume from punch areal roughness parameters.

Fig. 3. Global SHAP importance plots for multitask prediction of (a) worn area proportion and (b) normalized removed volume from punch areal roughness parameters.

While several parameters contribute to both targets, Table 3 highlights those punch areal roughness parameters that combine high SHAP importance, cross-target relevance, and stable contributions across folds. The reported SHAP standard deviation (denoted as "SHAP std" in the table) quantifies the variability of the fold-wise mean absolute SHAP values across the 5 CV folds and therefore reflects the stability of each feature's contribution under changing training-test splits. Parameters related to material volume and bearing ratio (Vmc, Smr1, Smr2) dominate both target wear metrics. In particular, Vmc consistently exhibits the highest importance for both the worn area proportion and the normalized removed volume, indicating that the defined wear metrics align mostly with the core material volume of the punch surface.

Table 3. Punch roughness parameters with highest SHAP importance for both punch wear metrics.

Punch roughness parameter | Worn area proportion | Normalized removed volume
| Mean |SHAP| | SHAP std | Rank | Mean |SHAP| | SHAP std | Rank
Vmc | 2.333 | 0.255 | 1 | 0.331 | 0.031 | 1
Smr1 | 2.123 | 0.300 | 2 | 0.127 | 0.030 | 8
Smr2 | 1.867 | 0.584 | 3 | 0.192 | 0.069 | 4
Vvv | 1.351 | 0.388 | 4 | 0.214 | 0.065 | 2
Vvc | 1.113 | 0.197 | 5 | 0.204 | 0.044 | 3
Svk | 0.910 | 0.175 | 6 | 0.175 | 0.018 | 5

The worn area proportion is primarily influenced by bearing-ratio-related parameters (Smr1, Smr2 ), and by volumetric descriptors such as Vmc and Vvv, which together describe how the contact area grows and how material spreads along the punch edge as the surface wears. This indicates that the worn area proportion predominately captures the spatial spread of wear and surface flattening. In contrast, the normalized removed volume shows stronger associations with valley- and volumerelated parameters, including Vmc,Vvc,Vvv, and Svk. These parameters characterize the amount of material available below the dominating surface level and the capacity of valleys to accommodate material removal. Accordingly, the removed volume index reflects the depth-related progression of wear, emphasizing material loss below the original surface.

While Task T1 demonstrates that the defined wear indices are consistently explained by physically plausible punch surface descriptors, the punch surface itself is not accessible for inline or in-process monitoring. Therefore, the subsequent task focuses on assessing whether the same wear indices can be inferred indirectly from the sheared surface characteristics of the scrap web.

For the second task, all 567 sequence-derived features extracted from scrap were used as input features, while the proportion of worn area and the normalized removed volume on the punch served as target variables. Similar to the task before, a multitask CatBoost regression model was employed to jointly learn both wear metrics, and model evaluation was again performed using 5 -fold group-
aware CV with substantial out-of-fold SHAP analysis. Table 4 reports the fold-wise cross-validated R2 values for this indirect prediction task.

Table 4. Group-stratified cross-validated R2 for predicting punch wear indices from scrap web sequence-derived features (Task T2).

Fold

Worn area

proportion

Normalized

removed volume

1 | 0.416 | 0.297
2 | 0.746 | 0.767
3 | 0.707 | 0.712
4 | 0.464 | 0.543
5 | 0.576 | 0.558

Compared to Task T1, the predictive performance is lower and exhibits higher fold-to-told variability. This behavior is expected, as Task T2 addresses a substantially more complex problem, that punch wear is not directly observed but must be inferred indirectly from surface features of the scrap web, which are influenced by additional factors such as local material flow, fracture behavior, lubrication and process variability. Consequently, moderate and variable R2 values reflect the natural difficulty of the indirect mapping. Despite the reduced predictability, the cross-validated performance remains consistently positive across folds, providing sufficient signal for meaningful SHAP-based identification of wear-related scrap web features.

Figure 4 shows the resulting global SHAP importance of scrap web roughness parameters for normalized removed volume and worn area proportion. In contrast to the previous task, where a small set of volumetric punch parameters clearly dominated, the scrap web-based models exhibit a broader distribution of contributing features, reflecting the indirect and more entangled nature of the information transfer from scrap web to punch.

[picture]

Fig. 4. Global SHAP importance plots for multitask prediction of (a) worn area proportion and (b) normalized removed volume from scrap web sequence-derived features.

Fig. 4. Global SHAP importance plots for multitask prediction of (a) worn area proportion and (b) normalized removed volume from scrap web sequence-derived features.

Across both wear metrics, descriptors related to valley void volume and depth on the sheared surface of the scrap web characteristics ( Vvv ) consistently appear as the most influential features. Statistical measures such as mean and root mean square (RMS) of Vvv dominate the SHAP rankings for both targets, indicating that punch wear is strongly reflected in the scrap web through changes in valley formation during the shearing process. Beyond Vvv, parameters related to core roughness depth ( Svk ) and bearing-ratio characteristics ( Smr2 ) also show relevant contributions, suggesting that wear progression affects not only the deepest valleys but also the transition region between plateaus and valleys. The presence of histogram-based and empirical cumulative distribution function (ECDF)based descriptors among the top-ranked features further suggests that wear information is encoded in changes to the overall distribution of surface heights and depths on the sheared surface of the scrap
web, rather than in simple shifts of average roughness alone. Table 5 summarizes those scrap web sequence-derived features that combine high SHAP importance, relevance across both wear metrics, and stable contributions across CV folds.

Table 5. Scrap web sequence-derived features with SHAP importance across both punch wear metrics.

Scrap web sequence-derived features | Worm area proportion | Normalized removed volume
| Mean |SHAP| | SHAP std | Rank | Mean |SHAP| | SHAP std | Rank
Mean(VVV) | 0.642 | 0.291 | 1 | 0.118 | 0.047 | 1
Max(Svk) | 0.475 | 0.240 | 2 | 0.079 | 0.041 | 3
RMS(VVV) | 0.463 | 0.247 | 3 | 0.087 | 0.045 | 2
RMS(Smr2) | 0.418 | 0.153 | 4 | 0.058 | 0.022 | 8
Min(Sq) | 0.367 | 0.194 | 7 | 0.066 | 0.035 | 5

The worn area proportion is most strongly influenced by features capturing the overall magnitude and spread of valley structures, such as Mean(Vvv) and RMS(Vvv). These descriptors reflect how extensively deep valleys are formed along the sheared surface and how uniformly they are distributed across the sequence. Their prominence suggests that the worn area proportion is primarily sensitive to the spatial extent and consistency of surface degradation, rather than a few isolated deep scratches or peaks. In contrast, the normalized removed volume shows relatively higher sensitivity to features related to local depth irregularities and pronounced spatial variability of surface height, such as Max(Svk) and Min(Sq). Increased material removal at the punch edge indicates a more advanced wear state, in which the punch no longer provides a sharp and well-defined shearing interface. It suggests that the initial shearing process becomes less uniform and less clearly localized due to weakened local shearing force, leading to a more irregular sheared surface on the scrap web. These effects are reflected in deeper valleys and increased depth variability rather than in changes of the overall contact extent.

Summary

The original version of this paper is available on https://www.scientific.net/SSP.389.125.pdf

This study investigated the spatially resolved measurements of worn punches and corresponding scrap web sheared surface across 12 punches with varying geometries, materials, lubricants, and production lengths to establish robust and physically interpretable indicators of punch wear. Two physically motivated wear indices, the worn area proportion and the normalized removed volume, were defined to describe representative aspects of punch wear. In Task T1, multitask regression analysis demonstrated that these wear indices can be consistently explained by a small set of punch surface roughness parameters, primarily related to material volume and bearing ratio. In Task T2, the same wear indices were inferred indirectly from scrap web sequence-derived features. Explainable SHAP analysis revealed stable and physically interpretable feature contributions, primarily related to valley depth and distribution, demonstrating that punch wear leaves a measurable and systematic imprint on the scrap web sheared surface across varying process conditions.

The presented approach has several limitations that point to directions for future work. First, while robust feature-level indicators were identified, the study does not yet provide a single aggregated wear index suitable for direct industrial deployment. Second, the indirect inference from scrap web surfaces remains sensitive to process variability, such as local material flow and fracture behavior, which were not explicitly modeled. Future research should therefore integrate additional process signals (e.g., force or AE) to further develop indirect wear inference. Moreover, extending the framework toward temporal modeling across tool life, rather than end-of-run characterization, would enable punch wear footprint assessment. Finally, validating the identified indicators in online or quasi-inline measurement setups will be essential to translate the proposed methodology into practical tool condition monitoring systems.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.125.pdf

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2023 Internet of Production - 390621612.

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The original version of this paper is available on https://www.scientific.net/SSP.389.125.pdf

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A. Frigge, M. Unterberg, T. Kaufmann, P. Niemietz, T. Bergs, Enhancing Crack Prediction in Fine Blanking Through Multi-sensor Data Fusion, in: W.-G. Drossel, S. Ihlenfeldt, M. Dix (Eds.), Production at the leading edge of technology: Proceedings of the 14th Congress of the German Academic Association for Production Technology (WGP), Chemnitz University of Technology, December 2024, Springer, Cham, 2025, pp. 153-161.

L. Ortjohann, M. Becker, P. Niemietz, T. Bergs, Material-data-driven prediction of sheared surface tears of fine blanked parts, in: Material Forming: ESAFORM 2024, Materials Research Forum LLC, 2024, pp. 1416-1425.

J. Moon, M. Unterberg, P. Niemietz, T. Bergs, Spatial Correlation Analysis between Punch and Scrap Web Sheared Surface Roughness for Indirect Punch Wear Assessment in Sheet-metal Forming, in: Congress of the German Academic Association for Production Technology WGP 2025 (accepted).

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This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 135-142

doi: 10.4028/p-Li672G

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-09

Revised:
2026-02-19

Accepted:
2026-02-24

Online:
2026-04-16

Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

João P. G. Magrinho 1,a*, Angela Cusanno 2, b, Miguel Jesus 1,c, Antonio Piccininni 2, d, Gianfranco Palumbo 2,e, M. Beatriz Silva 1,f

1 IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

2 Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona, 4, Bari, 70125, Italy

a* joao.magrinho@tecnico.ulisboa.pt, b angela.cusanno@poliba.it, c  miguel.lopes.jesus@tecnico.ulisboa.pt, dantonio.piccininni@poliba.it, e  gianfranco.palumbo@poliba.it, f  beatriz.silva@tecnico.ulisboa.pt

Keywords: sheet-bulk forming, sheet injection, laser heat treatment, tailored blanks.

Abstract

Integrating functional features into lightweight aluminium components remains a key challenge in advanced manufacturing, particularly when forming operations impose severe local deformation. This study focuses on the sheet injection process, a variant of Sheet-Bulk Forming (SBF), where thickening and lateral extrusion occur in previously bent aluminium sheets. The material investigated is AW6082-T6, a medium-strength Al−Mg−Si alloy widely used in transportation and structural applications due to its good strength-to-weight ratio and corrosion resistance.To improve formability and reduce the risk of defects such as fracture and folding, an approach based on Tailored Heat-Treated Blanks (THTB) was employed. Localised Laser Heat Treatment (LHT) was applied to selectively reduce strength and enhance ductility in critical deformation zones. Mechanical characterisation was performed via compression tests on both asreceived (T6) and heat-treated (HT) materials.Experiments were conducted on a flexible SBF demonstrator using a two-stage process: bending followed by sheet injection. Numerical simulations were performed to guide LHT pattern design and predict material flow. Among the tested LHT strategies, one demonstrated superior performance, enabling higher injection volumes and reducing process forces while avoiding failure. The experimental results confirm that THTB are an effective method for extending the process window of sheet injection in AW6082-T6, offering a promising solution for the production of complex aluminium components with enhanced functionality.

Introduction

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The increasing urgency of environmental challenges has intensified research into energy-efficient manufacturing solutions, particularly in the field of production engineering [1]. A lightweight design plays a crucial role in reducing energy consumption, CO2 emissions, and operating costs, particularly in transportation and industrial applications. Achieving lightweight structures often requires reduced sheet thicknesses and the integration of multiple functional features into single components, leading to complex geometries and demanding manufacturing processes.

Sheet-Bulk Forming (SBF) has emerged as a promising hybrid forming technology that combines conventional sheet forming with bulk forming operations [2]. This approach enables the production of geometrically complex components with localised features such as ribs, bosses, and thickened regions directly from sheet blanks, reducing the need for secondary operations or assembly steps [3]. Previous studies have demonstrated the potential of SBF for manufacturing high-performance lightweight components. However, its industrial application remains limited by challenges such as local thinning or thickening, high forming forces, and process instability [4].

Among the various SBF variants, sheet injection (combining deep drawing with controlled lateral material flow into a cavity) offers significant potential for creating local reinforcements extending out of the sheet plane [5]. Despite its advantages, experimental investigations on sheet injection,
particularly for medium-strength aluminium alloys, remain scarce, limiting its wider adoption in lightweight structural applications [6].

A promising strategy to overcome formability limitations in sheet injection is the local tailoring of material properties using short-duration heat treatments. Laser Heat Treatment (LHT) allows precise, localised softening of selected regions, enabling the production of Tailored Heat-Treated Blanks (THTB) with spatially adapted mechanical properties. While this approach has proven effective in conventional sheet forming [7], its application to SBF has not yet been systematically investigated.

This study addresses this research gap by experimentally and numerically investigating the use of LHT to create THTB from AW6082-T6 aluminium sheets for sheet injection processes. The work evaluates the influence of local heat treatment on formability, process forces, and defect formation. The results aim to demonstrate the potential of LHT-enabled THTB to expand the process window of sheet injection and to advance SBF as an efficient manufacturing technology for lightweight, multifunctional components.

Material and Methods

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Mechanical characterization. The work was carried out on AW6082-T6 aluminium alloy sheets with 3 mm thickness, selected for their favourable strength-to-weight ratio and suitability for lightweight structural applications. The as-received T6 condition is referred to as T6 material, while the locally heat-treated condition is denoted as HT material.

The study followed a four-step methodology: (i) mechanical characterisation of T6 and HT materials to provide input data for numerical simulations, (ii) finite element simulation of the sheet injection process to analyse force evolution and strain distribution, (iii) experimental laser heat treatment, and (iv) sheet injection experiments to validate the proposed approach.

Material behaviour was characterised using stack compression tests in accordance with ASTM E909 [8]. Specimens consisted of stacks of four circular discs ( 12 mm diameter) and were tested at room temperature on a 1200 kN hydraulic testing machine at a constant crosshead speed of 5 mm/min. The resulting true stress-strain curves (Fig. 1) show that LHT significantly reduces material strength while increasing ductility, confirming its effectiveness for improving formability in sheet injection.

[picture]

Fig. 1. True stress-true strain curves of aluminium AW6082-T6 and AW6082-HT obtained from stack compression (SC) tests.

Fig. 1. True stress-true strain curves of aluminium AW6082-T6 and AW6082-HT obtained from stack compression (SC) tests.

Numerical modelling.

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

The bending and upsetting stages of the sheet injection process were numerically modelled using the in-house finite element software i-form [9]. The simulations were based on a finite element flow formulation with an updated Eulerian approach, in which velocities are treated as primary variables, and equilibrium is achieved through iterative minimisation of residual forces. Material behaviour was
defined using the true stress - strain data obtained from stack compression tests, and a von Mises yield criterion was adopted.

All numerical simulations were performed under two-dimensional plane strain conditions, justified by the constant specimen width (50 mm). The deformable blank was discretised with approximately 4000 quadrilateral elements, while tools were modelled as rigid bodies. Friction at the tool workpiece interfaces was described using a constant friction law, with the friction factor calibrated to m=0.1 based on experimental force measurements.

For the bending stage, the specimen was clamped between fixed die and blank holder and deformed by a wiping punch moving at 1 mm/s, allowing accurate prediction of the force displacement and deformation evolutions (Fig. 2a). The subsequent upsetting stage simulated material flow into the die cavity using a two-piece blank holder ( A and B ) to control sidewall deformation and suppress folding (Fig. 2b). The simulations successfully reproduced the characteristic thickening and lateral material injection observed in SBF.

The numerical results identified a plastically deformed region of approximately 44 mm , which was used to define the laser heat-treated area in the experiments. In modelling THTB, a sharp transition between T6 and heat-treated zones was assumed to isolate the mechanical effects of local property modification on strain distribution and process forces.

[picture]

Fig. 2. Numerical model setup of the (a) sheet bending stage and (b) upsetting stage with identification of the main components.

Fig. 2. Numerical model setup of the (a) sheet bending stage and (b) upsetting stage with identification of the main components.

Laser heat treatment.

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

To locally improve formability in regions subjected to severe deformation during sheet injection, LHT was applied to selectively tailor the mechanical properties of the blanks. Short, localised laser exposure transformed the initial AW6082-T6 condition into an overaged state within the high-strain region, producing a stable reduction in yield strength and increased ductility. This controlled transition from T6 to HT material enables a direct assessment of the influence of LHT on material flow, forming forces, and defect formation under identical process conditions.

LHT was performed using a CO2 laser system with a top-hat energy distribution, allowing uniform heating over a square laser spot. A constant laser power and scanning speed were employed to achieve peak temperatures of approximately 450∘C, suitable for inducing local overaging. Based on numerical predictions, the heat-treated zone was designed to extend over a 44 mm region corresponding to the plastically deformed area during sheet injection.

Three LHT strategies were investigated in addition to the as-received T 6 condition. These strategies differed in scan path orientation (longitudinal or transverse) and track overlap, enabling controlled variation of the heat-affected zone geometry (Table 1).

Table 1. Nomenclature for the LHT strategies.

Case | LHT orientation | Overlap
T6 | - |
L_5mm | Longitudinal | 5 mm
L_0mm | Longitudinal | 0 mm
T_5mm | Transversal | 5 mm

Sheet injection experiments.

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

Sheet injection experiments were performed using a flexible sheet-bulk forming (SBF) demonstrator [5] mounted on a 1200 kN hydraulic testing machine. The setup employs a unit cell concept, in which straight bent slices are used to replicate the deformation behaviour of circular deepdrawn cups. This simplified geometry remains representative for sheet injection studies, as deformation and material flow are dominated by the bent sidewall region, where strain paths and thickness reduction are comparable to those in circular geometries [5].

The sheet injection process was investigated through two sequential stages: bending to define the pre-geometry, followed by upsetting, during which lateral material injection into the die cavity occurs. Separate tooling setups were used for each stage, incorporating a punch, blank holder, and die (Fig. 3). This modular approach enables controlled investigation of the combined deep drawing and injection mechanisms.

[picture]

Fig. 3. Overview of the experimental sheet injection setup with identification of the main active components, (a) bending setup, and (b) upsetting setup.

Fig. 3. Overview of the experimental sheet injection setup with identification of the main active components, (a) bending setup, and (b) upsetting setup.

Rectangular specimens (150×50×3 mm) were tested under four material conditions, including the T6 reference and three locally heat-treated variants. All experiments were conducted at room temperature under quasi-static conditions with a constant crosshead speed of 5 mm/min. Key process parameters for the bending and upsetting stages are schematically represented in Table 2.

Table 2. Overview of the experimental work plan, including die geometry for bending and upsetting stages.

Geometry | Dimensions
Bending stage | Bending stage geometry diagram showing r_p and r_d dimensions | rd = 9 mm rp = 3 mm
Upsetting stage | Upsetting stage geometry diagram showing t_d, l_d, and h_d dimensions | td = 5 mm ld = 12 mm hd = 10 mm

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

Bending stage.

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

The bending stage of the sheet injection process was carried out at room temperature under quasistatic conditions. For each material condition, three repeat tests confirmed good repeatability. Therefore, only representative force - displacement curves are shown. Experimental results were compared with finite element predictions, as illustrated in Fig. 4.

[picture]

Fig. 4. Experimental and numerical force-displacement curves for the bending stage under all material conditions: T6 (reference), L_5mm (Longitudinal, 5 mm overlap), L_ 0 mm (Longitudinal, 0 mm overlap), and T_5 mm (Vertical, 5 mm overlap).

Fig. 4. Experimental and numerical force-displacement curves for the bending stage under all material conditions: T6 (reference), L_5mm (Longitudinal, 5 mm overlap), L_ 0 mm (Longitudinal, 0 mm overlap), and T_5 mm (Vertical, 5 mm overlap).

For the T6 reference condition, numerical and experimental curves showed good agreement, with a maximum bending force of approximately 6.5 kN . Minor discrepancies in the initial slope and residual force at the end of the stroke were attributed to progressive contact development and springback, respectively, which are not fully captured by the numerical model. The measured springback angle was approximately 6∘.

For the LHT conditions, numerical simulations reproduced the general force trends but underestimated the experimental forces. This difference is attributed to the modelling assumption of a sharp transition between T6 and HT material, whereas the experimental blanks exhibited a gradual property gradient within the bent region. As a result, the effective material strength during bending was higher than predicted. Springback behaviour remained similar across all LHT strategies.

The L_ 0 mm strategy showed the highest maximum force among the LHT cases ( ~5.7kN ), corresponding to a reduction of approximately 12% compared to the T 6 reference condition (~6.5kN). In contrast, the transversal T_5mm strategy exhibited the lowest maximum force (~4.6kN), representing a reduction of about 29% relative to T6 and approximately 19% compared to L_ 0 mm . The longitudinal overlapping condition (L_ 5 mm ) resulted in intermediate values, confirming a progressive decrease in force with increasing effective softening. These quantitative differences demonstrate that LHT significantly reduces bending forces, with overlapping strategies, particularly the transversal configuration, providing the most pronounced improvement while maintaining stable deformation behaviour.

Upsetting stage.

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

The upsetting stage, during which material injection into the die cavity occurs, was performed under the same quasi-static conditions as bending. Experimental force - displacement curves were compared with numerical predictions for all material conditions (Fig. 5).

[picture]

Fig. 5. Experimental and numerical force displacement curves for the upsetting stage under all material conditions: T6 (reference), L_5mm (Longitudinal, 5 mm overlap), L_0mm (Longitudinal, 0 mm overlap), and V_5mm (Vertical, 5 mm overlap).

Fig. 5. Experimental and numerical force displacement curves for the upsetting stage under all material conditions: T6 (reference), L_5mm (Longitudinal, 5 mm overlap), L_0mm (Longitudinal, 0 mm overlap), and V_5mm (Vertical, 5 mm overlap).

For the T6 reference condition, numerical and experimental results agreed well in the early stage of deformation. Beyond a punch stroke of approximately 4 mm , differences emerged due to the activation of the two-piece blank holder, which promotes controlled material flow. At larger strokes, the experimental force remained lower than predicted as a result of sidewall folding, which reduced resistance and led to limited injection and premature fracture in the corner region.

For the LHT specimens, experimental and numerical curves followed similar trends up to the onset of injection. Slightly higher experimental forces were observed, attributed to gradual strength transitions within the heat-treated zone and friction effects not captured by the numerical model. During material injection, experimental forces increased more steeply due to burr formation along the sidewall, which locally increased friction but did not represent a critical defect.

Conditions with overlapping laser tracks (L_5mm and T_5mm) exhibited lower and more stable forces, consistent with their improved ductility, and resulted in defect-free geometries. In contrast, the non-overlapping condition ( L_0 mm ) leads to increased forces and corner fracture during the final stages of injection (Fig. 6).

Overall, the results demonstrate that LHT significantly improves formability during sheet injection by reducing forming forces and suppressing fracture. Overlapping LHT strategies provided the most favourable balance between material softening and process stability, while numerical predictions successfully captured the main trends, with deviations highlighting the influence of friction and property gradients that warrant further investigation.

[picture]

Fig. 6. Defects: (a) folding in T6 (reference); (b) fracture in T6; (c) fracture in L_0mm (Longitudinal, 0 mm overlap); and (d) burr in the LHT specimens.

Fig. 6. Defects: (a) folding in T6 (reference); (b) fracture in T6; (c) fracture in L_0mm (Longitudinal, 0 mm overlap); and (d) burr in the LHT specimens.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

This study demonstrated that LHT effectively tailors the mechanical properties of AW6082-T6 aluminium alloy for sheet injection processes. Mechanical characterisation showed a significant reduction in strength accompanied by enhanced formability, confirming the suitability of LHT for locally adapting material behaviour to high-strain forming operations.

Sheet injection experiments revealed that THTB substantially expand the process window compared to the T6 reference condition. While the untreated material exhibited early fracture, LHT strategies enabled increased material flow into the die cavity at reduced forming forces. Among the investigated approaches, the longitudinal strategy with overlapping tracks (L_5mm) provided the most stable behaviour, combining low forces, uniform softening, and defect-free geometries.

Overall, the results validate the feasibility of applying LHT to enable sheet injection of mediumstrength aluminium alloys, enhancing the industrial potential of sheet-bulk forming for lightweight, functionally integrated components in transportation and structural applications.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.135.pdf

A.E. Tekkaya, Energy saving by manufacturing technology, Procedia Manuf. 21 (2018) 392396.

M. Merklein, J.M. Allwood, B.A. Behrens, A. Brosius, H. Hagenah, K. Kuzman, K. Mori, A.E. Tekkaya, A. Weckenmann, Bulk forming of sheet metal, CIRP Ann. Manuf. Technol. 61(2) (2012) 725-745.

K. Mori, T. Nakano, State-of-the-art of plate forging in Japan, Prod. Eng. 10 (2016) 81-91.

T. Schneider, M. Merklein, Manufacturing of geared sheet metal components by a single-stage sheet-bulk metal forming process. In: D. Dimitrov, C. Schutte. Proceedings International Conference on Competitive Manufacturing, Stellenbosch (2013) 177-182.

J.P.G. Magrinho, M.B. Silva, P.A.F. Martins, A flexible sheet-bulk forming demonstrator, Int. J. Adv. Manuf. Tech. 103 (2019) 1405-1417.

J.P.G. Magrinho, M.B. Silva, P.A.F. Martins, Injection by sheet-bulk forming, Precis. Eng. 59 (2019) 73-80.

A. Piccininni, G. Palumbo, Design and Optimization of the Local Laser Treatment to Improve the Formability of Age Hardenable Aluminium Alloys. Materials 13(7) 2020.

ASTM International. Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature. ASTM E9-09:2018.

C.V. Nielsen, P.A.F. Martins, Metal forming: formability, simulation and tool design. Amsterdam: Academic Press, 2021.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 143-150

doi: 10.4028/p-Fi1xWZ

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-12

Revised:
2026-02-22

Accepted:
2026-02-24

Online:
2026-04-16

Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets

The original version of this paper is available on https://www.scientific.net/SSP.389.143.pdf

Karl J. Tilly 1,a*, Emad Scharifi 1,b and Junhe Lian 1,c

1 Institute of Metal Forming (IBF), RWTH Aachen University, Germany

a* karl.tilly@ibf.rwth-aachen.de, b emad.scharifi@ibf.rwth-aachen.de, c junhe.lian@ibf.rwth-aachen.de

*corresponding author

Keywords: hot metal gas forming, micro-channels, ultra-thin sheets.

Abstract

In carbon-free technologies, thin-walled components with microchannels from ultra-thin sheets, such as bipolar plates, cooling plates, and heat exchangers, are widely utilized. Using such components made of high-strength aluminum alloys further reduces the required wall thickness, thereby enhancing their lightweight potential. However, conventional forming methods for ultra-thin sheets, including elastomer-based deep drawing and hydroforming, are limited by process-induced phenomena such as springback, geometrical inaccuracies and reduced formability as well as localized thinning, which can necessitate a higher wall thickness or the use of a lower strength grade alloy. Gas-based hot sheet metal forming of high-strength aluminum alloys is introduced to improve formability and geometrical accuracy. In the present study, an isothermal, gas-based hot sheet metal forming process is developed for forming microchannels from AlMg 3 alloy sheets with a thickness of 0.4 mm . A 100 mm×100 mm blank is heated to 530∘C and formed under nitrogen gas pressure into a heated die featuring various channel geometries. The effects of blank-holder force, maximum gas pressure, wall angle, channel radius, and maximum channel depth on thinning and form filling are investigated. Additionally, the grain size of the final component is analyzed. A full form filling can be reached under a forming pressure of 200 bar. The thinning is dependent on the micro channel geometry and reaches a maximum of 29% for a channel depth of 1 mm . The grain size increases during the forming process, dependent on the introduced strain into the material. The proposed method enables forming of components without fracture and with high geometrical accuracy.

Introduction

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Thin-walled metallic components with integrated microchannel structures are widely employed as functional elements for heat and mass transfer, for example, as bipolar plates in fuel cells or as cooling plates for high-voltage batteries and power electronic systems [1]. In this context, aluminum alloys are particularly attractive, especially for mobile and aerospace applications, due to their favorable combination of high thermal conductivity, low density, and good chemical stability [2]. In recent years, the manufacturing of such aluminum components by sheet metal forming has been the subject of extensive research. Among the investigated forming technologies, Rubber-Pad-Forming (RPF), Flexible-Die-Forming (FDF), and hydroforming represent the most commonly applied processes. In RPF, the sheet metal is formed into a rigid die by means of a compliant elastomer punch, whereas FDF utilizes a rigid punch in combination with a flexible die medium [3]. In hydroforming, the sheet is shaped by hydraulic pressure acting on one side of the material [4]. Within the field of RPF, several studies have focused on the fabrication of aluminum bipolar plates with complex channel geometries. The forming of Archimedes screw-shaped microchannels in AA1050 sheets with a thickness of 0.3 mm was systematically investigated with respect to the influence of process parameters on achievable channel depth and local thickness reduction. The results indicate that both channel depth and thinning behavior are strongly dependent on the hardness of the elastomeric forming medium [5]. In addition, failure mechanisms during the RPF of metallic bipolar plates are analyzed using fracture-mechanicsbased criteria, enabling the prediction of crack initiation under critical forming conditions by means of the Cockcroft-Latham damage model [6]. To further reduce local thickness reduction, a modified two-step RPF strategy is proposed, demonstrating improved thickness distribution over the whole
component thickness compared to conventional single-step forming [7]. For FDF, research activities have primarily addressed the influence of size effects on form filling and achievable channel depth when forming microchannels in thin aluminum foils. Investigations on Al 1100 foils reveal that the ratio of sheet thickness to grain size significantly affects material flow and limits formability at the micro scale [3]. Furthermore, an alternative FDF concept employing a polymer powder medium as a flexible die is introduced [8]. This approach provides a more uniform pressure distribution and improved form filling while maintaining low tooling complexity. Hydroforming-based studies have mainly concentrated on process understanding and quality control for the industrial production of metallic bipolar plates. Design rules and quality criteria were derived through systematic variation of key process parameters such as internal pressure and tool geometry, with particular emphasis on channel definition, thickness uniformity, and process reproducibility [4]. In addition, the surface integrity of hydroformed bipolar plates was investigated, demonstrating that forming conditions have a pronounced influence on surface roughness, which is relevant for both electrical contact resistance and fluid flow behavior [9].
For conventional forming processes conducted at room temperature, the predominant research focus lies on formability, commonly quantified by the maximum achievable channel depth, and on minimizing local thickness reduction. These inherent limitations have motivated the development of advanced forming processes that incorporate controlled thermal energy input in order to extend the forming limits of thin aluminum sheets. Among these approaches, hot forming processes such as high-speed blow forming and hot metal gas forming (HMGF) have gained increasing attention. A defining characteristic of these processes is that the primary forming step is performed at elevated temperatures, resulting in reduced flow stress and enhanced forming limit. In the context of HMGF, the forming of metallic bipolar plates from AA8111 aluminum blanks with a thickness of 0.2 mm under isothermal conditions at approximately 500∘C is investigated [10]. The influence of gas pressure, channel width, and fillet radius on form filling was systematically analyzed. It was shown that form filling increases with gas pressure, reaching a maximum of approximately 80% at a pressure level of 4 MPa for a holding time of 15 minutes. Complementary studies addressed the fabrication of microchannel components from AA1070 sheets with a thickness of 0.1 mm using HMGF at temperatures between 300∘C and 400∘C [11]. By varying the channel depth-to-width ratio and fillet radius, optimal geometric conditions for maximum formability were identified, with the highest formability observed for a fillet radius of 7.5∘ and a depth-to-width ratio of 0.5 . Numerical investigations of the HMGF process applied to pin-shaped bipolar plates manufactured from 0.2 mm thick AA8111 blanks demonstrated that both gas pressure and fillet radius have a significant influence on thickness reduction and die filling behavior [12]. Further studies on AA6063 revealed that increasing the forming temperature leads to enhanced formability and promotes a more homogeneous grain size distribution due to thermally activated microstructural mechanisms [13]. In addition to experimental work, numerical process modeling has been addressed [14]. Suitable finite element discretization strategies for gas-based hot sheet metal forming were proposed, demonstrating that refined through-thickness discretization is required to accurately capture coupled thermal and mechanical gradients. Building on these findings, a hybrid hot forming process was developed that combines conventional hot deep drawing with subsequent gas-based forming, thereby exploiting the advantages of both approaches within a single process chain [15]. Finally, the evolution of microstructure and mechanical properties during gas-based hot sheet metal forming was investigated for the heat-treatable aluminum alloy AA6010. The results show that although deformation at elevated temperatures promotes grain growth, the final mechanical properties after artificial aging are not adversely affected. This indicates that gas-based hot forming can be effectively integrated into manufacturing routes for high-strength aluminum components [16].
While the production of microchannel components from high-strength aluminum alloys by means of HMGF has been investigated primarily with regard to the influence of geometrical tool design on form filling and thickness reduction, the associated microstructural evolution has received considerably less attention. In particular, deformation at elevated temperatures is known to promote grain growth in aluminum alloys, which may significantly affect the final mechanical performance of
thin sheet metal components. To date, the interplay between die geometry, local thinning, and grain size development during HMGF has not been systematically addressed for thin aluminum alloy sheets. To address the existing gap in the current literature, the present study proposes an HMGFbased process for the manufacture of microchannel components from thin aluminum alloy sheets and aims to investigate the influence of die geometry on both thickness reduction and grain size evolution during the forming process.

Experimental Setup

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For the experimental investigations, square blanks of an AlMg 3 alloy with a thickness of 0.4 mm and dimensions of 100 mm×100 mm were used for HMGF under uniform temperature conditions. The forming experiments were conducted using a servo-hydraulic press (Schenck) with a maximum nominal press force of 630 kN , Fig. 1 a). The forming tool insert consists of a die and a blank holder, Fig. 1 b). Both components are heated by an integrated heating ring and thermally insulated by an insulation plate and a cooling plate, respectively. The tool temperature was controlled and maintained at a constant value of 530∘C throughout the forming experiments. The blank holder force was applied by the servo-hydraulic press and simultaneously served as the sealing force for the gas-based forming process. The forming pressure was applied using nitrogen gas, supplied from an external gas cylinder, with a maximum available pressure of 25 MPa . The die features a circular overall contour with a diameter of 70 mm and a depth of 0.5 mm , as shown in Fig. 2 a) and b). Microchannel grooves were machined into the die surface within this contour. The geometric parameters of the microchannels were varied in terms of channel depth d , wall angle α, and lower corner radius, as defined schematically in Fig. 2 c). A sectional view of the die, depicted in Fig. 2 d), illustrates the spatial distribution of the microchannel geometries. Each microchannel groove is equipped with dedicated gas outlet holes, allowing residual air between the blank and the die to escape during forming and thereby promoting complete form filling. The gas outlets of each groove can be closed individually. This design enables continued forming of the remaining microchannels without loss of forming pressure in the event of local material rupture.
Prior to forming, each 100×100 mm2 blank was coated with a thin layer of boron nitride spray, which served as a high-temperature lubricant. The blank was then manually positioned between the die and the blank holder. Subsequently, the tool was closed using the servo-hydraulic press to ensure full contact between the tool surfaces and the specimen. During a holding period of 60 s , the blank was heated to the forming temperature of 530∘C. After reaching the target temperature, a blank holder force of 250 kN was applied. The forming process was initiated by opening the gas valve, resulting in a gradual increase in forming pressure. A maximum gas pressure of 20 MPa was reached after a forming time of 5 s . Upon completion of the forming step, the gas valve was closed, the tool was opened, and the formed specimen was manually removed from the die. The specimens were subsequently air-cooled to room temperature and prepared for further evaluation. For geometrical characterization, the formed specimens are first cleaned using cold water and isopropyl alcohol. Subsequently, the samples are sectioned perpendicular to the channel direction, as illustrated in Fig. 3 a). The sectioned samples are embedded and metallographically prepared by grinding and polishing. Geometrical measurements were then carried out using an optical microscope (Keyence VHX-7000). To characterize the grain size evolution, the embedded samples were electrochemically etched using a Barker-type electrolyte at an applied voltage of 20 V for 120 s . Grain size measurements were subsequently performed under polarized light using the Keyence VHX-7000 optical microscope. The grain size was quantified using the linear intercept method in accordance with ASTM E112.

[picture]

Fig. 1. a) Schenck hydraulic press with HMGF tool insert b) CAD design of tool insert.

Fig. 1. a) Schenck hydraulic press with HMGF tool insert b) CAD design of tool insert.

[picture]

Fig. 2. a) Die with micro channels b) sectional view of one die contour with geometrical values defining the micro channel c) sectional view of die and dimensions d) sectional view of all micro channels and geometrical dimensions.

Fig. 2. a) Die with micro channels b) sectional view of one die contour with geometrical values defining the micro channel c) sectional view of die and dimensions d) sectional view of all micro channels and geometrical dimensions.

Results - Shape and Dimension Analysis

The original version of this paper is available on https://www.scientific.net/SSP.389.143.pdf

In total, five specimens were produced and evaluated. The following geometrical parameters are determined, as defined in Fig. 3 b): Channel depth d , wall thickness tw, lower thickness tl, and upper thickness tu. For each of the investigated channel geometries, thickness reduction was evaluated as an average over all five specimens, with two channels analyzed per specimen. The resulting average thinning values for the three characteristic thickness locations are summarized in Fig. 3 c). The results indicate that the highest thickness reduction occurs in the channel wall region ( tw ). For channel depths of 0.5 mm and 0.75 mm , the wall thinning ranges between 16% and 18%, whereas a significantly higher thinning of approximately 29% is observed for channels with a depth of 1 mm . A qualitative comparison of the different channel geometries is presented in Fig. 3 d). In the transition region between the upper fillet radius and the channel wall, localized necking is observed for channels numbered 1 to 6, which are characterized by a wall angle of 45∘. In contrast, channels 7 to 10, featuring steeper wall angles of 60∘ and 75∘, do not exhibit visible necking in this region. Despite the occurrence of necking in channels with smaller wall angles, a direct comparison of wall thinning values does not indicate a pronounced increase in thickness reduction for geometries with similar
channel depths d . The thickness reduction in the lower channel region (t1) ranges from 7% to 8% for channels with a wall angle of 45∘ and from 6% to 7% for channels with steeper wall angles, suggesting a weak correlation between bottom thickness reduction and wall angle. In contrast, the upper thickness (tu) shows a slight increase of approximately 1% to 2% relative to the initial blank thickness. This effect can be attributed to measurement uncertainty and is therefore considered negligible. Based on the geometrical evaluation, it can be concluded that microchannels with a depth of 1 mm and a width of 1.5 mm can be successfully manufactured with a maximum thickness reduction of approximately 28%. For smaller channel depths, lower thickness reductions can be expected. Furthermore, steeper wall angles tend to result in slightly reduced wall thinning, which can be attributed to a decreased tendency for necking in the upper fillet region. However, these findings do not permit any conclusions regarding defect sensitivity.

[picture]

Fig. 3. a) Formed specimen b) microsection of formed specimen channel and areas of measurement c) thinning for measured areas for different geometrical dimensions d) close up of all microchannels of specimen no. 5 .

Fig. 3. a) Formed specimen b) microsection of formed specimen channel and areas of measurement c) thinning for measured areas for different geometrical dimensions d) close up of all microchannels of specimen no. 5 .

Results - Microstructural Investigation

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Measurements were conducted separately in the upper region, the lower region, and the wall region of the microchannel. The resulting grain size distributions are presented in Fig. 4. Overall, a pronounced increase in grain size is observed as a consequence of the forming process. The initial average grain size of 12.8μ m increases to 24.5μ m in the upper region of the microchannel and to 31.9μ m in the lower region. In contrast, the wall region exhibits a substantially larger increase in grain size, reaching an average value of 182.9μ m. In several cases, individual grains extend across nearly the entire wall thickness, as illustrated in Fig. 4 d). Considering the local wall thickness after forming, the ratio of grain size to wall thickness in the wall region approaches unity for these outliers. This indicates that the microstructure locally transitions from a polycrystalline to a quasi-columnar or single-grain-dominated state across the thickness. In comparison, the upper and lower regions remain clearly polycrystalline, with grain sizes that are small relative to the local sheet thickness. The pronounced grain growth in the wall region can be attributed to a combination of factors inherent to the HMGF process. First, the wall region undergoes increased local plastic deformation during the forming operation increasing the dislocation density, which promotes dynamic recovery and grain boundary mobility, as also observed for 2 XXX grade alloys in [17,18]. Second, prolonged contact with the heated die in this region leads to increased local thermal exposure compared to the upper and lower channel regions. The superposition of high level of localized strain and extended dwell time at elevated temperature provides favorable conditions for abnormal grain growth. From a materials perspective, such localized grain coarsening is expected to influence both the mechanical and functional properties of the formed component. A grain size approaching the local wall thickness may
result in reduced yield strength and altered strain hardening behavior, as well as increased anisotropy. In addition, coarse grains can affect corrosion behavior and surface stability, which are relevant aspects for microchannel components used in electrochemical or thermal management applications. In the context of process design, these results indicate that while HMGF enables the successful formation of microchannel geometries in thin aluminum alloy sheets, the associated thermomechanical history can lead to pronounced microstructural inhomogeneities. Consequently, the control of local temperature exposure, forming time, and die-sheet contact conditions appears critical to limit excessive grain growth in highly strained regions. This finding motivates a more detailed consideration of die geometry and process parameters not only with respect to form filling and thickness reduction, but also with regard to microstructural stability.

[picture]

Fig. 4. a) Grain size evaluation over all specimens and micro channels depending on the location of measurement b) microsection of initial blank as received c) microsection of final component in upper area d) microsection of final component in wall area.

Fig. 4. a) Grain size evaluation over all specimens and micro channels depending on the location of measurement b) microsection of initial blank as received c) microsection of final component in upper area d) microsection of final component in wall area.

Conclusion & Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.143.pdf

HMGF was successfully employed to manufacture thin-walled aluminum components with integrated microchannels from 0.4 mm thick AlMg 3 sheets at a forming temperature of 530∘C. Microchannels with a depth of up to 1 mm were produced with complete die filling using a maximum forming pressure of 20 MPa applied for 5 s . The magnitude of thickness reduction is primarily controlled by channel geometry, particularly channel depth and wall angle, and reaches a maximum of approximately 29% for a channel depth of 1 mm . Regions subjected to the highest local thinning exhibit pronounced grain growth, with grain sizes locally approaching the remaining wall thickness. These results indicate that, while HMGF enables the reliable forming of microchannel structures in thin aluminum sheets, careful control of process parameters is required to limit excessive grain coarsening in highly strained regions. Future work will therefore focus on optimizing the thermalmechanical process conditions and die design to improve microstructural stability and ensure consistent mechanical performance of the formed components.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.143.pdf

Zhang, X., Liu, J., Liu, Y., Zhang, G., 2025. Optimized Design and Testing of Enhanced Heat Transfer Secondary Micro-Channels on the Surface of Fuel Cell Bipolar Plate Flow Channels. Energies 18 (6), 1459.

Guo, K., Zhu, L., Li, Y., Yu, T.X., 2019. Numerical study on mechanical behavior of foam core sandwich plates under repeated impact loadings. Composite Structures 224, 111030.

Gau, J.-T., Gu, H., Liu, X., Huang, K.-M., Lin, B.-T., 2015. Forming micro channels on aluminum foils by using flexible die forming process. Journal of Manufacturing Processes 19, 102-111.

Zhang, J., Wang, R., Zeng, Y., 2022. Hydroforming rules and quality control parameters analysis for metal bipolar plate. Engineering Failure Analysis 132, 105919.

Hashemi, S.J., Roohi, A.H., 2021. Fabrication of aluminum bipolar plates with Archimedes' screw-shaped channels: a rubber pad forming process assessment. SN Appl. Sci. 3 (4).

Talebi-Ghadikolaee, H., Elyasi, M., Mirnia, M.J., 2020. Investigation of failure during rubber pad forming of metallic bipolar plates. Thin-Walled Structures 150, 106671.

Wang, C., Wang, H., Wang, Y., Chen, G., Zhu, Q., Zhang, P., 2022. Investigation on forming methods in rubber pad forming process used for fabricating clad foil microchannel. Journal of Manufacturing Processes 76, 771-785.

Zhang, C., Ma, J., Liang, X., Luo, F., Cheng, R., Gong, F., 2018. Fabrication of metallic bipolar plate for proton exchange membrane fuel cells by using polymer powder medium based flexible forming. Journal of Materials Processing Technology 262, 32-40.

Olayinka, A., Emblom, W.J., 2022. Surface roughness of AISI 1010 and AISI 304 of PEMFC bipolar plates with microscale hydroformed capillary channels. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 236 (10), 1332-1340.

Esmaeili, S., Hosseinipour, S.J., 2019. Experimental investigation of forming metallic bipolar plates by hot metal gas forming (HMGF). SN Appl. Sci. 1 (2).

Kargar-Pishbijari, H., Hosseinipour, S.J., Jamshidi Aval, H., 2020. A novel method for manufacturing microchannels of metallic bipolar plate fuel cell by the hot metal gas forming process. Journal of Manufacturing Processes 55, 268-275.

Esmaeili, S., Hosseinipour, S.J., Shamsi-Sarband, A., 2021. Numerical analyses of Manufacturing of an AA8111 Pin-shaped Bipolar Plate by Hot Metal Gas Forming. IJE 34 (8), 1994-2001.

Xu, Y., Lv, X.-W., Wang, Y., Zhang, S.-H., Xie, W.-L., Xia, L.-L., Chen, S.-F., 2023. Effect of Hot Metal Gas Forming Process on Formability and Microstructure of 6063 Aluminum Alloy Double Wave Tube. Materials (Basel, Switzerland) 16 (3).

Baru, N.K., Teeuwen, T., Teller, M., Hojda, S., Braun, A., Hirt, G., 2021. On appropriate Finite Element discretization in simulation of gas-based hot sheet metal forming processes. IOP Conf. Ser.: Mater. Sci. Eng. 1157 (1), 12027.

Baru, N.K., 2025. A novel hybrid hot forming process concept for high strength aluminum alloys, in: Sheet Metal 2025. Sheet Metal 2025. 04/01/2025. Materials Research Forum LLC, pp. 134-141.

Teeuwen, T., Baru, N.K., Bailly, D., Hirt, G., 2023. Investigation on evolution of microstructure and mechanical properties of heat-treatable 6010-S aluminium alloy during gas-based hot sheet metal forming process. IOP Conf. Ser.: Mater. Sci. Eng. 1284 (1), 12005.

Qiu, Y., Li, M., Wang, Y., Cao, H., Zheng, J.-H., Zheng, K., 2025. Effect of solution heat treatment on grain growth of pre-strained Al-Cu-Mn alloy: Experiment and modelling. Journal of Alloys and Compounds 1047, 184984.

Qiu, Y., Shi, J., Shen, K., Yu, Z., Shi, J., Han, Y., Xian, J., Zheng, K., Zheng, J.-H., 2025. Prestrain effect on the abnormal grain growth for aircraft 2219 aluminium alloy under indirect hot forming condition. Journal of Materials Research and Technology 36, 10563-10576.

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 151-158

doi: 10.4028/p-8pDJaR

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-13

Revised:
2026-02-19

Accepted:
2026-02-24

Online:
2026-04-16

Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

The original version of this paper is available on https://www.scientific.net/SSP.389.151.pdf

Cusanno Angela 1,a*, Magrinho João Pedro 2, b, Piccininni Antonio 1,c, Guglielmi Pasquale 3, d, Sorgente Donato 1,e, Palumbo Gianfranco 1,f and Silva Maria Beatriz 2,g

¹Department of Mechanics, Mathematics and Management, Politecnico di Bari, Bari, Italy

2 IDMEC, Instituto Superior Técnico, Lisboa, Portugal

3 Department of Engineering, University of Basilicata, Potenza, Italy

a* angela.cusanno@poliba.it, b  joao.magrinho@tecnico.ulisboa.pt, c  antonio.piccininni@poliba.it, d pasquale.guglielmi@unibas.it, e donato.sorgente@poliba.it, f gianfranco.palumbo@poliba.it, 9 beatriz.silva@tecnico.ulisboa.pt

Keywords: sheet-bulk forming, laser heat treatment, tailored blanks, profilometry-based indentation plastometry;experimentation.

Abstract

The sheet injection process, a hybrid sheet-bulk forming technique that integrates bending and injection to create complex features such as ribs, offers significant potential for advanced manufacturing applications. However, its implementation with lightweight aluminium alloys is hindered by their limited room-temperature formability. To address this, locally softened, tailored heat-treated blanks produced via laser heat treatment (LHT) can enhance local ductility while maintaining global strength. This study investigates the mechanical property gradients induced by LHT in 3 mm thick AW6082-T6 aluminium alloy sheets using Profilometry-based Indentation Plastometry (PIP). The laser treatment, performed with a 2.5 kWCO2 laser, produced localized heat treated regions, whose effectiveness was evaluated through microhardness testing. PIP enabled the direct extraction of local stress-strain curves without the need for specimen extraction and was validated against conventional tensile tests. Results showed that PIP accurately captured local variations in mechanical properties, with heat treated zones exhibiting increased ductility compared to the T6 condition.

Introduction

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In recent years, increasing demand for lightweight and, at the same time, high-performance components have driven the development of advanced metal forming processes capable of combining high geometric complexity with optimal mechanical properties [1]. Within this framework, sheetbulk forming processes have emerged as a promising solution, as they enable the integration of conventional sheet forming operations with localized bulk deformation, allowing the production of functional features such as ribs, bosses, and reinforcements directly from sheet materials [2]. Among these processes, sheet injection represents a hybrid forming approach that combines bending and upsetting, offering significant potential for applications in the automotive and transportation sectors [3]. Despite these advantages, the application of sheet injection to aluminium alloys remains challenging due to their limited formability at room temperature, particularly in precipitationhardened conditions such as T6 [4]. Alloys of the 6xxx series, widely used for their favorable strength-to-weight ratio and corrosion resistance, exhibit reduced ductility and early strain localization under complex loading paths, which can lead to cracking during forming [5]. To overcome these limitations, the use of tailored blanks with spatially graded mechanical properties has been increasingly investigated as an effective strategy to enhance local formability while preserving global structural performance [6].

Local modification of material properties can be achieved through different approaches, including partial annealing, mechanical processing, and thermal treatments. Among these, laser heat treatment (LHT) has attracted considerable attention due to its high flexibility and ease of integration into industrial production lines [7]. By locally controlling the thermal cycles, LHT enables the induction of softening in selected regions, resulting in a controlled reduction of strength and a corresponding increase in ductility [8].

The presence of strong gradients in mechanical properties, however, poses significant challenges for material characterization, which is particularly crucial when the forming process is reproduced numerically, as accurate local constitutive laws are required to predict material flow, strain distribution, and failure [9]. Conventional or even miniaturized tensile testing is often unsuitable, as it requires specimen extraction and provides only average properties over the specimen [10]. As a result, localized characterization techniques are required to accurately capture the mechanical behaviour within treated and untreated zones. Hardness testing is widely used as a first and rapid approach to assess local variations in mechanical properties and to qualitatively evaluate the presence of strength gradients induced by localized treatments [11]. Nevertheless, hardness measurements alone are not sufficient to fully describe the mechanical response, particularly in terms of strainhardening behaviour [12].

In this context, Profilometry-based Indentation Plastometry (PIP) has proven to be an effective semi-destructive method for determining local stress-strain curves from a single indentation test [13]. By combining residual indentation profile measurements with iterative finite element simulations, PIP enables the identification of yield stress, strain hardening behaviour, and ultimate tensile strength [14], making it particularly suitable for the assessment of tailored materials.

In the present work, the mechanical property gradients induced by different laser heat treatment strategies applied to 3 mm thick AW6082-T6 aluminium alloy sheets were investigated with specific reference to sheet injection applications. PIP was employed to extract local stress-strain curves in critical forming zones and was validated through comparison with conventional tensile testing on the base material. The effect of the LHT on the distribution of mechanical properties was analysed and correlated with microhardness measurements, providing insight into the potential of tailored heattreated blanks for advanced sheet-bulk forming processes.

Material and Methodology

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Material.

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An aluminium alloy (AW6082-T6) with a thickness of 3 mm was investigated. The mechanical properties are summarized in Table 1, with yield stress and ultimate tensile strength determined from tensile tests performed according to ASTM E8/E8M (2024).

Table 1. Mechanical properties of the investigated alloy.

Vickers Hardness [HV] | Yield Stress [MPa] | Ultimate Tensile Strength [MPa]
120 | 298 | 344

Laser Heat Treatments.

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To locally enhance the formability in regions that are critical during the sheet injection process, specifically during the bending and upsetting stages (see Fig. 1a), a Laser Heat Treatment (LHT) was applied to locally modify the material properties along the critical zones. The LHT was performed using a 2.5 kWCO2 laser source (Rofin Slab DC 025). The system consisted of a heat-treatment head moving along the vertical ( z ) axis and equipped with a Diffractive Optical Element (DOE) to generate a top-hat energy distribution over a 20 mm square spot. Motion in the horizontal plane was provided by a working table moving along the x - and y -axes. Fig. 1b shows the LHTed zone (highlighted in red), where the points A-F denote the start-end positions of the three laser tracks used to fully cover the treated area with the 20 mm square spot. Two different laser scanning strategies were adopted, referred to as S2 and S2R. In the S2 strategy, the laser followed a set of linear, parallel tracks moving
from left to right: the first track from point A to point B , the second from point C to point D , and the third from point E to point F . In contrast, the S2R strategy employed the same linear and parallel tracks but with a reversed scanning direction, moving from right to left. These two strategies were selected to generate different thermal histories and spatial temperature distributions, leading to different mechanical property distributions after the LHT. Before the laser heating, the side of the blank facing the laser beam was sprayed with a thin layer of black paint to reduce reflections. All tests were conducted with a constant laser power of 1350 W and a feed rate of 4 mm/s, with a 5 mm overlap between adjacent parallel tracks in both scanning strategies.

[picture]

Fig. 1. a) Schematic representation of the sheet injection process (adapted from [15]); schematic representation of the investigated LHT strategies; dimensions: mm .

Fig. 1. a) Schematic representation of the sheet injection process (adapted from [15]); schematic representation of the investigated LHT strategies; dimensions: mm .

Mechanical characterization of the heat-treated samples.

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Before each mechanical characterization test, the samples were cleaned to remove the black paint and subsequently polished. Vickers microhardness tests were conducted seven days after heat treatment to account for the hardness evolution due to natural ageing [16]. These tests were used to evaluate the effectiveness of the LHTs and to compare the two LHT strategies in terms of hardness distribution along the aluminium sheets. The tests were conducted in accordance with the EN ISO 6507-1:2018 standard using a fully automatic Qness Q10 A+ microhardness tester, with a load of 200 gf and a holding time of 15 s . Three key points were analyzed: (i) point P 1 , corresponding to the base material; (ii) point P 2 , corresponding to the critical zone during the bending stage and (iii) point P 3 , corresponding to the critical zone during the upsetting stage, according to the locations shown in Fig. 2a. Following the microhardness measurements, profilometry-based indentation plastometry (PIP) tests were conducted at the same three key points to obtain the stress-strain curves, yield stress, and ultimate tensile strength. PIP tests were carried out using the PLASTOMETREX PLX-Benchtop system shown in Fig. 2b. During the test, the sample was placed on the sample platform, and an indentation of approximately 100−200μ m deep was performed using a spherical Si3 N4 indenter with a radius of 1 mm . After indentation, the residual indent profile was scanned using the contacting stylus profilometer in four directions ( x,y,xy and yx ) through the central axis of the indent. The recorded maximum load and the residual indent profile were analyzed using the CORSICA software supplied with the PLX system. CORSICA performs an inverse analysis to identify the constitutive parameters that best reproduce the experimental response, providing the true stress-strain curve corresponding to the tested point. The Young's Modulus and Poisson's ratio were set to 69 GPa and
0.3 , respectively. The material behavior in the FE simulation was described using the Voce constitutive model [17], expressed in Eq. 1:

σ=σs−(σs−σY)exp(−ε/ε0).(1)

where σ is the true stress, ε the true strain, σY the yield stress, σs a saturation stress, and ε0 a characteristic strain.

[picture]

Fig. 2. a) Key points analyzed during microhardness and PIP test (dimensions: mm); b) Set-up for the PIP tests.

Fig. 2. a) Key points analyzed during microhardness and PIP test (dimensions: mm); b) Set-up for the PIP tests.

Results and Discussion

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Profilometry-based indentation plastometry results.

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The reliability of Profilometry-based Indentation Plastometry (PIP) in extracting local mechanical properties was first assessed by comparing the tensile parameters obtained from PIP with those measured by conventional uniaxial tensile tests on the base material, as shown in Fig. 3. The yield stress identified by PIP was found to be in the range of 312−340MPa, which is in very close agreement (percentage difference: 9.3%) with the tensile test value of approximately 298 MPa reported in Table 1, as well as UTS values (percentage difference: 1.5%).

[picture]

Fig. 3. Comparison between a) YS and UTS and b) flow stress curves obtained from PIP and from conventional uniaxial tensile tests on the base material.

Fig. 3. Comparison between a) YS and UTS and b) flow stress curves obtained from PIP and from conventional uniaxial tensile tests on the base material.

The overall agreement demonstrates that PIP can accurately reproduce the tensile response of the material, validating its use for local mechanical characterization in regions where standard tensile specimens cannot be extracted.
The effect of the two LHT strategies (S2 and S2R) on the resulting mechanical properties on the aluminium blanks is illustrated in Fig. 4, which shows the stress-strain curves identified by PIP at the base material location (P1) and at the critical zones corresponding to bending (P2) and upsetting (P3) for both S2 and S2R strategies. For both strategies, the laser heat treatment resulted in a clear reduction in yield stress and ultimate tensile strength, accompanied by an increase in strain at necking, compared to the T6 base material condition. This behaviour confirms the occurrence of local softening within the LHTed zone.

[picture]

Fig. 4. Stress-strain curves obtained by PIP for the different strategies.

Fig. 4. Stress-strain curves obtained by PIP for the different strategies.

For the S2 strategy, a gradual transition between the treated zone and the untreated region is observed. In particular, the stress-strain curve associated with point P2 (labelled as S2-P2 in Fig.4) remains close to that of the base material, whereas the curve corresponding to point P3 (S2-P3 in Fig.4) is significantly lower. This trend is quantitatively confirmed by the mean absolute percentage difference, calculated by comparing the stress values of P2 and P3 with those of the reference curve P1 at each common strain level, determining the absolute percentage deviation, and then averaging these deviations over the entire shared strain range. The S2−P2 curve exhibits a percentage difference of approximately 11% with respect to P1, while S2−P3 shows a substantially larger deviation of about 40%. This behaviour can be attributed to the processing sequence of the S 2 strategy, in which point P2 corresponds to the starting location of the laser track, whereas point P3 is located at the end of the track and is therefore exposed to higher temperatures. In contrast, in the S2R strategy, the stress-strain curve of point P2 (labelled as S2R-P2 in Fig.4) exhibited a more pronounced reduction (about 30%) compared to the S2 strategy. Moreover, the curves corresponding to points P2 and P3 are close to each other, indicating a more homogeneous thermal history along the laser tracks. Conversely, the S2 strategy led to a larger scatter among the identified curves, which can be associated with a less uniform temperature distribution induced by the laser heat treatment.

Comparison between PIP and hardness tests results.

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Vickers microhardness measurements performed after 7 days from the LHT at the same locations as the PIP tests are reported in Fig. 5 and show trends fully consistent with those observed for the tensile parameters identified by PIP. A clear reduction in hardness was measured in the laser-treated zones
compared to the base material, consistent with the decrease in yield stress and ultimate tensile strength extracted from the PIP analysis. This correlation highlights the effectiveness of the laser heat treatment in inducing controlled softening and validates hardness as a quick indicator of local strength variations. However, hardness measurements are not sufficient to capture changes in strain hardening behaviour. In contrast, PIP enabled the full reconstruction of local stress-strain curves, offering a more comprehensive mechanical characterization. This demonstrates the added value of combining hardness testing with PIP for the assessment of tailored heat-treated blanks.

[picture]

Fig. 5. Comparison between YS, UTS and hardness measured on the three key points.

Fig. 5. Comparison between YS, UTS and hardness measured on the three key points.

Conclusion

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This work investigated the mechanical property gradients induced by a laser heat treatment in 3 mm thick AW6082-T6 aluminium alloy sheets, with specific reference to applications in sheet injection processes. Profilometry-based Indentation Plastometry was employed as a local mechanical characterization technique and validated against conventional tensile testing.
The comparison between tensile tests and PIP demonstrated that the latter is capable of accurately identifying local stress-strain behaviour, confirming PIP as a reliable and semi-destructive tool for the characterization of tailored blanks, where standard tensile testing is not feasible due to spatial variations in material properties.
Both investigated laser scanning strategies successfully produced localized softened regions, resulting in a reduction in yield stress and an increase in local ductility compared to the T6 base material. Among the two strategies, the S2R approach provided a more uniform softening effect within the LHTed zone. This behaviour is particularly advantageous for sheet injection operations, as it promotes higher deformations corresponding to the critical zones of both bending and upsetting stages while preserving the overall strength of the component.
Hardness measurements confirmed the effectiveness of the laser heat treatment and showed a clear correlation with the strength reduction identified through PIP. However, hardness alone was insufficient to capture changes in ductility and strain hardening behaviour, highlighting the added value of PIP in providing full local mechanical characterization.
Thus, profilometry-based indentation plastometry represents an effective tool for the design and mechanical characterization of the laser heat treatment to produce tailored heat-treated aluminium
sheets to be subjected to sheet injection process. This work establishes a robust basis for future developments, notably process optimisation and advanced numerical modelling of the sheet injection process using tailored laser heat-treated aluminium sheets. In fact, PIP-based investigation will enable node-specific material properties in the FE model thus improving predictive accuracy.

Acknowledgement

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Financed by the European Union - NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033-17/06/2022, Spoke 11 Innovative Materials & Lightweighting). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them. The authors acknowledge Fundação para a Ciência e a Tecnologia (FCT) for its financial support via LAETA (project https://doi.org/10.54499/UID/50022/2025). Angela Cusanno also acknowledges the European Scientific Association for material FORMing for the support through the ESAFORM Mobility grant - project "Modelling sheet injection process using locally heat-treated blanks".

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 159-169

doi: 10.4028/p-j2TQc3

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-14

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Influence of Process Parameter Variations on Stamping-Bending Component Quality

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M. Buchner 1,a*, M. Damaškovič 1, b, L. Koller 2,c, W. Volk 1, d, M. Althoff 2,e and C. Hartmann 1,f

1 Chair of Metal Forming and Casting, Technical University of Munich, Walther-Meissner-Str. 4, 85748 Garching, Germany

2 Cyber-Physical Systems Group, Technical University of Munich, Boltzmannstraße 3, 85748 Garching, Germany

a* maximilian.buchner@tum.de, b  matej.damaskovic@tum.de, clukas.koller@tum.de, d  wolfram.volk@tum.de, e  althoff@in.tum.de, f  christoph.hartmann@utg.de

Keywords: leveling, stamping, bending sequence, parameter study, design of experiments.

Abstract

Achieving high geometric accuracy is crucial in stamping and bending processes. Key influencing factors include the position of the blank within the coiled sheet, leveling, strip lubrication, contour cutting, and the bending sequence. Currently, process design and parameter selection rely largely on the expertise of experienced engineers. A data-driven approach requires a detailed analysis of the effects and interactions of all process parameters. This analysis must include parameter settings, machine data and measurements of all manufactured parts. This study presents variance, interaction, and quality analyses based on long-term production trials for busbars. Process parameters were combined according to a statistical experimental design. The results indicate positive effects from slight pre-bending of sheet strips, active leveling, material removal through contour cutting, and simultaneous bending operations.

Introduction

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Stamping-bending components are typically produced from sheet coils through multiple stamping and bending operations in a single pass on automated stamping and bending machines. Common products with complex geometries include electrical conductors, terminals, contacts, and spring elements [1]. Component geometry is achieved either by loading beyond the yield strength or by modifying an already plastic state. Dimensional accuracy is critical for component quality and is strongly influenced by springback, residual stresses, bending sequence, and process uncertainties [2]. These uncertainties arise from material variations and interactions between process steps. To date, process design has relied heavily on implicit knowledge from experienced toolmakers and engineers. Such uncertainties, often referred to as process noise, should be captured and addressed by integrating sensors into the process chain. Understanding interactions within stamping-bending processes and assessing their generalizability is essential. While simulation approaches exist, FEM models are typically optimized for specific applications, limiting their broader validity. Therefore, statistical evaluations of data collected along the process chain and on finished components offer significant potential. They can reveal interactions between influencing parameters and resulting component properties. This enables inverse process tracing to determine the root causes of manufacturing quality for each part.

Approach

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Experimental Setup.

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A busbar is selected as the test component to analyze the influence of process parameters on geometry. Manufacturing is carried out on a Bihler GRM-NC stamping-bending machine, combining leveling, lubrication, cutting, free-form bending, and die bending operations (see Fig. 1). The machine is supplied with EN AW-5754 H22 aluminum alloy in strip form from a coil. An activatable leveling
process allows sheet strips to be flattened through alternating cold forming. Strip lubrication can be switched on or off via two rollers, using CLF 49 oil to prevent aluminum flake formation and adhesion. After the feed unit, the stamping unit punches pilot holes, cuts contours, and separates workpieces by shearing. The four cutting punches can be removed at any time to analyze the effect of contour cutting on component properties. The final module is a bending station, where the two legs of the busbar are first pre-bent freely. In the last step, the middle section is bent using a die, after which the finished busbar is ejected.

[picture]

Fig. 1. Manufacturing stations for busbar production on the Bihler GRM-NC stamping and bending machine.

Fig. 1. Manufacturing stations for busbar production on the Bihler GRM-NC stamping and bending machine.

The transformation of the component throughout the individual process steps is illustrated in Fig. 2. Initially, positioning holes are punched during the cutting operations, followed by contour cutting in a single stroke. In the third step, the connection surfaces of the busbar are pre-bent at both flank angles to ensure proper alignment. After the final step of die bending of the central section, the finished component contour is obtained.

[picture]

Fig. 2. Process steps in busbar manufacturing.

Fig. 2. Process steps in busbar manufacturing.

To enable a consistent quality assessment, a standardized geometric parameterization of the busbar is required. Therefore, the five planar sections are defined as lengths l1 to l5, the internal angles as a 1 to a4, and the corresponding radii as r1 to r4 (see Fig. 3).

[picture]

Fig. 3. Geometric parameterization of the busbar.

Fig. 3. Geometric parameterization of the busbar.

The target values corresponding to the 13 parameters are listed in Table 1. These values form the basis for designing the CAD model and the associated manufacturing process of the busbars.

Table 1. Nominal target values for the geometric parameters of the busbar.

Parameter | Unit | Target value
Length l₁ | mm | 18,00
Length l₂ | mm | 10,40
Length l₃ | mm | 23,90
Length l₄ | mm | 5,00
Length l₅ | mm | 18,00
Angle a₁ | ° | 120,00
Angle a₂ | ° | 120,00
Angle a₃ | ° | 90,00
Angle a₄ | ° | 90,00
Radius r₁ | mm | 3,00
Radius r₂ | mm | 3,00
Radius r₃ | mm | 3,00
Radius r₄ | mm | 3,00

These parameters are used to evaluate the manufacturing quality of each component based on its relative deviation from the nominal values. Combined with machine data and process settings, these measurements allow the identification of interactions between influencing factors. Dimensional measurements are performed using the in-line inspection system developed by Martinitz et al. [3]. Components are transported via a chute to a glass angle, where grayscale images are captured by two cameras from both profile and top views. High-quality optics and backlighting are employed to ensure optimal image resolution. The images are binarized using a MATLAB script and initially analyzed with the imfindcircles function. This approach was later replaced by a gradient-based evaluation method. This method segments the component into linear sections based on its slope. Angles and radii are then calculated between these sections. The gradient-based method proved significantly more robust, as the circle detection algorithm often failed when transition zones between contour segments exhibited elliptical rather than circular shapes. Since subsequent geometric evaluation depends on accurate arc identification, such failures previously caused complete analysis interruptions.

Influencing Parameters.

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The process parameters varied in this study include leveling, strip lubrication, contour cutting, and bending sequence. These factors are combined stochastically in accordance with the principles of statistical experimental design. Table 2 provides an overview of the factors and their levels.

Table 2. Combined factors and factor levels of the Design of Experiments.

Factor | Factor level
Coil | Coil 1- beginning Coil 1- middle Coil 1- end
Leveling | activated deactivated
Lubrication | activated deactivated
Notches contour | activated deactivated

Process sequence
simultaneous
left, right
right, left
left holding, right
right holding, left

The first factor relates to coil position, which is divided into three regions: the initial third, characterized by the largest mean radius, the middle section, and the end section, where the coil radius decreases. These regions differ significantly in pre-deformation, which may affect component geometry. Quach et al. demonstrated a direct correlation between residual stresses and springback [4]. His research found that residual stresses increase as the winding radius decreases. They also found that lower material strengths are associated with higher residual stresses in the component. Lee et al. have previously analyzed the resulting stress states using numerical models [5]. They demonstrated that, without leveling, there would be an increasing deviation from the geometric target values for the component. With a correctly adjusted leveling process, however, this should not occur. Investigations show that roll leveling homogenises the uneven distribution of residual stress. Leveling and lubrication can be manually activated or deactivated at the start of each test series. Comparing components produced with and without these settings reveals their direct impact on manufacturing quality. Fig. 4 illustrates two component variants used to study the influence of outer contour modifications. Variant A features four symmetrical cutouts, while Variant B retains an unmodified contour.

Part type A:

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Fig. 4. Component Variant A with outer contour cut and Component Variant B without outer contour cut.

Part type B:

This study thereby investigates the impact of strain hardening introduced during the stamping process on dimensional accuracy, as previously examined by Bolt et al. [6]. The associated residual stresses and reduction in component volume may influence springback behavior, as demonstrated by Kumar
et al. [7]. The final variable parameter concerns the bending sequence. While the last step, the die bending of the central section, is fixed, the sequence of pre-bending the busbar legs is adjustable. In this free-form bending process, the two punches can operate in different modes: simultaneously, rightfirst then left, or left-first then right. Alternatively, after the initial bend, the punch can remain engaged while the opposite leg is bent, resulting in five distinct bending sequences. These sequences are summarized in Fig. 5.

[picture]

Fig. 5. Positions of the bending punches for the five different bending sequences.

Fig. 5. Positions of the bending punches for the five different bending sequences.

Methods.

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The experimental design is structured according to the principles of the Design of Experiments, following a statistically valid random sequence of test runs. Variance, interaction, and quality analyses are used to examine interactions among process, machine, and component-geometry parameters. To classify the manufacturing quality of each component using a single metric, the dimensionless Overall Quality Indicator (OQI) is introduced. For normalization across different measurement scales, a z-transformation is applied to each geometric quality characteristic of the busbar. Subsequently, the absolute values of the z -scores are summed across all component parameters. The OQI therefore quantifies the overall deviation of a component's quality
characteristics from the dataset mean. A low OQI indicates consistently high product quality with minimal deviations, whereas a high OQI reflects greater variability in quality parameters. The OQI can be expressed by the following mathematical relationship:

OQIj=∑i=1n|xij−x¯isi|(1)

where
xij= value of quality parameter i in trial j
x¯i= mean of quality parameter i
si= standard deviation of quality parameter i
n= number of quality parameters

Results and Discussion

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Machine data.

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Based on the torque profiles of the spindle presses and bending units shown in Fig. 6, trends can be observed throughout the long-run production trials. These trends become particularly evident when considering the cleaning interventions for the active tool elements, which are also indicated in the graphs.

Process Variables

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[picture]

Fig. 6. Distribution of maximum torques per manufactured component at the two spindle presses for cutting ( 70% ), the two free-form bending axes ( 7% ), and the die bending axis ( e ).

Fig. 6. Distribution of maximum torques per manufactured component at the two spindle presses for cutting ( 70 % ), the two free-form bending axes ( 7 % ), and the die bending axis ( e ).

Overall, all press spindles show about 1% higher maximum torque when additional cutouts are stamped into the contour. Conversely, these components exhibit approximately l2 lower torque values at the bending units, as less material mass needs to be formed. The increasing torque after each cleaning cycle is caused by aluminum adhering to the tool surfaces. The adhesion reduces the cutting clearance and increases friction in the punch guides, resulting in higher process forces. After a certain number of produced parts, removal of these adhesions becomes essential, as the tool halves can no longer be separated for maintenance and cleaning. Immersion in a l4 sodium hydroxide solution for 2-3 hours dissolves the aluminum deposits, restoring tool functionality. However, the extent of adhesion increases after each cleaning cycle, which is reflected in the progressively steeper torque curves.

Analysis of Variance.

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To evaluate the average dispersion within individual factor levels, an analysis of variance (ANOVA) is performed. The objective is to identify which level of each factor exhibits the lowest variability. Lower variability in a quality characteristic indicates a more stable process. The results for the four investigated factors in the process chain are presented in Fig. 7.

[picture]

Fig. 7. Heatmaps for analyzing the variability of quality parameters for each parameter setting.

Fig. 7. Heatmaps for analyzing the variability of quality parameters for each parameter setting.

The heatmaps clearly show that all four radii and the lengths of the inner straight sections ( l1 to l5 ) exhibit low standard deviations. In contrast, pronounced fluctuations are observed for all four angles
as well as for s― and cμ. The high variability in angles is primarily attributed to springback. Standard deviations tend to be lower for bends with larger angles, i.e., those subjected to less severe deformation. The strong variation in the lengths of the two outer legs of the busbar is tool-related: when installing the entire cutting tool in the stamping-bending machine, its position along the process chain is not precisely fixed, as the distance to the part guides can be adjusted.

An isolated analysis of standard deviations under the factor bending sequence reveals that simultaneous bending provides the most stable process. Components with stamped cutouts also show reduced variability in quality parameters. For the factor leveling, angles exhibit lower standard deviations when leveling is active compared to when it is deactivated, confirming the effectiveness of leveling in reducing pre-deformation caused by coil winding. Similarly, the analysis of the coil section factor indicates that the initial coil region yields the lowest standard deviation. As coil radius decreases towards the end of the coil, standard deviations of component parameters increase, reflecting the growing pre-deformation of the strip and the resulting decline in process stability.

Interaction Analysis.

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As part of the interaction analysis, the relationships between individual factors are examined. The first step focuses on how leveling and contour cutouts influence the Overall Quality Indicator at different coil positions. The interactions between leveling and coil section, cutouts and coil section, as well as cutouts and leveling, are illustrated in Fig. 8.

[picture]

Fig. 8. Interaction analysis of the factors leveling, cutouts, and coil section on component quality.

Fig. 8. Interaction analysis of the factors leveling, cutouts, and coil section on component quality.

The interaction plots between leveling and coil position show similar trends to those between cutouts and coil position. This indicates that the contour cutting process exerts a comparable influence on the variability of quality parameters as the leveling process. This is particularly evident in the interaction between cutouts and leveling. When both are activated, the OQI reaches its minimum. Subsequently, the interactions between the factor bending sequence and the remaining investigated factors are analyzed. The corresponding interaction plots are presented in Fig. 9.

[picture]

Fig. 9. Interaction analysis of the factor bending sequence on component quality.

Fig. 9. Interaction analysis of the factor bending sequence on component quality.

The analysis confirms that the simultaneous bending sequence yields the lowest variability in quality parameters. In this case, the influence of leveling on the OQI is negligible. For all other bending sequences, an active leveling process reduces variability compared to a deactivated one. Similar findings emerge from the interaction between bending sequence and cutout stamping, with the exception that lower variability is observed even for the simultaneous sequence when cutouts are stamped. The cutout stamping process shows a particularly strong effect on the OQI for the right-left sequence. Conversely, an opposite trend is observed for the left hold-right sequence, where variability is lower when cutouts are not stamped. The interaction between bending sequence and coil section indicates that the simultaneous and left-right sequences are largely independent of coil position, whereas the remaining sequences exhibit a clear dependency on coil section.

Quality analysis.

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The quality analysis investigates which bending sequence provides the highest process capability and process control with respect to the component bending angles. For each test series, the mean and standard deviation of the four angles are calculated. To assess process capability, the mean of the standard deviations ( 32% ) of the individual angles within each test series is determined for each bending
sequence. The sequence with the smallest mean standard deviation corresponds to the process with the highest capability.

Process control is quantified by the deviation of the series means from the overall mean, referred to as the mean deviation of means and abbreviated as 32%. The sequence with the smallest average deviation represents the most controlled process. The results of the quality analysis are summarized in Table 3.

Table 3. Mean standard deviation ( a,b ) and mean deviation of means ( c,d ) of the bending angles for each bending sequence.

Process sequence | Parameter | x̄ | cμ | s̄
simultaneous | a₁ [°] | 126,02 | 0,198 | 0,270
| a₂ [°] | 121,42 | 0,213 | 0,234
| a₃ [°] | 97,34 | 0,375 | 0,340
| a₄ [°] | 98,44 | 0,527 | 0,390
left, right | a₁ [°] | 126,09 | 0,305 | 0,307
| a₂ [°] | 121,16 | 0,162 | 0,277
| a₃ [°] | 97,29 | 0,532 | 0,569
| a₄ [°] | 97,98 | 0,533 | 0,659
right, left | a₁ [°] | 126,07 | 0,251 | 0,312
| a₂ [°] | 121,26 | 0,201 | 0,308
| a₃ [°] | 97,48 | 0,494 | 0,545
| a₄ [°] | 98,18 | 0,506 | 0,687
left holding, right | a₁ [°] | 125,94 | 0,237 | 0,275
| a₂ [°] | 121,05 | 0,168 | 0,293
| a₃ [°] | 97,32 | 0,554 | 0,540
| a₄ [°] | 97,95 | 0,492 | 0,630
right holding, left | a₁ [°] | 125,93 | 0,268 | 0,336
| a₂ [°] | 121,08 | 0,188 | 0,273
| a₃ [°] | 97,22 | 0,647 | 0,573
| a₄ [°] | 97,79 | 0,667 | 0,665

Overall, the simultaneous bending sequence demonstrates the highest process control and capability. The mean standard deviation across all angles is, on average, superscript number lower during the simultaneous bending process compared to the other bending sequences. Only for the quality characteristic a2 do the other sequences perform slightly better. Notably, the low variations within individual test series for the simultaneous sequence indicate a high process capability. The lowest process control and capability are observed for the right hold-left sequence. This suggests that simultaneous bending ensures the most homogeneous material flow, which, according to Durmaz et al. [8], significantly influences the intensity and distribution of bending stresses.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.159.pdf

This study demonstrates how insights into interactions within stamping-bending processes can be extracted from large-scale experimental data. The parameters that varied include coil section, leveling, strip lubrication, contour cutting, and bending sequence. Combined with machine data and measured component geometries, these variations enable identification of the optimal parameter combination for minimizing geometric variability. A total of 2,400 busbars were produced in longterm production trials, with parameter settings changed after every 25 parts according to a statistical design. Components were measured in-line at the end of the process using an optical inspection system, ensuring complete traceability of each part to its dataset.

The results indicate a positive effect of leveling and contour cutting on dimensional accuracy. Components manufactured with these measures exhibit lower deviations from nominal geometry and reduced variability compared to those produced without them. Furthermore, dimensional accuracy tends to decrease as coil radius decreases, due to increasing pre-deformation. Regarding the bending sequence, simultaneous bending yields the smallest mean deviation and lowest variability of measured dimensions. The mean standard deviation is thereby reduced by superscript number in the simultaneous
bending process compared to the alternative bending sequences. Consequently, the highest process capability and control can be achieved with a large coil radius, active leveling, contour cutting, and simultaneous bending.

Further studies are required to verify the generalizability of these findings. These studies should include other components, extended process monitoring, and alternative inspection methods. Within the DFG Priority Program 2422 on data-driven process modeling, the experimental data will also be used to train neural networks. Machine learning will then enable the identification of process uncertainties and support inverse process tracing, allowing for continuous optimization and determination of the optimal parameter combination.

Statements and Declarations

The original version of this paper is available on https://www.scientific.net/SSP.389.159.pdf

Funding

The original version of this paper is available on https://www.scientific.net/SSP.389.159.pdf

This study was conducted as part of project No. 520459543, which is embedded in the Priority Program (SPP) 2422 funded by the German Research Foundation (DFG).

Conflict of Interest/Competing Interests

The original version of this paper is available on https://www.scientific.net/SSP.389.159.pdf

The authors declare no conflicts of interest.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.159.pdf

M. Paech, "Advanced semi-automatic straightening technology," vol. 41, pp. 74-79, 2008.

K. Richter, F. Reuther, R. Müller, and D. Landgrebe, "Investigating the Influence of Bending Parameters on the Springback Behavior of Ultra-High Strength Spring Strips," MSF, vol. 918, pp. 125-133, 2018, doi: 10.4028/www.scientific.net/MSF.918.125.

L. Martinitz, L. Koller, W. Volk, M. Althoff, and C. Hartmann, "An image-based, unified feature extraction framework for experimental and synthetic data for data-driven modelling in stamping and bending," J. Phys.: Conf. Ser., vol. 3104, no. 1, p. 12050, 2025, doi: 10.1088/1742-6596/3104/1/012050.

W. Quach, J. Teng, and K. Chung, "Residual stresses in steel sheets due to coiling and uncoiling: a closed-form analytical solution," Engineering Structures, vol. 26, no. 9, pp. 12491259, 2004, doi: 10.1016/j.engstruct.2004.04.005.

J. Lee and C. Lee, "An advanced model for the numerical analysis of the radial stress in centerwound rolls," International Journal of Mechanical Sciences, vol. 105, pp. 360-368, 2016, doi: 10.1016/j.ijmecsci.2015.11.016.

P. J. Bolt and W. H. Sillekens, "Prediction of shape aberrations due to punching, shearing and slitting," Journal of Materials Processing Technology, vol. 103, no. 1, pp. 87-94, 2000, doi: 10.1016/S0924-0136(00)00390-3.

D. Kumar, L. Zhigang, S. Jirathearanat, and A. Senthil Kumar, "Investigation of Residual Stresses Induced by Incremental Sheet Forming and Stamping in Aluminum Alloys," Journal of Materials Engineering and Performance, vol. 32, no. 7, pp. 2950-2962, 2023, doi: 10.1007/s11665-022-07304-3.

U. Durmaz, S. Heibel, T. Schweiker, A. Prabhakar, and M. Merklein, "Influence of the forming process on springback," IOP Conference Series: Materials Science and Engineering, vol. 1238, p. 12074, 2022, doi: 10.1088/1757-899X/1238/1/012074.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 171-180

doi: 10.4028/p-OHzO30

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-16

Revised:
2026-02-16

Accepted:
2026-02-24

Online:
2026-04-16

Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

Max Gröbel 1,a*, Karl J. Tilly 1,b, Emad Scharifi 1,c and Junhe Lian 1,d

1 Institute of Metal Forming (IBF), RWTH Aachen University, Intzestraße 10, 52072 Aachen, Germany

a  max.groebel@ibf.rwth-aachen.de, b  karl.tilly@ibf.rwth-aachen.de, c  emad.scharifi@ibf.rwth-aachen.de, djunhe.lian@ibf.rwth-aachen.de

Keywords: Sheet Metal forming, Gas-based hot forming, Precipitation hardening aluminum,

Abstract

Hybrid hot sheet forming routes that integrate heat treatment within the forming tool offer a promising pathway to manufacture complex geometries from precipitation-hardenable 7xxx aluminum alloys, but the resulting local deformation and thermal histories may generate pronounced spatial property variations. In this work, a gas-based hybrid forming process is demonstrated for EN AW-7020 sheets, combining in-tool solution heat treatment, isothermal forming at 500∘C with gas calibration and active pushing, followed by water quenching and artificial aging. A thermo-mechanically coupled finite-element model is used to identify regions of distinct equivalent plastic strain in a representative demonstrator geometry and to guide local specimen extraction. Tensile tests from low- and high-strain regions reveal clear location-dependent stress-strain responses after aging, with a reduction in ultimate tensile strength exceeding 20% in the more heavily deformed zones compared with reference material. Microstructural observations by optical microscopy indicate differences in grain morphology between component regions, consistent with the non-uniform thermo-mechanical history. The results highlight the need to account for local strain and process history when designing hybrid-formed 7xxx components and motivate targeted strategies for controlling property gradients through process parameter tuning and tailored post-forming heat treatment.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

The increasing demand for lightweight structural components in both automotive and aerospace industries has intensified research into forming processes for high-strength aluminum alloys of the 6xxx and especially the 7xxx series [1,2]. These alloys offer excellent strength-to-weight ratios and corrosion resistance, making them promising candidates for load-bearing structures in modern mobility applications. Despite their advantageous strength-to-weight ratio, 7xxx-series alloys exhibit limited ductility at room temperature, which results in localized thinning, reduced formability, and an increased risk of crack initiation during conventional cold forming [3, 4].

Recent studies highlight that warm and hot forming routes represent a viable solution to overcome these challenges. Comprehensive reviews of hot sheet metal forming for 7xxx alloys show that hot forming at 500∘C significantly improves formability while enabling the manufacture of geometrically complex components [2]. However, warm-forming routes cause heterogeneous microstructures that require subsequent heat treatments to obtain a homogenous microstructure and the desired mechanical performance [4]. Warm sheet forming studies using precipitation hardenable aluminum alloys AA7075 and AA7020 demonstrate that temperatures between 150∘C and 300∘C increase the drawability and limit strain localization, allowing components to reach up to 90% of the T6 strength after subsequent aging [1, 5]. Beyond conventional warm forming, hybrid thermomechanical process routes have gained substantial attention [6, 7]. For example, in [7], a hybrid hot forming process is developed consisting of solution heat treatment, immediate forming, quenching, and artificial aging to counteract the disadvantages of warm forming and positively influence the final properties with the integrated aging step. These developments align with industrial hot forming technologies such as Hot Forming and Quenching (HFQ ® ), which combines quenching and forming after solution heat treatment. In the case of precipitation hardenable aluminum alloys, artificial aging
is subsequently carried out to adjust the desired mechanical properties. HFQ®-based studies report significant springback reductions and improved dimensional accuracy for 7xxx-series alloys [8, 9]. Investigations on the forming-induced pre-deformation show that it strongly influences precipitation behavior during subsequent aging. Local pre-strain accelerates heterogeneous nucleation, lowering the achievable peak strength and altering the distribution of Guinier-Preston zones, particularly in Al−Zn−Mg alloys [5, 10]. This explains why even moderate plastic deformation can significantly reduce final strength after artificial aging [11].

However, the impact of the integrated gas-supported hot sheet forming process on the final mechanical properties of the complex-shaped components has not yet been evaluated. The present study, therefore, investigates this by means of tensile tests and grain size distribution to counteract the lack of knowledge for the combination of modern hot forming processes with the integrated heat treatment. This investigation aims to address microstructural changes to the forming operation and the mechanical properties.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

The material used in this study is the high-strength aluminum alloy EN-AW 7020 in the as-received H18 condition with a hardness level of 88HV2 and an ultimate tensile strength (UTS) of 257 MPa . Table 1 shows the chemical composition according to the supplier of the material. The sheet thickness investigated is 2 mm .

Table 1. Chemical composition of the investigated EN AW 7020

Si | Fe | Cu | Mn | Mg | Cr | Zn | Zr | Al
0.03 | 0.14 | 0.00 | 0.21 | 1.21 | 0.13 | 4.37 | 0.1138 | remaining

Experimental setup. The setup of the process is based on the process shown in [7] consisting of a die, a punch with gas channels, and a blank holder equipped with an active pushing system to increase the draw-in, as shown in Fig. 1. The active pushing system is based on eight cylinders, every 45∘ to push the sheet into the die. The pushers are controlled via LabView, which synchronizes the blank-holder position with the activation of the pneumatic system. The pushing system is divided into the x-pushers and the +-pushers, which can be controlled solely. After the completion of the deep drawing, a pressure valve opens and a pressure of max. 9 bar is applied to the cylinders, resulting in a max. pusher force of 1500 N . The end plates of the pushers are manufactured from TiAl6V4 because of its high strength combined with low thermal conductivity even at high temperatures. The tooling setup enables three different procedures to be performed: deep drawing, deep drawing with gas calibration, and deep drawing with active sheet pushing, as well as gas calibration. The present study deals with the complete forming process consisting of deep drawing, pushing, and gas calibration. Moreover, this set-up enables solution heat treatment within the forming tool up to 600∘C using heating cartridges (Mickenhagen high-performance heating cartridge 500 W−800 W ) in the punch, blank holder, and die, as well as additional heating coils (Mickenhagen flexible tubular heating element 2500 W−3320 W ) in the blank holder and die. Cooling channels are integrated into the frame to thermally decouple the heated tool components and ensure process stability.

[picture]

Fig. 1. Setup of the tool used for the experimental investigations

Fig. 1. Setup of the tool used for the experimental investigations

For the experimental procedure, the parts were lubricated with a graphite-based lubricant after being water cut to the proposed octagonal shape and cleaned up. To reduce the friction during hot forming, dies were lubricated as well as the pushers and the sheet material with graphite-based lubricant. The forming process is integrated into the heat treatment of the material; the sheet is placed in the center of the heated blank holder and conductively heated to the SHT temperature of 500∘C. The heat treatment is performed for 20 min to fully dissolve the alloying elements. Subsequently, the forming process starts and can be divided into two major steps. First deep drawing takes place within two seconds with a punch velocity of 30 mm/s and an increasing blank holder force of 3 kN to 6 kN applied by the gas springs, followed by the gas calibration supported by the pushing of the sheet with a force of 1500 N as shown in Fig. 2. The gas used for calibration is nitrogen with a pressure of 10 MPa .

[picture]

Fig. 2. Overview of the forming process and resulting parts

Fig. 2. Overview of the forming process and resulting parts

After fully forming, the part is directly quenched in water. To finally set the mechanical properties, the parts are artificially aged with another two-step heat treatment at 90∘C for 8 h and 145∘C for 8 h .

Fig. 3 shows the thermal reference cycle of the used alloy. For comparison, a section of sheet metal with the same temperature/time history is prepared and analyzed in the same way.

[picture]

Fig. 3. Thermal reference cycle

Fig. 3. Thermal reference cycle

The determination of the mechanical properties after forming is done by tensile tests. Therefore, tensile specimens are taken from identified regions by wire erosion and tested using the tensile testing machine Z100 with an optical strain measurement system by the ARAMIS-4M-system. Tests are performed at room temperature under quasistatic conditions with a crosshead speed of 0.9 mm/min for the large samples and 0.375 mm/min for the small samples, equivalent to a strain rate of 0.001 s−1. Fig. 4 shows the extracted specimens; the corresponding numerical investigations for identifying the relevant regions can be found in the results and discussion section. Furthermore, grain size is determined by the linear intercept method. For preparation, the samples are cold-embedded, ground, polished, and finally etched using Barker's reagent.

[picture]

Fig. 4. Tensile specimens extracted from the completely formed cross-die (dimensions in mm )

Fig. 4. Tensile specimens extracted from the completely formed cross-die (dimensions in mm )

Numerical setup. In addition to the experimental investigations, a numerical model is built in LS-DYNA R13 and pre- and post-processed in LS-PrePost 4.9 in accordance with [7]. The basic setup is shown in Fig. 5 at the beginning, during deep drawing with the pushers moving towards the sheet, and at the end of the process. Only one quarter of the setup is modelled to reduce calculation time.

[picture]

Fig. 5. Numerical model of the forming process as a function of process stage

Fig. 5. Numerical model of the forming process as a function of process stage

The sheet is modeled using 3D thermal shell elements with a fully integrated formulation and nine integration points through the thickness. Die, blank holder, punch, and the pushers are also modelled using thermal shell elements with reduced integration. Mechanical properties are assigned via the Thermo_Elastic_Viscoplastic_Creep card for the sheet and with the Thermal_Isotropic_material card for all other parts. The sheet is modeled as an elasto-plastic deformable body, while all tools and pushers are treated as rigid components. The flow curves for EN AW 7020 are taken by the isothermal stacked layer compression test directly after the solution heat treatment.

The process takes three seconds to complete and is divided into the deep drawing and the assisted calibration step. The die is fixed, and the punch is moving with a velocity of 30 mm/s, resulting in a deep drawing time of two seconds to reach the full drawing. The subsequent calibration takes one second with an increasing gas pressure, and the pushers are active during the deep drawing to get in contact at the start of the calibration.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

Based on the methodology described, components are successfully produced without cracks and initially numerically investigated to identify the strain distribution. Furthermore, tensile tests and grain size determination are carried out.

Local deformation behavior. With the help of the already validated numerical model from [7], local strains were extracted to identify regions with different forming histories. Fig. 6 illustrates the strain distribution of the formed part at the initial state, after deep drawing, and after subsequent gas calibration. After deep drawing, a maximum strain of ε=0.4 is observed in the wall region and in the corner, whereas the bottom region remains almost undeformed.

The subsequent gas calibration step leads to a pronounced localization of deformation in the corner area, where the strain increases to a maximum value of ε=1.08. This strong local strain accumulation is directly associated with a significant thickness reduction, resulting in a maximum thinning of 65% in the corner region. In contrast, the wall region experiences a moderate but continuous increase over both forming stages, while the bottom part is only marginally affected by the overall forming process.

An analysis of the forming history reveals that the deformation mechanisms differ distinctly between the individual regions of the component. The wall deformation is mainly induced during the tool-based deep drawing step, whereas the gas calibration predominantly contributes to the additional strain and thinning in the corner region. Overall, the induced deformation after the complete forming process is significantly higher in the wall and corner regions ( εWall ≥0.4 ) compared to the bottom region ( εBottom ≤0.05 ), clearly demonstrating the strong localization effects inherent to the multistage forming process.

[picture]

Fig. 6. Evolution of the numerically predicted strain distribution during multi-stage forming

Fig. 6. Evolution of the numerically predicted strain distribution during multi-stage forming

A geometric comparison of the experimentally manufactured component with the simulation model is based on the thinning along three symmetry lines to validate the plastic flow behavior, as shown in Fig. 7. The thinning behavior and its tendencies are represented quite well by the simulation model with minor deviations in the flanging area. As shown in the numerical analysis at the end of the complete forming process, the thinning along lines 1 and 2 in the bottom radius reaches its maximum, whereas this maximum is not pronounced along line 3. The greatest thinning can be detected in the corner area, which corresponds to the results of the numerical analysis. It can be seen that gas calibration causes the greatest change in shape in the area of the arms and the corners, and significantly increases thinning in this area. Furthermore, friction between the sheet metal and the forming tool restricts material flow, causing material to flow from regions that are not previously in contact with the die. This redistribution of material subsequently results in increased local thinning.

Line 3

Fig. 7. Thinning comparison along three symmetry lines of the completely formed cross-die

The deviations in the flanging area are due to the fact that the model is not considering the blank holder force compressing the sheet in this zone. Also, the high punch compression force acting on the bottom is not considered within the simulation model, resulting in less thinning at the bottom (Line 1 and Line 2). For inspection of the mechanical properties, tensile tests are carried out as mentioned in the Materials and methods section. The specimens are taken from the bottom region and the wall region.
Tensile tests. Fig. 8 a) illustrates the tensile behavior of the Al−Zn−Mg alloy after the complete thermo-mechanical processing route, comprising solution heat treatment (SHT), gas-based forming at 500∘C, and subsequent artificial aging at 90∘C for 8 h , followed by 145∘C for an additional 8 h . The resulting engineering stress-strain curves are shown for tensile specimens extracted from different regions of the formed component, namely the wall (dotted lines) and the bottom (solid line), to capture spatial variations in the mechanical response induced by the hot forming process. For comparison, the tensile properties of the reference sample are also included in the figure to assess the influence of the forming operation on the final mechanical properties. A yield strength of at least 215 MPa is observed in all samples, while the yield strength of the cross-die specimens remains below that of the reference sample.

The tensile strength decreases with increasing deformation, with a more pronounced reduction in the wall region compared to the bottom region. The elongation at fracture decreases in the base region and deteriorates significantly in the wall region. Fig. 8 b) shows the strain hardening rate as a function of the engineering strain. Strain hardening rate is calculated using formula (1), which measures the local gradient based on the differential stress and strain.

θ|i=dσdε|i=σ|i+1−σ|i−1ε|i+1−ε|i−1(1)

All samples exhibit a high initial strain-hardening rate followed by a continuous decrease with increasing strain. Specimens from the wall region show a more rapid decline and reach zero strain-hardening at lower strains, indicating an earlier onset of plastic instability. The black curve, representing the reference sheet material, exhibits the lowest strain-hardening rate.

[picture]

Fig. 8. True stress-strain behavior and corresponding strain hardening rate as a function of prior deformation state after artificial aging

Fig. 8. True stress-strain behavior and corresponding strain hardening rate as a function of prior deformation state after artificial aging

The mechanical behavior observed in the tensile tests reflects the strong coupling between the local deformation state and the subsequent precipitation kinetics of the 7xxx alloy within the hybrid hot forming route. The reduction of the UTS in the wall area is consistent with the high local strains identified in the numerical model and shown in Fig. 6. In Al−Zn−Mg alloys, such pre-deformation is known to accelerate heterogeneous nucleation during artificial aging, thereby reducing the achievable peak strength. This mechanism explains why the wall region, despite undergoing the same artificial aging treatment as the bottom region and the reference sheet, reaches noticeably lower tensile strength values. Furthermore, the earlier decline of strain hardening in the wall specimens indicates that the material enters the softening regime sooner due to the increased density of deformation-induced defects, as shown in Fig. 8 a). These defects act as preferential nucleation sites during aging and promote the formation of coarser precipitates, thereby lowering hardenability. In contrast, the bottom area in Fig. 6 shows only minor deformation and therefore preserves a precipitation sequence closer to that of the reference sheet, resulting in higher UTS. Regions with pronounced stretching exhibit locally increased dislocation density, which further influence the precipitation behavior. The black curve, representing the reference sheet material, shows the lowest strain-hardening rate over the entire strain range. This behavior reflects the absence of forming-induced dislocation structures, resulting in a reduced work-hardening capability compared to the formed specimens. As a result, the hybrid process introduces characteristic spatial variations in mechanical properties that follow directly from the strain distribution during forming. These results indicate that local deformation during forming directly affects precipitation and work-hardening, which must be accounted for in process optimization and component design to ensure consistent mechanical performance.

Grain size determination. In addition to the tensile tests, grain size is determined. For comparison Fig. 9 shows the development of the grain structure during the thermal stages of manufacturing the part including the heat treatment for the undeformed sheet. The rolling structure can clearly be identified in the delivery condition by the horizontally stretched grains. After solution heat treatment, a homogeneous grain size distribution emerges, which remains visible even after aging. The grain size decreases by approximately 10%. This confirms that the heat treatment effectively homogenizes the microstructure, providing a consistent starting point for the forming operation.

[picture]

Fig. 9. Effect of heat treatment without plastic deformation on the grain size distribution of the used sheet material

Fig. 9. Effect of heat treatment without plastic deformation on the grain size distribution of the used sheet material

o determine the influence of forming on the grain size distribution, samples are cut from the cross-die as shown in Fig. 10. The regions with maximum thinning exhibit slightly finer grains compared to the undeformed sheet, whereas areas with minimal pre-deformation as the bottom region tend to show slightly larger grains. These differences are small and close to the measurement scatter but consistent with the local deformation history. The wall region does not show measurable grain coarsening; instead, the grains appear elongated and locally refined due to the deformation introduced during forming. The corner of the cross-die is formed at the end of the process and therefore experiences the highest cooling rate due to forced convection. This rapid cooling suppresses grain growth after quenching, leading to a locally finer grain appearance relative to surrounding regions. Although no significant overall change in grain size is observed across the part, grain elongation is clearly visible in the areas of high thinning.

Fig. 9 illustrates that the microstructural variations follow the deformation history obtained from the numerical analysis in Fig. 6. The grain refinement in the highly thinned regions can be attributed to intense stretching during forming, which elongates and partially fragments the grains. This effect is most pronounced in the corner regions, where the highest cooling rates further restrict grain growth. In contrast, areas with minimal deformation as the bottom region cool more slowly, which allows for slightly more grain growth during the thermal cycle.
Overall, the combination of deformation and locally varying cooling conditions leads to a largely homogeneous grain-size distribution across the component, with regionally discernible grain elongation characteristic of hybrid hot sheet-forming processes. This uniform microstructure shows process robustness, ensuring predictable mechanical performance and consistent quality in hybrid hot sheet-forming of single components.

[picture]

Fig. 10. Regional influence on post-ageing grain size distribution within the cross-die

Fig. 10. Regional influence on post-ageing grain size distribution within the cross-die

Summary

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

Within this study the influence of forming on mechanical properties of the precipitation hardenable aluminum alloy EN AW 7020 has been investigated on the hybrid hot sheet forming process [7]. To determine relevant regions and correspond them to the mechanical properties, a numerical identification was carried out. Based on the obtained results the following key findings can be drawn:

The forming operation followed by the artificial aging reduces the ultimate tensile strength. It can be stated that the degree of plastic deformation further reduces the UTS, lowering the UTS more than 20% compared to the non-deformed sheet.

Grain refinement can only be observed in regions with maximum thinning, resulting in elongation of grains. This elongation can also be observed in the wall regions due to the stretching.

The hybrid hot sheet forming process introduces characteristic mechanical and microstructural gradients that directly correlate with the local strain distribution. These gradients must be considered in the design of load-bearing components made from 7xxx aluminum alloys.
Further research should focus on the detailed influence of pre-deformation on precipitation kinetics and local hardness evolution in EN AW 7020. Optimizing hybrid hot forming parameters, such as temperature, strain rate, and cooling, could help reduce UTS loss and control grain growth. The correlation between microstructural gradients and mechanical performance, including fatigue and
fracture behavior, should be further investigated. Finally, predictive models and design guidelines for load-bearing components made from 7xxx aluminum alloys could be developed based on these findings.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

This project (Lightness.NRW) was funded by "Europäischer Fonds für regionale Entwicklung" (EFRE). The authors of IBF further acknowledge excellent collaboration with the project partners SMS group GmbH, Ford-Werke GmbH, Hydro Extruded Solutions GmbH, Hydro Aluminum Rolled Products GmbH, HoDforming GmbH, CTES and Automotive Laboratory of FH Aachen. The authors would like to thank Stefan Seidel for the preparation of the tensile specimens.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.171.pdf

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K. Zheng, D. J. Politis, L. Wang, and J. Lin, A review on forming techniques for manufacturing lightweight complex-shaped aluminium panel components. International Journal of Lightweight Materials and Manufacture, 2 (2018) 55-80.

J. A. Österreicher, M. A. Tunes, F. Grabner, A. Arnoldt, T. Kremmer, S. Pogatscher, and C. M. Schlögl, Warm-forming of pre-aged Al-Zn-Mg-Cu alloy sheet. Materials & Design (2020) 108837.

S. Lotz, E. Scharifi, U. Weidig, and K. Steinhoff, Effect of Combined Forming and Aging Processes on the Mechanical Properties of the Precipitation-Hardenable High-Strength Aluminum Alloys AA6082 and AA7075. Metals, 8 (2022) 1250.

N. K. Baru, T. Teeuwen, D. Bailly, and E. Scharifi, A novel hybrid hot forming process concept for high strength aluminum alloys. Materials Research Proceedings, 52 (2025) 134-141.

R. Wu, W. Dai, J. Luo, M. Li, Y. Liu, and H. Li, Aluminum Alloy Hot Stamping and Forming Technology: A Review. Materials (Basel, Switzerland), 8 (2025).

E. Scharifi, V. A. Yardley, U. Weidig, D. Szegda, J. Lin, and K. Steinhoff, Hot Sheet Metal Forming Strategies for High-Strength Aluminum Alloys: A Review-Fundamentals and Applications. Adv Eng Mater, 16 (2023).

M. C. Paulisch, N. Wanderka, M. Haupt, S. Selve, I. Driehorst, and W. Reimers, The influence of heat treatments on the microstructure and the mechanical properties in commercial 7020 alloys. Materials Science and Engineering: A (2015) 254-262.

A. Deschamps, F. Livet, and Y. Bréchet, Influence of predeformation on ageing in an Mg alloy-I. Microstructure evolution and mechanical properties. Acta Materialia, 1 (1998) 281-292.

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 181-189

doi: 10.4028/p-f59c2L

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Accepted:
2026-02-16

Online:
2026-04-16

Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

Zixuan Mu 1,a*, Youngrok Lee 1, b, Jeffrey Abell 1,c, Alan Taub 1,2, d, Mihaela Banu 1,e

¹Department of Mechanical Engineering, University of Michigan, 2350 Hayward St, Ann Arbor, MI, USA

2 Department of Materials Science and Engineering, University of Michigan, 2300 Hayward St, Ann Arbor, MI, USA

a  zixuanmu@umich.edu, b  yroklee@umich.edu, cjaabell@umich.edu, d  alantaub@umich.edu,  embanu@umich.edu

Keywords: incremental sheet forming (ISF), toolpath strategies, curvilinear, springback, bulge, pillow effect, bending moments

Abstract

Geometric deviations remain a major barrier to the widespread industrial adoption of incremental sheet forming (ISF). Compared with conventional toolpath compensation that rely on extensive data generation and trial-and-error procedures, variation of toolpath styles offers a more direct and efficient strategy for mitigating geometric defects. In this study, multiple curvilinear toolpath strategies were investigated for a standard closed-contour ISF part to evaluate their effectiveness in reducing geometric deviations. Six toolpaths were examined, including three established types - convex, concave, and wavy - and three novel toolpaths proposed in this work: adaptive, cusp, and sine. The convex toolpath achieved the largest side-wall springback reduction relative to the linear baseline but introduced a significant bottom pillow effect and reduced formability. While the cusp toolpath effectively suppressed both springback and pillow formation, it resulted in local thickening and degraded surface finish. Overall, the sine toolpath provided the most balanced performance, achieving effective reduction of all major geometric defects. Numerical simulations reveal an inherent tradeoff between side-wall springback reduction and bottom pillow formation, as positive residual bending moments formed in the pillow region contribute to springback mitigation by promoting outward bending of the side walls.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

Incremental sheet forming (ISF) has been extensively investigated over the past two decades and has demonstrated significant potential for small-batch manufacturing and rapid prototyping. Nevertheless, its relatively low geometric accuracy remains a major limitation that restricts broader industrial adoption. Such inaccuracies are commonly referred to sheet bending, springback, and pillow effect [1,2]. Multiple approaches have been proposed to tackle this challenge [1], with toolpath compensation being the most commonly adopted strategy.

On one hand, geometric inaccuracies can arise from machine compliance effects, such as tool deflection, which are particularly significant in two-point incremental forming (TPIF) and robotic incremental forming [3, 4]. These compliance-induced errors can be systematically mitigated using compliance-based compensation strategies without extensive trial-and-error [3]. On the other hand, additional geometric inaccuracies stem from variations in the sheet stress mechanics during forming, which are often feature-dependent and difficult to compensate uniformly. This has motivated the development of predictive models for geometric deviation estimation. For instance, regression-based [5], simulation-assisted in-situ [6], and deep learning-based [7] approaches have been proposed to enable toolpath correction. While these studies have demonstrated significant success in reducing geometric deviations, most existing toolpath compensation strategies rely on extensive trial-and-error procedures or data-driven approaches that require large amounts of training data, which can be prohibitively expensive for sophisticated models.

As an alternative to explicit toolpath compensation, recent studies have increasingly focused on the design of toolpath strategies in ISF to influence stress evolution and deformation mechanisms during forming, thereby inherently improving geometric accuracy without iterative correction. While contour (Z-level) and spiral toolpaths remain the most conventional approaches, Lu et al. [8] developed a feature-based toolpath generation algorithm and demonstrated improved geometric accuracy for critical edges and non-symmetric parts. Other studies have explored alternative strategies, including muti-step [9, 10], zigzag [11], radial [12], point contact [13] toolpaths. Among these approaches, curvilinear toolpath strategies have attracted particular attention for their potential to influence the deformation behavior.

The concept of curvilinear toolpaths was first introduced by Grimm et al. [14], inspired by vibration-assisted forming, who showed that wavy toolpaths could improve surface variability. Building on this idea, Bremen and Bailly [15] investigated global springback by proposing convex and concave curvilinear toolpaths with superimposed wavy patterns. They showed that the wavy convex toolpath led to the minimum springback, as it effectively hindered the accumulation of local bending moments along the toolpath, resulting in a much smaller net residual bending moment prior to unclamping. However, their investigation was limited to open-contour parts clamped along two edges, which are more susceptible to large springback. In contrast, closed-contour parts, although generally stiffer and less prone to geometric inaccuracies, are more commonly used in ISF and exhibit distinct internal deformation mechanisms. The influence of curvilinear toolpaths on geometric deviations in closed-contour parts therefore remains insufficiently elaborated.

Consequently, this work follows a framework similar to that of Bremen and Bailly [15] and aims to examine the effects of different curvilinear toolpath strategies on the geometric deviation of a standard closed-contour ISF part, with the objective of identifying an effective strategy for reducing various geometric deviations and clarifying the underlying deformation mechanisms.

Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

In this work, aluminum alloy 7075-O (Kaiser Aluminum, USA) was used to form all parts, and its tensile behavior was characterized using the Voce hardening law, as given in Eq. 1, with the corresponding parameters listed in Table 1 [16], where σ¯ is the equivalent stress and εp is the equivalent plastic strain.

σ¯=k0+Q(1−e−βεp)(1)

Table 1. Elastic properties and Voce law parameters of AA7075-O

Density mathematical formula

Modulus

Poisson's

ratio

Yield strength

2810 | 69.74 | 0.33 | 89 | 91.30 | 149.34 | 26.71

The truncated pyramid was chosen as the standard closed-contour target geometry in this study, with its dimensions and a representative formed part shown in Fig. 1 (a) and (b). Single point incremental forming (SPIF) experiments were performed on a 3 -axis HAAS VF-2 CNC milling machine (Haas Automation, USA) using a 12.7 mm diameter hemispherical forming tool, as illustrated in Fig. 1 (c). The lubrication grease molybdenum disulfide (MoS2) was applied prior to forming to reduce friction. All tests with different toolpaths were conducted at a feed rate of 42 mm/s and a step size of 0.5 mm . The formed geometries were measured using a Romer Absolute Arm with Integrated Scanner 7525SI (Hexagon Manufacturing Intelligence, USA).

Finite element simulations were performed using ABAQUS/Explicit. The forming tool and clamping frames were modeled as rigid bodies, while the sheet was discretized using 3D reducedintegration solid elements (C3D8R). A mesh size of 0.5 mm×0.5 mm was adopted in the forming region, which has been shown to be appropriate based on a mesh sensitivity study in previous work
[16]. Five elements were used through the sheet thickness. The material behavior was modeled using the von Mises yield criterion with isotropic hardening.

[picture]

Fig. 1. Target geometry and experimental configuration: (a) CAD definition and dimensions of the truncated pyramid, (b) formed pyramidal part, and (c) ISF test setup.

Fig. 1. Target geometry and experimental configuration: (a) CAD definition and dimensions of the truncated pyramid, (b) formed pyramidal part, and (c) ISF test setup.

Owing to the high rigidity of the target geometry, local springback following tool passage dominates over global springback during unclamping and trimming, leading to negligible differences in geometry before and after unclamping. Accordingly, all geometric defects considered in this study are treated as developing progressively during the forming process rather than occurring abruptly after forming. Since the magnitude of springback is directly governed by bending moments [17], and bending moment is not available as a direct field output for solid elements, bending moments, were therefore computed in the simulation using the simplified expression given in Eq. 2,

SM=∫−t/2t/2σzdz≈∑e=1NσezeΔze(2)

where SM is the section bending moment, σ is the normal stress, z is the through-thickness coordinate measured from the mid-plane, t is the deformed sheet thickness, e denotes the throughthickness element index, N is the number of elements through the thickness, and Δz refers to deformed element thickness.

[picture]

Fig. 2. Schematics of different curvilinear toolpath strategies (pyramid's side wall projection): (a) convex, (b) concave, (c) wavy, (d) adaptive, (e) cusp, and (f) sine

Fig. 2. Schematics of different curvilinear toolpath strategies (pyramid's side wall projection): (a) convex, (b) concave, (c) wavy, (d) adaptive, (e) cusp, and (f) sine

Different curvilinear toolpath strategies were implemented in this study, including three basic shapes proposed in previous works [14, 15] - namely convex, concave, and wavy - as well as three
newly developed variants: adaptive convex, cusp convex, and single-period sine. These variants were introduced to mitigate geometric defects observed with the basic shapes. Schematics of all toolpaths are shown in Fig. 2. The convex and concave toolpaths correspond to downward- and upwardopening parabolic profiles, respectively. For consistency and fair comparison, their amplitudes were set to the same value. The wavy toolpath is defined as a continuous sinusoidal profile with multiple periods. The adaptive convex toolpath is a modified convex profile with curvature progressively decreasing with depth. The cusp convex toolpath is defined as a convex profile with a sharp apex formed by the intersection of two parabolic segments. The single-period sine toolpath consists of one complete sinusoidal period starting and ending at valleys, with two symmetric inflection points and asymmetric convex and concave segments defined by different amplitudes or wavelengths. For consistency, the curvature of the convex segment was set to be consistent with that of the convex and concave parabolic toolpaths. A reference linear toolpath was generated in Fusion 360, from which all curvilinear toolpaths were derived. Each curvilinear strategy began and ended with several linear passes to ensure smooth transitions.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

[picture]

Fig. 3. Cross-sectional profile comparison of experimental results: (a) basic curvilinear toolpaths, (b) detailed view of the mid region in (a), (c) novel curvilinear toolpaths, and (d) detailed view of the mid region in (c)

Fig. 3. Cross-sectional profile comparison of experimental results: (a) basic curvilinear toolpaths, (b) detailed view of the mid region in (a), (c) novel curvilinear toolpaths, and (d) detailed view of the mid region in (c)

Fig. 3 compares the cross-sectional profiles of experimentally formed parts produced using different curvilinear toolpaths. The profiles are divided into three regions: top, mid, and bottom. As shown in Fig. 3 (a) and Fig. 3 (c), substantial deviations from the target CAD geometry are observed in the top region for all toolpath strategies. This behavior is primarily attributed to sheet bending effects inherent to SPIF, and therefore the present analysis focuses on springback in the mid region and the pillow effect in the bottom region of the truncated pyramid. Among the basic curvilinear toolpaths (Fig. 3 (b) and Table 2), the convex toolpath exhibits the largest reduction in springback ( −74.0% ) relative to the conventional linear toolpath. In contrast, the concave and wavy toolpaths result in only minor changes in springback compared to the linear case, consistent with previously reported global springback trends after unclamping in open-contour parts [15]. The springback observed in the pyramid is reflected by an inward bulging of the side walls, as shown in Fig. 4, with a magnitude consistent with the springback levels observed in Fig. 3.

Table 2. Maximum springback and pillow height relative to the CAD profile

Toolpath style | Max springback [mm] | Percentage change [%] | Max pillow height [mm] | Percentage change [%]
Linear | 3.651 | 0.0 | 0.509 | 0
Convex | 0.948 | -74.0 | 3.227 | +534.1
Concave | 4.270 | +17.0 | 1.052 | +106.7
Wavy | 3.299 | -9.6 | 0.468 | -8.1
Adaptive | 3.168 | -13.2 | 0.562 | +10.4
Cusp | 1.089 | -70.2 | 1.193 | +134.4
Sine | 2.147 | -41.2 | 0.866 | +70.1

[picture]

Fig. 4. Horizontal cross-sectional profile ( z=−30 mm ) comparison of experimental results: (a) full view, (b) detailed view of selected edge section in (a)

Fig. 4. Horizontal cross-sectional profile ( z = − 30 m m ) comparison of experimental results: (a) full view, (b) detailed view of selected edge section in (a)

Despite its effectiveness in reducing springback, the convex toolpath introduces a substantially more pronounced pillow effect and reduced formability. Specifically, the convex toolpath results in a 534.1% increase in pillow height, and fracture occurred at a forming depth of approximately 70 mm during the 80 mm -deep pyramid tests, as shown in Fig. 5 (b). To mitigate these issues while maintaining low springback, three convex-inspired toolpath strategies - adaptive cusp, and sine were proposed and evaluated, with results presented in Fig. 3 (c) and (d), Fig. 4, and Table 2. Although the adaptive toolpath effectively reduces the pillow effect, it largely restores the springback level to that of the linear toolpath, rendering it redundant compared to the baseline case. The cusp toolpath achieves substantial reductions in both springback ( −70.2% ) and pillow height ( +134.4% ); however,
it introduces a surface finish defect, as shown in Fig. 5 (a), characterized by localized thickening at the midsection of each side wall due to inhomogeneous material flow caused by the sharp change in toolpath slope at the cusp apex. The sine toolpath also provides notable reductions in springback ( −41.2% ) and pillow height ( +70.1% ) and, although slightly less effective than the cusp toolpath, produces a smoother surface without introducing additional surface finish defects. Therefore, the sine toolpath is identified as the most balanced curvilinear strategy, offering an effective compromise between springback reduction, pillow mitigation, and surface finish.

[picture]

Fig. 5. Pyramidal parts formed using different curvilinear toolpaths: (a) cusp, (b) convex ( 80 mm depth), and (c) sine ( 80 mm depth)

Fig. 5. Pyramidal parts formed using different curvilinear toolpaths: (a) cusp, (b) convex ( 80 mm depth), and (c) sine ( 80 mm depth)

To further assess the formability of the sine toolpath, an 80 mm -deep pyramid was formed using this strategy, whereas the convex toolpath failed due to severe thinning and fracture during forming. As shown in Fig. 5 (c), the pyramid was successfully formed to the full 80 mm depth without fracture, demonstrating improved formability relative to the convex toolpath. Furthermore, as shown in Fig. 6, during the forming of the 80 mm -deep pyramid, the sine toolpath achieves an overall springback reduction exceeding 50% and exhibits a negligible pillow effect compared to the linear toolpath.

[picture]

Fig. 6. Cross-sectional profile comparison of experimental results of 80 mm -depth: (a) full view, and (b) detailed view of mid region in (a)

Fig. 6. Cross-sectional profile comparison of experimental results of 80 mm -depth: (a) full view, and (b) detailed view of mid region in (a)

The simulated snapshots of bending moment distribution about the y -axis, SM22, during forming are shown in Fig. 7. For the linear toolpath (Fig. 7 (a)), each parallel pass of the tool in the x direction leaves a positive residual bending moment (positive curvature) along the tool track. These moments accumulate along the side walls (blue circle), leading to a pronounced bulge springback, consistent
with the geometric deviations observed in Fig. 3 and 4. Although previous work [15] reported that convex toolpaths significantly reduce overall bending moments for open-contour parts prior to unclamping, Fig. 7 (b) shows that, for the closed-contour pyramid studied here, the residual bending moment along the toolpath is not markedly reduced compared to the linear case. Instead, a substantial positive residual bending moment develops in the bottom pillow region, which acts against the side walls and enhances bending near the forming edges (black circle), thereby mitigating sidewall bulging. In contrast, the concave toolpath (Fig. 7 (c)) generates negative residual bending moments in the pillow region, which do not promote edge bending (black circle) and therefore offer limited springback reduction. As shown in Fig. 7 (d), the sine toolpath produces a smaller pillow region and lower residual bending moments than the convex toolpath, which in turn leads to a moderate reduction in edge bending (black circle). Despite this reduction, the induced bending remains substantially higher than in the linear and concave cases, resulting in effective springback mitigation.

These results highlight a fundamental tradeoff between sidewall springback reduction and pillow height in closed-contour forming. Curvilinear toolpaths that induce larger positive bending moments in the pillow region tend to provide more effective springback mitigation, but excessive pillow formation can adversely affect formability. Consequently, toolpath design must balance springback control and pillow suppression based on product-specific tolerance requirements. Within this study, the sine toolpath offers the most favorable compromise, achieving substantial springback reduction while limiting pillow height and preserving formability.

[picture]

Fig. 7. Bending moment distribution for different styles of toolpaths: (a) linear, (b) convex, (c) concave, and (d) sine

Fig. 7. Bending moment distribution for different styles of toolpaths: (a) linear, (b) convex, (c) concave, and (d) sine

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

In this study, multiple curvilinear toolpath strategies were applied to a closed-contour part using SPIF to evaluate their effectiveness in mitigating geometric defects. Three established toolpaths convex, concave, and wavy - were examined alongside three novel toolpaths proposed in this work: adaptive, cusp, and sine. Among these, the convex toolpath achieved the greatest springback reduction in the mid-wall region; however, this benefit came at the expense of a pronounced pillow
effect and reduced formability. The cusp toolpath effectively reduced both springback and pillow height but introduced surface finish defects. Overall, the sine toolpath provided the most balanced performance, achieving effective mitigation of springback while limiting pillow formation and maintaining good formability. Deformation analysis revealed that positive sectional bending moments accumulated along the toolpath are responsible for inward bulging springback on the side walls, while positive residual bending moments in the pillow region play a critical role in springback reduction. These findings highlight an inherent tradeoff between springback mitigation and pillow severity in closed-contour part forming.

Future work may focus on the parametric optimization of curvilinear toolpath geometries to establish quantitative relationships between key mathematical features, such as amplitude and curvature, and geometric accuracy. More detailed deformation analyses could also be performed to identify the dominant deformation mechanisms associated with each toolpath type and to clarify the evolution and accumulation of residual bending moments throughout the formed part. In addition, the application of curvilinear toolpaths to closed-contour parts with curved internal wall surfaces could be investigated to assess their effectiveness in mitigating geometric defects.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.181.pdf

Lu, H., Liu, H. and Wang, C., 2019. Review on strategies for geometric accuracy improvement in incremental sheet forming. The International Journal of Advanced Manufacturing Technology, 102(9), pp.3381-3417.

Vanhulst, M. et al., 2025. ESAFORM benchmark 2024: study on the geometric accuracy of a complex shape with single point incremental forming. International Journal of Material Forming, 18(3), p.72.

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Bharti, S., Paul, E., Uthaman, A., Krishnaswamy, H., Klimchik, A. and Abraham Boby, R., 2024. Systematic analysis of geometric inaccuracy and its contributing factors in roboforming. Scientific Reports, 14(1), p.20291.

Behera, A.K., Verbert, J., Lauwers, B. and Duflou, J.R., 2013. Tool path compensation strategies for single point incremental sheet forming using multivariate adaptive regression splines. Computer-Aided Design, 45(3), pp.575-590.

Ren, H., Xie, J., Liao, S., Leem, D., Ehmann, K. and Cao, J., 2019. In-situ springback compensation in incremental sheet forming. CIRP Annals, 68(1), pp.317-320.

Bingqian, Y., Zeng, Y., Yang, H., Oscoz, M.P., Ortiz, M., Coenen, F. and Nguyen, A., 2024. Springback prediction using point series and deep learning. The International Journal of Advanced Manufacturing Technology, 132(9), pp.4723-4735.

Lu, B., Chen, J., Ou, H. and Cao, J., 2013. Feature-based tool path generation approach for incremental sheet forming process. Journal of Materials Processing Technology, 213(7), pp.1221-1233.

Cappellini, C., D'Urso, G. and Giardini, C., 2025. Multi-Step Tool Paths Development for Reducing Geometric Deviation and Pillow Effect in the Single-Point Incremental Forming. Journal of Manufacturing Science and Engineering, 147(7), p.071005.

Vanhulst, M., Vanhove, H., Duflou, J.R., Araujo, A.C., Cantarel, A., Chabert, F., Korycki, A., Olivier, P. and Schmidt, F., 2024. Influence of toolpath strategies on the final accuracy and thickness distributions in multi-stage incremental forming. MATERIAL FORMING, ESAFORM 2024, 41, pp.1498-1506.

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Grimm, T.J. and Mears, L., 2020. Investigation of a radial toolpath in single point incremental forming. Procedia Manufacturing, 48, pp.215-222.

Chang, Z., Huang, W. and Chen, J., 2020. A new tool path with point contact and its effect on incremental sheet forming process. The International Journal of Advanced Manufacturing Technology, 110(5), pp. 1515-1525.

Grimm, T.J., Ragai, I. and Roth, J.T., 2018. Utilization of wavy toolpath in single-point incremental forming. In ASME International Mechanical Engineering Congress and Exposition (Vol. 52019, p. V002T02A029). American Society of Mechanical Engineers.

Bremen, T. and Bailly, D.B., 2024. On the Influence of Wave-Shaped Tool Path Strategies on Geometric Accuracy in Incremental Sheet Forming. Journal of Manufacturing and Materials Processing, 8(1), p.27.

Shin, J., 2021. Investigation of Incremental Sheet Forming (ISF) using Advanced Numerical and Analytical Approaches. PhD thesis, University of Michigan.

Burchitz, I.A., 2008. Improvement of springback prediction in sheet metal forming. PhD thesis, University of Twente.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 191-206

doi: 10.4028/p-Y78kVu

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-22

Accepted:
2026-02-24

Online:
2026-04-16

Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

Maziar Khademi 1,a*, Peng Neo Zhang 1, b, Michael P. Pereira 2,c and Matthias Weiss 1,d

1 Institute for Frontier Materials, Deakin University, 75 Pigdons Rd., Waurn Ponds, Geelong, VIC 3216, Australia

2 School of Engineering, Deakin University, 75 Pigdons Rd., Waurn Ponds, Geelong, VIC 3216, Australia

a  m.khademi@deakin.edu.au, b  peng.neo.zhang@deakin.edu.au, c  michael.pereira@deakin.edu.au

dmatthias.weiss@deakin.edu.au,

Keywords: Bipolar plates; 3D Printed tool; Micro-roller embossing; Fuel cell; Multi stage forming.

Abstract

Bipolar plates are key components in fuel cells, and their performance strongly depends on the geometry of the microchannels used to distribute reactant gases. Producing channels with sufficient depth in thin metal sheets remains challenging, particularly when cost-effective manufacturing routes are required. This work investigates a multi-stage roller embossing process for forming bipolar plate channels using additively manufactured polymer tools. By dividing the total deformation into multiple forming stages, the process reduces tool deflection that typically limits channel depth in single-pass embossing. Experiments conducted on 0.1 mm stainless steel foil show that the multi-stage approach increases the achievable average channel depth from approximately 0.25 mm in a single pass to approximately 0.34 mm , resulting in a maximum aspect ratio (channel depth to width) of 0.314 . These results indicate that combining multi-stage forming with 3D-printed tooling provides a practical route for flexible and low-cost fabrication of metallic bipolar plates, especially for low volume production.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

Proton Exchange Membrane Fuel Cells (PEMFCs) generate electricity from hydrogen and oxygen and only produce water as a byproduct. A typical PEMFC stack unit consists of different components, including the bipolar plates (BPPs), which have a large number of small flow channels (microchannels) for the gases to interact [1]. The performance of the fuel cell is influenced by the geometry of the microchannels within the BPPs. A key geometrical parameter is the aspect ratio (AR) of the channels, which is the ratio of channel depth to width, which directly influences the efficiency of fuel cells [2]. Despite extensive research on bipolar plate fabrication, achieving high aspect ratio microchannels in thin metallic foils remains a key manufacturing challenge. Mass production of metal BPPs is often achieved using micro-stamping, but this process can lead to issues such as wrinkling defects and material thinning or even rupture [3]. Research has shown that the maximum achievable aspect ratio for stainless steel with thickness of 0.1 mm using micro-stamping is 0.43 [4]-i.e., micro-stamping is limited by the maximum aspect ratio that can be achieved. These limitations motivate the exploration of alternative forming processes that can reduce material thinning and forming defects, while enabling greater channel depths and hence higher aspect ratios.

Micro roll forming has been shown to reduce material thinning [1] and Bauer et al. [5] has shown that the micro roller embossing process can be used to form BPPs on an industrial scale. By utilizing a rolling mill, Bauer et al. [5] formed 0.1 mm -thick stainless steel foils successfully in a single pass. However, the process showed forming defects in the form of wrinkles. The main challenge in the work by Bauer et al. [5] is that the reported formed depth of 0.31 mm is lower than the target depth of 0.5 mm . A similar limitation was observed when forming more complex channel patterns using roller embossing [6]. This issue appears to be related to structural deflection, particularly shaft deflection, occurring during the roller embossing process even when steel tools are used. This
observation indicates that tool and shaft deflection can play a dominant role in limiting the achievable channel depth.

In general, increasing the forming depth requires higher forming forces, which in turn increases the stresses that must be transferred at the channel corner radii. Rather than increasing forming forces in a single pass, distributing deformation over multiple forming steps provides a promising strategy to overcome depth and deflection limitations.

One effective way to reduce stress and thereby increase the achievable aspect ratio is to increase the number of forming steps. Multi-stage forming reduces the forming force that must be transferred in each step. It also enables the creation of intermediate shapes that promote material flow and allows higher stresses to be transferred at the channel corners [7, 8]. As a result, multi-stage forming has the potential to increase the achievable aspect ratio while reducing peak stresses on both the material and the forming tools.

In recent years, additive manufacturing has gained recognition as a viable technology for rapid prototyping of forming tools [9]. Various studies have explored the use of 3D-printed tools for sheet metal forming processes, such as V-bending of aluminum [10] and deep drawing of aluminum and steel [8]. The findings indicate that 3D-printed plastic tools are capable of forming metal sheets, but tool deflection during forming presents a major challenge [11]. This challenge is particularly critical in micro-forming applications, where the magnitude of small tool deflections (e.g. fractions of a millimeter) can be a large percentage of the total forming height; thus, leading to large deviations in the formed channel geometry. Cyron et al. [12] investigated the fabrication of BPPs using plastic dies, demonstrating that 3D-printed plastic tools can be employed for micro-component forming. However, a comparison between conventionally machined steel dies and 3D-printed plastic dies revealed notable discrepancies between the designed and actual plate shapes that were formed with plastic tools. The underlying causes of these deviations were not analysed.

To date, no work has systematically combined multi-stage roller embossing with additively manufactured tooling, while explicitly accounting for tool deflection effects. In this study, the 3D printing concept is applied to a new concept of the roller embossing process (named multi-stage roller embossing), to form a representative BBP geometry using stainless steel foil. Three forming strategies are examined: single-stage forming with ABS tooling, multi-stage forming with ABS tooling, and multi-stage forming with a stiffer photopolymer resin insert in the final stage. A Finite Element Analysis (FEA) model was developed and used to prove the concept and validated with experimental results. The FEA model was then used to develop a solution for redesigning the tool setup and geometry to reduce tool deflection effects and reduce the forming force in the roller embossing process to increase the forming depth. The results of this study suggests that 3D printed plastic forming tools can be used to form microchannels relevant to BPP production if tool deflection is accounted for.

Experiment Set Up

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Material. The study utilised bright-annealed 316L stainless steel foil with a thickness of 0.1 mm . The mechanical properties of the 316L stainless steel were obtained from a previous study [13] where the true stress-strain curve was determined and fitted with the Swift law (Eq. 1):

σ=k(ε0+ε)n(1)

where K,ε0 and n, are the strength coefficient, strain shift parameter, and hardening exponent, respectively. The anisotropic plastic behaviour was characterised using the Lankford coefficients ro, r45, and r90, corresponding to rolling, diagonal, and transverse directions, respectively. The elastic and plastic properties are presented in Table 1.

Table 1. Elastic and plastic property parameters of the 316 L stainless steel sheet [13].

E (GPa) | K | n | ε₀ | r₀ | r₄₅ | r₉₀
190 | 1534 | 0.516 | 0.047 | 0.85 | 1.22 | 1.21

Acrylonitrile butadiene styrene (ABS) and a rigid photopolymer resin (Formlabs Rigid 10K resin [14]) were used for the 3D-printed tools. The ABS material was supplied by Stratasys Ltd [15]. All ABS parts in this study were additively manufactured using a Stratasys F190 fused deposition modelling 3D printer, with a 100% infill strategy and a layer thickness of 0.127 mm . The Rigid 10K resin is a glass-filled photopolymer with high stiffness and strength, designed for tooling and functional prototyping applications, and was supplied by Formlabs Inc. All Rigid 10k resin parts in this study were additively manufactured using a Formlabs 3L 3D printer, which uses low force stereolithography technology, with a layer height of 50μ m. After printing, all Rigid 10 K resin specimens were post-cured using the manufacturer's recommended procedure. The post-curing process was conducted at a temperature of 70∘C for a duration of 60 minutes to ensure complete polymerization, enabling the material to reach its intended stiffness, strength, and heat resistance.

The ABS and Rigid 10k resin materials were tested in compression according to ASTM-D1621 standard [16] using cuboid samples (Fig. 1). The compressive load was applied parallel to the material stacking direction (z-axis). The specimens were printed with the build direction aligned with the zaxis, such that the layer stacking direction was parallel to the applied compressive load.

Fig. 2 shows the resulting compressive stress-strain curve. The elastic modulus determined from the stress strain response was 1.3 GPa and 5.7 GPa for ABS and Rigid 10 K resin, respectively, where the reported values represent the average of five tested specimens for each material. When manufactured using 3D printing, the Poisson's ratio of the ABS material is reported to be 0.37 [17], and 0.36 for Rigid 10k resin [18].

[picture]

Fig. 1. Schematic of the compression tests and compression test samples used to characterise the 3D printed materials.

Fig. 1. Schematic of the compression tests and compression test samples used to characterise the 3D printed materials.

[picture]

Fig. 2. Engineering stress-strain curves, determined in the compression tests, for the 3Dprinted materials: a) ABS, b) Rigid 10 K resin.

Fig. 2. Engineering stress-strain curves, determined in the compression tests, for the 3Dprinted materials: a) ABS, b) Rigid 10 K resin.

Experimental micro roller embossing trials. The ideal cross-section of the microchannels, formed with an aspect ratio of 0.462 calculated based on the method described in [19], is shown in

Fig. 3. This profile was selected based on previous research [5] performed on BPP forming with steel tools, enabling a comparison of the results. The dimensions of the forming rollers are shown in Fig. 4(a). The forming was conducted on a mini roll former that is chain-driven using three stations (see Fig. 4(c) and (d)). Stations 1, 2, and 3 are used sequentially in the multi-stage forming process, with each station contributing to the progressive forming of the microchannels in the sheet. In addition, the guide stations ensure stable sheet alignment and controlled material feeding between forming stages. The roller gap between the top and bottom rollers was set at 0.1 mm and a flat sheet ( 170 mm length × 27 mm width) was fed into the roller former.

[picture]

Fig. 3. Schematic of the target microchannel profile, units of the linear dimensions in millimetres.

Fig. 3. Schematic of the target microchannel profile, units of the linear dimensions in millimetres.

(a)

(b)

Station 1

Station 2

Station 3

[picture]

Fig. 4. a) Schematic of the micro roller embossing tooling for single roller station. b) Desired cross-section of tool in each station (dimensions in mm). c) Schematic of the three-station roller embossing layout, illustrating the relative position of the top and bottom rollers and the stainlesssteel foil feed path through the guide station. d) Photograph from the top of the experimental roller former.

Fig. 4. a) Schematic of the micro roller embossing tooling for single roller station. b) Desired cross-section of tool in each station (dimensions in mm). c) Schematic of the three-station roller embossing layout, illustrating the relative position of the top and bottom rollers and the stainlesssteel foil feed path through the guide station. d) Photograph from the top of the experimental roller former.

To evaluate the influence of multi-stage forming on channel quality, three sequential forming depths of 0.15 mm,0.30 mm and 0.50 mm (shown in Fig. 4(b)) were first tested using ABS-based 3D-printed tooling. This series was designed to quantify the effect of incrementally increasing deformation during the forming process. Following this, an additional sequence was conducted in which the initial two steps ( 0.15 mm and 0.30 mm depth) were performed with ABS tooling, while the final forming step ( 0.50 mm depth) was conducted using a resin-based tool. This second test condition was intended to demonstrate the feasibility of forming micro-channels using hybrid 3Dprinted tooling materials and to provide evidence supporting the applicability of resin tooling for the final, higher-load forming stage. The three investigated forming strategies are defined as Cases A-C and summarised in Table 2, which introduces the case labels, forming strategies, and corresponding tooling configurations used throughout the remainder of the study.

Table 2. Summary of the different forming strategies and tooling configurations used in this study, which are designed to achieve increased forming depth.

Case | Forming strategy | Tooling configuration
A | Single-stage forming | ABS inserts
B | Multi-stage forming (3 stages) | ABS inserts (all 3 stages)
C | Multi-stage forming (3 stages) | ABS inserts + Rigid 10k resin (final stage)

The final shape of the profiles and the dimensional accuracy of the 3D-printed rollers were analysed using a non-contact optical surface profilometer Alicona (R), with a 5× magnification optical lens, a vertical resolution of 360 nm and a lateral resolution of 3.91μ m. The Mean Absolute Error (MAE) [20] value was determined to quantify the deviation between the actual and printed roller profiles. Following the methodology outlined in [20], the MAE determined for the top and bottom roller profiles was 37μ m and 26μ m, and 19μ m and 29μ m for Rigid 10k resin tools respectively, suggesting that the rollers were printed with high precision.

Numerical Analysis

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

FEA of the roller embossing forming process was conducted with ABAQUS. All parts of the experimental micro roller embossing set up were replicated in the numerical model, including the dimensions of the rollers, sheet length, and roller gap. The FEA model is shown in Fig. 5. As shown, each roller consists of two parts: the main rollers and the inserts. The main rollers are made of ABS; however, depending on the forming strategy, the material of the inserts differs. Therefore, in the numerical simulation, separate sections were defined to assign different material properties to the rollers and inserts.

[picture]

Fig. 5. FEA model of the multi-stage micro roller embossing process.

Fig. 5. FEA model of the multi-stage micro roller embossing process.

The sheet was meshed with S4R shell elements, with 5 integration points through the material thickness. Based on the mesh sensitivity analysis shown in Fig. 6, the mesh was refined to a size of 0.1 mm , specifically in the channel-forming region (shown in Fig. 5) to improve accuracy. In the mesh convergence analysis, the reaction force in single-stage forming was considered to evaluate the effect of mesh refinement on the simulation results. While a 0.2 mm mesh also provided good accuracy, a mesh size of 0.1 mm was ultimately selected to more accurately represent local contact conditions.

[picture]

Fig. 6. Mesh sensitivity analysis of the FEA model, showing the influence of the sheet mesh size on the predicted forming force. The reported force corresponds to the reaction force acting on the forming rollers during single-stage micro-roller embossing.

Fig. 6. Mesh sensitivity analysis of the FEA model, showing the influence of the sheet mesh size on the predicted forming force. The reported force corresponds to the reaction force acting on the forming rollers during single-stage micro-roller embossing.

The forming rollers were meshed as deformable bodies with C3D8R elements. A refined mesh size of 0.15 mm was applied in the critical contact locations of the rollers. In the tool corner areas, where the smallest geometric features exist, the mesh was further refined to approximately 0.04 mm to properly capture the geometry. In all other tool regions, the mesh size was set to 1 mm . Symmetry boundary conditions were applied along the centreline, thus allowing only half of the sheet and rollers to be modelled. To define the sheet material properties, an anisotropic Hill48 material model was applied, using the material data from Table 1. The material properties of the rollers were defined based on Fig. 2, using von Mises elasto-plastic isotropic yielding.

The boundary conditions were defined so that the bottom rollers rotated about their axes at 1.5 radians per second, while the top rollers rotated at -1.5 radians (negative indicating the opposite direction to the bottom rollers). In the FEA model, the shafts were modelled as deformable highstrength steel components with high stiffness, rather than as rigid bodies. This approach allows shaft deflection to be captured accurately. The shafts are constrained at the support/bearing locations through the boundary conditions. The interaction algorithm "surface to surface contact" with hard normal contact and Coulomb friction law were defined between the rollers and the sheet surface, and the coefficient of friction was set to 0.2 [21]. The roller embossing process simulation was solved using the ABAQUS/Explicit solver with step time of 3 seconds and a mass scale factor of 5000 , resulting in quasi-static conditions with a kinetic energy of less than 10% of the internal energy throughout the forming process. The deformation history of the sheet after the ABAQUS/Explicit steps was imported into ABAQUS/Implicit for a springback analysis. For the springback analysis, all contact conditions were removed to release the formed component in space.

Results and discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

Single-stage forming. A comparison of the simulation (FEA) and experimental results of the formed part in single-stage forming with equivalent plastic strain (PEEQ) is demonstrated in Fig. 7. This shows close agreement between the simulated and experimental deformed shapes and validates the FEA model predictions.

[picture]

Fig. 7. Comparison of FEA and experimental results of the formed part after the roller embossing process for single-stage forming (target depth =0.5 mm ).

Fig. 7. Comparison of FEA and experimental results of the formed part after the roller embossing process for single-stage forming (target depth = 0.5 m m ).

The experimental and the predicted cross-sectional profile shape after forming (and springback) are compared in Fig. 8(b). The comparison is performed using the top surface of the formed part, which is consistently used for all profile evaluations presented in this study. The results indicate that the FEA model can provide a reasonable representation of the experiments. In Fig. 8(b), the first valley shows a small deviation in 2D shape between the experiment and the FEA near the start of the first corrugation (at approximately x=9 mm ). In this forming region, the material is not fully constrained by the forming rollers which is different to the symmetry centre area. The thickness distribution of the formed component is shown in Fig. 8(c). For each thickness location, measurements were performed at two corresponding points on two samples. The reported thickness values represent the average of these measurements, and the standard deviation was calculated to quantify experimental variation. The simulation and experimental results are closely aligned and only a small discrepancy exists which may be due to measurement error.
(a)

(b)

[picture]

Fig. 8. a) Profile path defined for cross section profile and thinning measurements, b) comparison of the cross-section profile of the formed part between FEA and experiment, c) comparison of the thickness distribution between FEA and experiment.

Fig. 8. a) Profile path defined for cross section profile and thinning measurements, b) comparison of the cross-section profile of the formed part between FEA and experiment, c) comparison of the thickness distribution between FEA and experiment.

For the remainder of this paper, for all comparisons, only the profile of the middle channel is considered (Fig. 9(a)), since all channels are relatively consistent as shown in Fig. 8(b). A comparison of the ideal cross-sectional profile and the formed part for single-stage forming (Case A) is shown in Fig. 9(b). The maximum depth of the formed parts was 0.25 mm on average for the eight channels experimentally formed in each part. This result indicates that only 50% of the desired depth was formed and that the channel top had a curved shape instead of the designed (ideal) flat surface.

[picture]

Fig. 9. a) Cross-section of the 3D model, b) FEA cross-section profile of the part compared to the ideal shape for single-stage forming.

Fig. 9. a) Cross-section of the 3D model, b) FEA cross-section profile of the part compared to the ideal shape for single-stage forming.

Fig. 10 shows a cross-section view of the roller gap (located at the centreline of the rollers), predicted by the FEA model at the location and time where the sheet is positioned between the two rollers. The contour plot shows the equivalent plastic strain (PEEQ) distribution in the rollers. At this location, the rollers should be separated only by the sheet thickness of 0.1 mm . However, the predicted gap is much larger than this (0.292 mm), as shown by the measurements in Fig. 11.

[picture]

Fig. 10. FEA predicted gap between two rollers at the location where the sheet is formed in the tool gap.

Fig. 10. FEA predicted gap between two rollers at the location where the sheet is formed in the tool gap.

Fig. 10 shows that there is plastic deformation of the rollers near the surface of the roller profiles. However, analysis of the deformation over the entire cross-section of the roller during the forming process revealed that the deflection is not confined solely to this forming region. Instead, the entire roller undergoes deformation (which is mostly elastic deformation). As illustrated in Fig. 11, the roller predominantly experiences deflection in the vertical direction, aligned with the radial direction of the rollers. This deflection prevents full contact between the two roller profiles, contributing to the gap shown in Fig. 10, and limits the maximum achievable forming depth.

[picture]

Fig. 11. Schematic illustration of the gap condition between the two embossing rollers during the forming stage.

Fig. 11. Schematic illustration of the gap condition between the two embossing rollers during the forming stage.

Another issue is the curved shape of the formed cross-section. One reason for this curvature is that the channel does not reach the designed maximum depth, as shown in Fig. 10 and 11. A second contributing factor is the local deflection of the roller during forming, which results in the deformed shape of the roller profiles deviating from the ideal profile shape. Fig. 12 shows the FEA prediction of the two-dimensional profiles for the centre corrugation of the forming roller surfaces at the point where the sheet metal is being formed in the tool gap (for Case A). The black line represents the designed (ideal) roller profile. The results show deflection at the corner radius of the corrugation due to the forming forces, which leads to curvature in the formed channel profile. For this case, the maximum deviation between the ideal and the deformed roller shape is approximately 0.04 mm at the roller corners.

[picture]

Fig. 12. Cross-section profile of a) top rollers, and b) bottom rollers during the forming stage (for Case A, single-stage forming condition).

Fig. 12. Cross-section profile of a) top rollers, and b) bottom rollers during the forming stage (for Case A, single-stage forming condition).

Multi-stage forming. A multi-stage forming approach was then applied to try to increase the achievable forming depth, by attempting to reduce the elastic deflection of the entire roller. Instead of a single forming pass, the channels were formed in three stages with target depths of 0.15 mm , 0.30 mm , and 0.50 mm , as shown in Fig. 4(b). In all stages, ABS inserts were used as the forming tools (i.e. Case B in Table 2). This approach led to a reduced roller gap by approximately 17% during forming at the last stage where the target depth is 0.5 mm , as illustrated in Fig. 13(a). Comparison of the effect of the multi-stage forming process is shown in Fig. 13(b). As demonstrated, the forming depth increases from 0.25 mm to 0.30 mm , representing an improvement of approximately 25%.

[picture]

Fig. 13. a) FEA prediction showing a reduction in the tool gap between the top and bottom roller surfaces during the last stage of multi-stage forming (Case B). b) Comparison of the cross-section profile of the formed part with the ideal shape for single and multi-stage forming (experimental results for Cases A and B).

Fig. 13. a) FEA prediction showing a reduction in the tool gap between the top and bottom roller surfaces during the last stage of multi-stage forming (Case B). b) Comparison of the cross-section profile of the formed part with the ideal shape for single and multi-stage forming (experimental results for Cases A and B).

In multi-stage forming, the maximum required forming force is distributed over multiple stages, thereby reducing the stresses that must be transferred by the material. As shown in Fig. 15, this multistage forming approach reduces stress concentrations at both the top and bottom rollers. This results
in lower deflection at the corner radii from 0.04 mm (shown in Fig. 12) to 0.03 mm in Fig. 14. Although the reduction in local corner deflection is relatively small, the dominant contribution to the increased forming depth arises from the reduction in global roller deflection, which directly decreases the effective tool gap during multi-stage forming.

The reduction in global roller deflection (Fig. 14 (a) & (b)) leads not only to a smaller effective roller gap (as shown in Fig. 13 (a)), but also to a reduction in local stress concentrations at the channel corners of the rollers (as observed in Fig. 15 (c) & (d)). Consequently, the combined reduction in global tool deflection and local corner stresses enables greater achievable forming depth compared with the single-stage case shown in Fig. 13 (b).

[picture]

Fig. 14. FEA prediction showing a reduction in corner radius deflection in Case B compared with Case A for a) top roller and b) bottom roller.

Fig. 14. FEA prediction showing a reduction in corner radius deflection in Case B compared with Case A for a) top roller and b) bottom roller.

(a)

(b)

[picture]

Fig. 15. Von Mises stress distribution [units: MPa] in the forming rollers during a) & c) singlestage forming (Case A), and b) & d) multi-stage forming (Case B), illustrating the reduction in stress concentration at the rollers and the channel corners when deformation is distributed over multiple stages using ABS rollers.

Fig. 15. Von Mises stress distribution [units: MPa] in the forming rollers during a) & c) singlestage forming (Case A), and b) & d) multi-stage forming (Case B), illustrating the reduction in stress concentration at the rollers and the channel corners when deformation is distributed over multiple stages using ABS rollers.

Multi-stage forming with Rigid 10k resin in the final stage. After demonstrating that multistage roller embossing increases forming depth, a further study case was conducted in which the multi-stage process was repeated with one key difference: in the final forming stage, a Rigid 10k resin insert was used instead of ABS. The aim was to form channels with tighter corner radii and a flatter bottom surface, due to the higher stiffness of the Rigid 10k material. In this approach, the first two stages acted as pre-forming steps, while the final stage employed a stiffer tool (i.e. Case C in Table 2 ). The higher stiffness reduced local channel deflection, resulting in a 13% increase in forming depth to approximately 0.34 mm as shown in Fig. 16. However, deflection of the main roller, which was manufactured from ABS, still limited the ability to reach the maximum target depth. In multi-stage forming processes, the creation of pre-shapes increases tool contact during the early forming stages and thereby enhances the maximum transferable stress. This is typically followed by a final forming step in which tight corner radii are produced under lower forming forces. As a result, material is more effectively redistributed during the process, leading to an increased forming depth [22,23].

The achieved forming depth of 0.34 mm corresponds to approximately 68% of the target profile depth and exceeds the depths reported in previous studies [5] that used steel tools to form the same channel geometry. The 0.34 mm forming depth results in a maximum aspect ratio of 0.314 and also corresponds to much flatter geometry in the channel profiles at the top and bottom surfaces (see Fig. 16).

[picture]

Fig. 16. Comparison of the cross-section profile of the formed part with the ideal shape for single and multi-stage forming (experimental results).

Fig. 16. Comparison of the cross-section profile of the formed part with the ideal shape for single and multi-stage forming (experimental results).

To evaluate repeatability and channel-to-channel consistency, depth measurements were performed for channels 1−4 in the multi-stage forming cases. The FEA results are shown in Fig. 17. The variation across channels is small for both Case B and Case C, indicating uniform deformation across the plate width. The calculated standard deviation across channels was ±0.0205 mm for Case B and ±0.005 mm for Case C, confirming good geometric consistency.

[picture]

Fig. 17. Channel-to-channel depth distribution for multi-stage forming using ABS inserts (Case B) and hybrid ABS + Rigid 10K resin tooling (Case C). Error bars represent the standard deviation calculated across channels 1−4 for each case.

Fig. 17. Channel-to-channel depth distribution for multi-stage forming using ABS inserts (Case B) and hybrid ABS + Rigid 10K resin tooling (Case C). Error bars represent the standard deviation calculated across channels 1 − 4 for each case.

Table 3 summarises the achieved channel depths and corresponding improvements for the different forming strategies investigated in this study. The results clearly show a progressive increase in forming depth from single-stage forming to multi-stage forming with ABS tooling, and a further improvement when a stiffer resin insert is used in the final stage. This comparison highlights the individual contributions of multi-stage forming and tooling stiffness to improving channel depth. The forming force results in Table 3 further clarify the underlying mechanisms governing channel formation. For ABS tooling, the transition from single-stage to multi-stage forming leads to a reduction in the maximum forming force at the final stage, as the total deformation is distributed over multiple steps and the effective contact stresses are reduced. In contrast, when a stiffer resin insert is employed in the final stage (Case C), the maximum forming force increases despite the improved channel depth. This increase is attributed to the formation of a flatter channel bottom and sharper corner radii, which enhance contact between the sheet and the tool and require higher local forming forces. Nevertheless, the increased stiffness of the resin tool limits tool deflection, allowing the higher forming force to be effectively transferred into material deformation.

Although the use of a stiffer insert improves forming depth, the maximum achievable depth remains limited by global compliance of the roller-shaft assembly. Elastic deflection of the roller body and shafts increases the effective tool gap under load, thereby restricting further depth increase. Future optimisation should therefore focus on stiffening the complete load path, including shafts, roller bodies.

Table 3. Summary of forming depth improvements for different forming strategies

Case | Forming strategy | Tooling configuration | Achieved depth (mm) (average) | Percentage of target depth (0.50 mm) | Relative improvement in forming depth | Maximum forming force at final stage (N)
A | Single-stage forming | ABS inserts | 0.25 | ~50% | Baseline | 1921
B | Multi-stage forming (3 stages) | ABS inserts (all 3 stages) | 0.30 | ~60% | 25% increase vs. Case A | 1610
C | Multi-stage forming (3 stages) | ABS inserts + rigid 10k resin (final stage) | 0.35 | ~68% | 13% increase vs. Case B | 2665

The results obtained using the Rigid 10 K resin insert in the final forming stage suggest that a hybrid tooling strategy may provide further performance improvements. Extending this concept, a hybrid configuration combining polymer-based pre-forming stages with a final metallic finishing pass could further minimise global tool deflection while preserving the flexibility and cost advantages of additively manufactured tools. In such an approach, the polymer tools would be used to generate intermediate channel geometries under reduced load, and a high-stiffness metallic insert in the final stage would ensure accurate corner radii and target depth. This strategy could be particularly attractive for low-volume production or prototyping, where rapid tool iteration is required but final dimensional accuracy remains critical.

Conclusions

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

A multi-stage micro roller embossing process, relevant to fuel cell bipolar plates, using 3D-printed plastic tools was studied. A FEA model was developed and validated by experimental results and applied to investigate the effect of multi-stage forming on forming depth, and hence aspect ratio. This study demonstrates the feasibility of multi-stage micro-roller embossing of metallic bipolar plate channels using additively manufactured polymer tooling. The results highlight that accurate channel formation requires explicit consideration of tool compliance when applying 3D-printed tools to micro-scale forming processes.

It is possible to use 3D-printed plastic prototype tools for roller embossing microchannel profiles produced from 0.1 mm stainless steel foil. With the initial tool design, the designed channel profile depth was not achieved. This was due to excessive tool deflection, which led to an oversized tool gap between the forming rollers. Using the multi-stage forming, the tooling deflection was reduced. This led to an increase in the achievable channel depth of 25%. In the next step, using tools with higher stiffness in the final stage of forming resulted in a 13% increase in forming depth and improved flatness of the bottom surfaces of the channel profiles.

These findings highlight the importance of accounting for tool compliance in the design of additively manufactured tooling via the simulation of the roller embossing process. To further improve the profile shapes formed, local deflection of the rollers must be accounted for and/or material solutions developed to overcome this deformation.

The observed benefits of increased tool stiffness in the final stage indicate that hybrid tooling strategies, combining compliant polymer pre-forming with a high-stiffness metallic finishing pass, represent a promising direction for future work. Such an approach may enable further increases in achievable channel depth while maintaining cost-effective and flexible tooling solutions.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.191.pdf

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Reuther, F., Dix, M., Kräusel, V., Psyk, V., & Porstmann, S., Model validation of hollow embossing rolling for bipolar plate forming, Int. J. Mater. Form. 17 (2024) 17.

Z. Xu, Z. Li, R. Zhang, T. Jiang, L. Peng, Fabrication of micro channels for titanium PEMFC bipolar plates by multistage forming process, Int. J. Hydrogen Energy 46 (2021) 11092-11103.

Q. Zhong, R. Hua, C. Wang, L. Cheng, Z. Ma, H. He, F. Chen, Investigation on three-stage stamping of micro-channels with titanium ultra-thin sheet used for PEM fuel cell bipolar plates, Int. J. Adv. Manuf. Technol. 127 (2023) 1377-1389.

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Information on .

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A. Bhattacharjee, T. Loghmani, S. Anwar, Finite element simulation and analysis of drop tests to improve the mechanical design of a handheld QSTM medical device, Proc. ASME Int. Mech. Eng. Congr. Expo. (2022) ASME.

Y. Xu, L. Peng, P. Yi, X. Lai, Analysis of the flow distribution for thin stamped bipolar plates with tapered channel shape, Int. J. Hydrogen Energy 41 (2016) 5084-5095.

A. Essa, B. Abeyrathna, B. Rolfe, M. Weiss, Incremental shape rolling of a variable depth profile, J. Mater. Process. Technol. 316 (2023) 117964.

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This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 207-215

doi: 10.4028/p-kh92Rm

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-18

Accepted:
2026-02-24

Online:
2026-04-16

Experimental and Numerical Investigation of AA6061 Tube Flowformability

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

Katia Mocellin 1,a*, Nagasai Meghana Rani Kauta 1, b and Pierre-Olivier Bouchard 1,c

¹Mines Paris, Université PSL, Centre de Mise en Forme des Matériaux (CEMEF), UMR CNRS, 06904 Sophia Antipolis, France

a*katia.mocellin@minesparis.psl.eu, b  meghanakns@gmail.com, c  pierre-olivier.bouchard@minesparis.psl.eu

Keywords: flowforming, tube flowformability, AA6061, finite element simulation.

Abstract

This study introduces a novel flowformability test aimed at replicating the complex loading conditions of industrial flowforming processes-alternating stress triaxiality, large plastic strains, and high strain rates. A novel Conical Flowformability Test (CFT) configuration was selected for experimental validation due to its ability to achieve a high theoretical thickness reduction while respecting machine constraints. Experiments conducted on AA6061 in O-temper and W+3h states demonstrated substantial thickness reductions. Comparison between the numerical simulations using the software FORGE® and the experimental results is satisfactory despite certain unquantifiable experimental defects such as fish scales and material build-up. The current study paves way to establish a robust framework for assessing material flowformability and damage evolution under realistic process conditions.

1. Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

Flowforming is a near-net-shape manufacturing process widely used for producing high-performance tubular and conical components in aerospace, defense, and energy sectors. Its major advantage lies in achieving large plastic strains under controlled incremental deformation, resulting in superior mechanical properties and dimensional accuracy [1]. However, the process imposes highly complex loading paths characterized by alternating positive and negative stress triaxiality, very high strain rates, and severe plastic deformation [2]. These conditions complicate damage prediction, as conventional material characterization tests-such as tensile, compression, or torsion tests-are unable to replicate the incremental and non-proportional loading inherent in flow forming; moreover, these tests tend to predict final fracture at plastic strain levels significantly lower than those typically attained during flowforming.

Several mechanical tests have been proposed in the literature to evaluate ductile fracture under conditions approaching those encountered in flow forming. Common approaches include conventional tensile tests [3], in-plane torsion tests [4], and TELE test [5], which aim to correlate fracture strain with stress state parameters such as triaxiality and Lode angle. While the conventional tests provide valuable insights for monotonic or proportional loading, they fall short in reproducing the cyclic stress state and alternating triaxiality observed in flowforming. On the other hand, in-plane torsion tests reproduce very large strains and cyclic loading while lacking to produce non-proportional alternate tensile - compressive loading.

To address these limitations, a dedicated damage test is required - one that can mimic the essential features of flowforming:

Alternating stress triaxiality (compressive under roller contact, tensile during material flow),

Large plastic strain accumulation over multiple tool passes, and

High strain rates induced by combined rotation and axial feed.

Such a test should also provide a measurable experimental observable-typically the final thickness at fracture-linked to flowformability or spinnability as discussed in [6], [7]. This observable serves as a practical indicator for process design and material selection.

In this context, the present work introduces a novel Conical Flowformability Test (CFT), specifically designed to replicate flowforming conditions under laboratory constraints. Unlike conventional tube flowformability tests, which require radial roller motion, the CFT adapts to the axial-only roller movement of the laboratory FluoTi device by modifying the preform and mandrel geometry. This configuration enables high thickness reduction ratios (up to 80% ) while respecting machine limitations, thereby providing a robust platform for experimental damage characterization and numerical validation. The following sections detail the experimental setup, modelling approach, and hybrid methodology adopted to evaluate flowformability and identify critical damage thresholds.

2. Methodology

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

2.1 Conceptual Design

The laboratory Fluoti test device (see Fig. 1) has certain limitations with respect to flowformability testing. Conical Flowformability Test (see Fig. 2) was selected because it can reach high thickness reductions ( TR ) up to 80% while remaining compatible with these limitations. Flowformability (TRmax) which is the maximum thickness reduction that can be obtained before failure of the specimen, can be mathematically defined as seen in Eq. 1, where e0 and ef are the initial and final specimen thickness respectively.

TRmax=e0−efe0×100(1)

[picture]

Fig. 1. FluoTi machine set up (a) Experimental, (b) Schematic representation.

Fig. 1. FluoTi machine set up (a) Experimental, (b) Schematic representation.

[picture]

Fig. 2. Schematic representation of CFT in its initial (left) and final (right) stages.

Fig. 2. Schematic representation of CFT in its initial (left) and final (right) stages.

2.2 Experimental Setup

The conical preform is mounted on the cylindrical mandrel and fixed in position using sockets. The rollers are then adjusted so that their tips are positioned at the desired positions as shown in Fig.3. Distances between the tips of the three rollers are dbc=3.44 mm and dac=6.44 mm. The reference
roller chosen for the experiments is Roller A. It is adjusted axially such that the tip of the roller aligns with the starting point. The other two rollers are adjusted according to the distance indicated in Table 1.

[picture]

Fig. 3. Illustration of axial distance between rollers (left) and roller tip point (right).

Fig. 3. Illustration of axial distance between rollers (left) and roller tip point (right).

Mandrel rotational speed was set to 205 rpm and roller feed ratios varied between 0.1 and 0.3 mm/tr. Further, the test is performed on two material states of the preform - AA6061 alloy in O-temper (mat-O) and solution-treated and 3 hour-aged state (mat-W+3h). The true stress-strain curves of these two states have been evaluated from force-displacement curves obtained using simple compression tests. This material testing methodology is presented in detail in [8].

At the end of each experiment, thickness profiles, roller forces and torque were measured and failure locations were identified visually.

2.3 Numerical Modelling

Simulations were performed in FORGE® NxT 3.1 using a Classic Lagrangian formulation. To reduce CPU time, the preform geometry consists of a 90∘ symmetrical geometry configuration. A comparative simulation study between 90∘,120∘ and 360∘ symmetry geometry configurations is made in [9] and shows that symmetry planes can be introduced to significantly reduce CPU time. The material behaviour law parameters used in the simulation studied in this section are based on the Johnson-Cook (J-C) phenomenological material behaviour law given by Eq. 2. The identified J-C law parameters for mat- W+3 h specimen are given in Table-1. During the process, self-heating in the deformed part is considered by means of the thermomechanical material behaviour law. In addition, the friction law used is given in Eq. 3 with the friction law parameters of m¯=0.4 and μ=0.2. The experiment is carried out at ambient temperature conditions. Important simulation outputs include thickness evolution, roller forces and local damage metrics.

σ=[σ0+Kε¯n][1+Clnε¯˙ε¯˙0][1−(T−T0Tm−T0)m](2)

Where σ is the equivalent stress, σ0 corresponds to yield stress, ε¯ and ε¯˙ are respectively the plastic strain and strain rate, T the temperature, ε¯˙0 and T0 are respectively a reference (or base) temperature and a reference strain rate. Tm is the material melting temperature. C is an experimentally determined parameter considering the strain rate effect, n is the strain-hardening exponent, m is a strain rate sensitivity and K is a parameter determined experimentally.

Table 1. Johnson Cook law parameters for mat-W+3h state.

σ₀ [MPa] | K [MPa] | n | C | m
65.58 | 261.5 | 0.27 | 7.10⁻⁴ | 1.09

τfr=min(μσn;−m¯σ03)(3)

A two-tier mesh is used as part of the conical flowformability simulations as seen in [9]. The preform is meshed with two different mesh sizes of respectively 1.25 - and 3−mm. Mesh zone 1 contains more refined elements as this part of the preform is directly in contact with the rollers. The mesh size of 1.25 mm is chosen based on a preliminary convergency study.

Due to very high strain magnitudes observed during the simulation, mesh elements can degenerate. Remeshing takes place at such points to avoid such mesh degeneration. At least 4 elements in the part thickness below the roller is maintained throughout the process.

The time step, Δt chosen for the simulations is based on the condition that the distance travelled by the roller at the given rotational velocity, ωM during the time step Δt does not exceed the length of the mesh element in the orthoradial direction, eθ. The expression is given in Eq. 4.

Δt<eθωM(4)

The simulations are run on 12 CPUs of a calculation computer 1. For the given numerical and process parameters, the computation time taken for each simulation case is nearly 40 h .

3. Results

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

3.1 Experimental Observations

Maximum thickness reduction before fracture was achieved approximately 78% for mat-O and 68% for mat-W+3h. Failure modes included pile-up and macro-cracking (mat-O) and fish-scale defects with macro-cracks near Roller C (mat-W+3h) as can be seen in Fig. 4.

[picture]

Fig. 4. Deformed parts at the end of CFT experiments on (a) mat-W +3 h and (b) mat-O specimens.

Fig. 4. Deformed parts at the end of CFT experiments on (a) mat-W +3 h and (b) mat-O specimens.

[picture]

Fig. 5. Evolution of material pile-up at the three specific stages- 1 (initial), 2 (intermediate), 3 (final) for Mat-O. Blue double arrow represents the distance from the reference roller to the fixed end of the part; Red arrow, the displacement vector of the roller during the process.

Fig. 5. Evolution of material pile-up at the three specific stages- 1 (initial), 2 (intermediate), 3 (final) for Mat-O. Blue double arrow represents the distance from the reference roller to the fixed end of the part; Red arrow, the displacement vector of the roller during the process.

Failure on the specimens can be tracked through a combination of visual inspection of the specimens and the force-displacement curves. Three stages during the conical flowformability test are shown in Fig. 5 corresponding to the respective points indicated in the force-displacement curves
in Fig. 6. The initial stage of the experiment is characterized by the near linear force-displacement experimental curve. The intermediate stage of the experiment is where the slope of the forcedisplacement curve increases, and the pile-up begins on the material specimen. In the final stage of the experiment, cracks are observed on the surface of specimens in both material states.

[picture]

Fig. 6. Comparison of (left) radial and (right) axial roller forces obtained in the experiments on two material states, mat-O and mat-W+3h.

Fig. 6. Comparison of (left) radial and (right) axial roller forces obtained in the experiments on two material states, mat-O and mat-W+3h.

Mat-O being much softer than mat-W+3h, the formation of the pile-up is facilitated. This pile-up forms a collar whose diameter becomes high enough to enter in the planar vertical area of rollers as can be seen in Fig. 4 (a). This may explain the higher axial force observed for this mat-O in Fig. 6. It is indeed difficult to flow-form softer materials and rollers geometries need to be adapted accordingly. In the end, and despite the small cracks observed in the collar pile-up, final thickness reduction is higher for mat-O than for mat-W+3h, meaning higher flowformability.

3.2 Simulation vs Experiment

A material build-up is observed during the experiment as seen in Fig. 7. There is a deviation in the radial positions of the roller tips due to the material-build up in the final stage of the experiment. This difference in the radial positions of the roller tip point is evaluated between the initial and final stages of each experiment case as seen in Fig. 8. To consider this deviation, in the simulation, a linear roller trajectory in the axial direction is assumed between the experimentally measured initial and the final positions of the roller tip positions.

[picture]

Fig. 7. Mat-O CFT specimen at (a) initial, (b) intermediate and (c) final stages of the conical flowformability experiment. In (d), experimental thickness measurements along part length at intermediate stage (upper) and at final stage (lower).

Fig. 7. Mat-O CFT specimen at (a) initial, (b) intermediate and (c) final stages of the conical flowformability experiment. In (d), experimental thickness measurements along part length at intermediate stage (upper) and at final stage (lower).

(d)

[picture]

Fig. 8. Illustration of the deviation in radial tip positions of rollers A and B from C at the end of the experiment. The blue zone is the illustration of cracked zone with respect to the experiment. The dashed red line is the trajectory designed for all three rollers with their initial positions presented at the start end of the line. In the inset figure, the location of the fractured zone and final position of Roller C (in blue) are indicated with respect to the whole geometry.

Fig. 8. Illustration of the deviation in radial tip positions of rollers A and B from C at the end of the experiment. The blue zone is the illustration of cracked zone with respect to the experiment. The dashed red line is the trajectory designed for all three rollers with their initial positions presented at the start end of the line. In the inset figure, the location of the fractured zone and final position of Roller C (in blue) are indicated with respect to the whole geometry.

The radial and axial force-displacement curves are compared between simulation and experiment for mat-W +3 h specimen in Fig. 9. Axial roller displacement, dZ and distance from fixed end, ΔZ′ are presented on the top and the bottom horizontal axes respectively. They correspond to the axial distance covered by the rollers with respect to the starting point as shown in Fig. 7. Here, both the radial and axial forces on Roller A are perfectly represented by the force curves from simulation until dZ=30 mm. Further, points 1 and 2 on the experimental curve correspond to the points at which the axial roller displacement magnitudes are equal to dz=60 mm and dz=75 mm respectively. At point 1, the radial force is underestimated by 5.25 kN which represents an error of approximately 32%. At the same point, the axial force is underestimated marginally by 0.29 kN with respect to the experiment.

[picture]

Fig. 9. Comparison of (left) axial and (right) radial Roller A forces in simulation (Sim. II) with experimental values. Point 1 and Point 2 correspond to the intermediate and the end stages of experiment on mat- W+3 h specimen.

Fig. 9. Comparison of (left) axial and (right) radial Roller A forces in simulation (Sim. II) with experimental values. Point 1 and Point 2 correspond to the intermediate and the end stages of experiment on mat- W + 3 h specimen.

The part profiles and thickness distribution along their length at these points are compared in Fig. 10. The thickness under Roller A corresponds well with the experimental value at point 1. But at point 2, the thickness under Roller A is overestimated by 0.4 mm in the simulation which is equal to about 12% error with respect to the average value of the experiment. However, this value is within the error range of 0.5 mm calculated based on experimental measurements. As a reminder, despite the horizontal roller trajectory, the experimental thickness measurements decrease with increase in the axial roller displacement, dz due to the conical mandrel geometry.

[picture]

Fig. 10. In (1a) -(lb), Deformed part profile at initial and at dz=60 mm obtained from simulation (upper). Comparison of thickness in CFT-int experiment and during simulation at dz= 60 mm along part length (lower). In (2a) -(2b), preform profile at initial and at dz=75 mm obtained from simulation (upper). Comparison of thickness in CFT-int experiment and during simulation at dz=75 mm along the part length (lower).

Fig. 10. In (1a) -(lb), Deformed part profile at initial and at d z = 60 m m obtained from simulation (upper). Comparison of thickness in CFT-int experiment and during simulation at d z = 60 mm along part length (lower). In (2a) -(2b), preform profile at initial and at d z = 75 m m obtained from simulation (upper). Comparison of thickness in CFT-int experiment and during simulation at d z = 75 m m along the part length (lower).

Thickness profiles were predicted accurately in regions dominated by Roller A. Discrepancies in roller force magnitudes are attributed to machine stiffness and friction parameter uncertainties. In addition, a better understanding of phenomena such as fish-scale formation and material build-up is required. Further research on material behavior testing and identification methodologies, capable of accounting for very large strains and strain rates, would help improve these predictions. The flowformability magnitude evaluated for the two material states at the two different stages of the test is presented in Fig. 11.

[picture]

Fig. 11. Comparison of theoretical, experimental and prediction of simulation of TRmax (red) and final part thickness at fracture, efrup  (black).

Fig. 11. Comparison of theoretical, experimental and prediction of simulation of T R max (red) and final part thickness at fracture, e f rup (black).

4. Discussion and Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

The proposed novel Conical Flowformability Test (CFT) demonstrates its capability to reproduce the alternating stress states and significant strain accumulation characteristic of flowforming, while remaining compatible with the laboratory FluoTi experimental device capabilities. The hybrid experimental-numerical flowformability testing helps in providing a robust framework for damage evaluation under realistic process conditions in the future. Nevertheless, the study acknowledges limitations related to machine stiffness characterization, friction law calibration, and the accuracy of predicted roller trajectories, which influence the reliability of force and thickness predictions. Furthermore, phenomena such as fish scale formation and material build-up, observed experimentally, require deeper investigation to enhance predictive accuracy. Despite these limitations, the proposed approach constitutes a significant advancement in reliable flowformability testing assessment and sets a strong foundation for a future study on ductile fracture characterization, offering a foundation for future research aimed at refining damage models and improving process simulations across a broader range of kinematic configurations.
Future work on flowformability testing should focus on:

Quantifying machine frame stiffness and integrating its effect into simulation models to improve roller force prediction.

Developing advanced friction calibration procedures for more accurate representation of contact conditions.

Investigating surface phenomena such as fish scales and material pile-up through dedicated experimental and numerical studies.

Applying the methodology to ductile damage models and multi-parameter fracture criteria for enhanced predictive capability.

Validating the approach across different geometries and material states to ensure applicability to industrial flowforming processes.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

This work was carried out at CEMEF, Mines Paris - PSL, as part of the FluoFAB project funded by BPI France.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.207.pdf

Wong, C. C., Dean, T. A., & Lin, J. (2003). A review of spinning, shear forming and flow forming processes. International Journal of Machine Tools and Manufacture, 43(14), 14191435. https://doi.org/10.1016/S0890-6955(03)00172-X.

Roula, A. M., Mocellin, K., Traphöner, H., Tekkaya, A. E., & Bouchard, P. O. (2022). Influence of mechanical characterization on the prediction of necking issues during sheet flow forming process. Journal of Materials Processing Technology, 306. .

Xu, W., Wu, H., Ma, H., & Shan, D. (2018). Damage evolution and ductile fracture prediction during tube spinning of titanium alloy. International Journal of Mechanical Sciences, 135, 226239. .

Yin, Q., Soyarslan, C., Isik, K., & Tekkaya, A. E. (2015). A grooved in-plane torsion test for the investigation of shear fracture in sheet materials. International Journal of Solids and Structures, 66, 121-132. .

Bourgeon, L. (2009). Etude et modélisation des mécanismes d'endommagement en forge à froid [Doctoral dissertation, Ecole Nationale Supérieure des Mines de Paris]. .

Ma, H., Xu, W., Jin, B. C., Shan, D., & Nutt, S. R. (2015b). Damage evaluation in tube spinnability test with ductile fracture criteria. International Journal of Mechanical Sciences, 100, 99-111. .

Bylya, O. I., Khismatullin, T., Blackwell, P., & Vasin, R. A. (2018). The effect of elasto-plastic properties of materials on their formability by flow forming. Journal of Materials Processing Technology, 252, 34-44. .

Kauta, N. (2024). Analysis and modelling of flowformability through a hybrid experimentalnumerical approach. [Doctoral dissertation, Ecole Nationale Supérieure des Mines de Paris]. .

Kauta, N. M. R., Bouchard, P.-O., & Mocellin, K. (2022). Relevance of Symmetry Assumptions in the 3D Numerical Modeling of a Flowformability Test. Key Engineering Materials, 926, 776-783. .

Tekkaya, A. E., Bouchard, P.-O., Bruschi, S., & Tasan, C. C. (2020). Damage in metal forming. CIRP Annals, 69(2), 600-623. .

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 217-225

doi: 10.4028/p-cl9cUk

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-16

Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

Bernd-Arno Behrens 1,a, Sven Hübner 1, b, Ulrich Holländer 2,c, André Langohr 2, d, Alexander Schnettger 2,e, Henrik Depke 1,f and Lorenz Albracht 1, g*

1 Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

2 Leibniz University Hannover, Institute of Materials Science, An der Universität 2, 30823 Garbsen, Germany

abehrens @ifum.uni−hannover.de,b huebner@ifum.uni−hannover.de,c  hollaender@iw.uni-hannover.de, d  langohr@iw.uni-hannover.de, e  schnettger@iw.uni-hannover.de, f  depke@ifum.uni-hannover.de, g  albracht@ifum.uni-hannover.de

Keywords: resistance heating; hot stamping; coating

Abstract

Hot stamping of manganese-boron steels is widely used in automotive manufacturing to produce ultra-high-strength components with tensile strengths exceeding 1500MPa[1,2]. Conventional industrial heating relies on gas-fired roller hearth furnaces, which require 5-10 min to reach austenitization and exhibit low energy efficiency [3,4]. Resistance heating offers a compact and energy-efficient alternative, enabling heating rates above 100 K/s and full austenitization within seconds. However, rapid heating of uncoated steels leads to severe oxidation, and established coating systems such as AlSi are not designed for diffusion-controlled bonding within such short times [5]. This study demonstrates that resistance heating in an XHV-adequate atmosphere - consisting of nitrogen and monosilane - suppresses oxidation while simultaneously enabling adhesion of a prelaminated aluminum foil to the steel substrate. For coating preparation, 22 MnB 5 sheets were roughened by corundum blasting, cleaned, and laminated with an aluminum foil using a flat-die pressing tool. The pre-coated blanks were heated in a self-developed resistance-heating chamber, in which the oxygen concentration was reduced to an XHV-adequate level. Several heating profiles were investigated to determine suitable process windows for coating formation. The results show that resistance heating achieves austenitization within a few seconds, reducing heating times by more than an order of magnitude compared to furnace heating. The XHV-adequate atmosphere reliably prevents scale formation, enabling completely oxidation-free surfaces during rapid heating. Under these conditions, the laminated aluminum foil bonds uniformly to the substrate, forming a continuous coating layer. Metallographic cross-sections and SEM analyses confirm the formation of Al−Fe intermetallic phases at the interface, demonstrating robust metallurgical bonding suitable for subsequent hot stamping operations. Overall, the combination of resistance rapid heating and an XHV-adequate atmosphere provides a highly energy-efficient process route for hot stamping while offering an opportunity to integrate aluminum-based protective coatings directly into the heating step. This approach addresses the limitations of current furnace-based heating and coating technologies and opens a promising pathway toward more flexible, sustainable, and functionally integrated hotstamping process chains.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

Hot stamping has become one of the most important manufacturing routes for producing ultra-highstrength components in the automotive industry. By heating manganese-boron steels above the austenitization temperature and subsequently forming and quenching them in cooled die, tensile strengths exceeding 1.500 MPa can be achieved [2]. These properties are essential for safety-relevant structures such as A- and B-pillars, bumpers, and intrusion-resistant components. Industrial heating is typically carried out in gas-fired roller hearth furnaces, which require 5−10 min to reach the target temperature of approximately 950∘C[3,4]. The slow heating rate is primarily dictated by the AlSi
protective coating, which requires sufficient time to form diffusion-controlled intermetallic phases that prevent scale formation during heating [7]. As a consequence, furnace systems are large, energyintensive, and limit the flexibility of the overall hot-stamping process chain [8]. Resistance heating represents a highly efficient alternative, as Joule heating enables heating rates above 100 K/s and full austenitization within seconds [9]. Due to the direct power input into the material, high energy savings are achievable, and the compact design of the equipment significantly reduces required installation space [10]. However, the extreme heating rates pose a substantial challenge to conventional coating systems. The diffusion time required for AlSi coatings to bond with the substrate is not available during rapid resistance heating, while uncoated steels suffer from severe oxidation, leading to surface degradation and reduced mechanical performance. A promising solution is the use of an oxygen-free process atmosphere. By employing a nitrogen-monosilane gas mixture, the oxygen concentration in the heating chamber can be reduced to levels equivalent to an extreme high vacuum (XHV), preventing the formation of scale even during rapid heating. At the same time, this environment opens the possibility of applying alternative coating systems that can bond within seconds [11]. In this study, we investigate the feasibility of combining resistance rapid heating with an XHV-adequate atmosphere to enable scale-free austenitization and simultaneous bonding of a mechanically prelaminated aluminum foil to 22 MnB 5 steel. The resulting process route aims to combine high energy efficiency, compact equipment layout, and integrated surface functionalization, thereby addressing key limitations of conventional hot-stamping technology.

Materials and Methods

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The experimental investigations were carried out using a resistance heating system specifically developed to enable rapid austenitization of manganese-boron steel sheets under XHV-adequate conditions. Shown in fig. 1 the core of the setup is a sealed high-temperature process chamber manufactured from stainless steel, in which the sheet is positioned such that the active heating zone lies fully inside the controlled atmosphere. Quartz-glass observation windows allow optical access as well as pyrometric temperature measurement, while an exhaust and sampling port positioned above the sheet continuously supplies gas to an external lambda probe for oxygen monitoring. Heating is achieved by direct current flow through the sheet, which is clamped between two water-cooled copper electrodes. The left electrode is fixed, whereas the right electrode is mounted on a motorised ballscrew spindle. This enables continuous compensation for thermal expansion during heating, ensures a stable and planar sheet position, and allows defined plastic stretching to be introduced during selected experiments. The electrical power is supplied through a water-cooled thyristor unit and a high-current transformer that reduces the mains voltage to approximately 30 V , enabling currents of several tens of kiloamperes. These conditions allow heating rates exceeding 100 K/s and peak temperatures of 950−1050∘C within only a few seconds.
To generate an XHV-adequate environment, the system is equipped with a dedicated gas management unit capable of metering nitrogen and controlled amounts of silane. The atmosphere is established through a two-step process. First, nitrogen ( N25.0 ) is introduced at a high flow rate to displace the ambient atmosphere inside the chamber. Within 60−120 s, this purge reduces the oxygen concentration to below 10−3 vol. %. Subsequently, a nitrogen-silane mixture containing approximately 100 ppm SiH 4 is fed into the chamber. Monosilane reacts spontaneously and selectively with residual oxygen according to the reaction SiH4+2O2→SiO2+2H2O, thereby chemically binding the oxygen in the form of solid silica particles and water vapour. In a second, temperature-triggered reaction step, the resulting H2O is further converted by silane into H2, again forming inert SiO2[12,13]. This reaction mechanism enables a further reduction of the initial oxygen concentration to −10−15vol.%, equivalent to the conditions of an extreme high vacuum (XHV) without the need for mechanical vacuum generation. As the reaction rate increases with temperature, the oxygen content continues to decrease during the subsequent heating stage. Once XHV-adequate conditions are reached, resistance heating is initiated. The sheet was heated to 950∘C within 12 s . Subsequently, the temperature was maintained for an additional 30 s in order to reduce temperature gradients and promote a more homogeneous temperature distribution within the sheet. The XHV-
adequate atmosphere suppresses any formation of oxide scale, even at temperatures exceeding 1000∘C, enabling metallurgical surface reactions to proceed without interference from oxidation. These conditions also allow the integration of coating processes directly into the heating step. Two coating strategies were investigated. In the first approach, nickel-based brazing powders (alloys Ni700, Ni710 and Ni720) were applied to the sheet surface. Their melting ranges between 875∘C and 950∘C make them suitable for rapid bonding during short holding times [14].

[picture]

Fig. 1. Resistance heating device with XHV-adequate atmosphere

Fig. 1. Resistance heating device with XHV-adequate atmosphere

The investigations were carried out using an uncoated manganese-boron steel of grade 22 MnB , which was provided by Salzgitter Mannesmann Forschung with a nominal thickness of 1.5 mm . The chemical composition of the steel corresponds to the typical specification of 22 MnB 5 and is summarized in tab. 1. It is characterized by a carbon content of 0.19−0.25wt.% and a manganese content of 1.10−1.40wt.%, ensuring sufficient hardenability for press-hardening applications. The boron content in the range of 0.0008−0.0050wt.% enhances the hardenability, while minor alloying elements such as silicon, chromium, aluminum and titanium are present within standard limits to stabilize the microstructure and maintain the effectiveness of boron through nitrogen fixation. The contents of phosphorus and sulfur are restricted to low levels to preserve good formability and mechanical performance. The selected material grade and sheet thickness represent an industryrelevant reference for hot stamping applications and allow direct comparison with established hot stamping processes

Table 1. Chemical composition of the investigated 22 MnB 5 steel (wt.%)

Element | Carbon | Manganese | Boron | Silicon | Phosphorus | Sulfur | Chromium | Aluminum | Titanium
Content [wt. %] | 0.19 – 0.25 | 1.10 – 1.40 | 0.0008 – 0.0050 | ≤ 0.40 | 0.025 | 0.015 | 0.15 – 0.35 | 0.020 – 0.060 | 0.020 – 0.050

A further process route is illustrated in fig. 2 and aims to investigate the feasibility of rapid heating of coatings that form intermetallic phases. For this purpose, aluminum thin foils (thickness 8−14μ m ) were applied prior to heating. The process begins with a targeted surface roughening of the steel sheet. To this end, the sheet surface was manually treated with corundum in order to increase the surface roughness and to prepare improved mechanical interlocking between the steel substrate and the aluminum foil. This step increases the effective contact area and establishes the prerequisite for a form- and force-fitting bond in the subsequent joining step. Subsequently, both the roughened steel
sheet and the aluminum thin foil were cleaned. Cleaning was carried out manually using acetone and served to remove contaminants such as abrasion debris, residual corundum particles, grease, or oil in order to ensure clean interfaces for the pressing operation. In the next process step, the prepared steel sheet and the aluminum thin foil were pressed together. The pressing operation was performed on a servo-hydraulic press of type Dunkes HDZ 400 using a flat die tool. An applied pressing force in the range of 2.000 to 3.000 kN was used. The objective of this step is to establish a uniform and reproducible contact between the aluminum foil and the steel substrate without inducing any intentional forming. The suitability of the pressing process was assessed based on visual criteria, with particular emphasis on whether the roughness structure of the previously roughened steel sheet was locally discernible through the aluminum foil after pressing. This imprinting of the surface structure was interpreted as an indicator of sufficiently high local contact pressure and effective mechanical interlocking.
The prepared specimens were subsequently heated by resistance heating. Heating was carried out in an XHV-adequate atmosphere, resulting in an extremely low oxygen activity and enabling oxidationand scale-free heating of the specimens. In particular, undesired oxidation at the interface between the steel sheet and the aluminum foil during the rapid heating phase could thus be prevented. After completion of resistance heating, the specimens were transferred under ambient air conditions. The subsequent pressing operation was again performed using a flat plate tool, without any geometric forming of the specimens. This final process step serves exclusively to ensure contact and controlled cooling of the specimens without any forming component and concludes the process chain depicted in fig. 2.

[picture]

Fig 2. Process chain hot stamping with applied aluminum foil

Fig 2. Process chain hot stamping with applied aluminum foil

The experimental matrix, shown in tab. 2, comprises a total of four pressing trials in which both the applied pressing force and the effective pressing area were systematically varied. In experiments 1 to 3, the pressing area was kept constant at 420 mm×140 mm, while the applied force was increased stepwise from 2.000 kN to 2.500 kN and finally to 3.000 kN . This resulted in surface pressures of 34.0MPa,42.5MPa, and 51.0 MPa , respectively. This series of experiments served to investigate the influence of increasing surface pressure at a constant contact area on the mechanical interlocking between the aluminum foil and the steel substrate. In experiment 4, the maximum applied force of 3.000 kN was maintained while the pressing area was reduced to 140×140 mm. As a result, the corresponding surface pressure increased significantly to 153.1 MPa . This experiment was deliberately conducted to analyze the effect of a strongly increased local surface pressure on the quality and homogeneity of the mechanical interlocking and to enable a direct comparison with the results obtained for larger pressing areas.

Table 2. Experimental matrix of the pressing trials

Test | Applied force F (kN) | Contact area (mm × mm) | Contact pressure p (MPa = N/mm²)
1 | 2.000 | 420 × 140 | 34.0
2 | 2.500 | 420 × 140 | 42.5
3 | 3.000 | 420 × 140 | 51.0
4 | 3.000 | 140 × 140 | 153.1

From the well-adhering coated sheets, cross-sections were prepared by metallographic sectioning, mounting, grinding, and polishing. The cross-sectional specimens were subsequently examined using a Zeiss SUPRA 55VP field emission scanning electron microscope (FE-SEM) equipped with an energy-dispersive X-ray spectroscopy (EDX) system. Backscattered electron (BSE) imaging was employed to resolve phase contrasts across the coating-substrate interface, and elemental line scans were recorded along defined measurement paths at constant accelerating voltage to characterize compositional gradients. Depending on the accelerating voltage and material properties, the lateral spatial resolution of the EDX measurements was approximately 1μ m, with a quantitative accuracy within a few atomic percent.

Results

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

Fig. 3 shows the results of the pressing trials with varying pressing force and pressing area. In experiments 1 to 3, it can be observed that the mechanical interlocking between the aluminum foil and the steel substrate is predominantly limited to the edge regions. The central areas exhibit large non-bonded zones, which are marked in green in the figure. These regions can lead to poor bonding, as no mechanical interlocking between the coating foil and the steel blank occurred there, preventing the formation of a metallurgical bond. With increasing pressing force from experiment 1 to experiment 3, the extent of these non-interlocked areas visibly decreases. This indicates that an increase in surface pressure generally leads to improved mechanical bonding; however, for the selected large pressing area, it is not sufficient to achieve continuous interlocking over the entire surface. The preferential bonding in the edge regions suggests locally increased surface pressures caused by edge and stiffness effects of the flat plate tool. In experiment 4, in which the pressing area was significantly reduced while the maximum pressing force was applied, a markedly different behavior is observed. The previously large non-interlocked zones are largely eliminated. Instead, only locally confined, millimeter-scale areas without interlocking remain, which are sporadically distributed within the coated region. Overall, the mechanical interlocking in experiment 4 is substantially more homogeneous than in the trials conducted with a larger pressing area. The results clearly demonstrate that local surface pressure is a dominant influencing factor for the quality of interlocking and that a reduction of the pressing area at a constant high pressing force significantly improves the areal bonding. Overall, the results show that only from test 4(153.1MPa), where a significantly increased surface pressure was applied due to the reduced pressing area, the aluminum foil was largely bonded to the steel substrate. Lower surface pressures applied in the preceding tests were insufficient to establish continuous contact, highlighting that adequate surface pressure is a key requirement for effective foil-steel bonding.

[picture]

Fig. 3. Results of the pressing trials of aluminum thin foil with a 1.5 mm thick 22 MnB 5 sheet

Fig. 3. Results of the pressing trials of aluminum thin foil with a 1.5 mm thick 22 MnB 5 sheet

The resistance-heated specimen processed in an XHV-adequate atmosphere of experiment 4 is shown in fig. 4. This figure exemplarily illustrates the results of the thin-foil coating and its analysis after resistance heating under an XHV-adequate atmosphere. In (a), a photographic image of the heated steel sheet is presented. On both lateral edge regions, zones can be identified that were not heated. These areas correspond to the contact regions where the electrodes were pressed onto the sheet during resistance heating. Between these edge zones lies the actual heated region, which is characterized by a dark blue coloration. This region represents the coated area in which the aluminum thin foil reacted during heating and formed a coating layer. The area marked in green indicates the measurement region selected for subsequent microstructural investigations. In (b), an SEM cross-section taken from this coated region is shown. It can be observed that a metallurgical bond has formed between the 22 MnB 5 substrate and the aluminum foil. However, the resulting layer exhibits pronounced porosity and appears locally not fully bonded. The intermetallic phase is not homogeneously formed over the entire area but occurs in a partially discontinuous manner, indicating an as-yet insufficient consolidation of the layer. The results of the EDS line scan shown in (c) confirm the reaction mechanism observed in the microstructure. The line profile reveals a pronounced mutual diffusion of aluminum and iron across the layer thickness. With increasing penetration depth, the aluminum content decreases while the iron content correspondingly increases, indicating the formation of an intermetallic phase in the interfacial region between the aluminum foil and the steel substrate. The layer formation was not affected by the XHV-adequate atmosphere, which is evidenced by the absence of a detectable oxygen signal in the line-scan analysis. This clearly demonstrates that, under an XHV-adequate atmosphere, an intermetallic phase forms during resistance heating. This metallurgical bonding occurs entirely within the heating interval of approximately 40 s that is already required for hot stamping and is therefore significantly faster than the established AlSi bonding process, which typically requires 6−10 min to form a load-bearing intermetallic layer. This highlights
the considerable potential of combining the coating and heating processes and substantially reducing process time. At the same time, a limitation of the current process state becomes evident. The produced layers exhibit locally incomplete bonding and appear highly porous overall. These inhomogeneities can primarily be attributed to the current surface pre-treatment of the sheets. Surface roughening is performed manually by corundum blasting, which does not ensure a reproducible and uniformly distributed surface roughness. A non-homogeneous surface topography leads to locally reduced contact areas and, consequently, to incomplete diffusion zones. Another significant influencing factor lies in the current method used to apply the aluminum foil. The foil application was carried out by sequential flat pressing rather than by a continuous pressing process. As a result, the contact between foil and substrate is established locally in discrete steps, which has a significant influence on the uniformity of the bonding conditions. The individual pressing steps remain clearly discernible on the sheet surface. This pressing operation results in inhomogeneous contact conditions, as the contact pressure varies across the surface and, in particular, local micro-scale air gaps are not reliably closed. In these regions, diffusion during heating is impeded, preventing the formation of a continuous metallurgical bond. Overall, the results demonstrate that the XHV-adequate atmosphere fundamentally enables rapid and effective intermetallic phase formation suitable for rapid resistance heating. At the same time, it becomes clear that the quality and homogeneity of the coating are strongly governed by the mechanical surface pre-treatment and the application method of the aluminum foil. With a more process-stable and reproducible surface preparation as well as a defined and uniform lamination process, a significantly more homogeneous and full-area bonding of the coating can be expected.

[picture]

Fig. 4. Results of hot stamping of 22 MnB 5 sheets with aluminum thin-foil coating

Fig. 4. Results of hot stamping of 22 MnB 5 sheets with aluminum thin-foil coating

Conclusions & Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

Within the scope of the investigations conducted, it was demonstrated for the first time that aluminum thin coatings can be successfully heated by rapid resistance heating under an XHV-adequate atmosphere and subsequently hot stamped. The results show that, during resistance heating, an intermetallic phase forms between the aluminum foil and the 22 MnB 5 substrate within the heating interval that is already required for hot stamping. This proves that the formation of a metallurgically effective coating is not limited to long-duration furnace processes, but can also be realized under the extremely short process times of rapid resistance heating. Compared to established coating systems such as AlSi furnace coatings, which typically require heating times of several minutes to form a load-bearing intermetallic layer, the approach presented here represents a significant reduction in process time.
In addition, the combination of thin aluminium foil coating and heating offers substantial potential for energy savings and reducing long heating times. Particularly in the context of the ongoing electrification of industrial processes and the increasing transition from fossil energy carriers to electrically driven systems, resistance heating represents an energy-efficient and future-oriented alternative for hot stamping.
At the same time, the investigations reveal that the current process route still exhibits limitations with regard to the homogeneity and continuity of the coating. In particular, the occurrence of locally noninterlocked areas demonstrates that the quality of the aluminum thin coating is strongly governed by the application and joining process. These regions can be interpreted as failure cases of the current process chain, since they represent local outliers from the otherwise continuous intermetallic bonding and may lead to reduced coating adhesion and locally impaired corrosion protection. Sheets with clearly missing mechanical interlocking between the aluminum foil and the steel blank correspondingly showed no metallurgical bonding. The currently employed flat pressing process results in inhomogeneous contact conditions and locally varying surface pressures, which prevents a uniform mechanical interlocking over the entire area from being achieved reliably. For future research and development, the application process of the aluminum foil should therefore be further optimized in a targeted manner. In particular, the use of a roller-based lamination process offers significant potential to apply the aluminum foil under a constant and well-defined contact pressure. Such a process can reduce local pressure fluctuations, close micro-scale air gaps, and minimize the occurrence of bonding outliers, thereby achieving a substantially more homogeneous mechanical interlocking between the foil and the substrate. In combination with XHV-adequate rapid heating, this is expected to enable a continuous, reproducible, and industrially scalable coating, paving the way for new energy-efficient process chains in hot stamping.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 394563137 - SFB 1368

References

The original version of this paper is available on https://www.scientific.net/SSP.389.217.pdf

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Pfeifer F, Knorr L, Schlosser F, Marten T, Tröster T. Ecological and Economic Feasibility of Inductive Heating for Sustainable Press Hardening Processes. J. sustain. dev. energy water environ. syst. 2023; 11(3): 1-20 []

Wieland Michael. Entwicklung einer Methode zur Prognose adhäsiven Verschleißes an Werkzeugen für das direkte Presshärten 2015.

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Gerhardt KW. Untersuchungen zur konduktiven Erwärmung für Warmzugversuche an Blechen. DissertationShaker Verlag.

Christian Gebel. Bewertung von martensitischen Chromstählen für die Warmumformung der automobilen Großserienfertigung 2021.

Philipp Olle. Numerische und experimentelle Untersuchungen zum Presshärten 2010.

Yilkiran D. Abschlussbericht Konduktive Erwärmung von Formplatinen für das Presshärten 2014.

Mori K, Maeno T, Yamada H, Matsumoto H. 1-Shot hot stamping of ultra-high strength steel parts consisting of resistance heating, forming, shearing and die quenching. International Journal of Machine Tools and Manufacture 2015; 89: 124-31 [ j.ijmachtools.2014.10.008]

Behrens B-A, Langohr A, Farahmand E, et al. Resistance Heating in XHV-Adequate Atmosphere: An Energy-Efficient Heating Process for Hot Stamping. In: Resistance Heating in XHV-Adequate Atmosphere: An Energy-Efficient Heating Process for Hot Stamping; 2024. AIST; 126-32.

Behrens B-A, Hübner S, Holländer U, Langohr A, Pfeffer C, Albracht L. Increasing the energy absorption of monolithic manganese boron steels in oxygen-free environment. IOP Conf. Ser.: Mater. Sci. Eng. 2021; 1157 (1): 12021 []

Holländer, U.; Wulff, D.; Langohr, A.; Möhwald, K.; Maier, H. J. (2019): Brazing in SiH4Doped Inert Gases - A New Approach to an Environment Friendly Production Process, Int. J. of Precis. Eng. and Manuf.-Green Tech. 495, 2019 (1), 187 [ /10.1007/s40684-019-00109-1]

Szafarska, M.; Olszok, V.; Holländer, U.; Gustus, R.; Weber, A. P.; Maus-Friedrich, W. (2023): Gas Phase Reaction of Silane with Water at Different Temperatures and Supported by Plasma, ACS Omega, 2023, 8, 9, 8388-8396 [ /10.1021/acsomega.2c07209]

Behrens B-A, Hübner S, Holländer U, et al. Oxygen-free resistance heating with nitrogen and silane as an energy-efficient heating process for hot stamping. IOP Conf. Ser.: Mater. Sci. Eng. 2023; 1284 (1): 12007 []

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The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 227-241

doi: 10.4028/p-k4HkEk

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

Bernd-Arno Behrens 1,a, Sven Hübner 1, b, Simon Pauli 2,c, Henner Rüschkamp 2, d, Simon Kimmina 1,e, Denis Fink 1,f, Behdad Yaalimadad 1, g*

1 Leibniz University Hanover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

2 Aspens GmbH, Feodor-Lynen-Straße 27, 30625 Hanover, Germany

abehrens@ifum.uni-hannover.de, b  huebner@ifum.uni-hannover.de, c  s.pauli@aspens.de, d  h.rueschkamp@aspens.de, e  s.kimmina@stud.uni-hannover.de, f  fink@ifum.uni-hannover.de, g * yaalimadad@ifum.uni-hannover.de

Keywords: fuel cell systems, bipolar plates, sheet metal forming, rubber forming.

Abstract

Hydrogen-based energy systems are considered a key pillar of the energy transition, yet the cost-efficient, mass production of metallic bipolar plates (BPPs) for proton exchange membrane fuel cells (PEMFCs) remains challenging, as conventional processes are limited by comparatively long cycle times and forming-related instabilities. This paper investigates the rubber drawing process as a cost-efficient manufacturing method for metallic bipolar plates, proposed as an alternative to the commonly applied hydroforming process, analysing the influence of pressing force, rubber hardness and thickness, tool modifications for varying pressure distribution, and the suitability of additively manufactured tool dies made from Maraging Steel 1 (X3NiCoMoTi 18-9-5) or ceramic-filled UV resin. The results show that precise and stable tool guidance, as well as a well-adapted tool setup, are required to achieve reproducible component quality; targeted adjustments of process and rubber parameters improved channel dimensional accuracy, but revealed limited forming capability in certain areas. Furthermore, concavely and convexly modified rubber dies reduced component warping in specific directions, and steel dies exhibited higher precision and less distortion compared to ceramic-filled UV resin dies. These findings highlight the potential of the rubber drawing process for cost-effective production of bipolar plates, while identifying key parameters for further optimization toward industrial-scale manufacturing.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

Fuel cells are considered a key technology for sustainable mobility and a promising option for reducing emissions in the transport sector. Compared to conventional internal combustion engines, fuel cell systems enable locally emission-free operation and higher overall energy efficiency. In addition to battery electric vehicles, hydrogen-based mobility concepts offer advantages such as high energy density and short refueling times, making them particularly suitable for applications with extended range requirements [1,2]. A widely used fuel cell technology is the proton exchange membrane fuel cell (PEMFC). In PEMFCs, electrical energy is generated through the electrochemical reaction of hydrogen and oxygen to form water, ensuring a continuous on-board power supply in fuel cell electric vehicles (FCEVs). This addresses key limitations of pure electromobility, including limited driving range and long charging times, while maintaining high system efficiency [1,2]. Fig. 1 illustrates the exemplary structure of a fuel cell stack composed of multiple individual cells connected in series to achieve a nominal voltage of approximately 400 V . Each single cell comprises a membrane electrode assembly (MEA), which consists of a catalyst-coated membrane and adjacent gas diffusion layers, as well as bipolar half plates that enable reactant distribution and electrical conduction. Together with the current collectors, these components facilitate the electrochemical conversion of hydrogen and oxygen into electrical energy [3, 19]. The individual cells are stacked in
series and electrically interconnected, while the entire fuel cell stack is mechanically clamped and electrically contacted by current collectors and end plates, as shown in Fig. 1 [19].

[picture]

Fig. 1. Fuel cell stack [19].

Fig. 1. Fuel cell stack [19].

The bipolar plate (BPP), consisting of two monopolar plates (MPP), is a central structural component of the cell. It performs essential functions such as charge transport, gas supply, removal of reaction products, cooling, and separation of media [4]. These diverse tasks place high demands on corrosion resistance, electrical conductivity, and dimensional accuracy. At the same time, BPPs account for about 80% of the stack weight and 45% of the stack costs [5]. The high costs result primarily from the complex manufacturing processes, which require high precision due to the intricate microchannel structures of bipolar plates. Fig. 2 shows a cross-sectional view of a BPP, illustrating the characteristic channel geometry from a side perspective and highlighting the stringent geometric requirements involved (dimensions in mm ) [6,20]. Conventional processes such as hollow stamping reach their limits when it comes to complex channel geometries and thin-walled materials. Alternative forming processes such as hydroforming can provide improved dimensional accuracy and surface quality for metallic bipolar plates. However, the process is characterized by long cycle times due to the need for pressure build-up, controlled fluid flow, and pressure holding phases, which significantly limits productivity in high-volume manufacturing [7]. In addition, the requirement for high-pressurecapable tooling and sealing systems results in elevated tool complexity and costs, making hydroforming economically unattractive for large-scale production [7]. Therefore, intensive research is being conducted into alternative manufacturing technologies, including continuous hollow spinning or roll spinning, which offer high automation potential [1,8]. Although these processes enable high production rates (up to 120MPP/min ), they have limitations in terms of flexibility and component homogeneity [9].

Rubber pad forming is a particularly promising alternative, as it employs a highly compliant, entropically elastic medium instead of a geometrically rigid metallic die. This enables a more uniform and adaptive pressure distribution, allowing gentle and flexible forming of sensitive surfaces. Originally known from the aviation industry, the process was developed specifically for large sheet metal components and prototypes [2,10]. Due to the simple tool design (no sealing of the pressure medium required) and the potentially shorter cycle times, it offers cost advantages over processes such as hydroforming [11]. In addition, the elastic pressure distribution is expected to reduce material thinning and improve surface quality - a decisive advantage for coated or polished materials [12].

In recent years, an increasing number of scientific papers have been published on the application of the rubber stamping process to the manufacture of metallic

[picture]

Fig. 2. MPP channel geometry [20].

Fig. 2. MPP channel geometry [20].

bipolar plates. Elyasi et al. (2017) investigated the production of stainless steel BPPs using semistamp rubber forming and demonstrated a significant improvement in the fill ratio ( +11.7% ), thickness distribution, and dimensional accuracy compared to conventional rubber pad forming [13]. Hashemi and Roohi (2021) evaluated the influence of process parameters such as rubber hardness, pressing force, and stamp speed on aluminum BPP with helical channels and identified a Shore A hardness of 60 as optimal for maximum channel depth [14]. Elyasi et al. (2016) additionally showed that the design of the tool gap (the so-called "die clearance") significantly influences the dimensional accuracy and service life of the rubber die [15]. More recent work, such as that by Albers and Ngondji (2025), combines rubber pad forming with stampinging technologies ("hybrid forming") and demonstrates an increase in process accuracy while reducing tool complexity [16].

Furthermore, recent studies indicate that the nonlinear pressure behavior of the elastic medium in the rubber stretching process can lead to local mold instabilities, especially in thin-walled sheets. Groche et al. (2014) identified uneven pressure distributions as the cause of elastic springback and local warping [17], while Kim and Kim (2018) confirmed that the hardness and pressure curve of the elastomer are decisive for the flatness and dimensional accuracy of the components [18]. However, a targeted examination of these instabilities - in particular the so called 'snap-through' effect - in the manufacture of metallic bipolar plates has not yet been carried out, which underlines the existing research gap and the relevance of the present work.

This work deals with the investigation of the dimensional and shape accuracy of metallic bipolar plates (BPP) in the rubber drawing process as a function of various process parameters. The focus is on analyzing the influences of pressing force, holding time, rubber hardness, and rubber thickness on the resulting component geometry as well as on local shape instabilities such as warping and the 'snap-through' effect. Geometric features such as draw depth, edge sharpness, flatness, and reproducibility of the channel structures were evaluated. In addition, the occurrence of elastic springback and local deformations was investigated in order to identify correlations between pressure distribution, material properties of the rubber, and component distortion.

Various tool materials were used to carry out the tests, including ceramic-filled UV-cured resin (CR) and Maraging Steel 1 (MS1), each of which was additively manufactured. The manufacturability of additively manufactured matrices, like those depicted (CR and steel), and their suitability for the production process in terms of feasibility were evaluated. Furthermore, the reproducibility and cost-effectiveness of the process were also evaluated. In addition, the test and tool setup was specifically modified, e.g., by using convex and concave steel masks placed on the rubber pad (Fig. 4). These modifications influence the local pressure distribution during the forming process and its development over time in the course of the process. The aim was to analyse the influence of this coupled spatial-temporal pressure distribution on the flatness of the components, as it contributes significantly to the development of nonlinear form instabilities (cf. [17, 18]).

The aim of the investigations is to quantify the influence of these parameters on dimensional accuracy and dimensional stability and to develop strategies for minimizing warping. For the experimental implementation, a simplified channel design and a reduced component size were chosen in order to enable a high number of reproducible test runs with low material consumption.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

The rubber materials used for the forming experiments were based on polyurethane (PU). Polyurethane sheets and mats were supplied by Fibro GmbH , including thin mats with thickness of 1 mm and hardness of 90 and 95 Shore A, as well as Fibroelast and Fibroflex sheets with thickness of 20 mm and hardnesses of 65 Shore A (Fibroelast) and 80-95 Shore A (Fibroflex). All rubber materials were cut to a stamp size of 50×50 mm, corresponding to the selected demonstrative component geometry. The Fibroelast and Fibroflex plates were also prepared in thicknesses of 5, 10, and 15 mm . The CR dies were manufactured by Aspens through 3D printing and provided for the investigations. After UV-curing, they were additionally heat-treated at 150∘C. The size of each die was 50 x 50 x 10 mm . The CAD geometry shown in Fig. 3 represents a simplified channel design developed by Aspens and used for the investigations. In addition, steel dies with equal size made of MS1
(X3NiCoMoTi 18-9-5), a high-strength, precipitation-hardening steel, were printed by IPEG (Institute for Product Development and Device Engineering) using a powder laser process. The material used to manufacture the MPP was X2CrNiMo17-12-2 (1.4404) austenitic stainless steel. The 0.1 mm thick sheet metal blanks were also cut to a size of 50×50 mm.

For the forming experiments a hydraulic press Hydrap HPDZb 63 was used. The system has a CNC press control with a monitor for precise input of process and tool parameters and enables ram forces of 63−630kN, drawing cushion forces of 40−400kN, and stroke speeds of 0−410 mm/s. Fig. 4 shows the hydraulic press, along with the corresponding schematic representation of the experimental setup used for the rubber pad forming

[picture]

Fig. 3. CAD model of the die with simplified channel geometry.

Fig. 3. CAD model of the die with simplified channel geometry.

experiments investigating the influence of rubber hardness, rubber thickness, and pressing force. The schematic illustrates the arrangement of the base plate, draw edge, die, sheet blank, rubber pad, and stamp. On the right-hand side, a modified setup is additionally shown, exemplified by a convex steel mask positioned on top of the rubber pad.

[picture]

Fig. 4. Schematic representation of the experimental setup without and with mask.

Fig. 4. Schematic representation of the experimental setup without and with mask.

The draw edge tool was manufactured from 1.2740 tool steel based on a CAD model. Fig. 5 shows the CAD representation of the draw edge tool as well as its installation in the hydraulic press, mounted above a load cell with signal amplifier for measuring the actual forming force. The tool consists of a base plate, a bolted draw-edge component, a stamp, and features the dimensions shown in Fig. 5.

[picture]

Fig. 5. Draw-edge tool CAD model and installation in the press.

Fig. 5. Draw-edge tool CAD model and installation in the press.

Rubber pads with a hardness of 80 Shore A and a thickness of 10 mm were used to investigate modified concave and convex tool geometries and the resulting force transmission. Concave refers to indentations that are curved inward, while convex describes elevations that are curved outward. These shapes influence the tool geometry and thus the resulting local and temporal pressure distribution during the forming process: Concave areas lead to locally higher pressure and longer contact time,
while convex areas lead to lower pressure and shorter contact time. The elevations were created using steel masks with thicknesses between 1 and 3 mm , which were positioned as shown in Fig 4. They were also produced by milling material out of the rubber pad, resulting in a convex or concave elevation of 2 mm . The planned mask and pad geometries included square, ring-shaped, and grid-like structures are shown in Fig. 6. So far, the square variants have been manufactured and examined; further investigations will address the analysis of ring and grid geometries. Such test parameters that have not yet been carried out are marked with an asterisk (*) in the following figures and tables. The steel mask geometries are shown in their concave configuration. For each geometry, a corresponding negative part remains after removal of the raised structure; this negative directly represents the complementary convex configuration and is likewise used in the experiments.

[picture]

Fig. 6. Representative concave steel mask geometries: (1) square, (2) ring, (3) grid and milled rubber pads: (4) concave (5) convex.

Fig. 6. Representative concave steel mask geometries: (1) square, (2) ring, (3) grid and milled rubber pads: (4) concave (5) convex.

Table 1 provides an overview of the material parameters of the rubber pads, including rubber hardness and thickness, as well as those of the sheet metal blanks and dies. In addition, the investigated process parameters and modifications, such as pressing force, dwell time, and mask geometry, are summarized. Three tests were carried out for each parameter variation in order to assess the reproducibility of the results and identify outliers.

Table 1. Experimental matrix for the parameter study to improve component geometry.

Parameter | Levels / Variants
Rubber hardness [Shore A] | 65 | 80 | 95
Rubber thickness [mm] | 5 | 10 | 15
Pressing force [kN] | 300 | 400 | 500
Dwell time [s] | 0 | 2
Mask geometry | Convex | Square | Ring (*) | Grid (*)
Conkave
Die material | Ceramic-filled UV-cured | Maraging Steel I

The formed MPPs were then indexed and measured using the Keyence VR-3200 3D profilometer. The system works on the principle of fringe projection and enables non-contact, high-resolution surface characterization. With a height measurement accuracy of 3μ m, a width measurement accuracy of 2μ m, and a repeatability of 0.5μ m, it allows precise 2D and 3D measurements at up to 160x digital magnification. Despite the profile meter's anti-reflection settings, these could not be completely eliminated without additional matting. Attempts at matting using airbrush technology showed that this enables reflection-free 3D measurement. However, due to the large number of samples, matting was not used, as the geometry parameters could be reliably evaluated despite the remaining measurement artifacts.

The component geometry was evaluated based on the measured 2D and 3D height profiles. Characteristic values such as channel depth and geometry, surface quality, and component warping were determined and compared. Further data analysis was performed using Microsoft Excel and
creating response surface plots in Minitab. For the quantitative evaluation of the channel geometry and drawing depth, four characteristic reference measurement points ( P1−P4 ) were defined representing both wide and narrow channels as well as central and outer areas of the component. To determine component warping, four profile lines were defined across the optically measured sheet metal. The profile lines include a vertical line, a horizontal line, and two diagonal lines, where TL - BR stands for top left to bottom right and BL - TR stands for bottom left to top right. Based on these profiles, the height difference between the highest point at the center of the component surface and a reference line connecting the outer corner points at the edge of the forming zone was determined. In this context, a comparison was carried out between the target geometry (steel die), a standard rubber pad with a thickness of 10 mm and a hardness of 80 Shore A, and the modified setup described above featuring convex and concave elevations. The experiments on component warping were conducted exclusively using the steel die to ensure improved reproducibility and comparability.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

Using the materials and equipment previously described, all experiments were conducted within the framework of parameter studies and subsequently analyzed and evaluated optically. At the beginning of the investigations, the actual geometries of the CR and steel dies were measured using a Keyence light microscope. Fig. 7 shows such an image capture and measurement. From left to right, real photographic images of the CR and steel dies are displayed first. Next, the determined 3D height profile of these dies can be seen. On the right side, the 2D side-height profile of both dies is depicted, which was determined along the vertical blue arrow in the original image. The labels P1 to P4 in the right image are the measurement points selected for the subsequent analysis to evaluate the channel or drawing depth. Qualitatively, it can be observed in both the 3D and 2D height profiles that the steel die possesses distinctly sharper and deeper channels. While the channel depths of the CR die range from 0.219 to 0.374 mm , the steel dies have channel depths between 0.425 and 0.561 mm . From the 3D height profile representation of the entire component, it can also be seen from the color areas that the channel depths of the CR die lie in a similar range, whereas the steel die exhibits clear height differences in certain channel areas. The gradations of the channels in the middle area (green and blue) are desired recesses that are clearly better manufactured in the steel die. The right section of the image also shows that on a micrometer scale, both dies exhibit global unevenness, both in the surface area and in the channel bottoms. However, locally, the CR die has flatter, smoother surfaces compared to the steel die, which tends to have a wavy surface.

[picture]

Fig. 7. Optical analysis of the manufactured CR and steel dies.

Fig. 7. Optical analysis of the manufactured CR and steel dies.

Fig. 8 presents a detailed comparison of the side profiles from exemplary channel sections (P2) of the two manufactured dies made from CR and steel. This figure highlights the significantly different channel geometries of the CR and steel dies. Apart from channel depths, these differ primarily in their overall geometry. The CR die exhibits a more conical channel geometry with a central low point, whereas the steel die has a more trapezoidal geometry with a flat channel bottom. In comparison with
the target geometry from the state of the art (Fig. 2), it is observed that the steel die features a much better, more precisely manufactured geometry and is closer to the reference geometry from the polished section. Apart from differences in the slope of the edge regions, the channel width at P2 is approximately the same for both dies, while the CR die achieves a channel depth of 0.264 mm and the steel die reaches a channel depth of 0.561 mm . However, the actual channel depths are to be disregarded, and instead, a qualitative assessment of the geometry should be employed, as the CAD geometry (target geometry) used for die fabrication was only constructed in reference to the actual target geometry in order to facilitate representative qualitative executions and evaluations.

[picture]

Fig. 8. Comparison of the channel geometry of the CR and steel die at P2.

Fig. 8. Comparison of the channel geometry of the CR and steel die at P2.

In summary, the comparison between the CR and steel dies demonstrates a higher geometric conformity to the CAD geometry for the steel die. The observed deviations of the CR die can largely be attributed to process-related limitations of resin-based additive manufacturing, including limited resolution, light scattering caused by ceramic fillers, and additional smoothing effects during UV post-curing, which particularly affect edge sharpness and fine channel geometries. The remaining deviations of the steel die from the CAD geometry, such as unevenness and variations in channel depth, are mainly associated with a previously identified manufacturing inaccuracy of approximately 0.1 mm . are attributed to a previously noted inaccuracy of about 0.1 mm in the additive manufacturing at IPEG.

The sheet metal blanks were successfully formed without cracking in the first test series. The pure pressing time was 4−5 s; however, additional time had to be considered within the overall cycle for loading and unloading the components. Consequently, the total cycle time from one experiment to the next was approximately 20 s . Fig. 9 shows a representative MPP manufactured with a steel die. The previously defined measurement points P1 to P4 and the derived 2D height profile along the marked measurement path (blue arrow) are shown. From the 2D height profile, it can be seen that channel depths between 0.219 and 0.374 mm were achieved. The highest values were measured in the wider channels P1 and P4. The narrow channels P2 and P3 show a difference of 0.110 mm(P2) and 0.155 mm (P3) compared to the highest channel depth of P1, which is about 30 to 42% lower than the maximum drawing depth achieved by P 1 .

[picture]

Fig. 9. Representative formed MPP with measurement points and extracted 2D height profile.

Fig. 9. Representative formed MPP with measurement points and extracted 2D height profile.

Fig. 10 shows an exemplary comparison of the actual and target geometries of MPPs manufactured with CR and steel dies. This is a detailed view from the area of the MPP marked on the right. Qualitatively, it can be observed that the channel geometries of the sheets formed with the CR die are closer to the respective target geometry of the die. However, the achieved drawing depths with the steel die are correspondingly higher, and the channel geometry more closely matches the overarching target geometry (reference geometry) that was established as the target dimension before the fabrication of the dies.

[picture]

Fig. 10. Comparison of die geometry and component geometry for the (1.) CR and (r.) steel dies.

Fig. 10. Comparison of die geometry and component geometry for the (1.) CR and (r.) steel dies.

For a qualitative comparison of the actual and target geometry of the MPP and the die, Fig. 11 presents the evaluation of the determined drawing depths in relation to the target drawing depth of the respective dies (CR and steel) graphically using a boxplot diagram. As shown in Fig. 11, MPPs manufactured with CR dies achieve higher relative drawing depths relative to the die geometry compared to components made with steel dies. In some cases, the achieved channel depths exceeded 100%. Overall, MPPs produced with the steel die show higher absolute drawing depths than those made with CR. However, except for measurement point P1 ( >90 %), these are significantly below the target depth, ranging between 65% and 83%. Generally, wider channels achieved higher relative drawing depths and better dimensional accuracy of the entire channel geometry compared to narrow channels (Figs. 10 and 11).

[picture]

Fig. 11. Comparison of the achieved drawing depths between CR and steel dies for different measurement points.

Fig. 11. Comparison of the achieved drawing depths between CR and steel dies for different measurement points.

The overall cycle time of about 20 s (with the exception of failure-related trials involving increased removal times due to required tool disassembly) is primarily determined by tooling and equipment constraints rather than by the forming process itself. Since the actual forming process, defined by the start and end of the press stroke, lasted approximately 4−5 s, a cycle time of less than 7 s appears feasible with optimized equipment, process technology, and automation.

The comparison of the channel depths of the fabricated MPPs reveals a strong dependence on the target geometry of the die and the limitations imposed by the respective manufacturing process. While the CR die shows a higher relative fulfillment of the prescribed channel depth, this is mainly a consequence of its insufficient absolute channel depth and elastic deformation caused by an inhomogeneous modulus of elasticity, which in some cases even results in drawing depths exceeding the die geometry. In contrast, the steel die exhibits lower relative form filling, primarily due to its deeper and sharper channel geometry, which places increased demands on material flow and formability.

Local variations in channel fulfillment are further governed by the spatial position on the MPP and the channel width, as demonstrated by the high degree of filling observed at P1. Enhanced material inflow and more favorable stress conditions in outer regions support forming, whereas narrow channels and sharp edges are adversely affected by the viscoelastic behavior of the rubber, which resists penetration under low holding time and room temperature. To counteract this effect, an increase in holding time was experimentally investigated in order to improve rubber flowability under sustained static pressure. However, longer holding times led to pronounced rubber intrusion into gaps between the die and the draw edge, which prevented non-destructive demolding and caused damage to the components. As a result, this approach could not be further pursued with the current tool configuration. An alternative approach to improve rubber flowability would be tempering the rubber; however, this would significantly increase cycle time and tooling complexity, thereby reducing the economic viability of the process. In addition, the rubber hardness is expected to influence the achievable form filling and channel geometry. This effect was therefore investigated within the parameter study presented in the following section.

The evaluation of the parameter study by creating response surface plots in Minitab shows the influences of rubber hardness, rubber thickness, and pressing force on the achieved drawing depth, as illustrated in Fig. 12 using the example of measuring point P 1 . The response surface plots each hold one variable constant while relating two others to each other, highlighting the achieved drawing depth. The plots indicate that the greatest drawing depths of approximately 0.397 mm were attained with a rubber thickness of 10 mm . The optimal rubber hardness is 80 Shore A in combination with a pressing force of 300 kN . Additionally, the middle plot shows that the optimal pressing force increases with higher rubber hardness. The smallest drawing depths, below 0.385 mm , were observed with a pressing force of 500 kN in combination with a rubber hardness of 65 Shore A . Both higher and lower rubber hardness than 80 Shore A generally resulted in reduced drawing depths; the same applies for a rubber thickness of 10 mm . The influence of the pressing force depends on the other parameters. With exceptions, the smallest drawing depths occur at a pressing force of 500 kN . Overall, the influence of the varied process parameters on the drawing depth remained limited to a range of 6 to 13μ m.

[picture]

Fig. 12. Influence of pressing force, rubber hardness, and rubber thickness on the drawing depth.

Fig. 12. Influence of pressing force, rubber hardness, and rubber thickness on the drawing depth.

In contrast to the expectations promising a better forming quality with lower rubber hardness, observations showed that the best results were achieved at a Shore A hardness of 80. This is similar to the issue with increased holding time. Softer rubber also increases the risk of jamming and tends to flow into undesirable areas, which can negatively affect component quality as the rubber tends to displace its volume into all cavities, serving only a small portion of the die filling. At the same time, rubber with higher hardness, such as 90 Shore A, would also be disadvantageous, as it offers greater resistance to deformation. This explains the observed dependence of pressing force on rubber hardness: The higher the rubber hardness, the greater the pressing force required to achieve similar drawing depths (see Fig. 12, center). For ongoing investigations, considering effort, feasibility, and especially the scalability of the resulting surface pressure, a rubber hardness of 80 Shore A , a rubber thickness of 10 mm , and a pressing force of 300 kN were selected as suitable. Nevertheless, it should be noted that in the entire parameter study, the range of maximum 13μ m is very limited, which reduces the sensitivity of the measurement values to the parameters. Therefore, further influencing factors and challenges of the currently developed process are addressed in subsequent sections.

In summary, the successful formation of sheet metal blanks without cracking suggests that the chosen process parameters were generally effective. However, the comparison of channel geometries between CR and steel dies reveals important distinctions in their performance and influence on forming behavior.

For the investigation of component warping, forming tests were conducted with a steel die using constant rubber and process parameters, and the results were analyzed as described below. The investigations typically showed a rise in the component center compared to the outer areas. Fig. 13 exemplarily illustrates such a measurement, where the reference lines described in the methodology are shown. A resulting 2D height profile is depicted on the right side and shows a central elevation of 0.248 mm based on the BL-TR line.

[picture]

Reference lines on sheet

Figure 13. Reference lines on sheet

Fig. 13. Optical analysis for determining component warpage.

Fig. 14 shows a representative 3D height profile used for a comprehensive examination of component warping. From the perspective depicted, the central elevation of the component compared to its corner points is evident. The component exhibits asymmetric behavior across its entire surface, as can be seen in the edge areas of the 3D profile in Fig, 14. Moreover, it becomes clear that the degree of warping intensifies disproportionately towards the outer and corner areas.

[picture]

Fig. 14. Representative 3D height map for evaluating component warpage.

Fig. 14. Representative 3D height map for evaluating component warpage.

The inhomogeneous warping behavior of the components indicates non-uniform stress states in the sheet metal during and after forming, which can mainly be attributed to the asymmetric channel geometry and the resulting uneven stress distribution. Local differences in deformation lead to varying springback behavior and should therefore be considered in future adjustments of the mask geometry. The pronounced deformation observed in corner regions is likely related to the absence of beading structures, which reduces local stiffness and resistance to elastic deformation compared to reinforced areas, thereby promoting increased springback. In addition, these effects may be intensified by an earlier transition to plastic deformation in certain regions or by deformation and partial failure of the rubber, as evidenced by damage observed in the rubber in corner areas after several forming cycles.

Fig. 15 presents an overview of the results related to component warping. In addition to the measurements of the target geometry (Target Steel), it compares the measurement values from the reference experiment with rubber pads (RP) and the various modifications of the experimental setup across all four considered measurement areas. Based on the figure, it is apparent that except for a few exceptions with RV 2 mm , all experiments show positive values, indicating an elevation of the component center compared to the outer areas. In contrast, the target geometry displays exclusively negative values between 0,02 and -0.13 mm . The measurement values from all experiments range from approximately -0.29 to 0.52 mm . The test series RSX 2 mm and RV 2 mm exhibit high variability compared to the other measurements, with a standard deviation of up to 0.179 mm (RV 2 mm , vertical). The figure clearly shows that the diagonal TL - BR has the highest values, suggesting that component warping is most pronounced along this line. The lowest values most frequently occur in the horizontal measurement, followed by the vertical measurement. These two measurement areas also show relatively small variations between the different parameters, within a range between 0.08 and 0.18 mm , apart from RSX 2 mm and RV 2 mm . The progression of values along the vertical line shows no clear trend, while on the horizontal line a slight decrease is observed from the pure rubber pad to the convex elevation via the steel mask, where the value tends to decrease with increasing mask height. With the increase of the concave steel mask, the horizontal value increases slightly. Apart from outliers, the lowest value of 0.075 mm is observed in the diagonal BL - TR of the RSX 3 mm test series. As can be seen in Fig. 15, all measurement areas, except for the diagonal TL - BR, show relatively low values. In the RV 2 mm measurement, when including outliers, the lowest values are seen by far, including negative areas, with the lowest value being -0.285 mm and the mean of the measurement series at -0.065 mm . Comparing the RX 2 mm and RV 2 mm measurements, it is evident that the concavely milled rubber pad leads to predominantly less component warping, although the significance is limited due to the high measurement variability in RV 2 mm . Another notable observation is the progression of warping values along the two diagonals, starting with the standard rubber pad through to the combination with the convex and particularly the concave steel mask (GSV) with mask thicknesses of 1,2 , and 3 mm : Except for the RSX 3 mm measurement, the warping intensifies in the OL-UR direction with increasing mask height, while it decreases in the UL-OR direction. It can be observed that the values of the two diagonals consistently exhibit an inverse relationship, reflected in a symmetrical progression of measurements parallel to the x -axis at y=0.25 mm.

[picture]

Fig. 15. Influence analysis of convex (RSX) and concave (RSV) steel masks at heights 1,2,3 mm, and milled rubber pads with 2 mm elevation (RX) or recess (RV) on warpage compared to target geometry of steel die (Target Steel) and standard rubber pad reference (RP).

Fig. 15. Influence analysis of convex (RSX) and concave (RSV) steel masks at heights 1 , 2 , 3 m m , and milled rubber pads with 2 mm elevation (RX) or recess (RV) on warpage compared to target geometry of steel die (Target Steel) and standard rubber pad reference (RP).

Deviations between vertical, horizontal, and diagonal warping measurements can partly be explained by geometric effects described by the intercept theorem, which predicts more pronounced bending along diagonal directions for identical curvature radii. This behavior further suggests an increased stress gradient between the component center and edge regions along the diagonals, particularly towards the corners. This assumption is confirmed by the three-dimensional component geometry analysis and is consistent with the previously discussed interpretations.

Despite partly ambiguous trends associated with convex and concave tool modifications, distinct correlations are observed. Horizontal warping decreases with increasing convex steel mask height and increases with increasing concave mask height, indicating a clear influence of stress redistribution induced by tool geometry. These findings support the assumption that a time-dependent redistribution of stresses significantly affects forming behavior and final component flatness. Notably, negative warping values observed in parts of the RV 2 mm test series, where the component center exhibits downward deformation, warrant further investigation to assess measurement reproducibility and to derive targeted measures for reducing warping. Reproducibility is therefore identified as a key prerequisite for reliably evaluating parameter-dependent trends.

An additional relevant observation is the inverse relationship between different measurement areas, particularly between the two diagonal height profiles. This suggests that warping induced by the mask geometry in one diagonal direction can partially compensate for warping in the orthogonal diagonal. The mechanical origin of this behavior lies in the targeted modification of the pressure distribution by the steel masks, which can geometrically direct warping into preferred directions. As a result, one diagonal exhibits increased warping while the orthogonal diagonal shows reduced deformation. This effect may offer advantages during component assembly and has the potential to mitigate snap-through behavior, which depends on the existing residual stress state. The influence of mask geometry on local stress and strain distributions during forming thus directly explains the observed changes in the height profiles and will be further investigated in subsequent work packages.

Conclusion

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

This study investigated the potential of the rubber drawing process for the production of metallic MPPs for use in PEMFCs. The focus was on dimensional and form accuracy in relation to process parameters such as pressing force, holding time, rubber hardness, rubber thickness, and the influence of concavely and convexly modified rubber pads. Additionally, the quality and suitability of additively manufactured CR and steel dies were analyzed.

The investigation of the additively manufactured dies revealed that dies made from CR were not suitable for use due to an insufficient and inhomogeneous modulus of elasticity. Furthermore, the

CAD geometry could not be precisely realized with these materials, which further restricted the quality of the MPPs produced with them. In contrast, steel dies showed higher precision and less distortion during fabrication, making them more suitable for use, although there is still potential for optimization in manufacturing accuracy.

The experimental investigations demonstrated the potential of the rubber pad forming process to offer economic advantages over the competing hydroforming process, particularly in terms of reduced equipment and tooling costs as well as potentially shorter cycle times. However, the major challenge remains the reliable fulfillment of the geometric requirements of the manufactured components. The examination of rubber and process parameters demonstrated that targeted adjustments, particularly of rubber materials in terms of hardness and thickness, achieved improvements in the dimensional accuracy of the MPPs. A Shore A hardness of 80, in combination with a thickness of 10 mm and a pressing force of 300 kN , was identified as optimal, as this parameter set provides a balanced compromise between sufficient stiffness and adequate flowability of the rubber. This configuration allowed for the best possible dimensional accuracy, with values of nearly 95% of the tool's specified target value being reached for the wide outer channels, which can be attributed to improved material inflow and more favorable stress conditions in these regions, while measurement sensitivity ranged from 6 to 13μ m. The analysis also highlighted that both the hardness and viscoelastic properties of the rubber are critical factors for dimensional accuracy, since they directly govern elastic deformation, flow resistance, and local form filling. Lower Shore A hardness and extended holding times improve flow capacity, particularly in deeper or sharper channel geometries, but simultaneously increase the risk of jamming and undesirable flowing into cavities, caused by excessive elastic deformation and uncontrolled material migration, negatively impacting component quality.

Another significant finding was achieved through the modification of rubber pads and the associated shift in stress distribution. The use of concavely and convexly modified rubber pads enabled the targeted manipulation of local pressure distribution. This led to a reduction in component warping in certain areas of the plate structure. In some cases, these effects were offset by increases in other directions, indicating an inverse relationship, for example, between warping values along different diagonals. This effect could help direct component warping in a specific direction, reduce local stresses, and thus improve the overall stability of the MPPs. This could also minimize the 'snapthrough' effect, which is associated with residual stresses in the components.

Overall, the study demonstrates the potential of the rubber drawing process for the production of MPPs, but it also emphasizes that further optimizations in material selection, tool geometry, and process control are necessary. These adjustments are critical to further improve dimensional accuracy, process stability, and reproducibility, and to promote the economical use of the process in large-scale applications.

Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

The current investigations have shown that optimizing process conditions can significantly improve the component quality in the production of metallic MPPs. In particular, the results suggest that precise control of process parameters such as Shore hardness, pressing force, holding time, and mask geometry is essential for achieving more accurate form filling and improved dimensional accuracy, as these parameters collectively govern the viscoelastic deformation, flow resistance, and elastic recovery of the rubber, which in turn determine local material inflow and geometric fidelity during forming.

However, the use of high-precision techniques, such as CNC micro-milling or more precise 3D printing for die manufacturing, could further enhance the control over component geometries. Simultaneously, more modern presses and the implementation of an optimized rubber housing design could facilitate longer holding times without causing blockages.

Moreover, a key approach lies in further developing die and channel geometries. Targeted recesses or undercuts can help compensate for the springback effect of stainless steel. Additionally, concave and convex mask geometries could be advanced to ensure even stress distribution and prevent uneven component deformation.

Additional approaches include the use of lubricants, such as spray water, to minimize friction between rubber and sheet metal as well as tool wear. Furthermore, simulation-based approaches employing hyperelastic material models could enable more precise process control by better accounting for complex material properties.

Looking ahead, the current research project envisages the production of milled dies and the adjustment of die geometries to effectively reduce component warping. Additionally, the project plans to determine the wear limits of different rubber variants through fatigue tests.

Combining these measures could not only significantly optimize the quality and efficiency of MPP manufacturing but also support their application in sustainable mobility.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

This research project was carried out as a cooperative project between companies (Aspens) and research institutions (IFUM) within the Central Innovation Programme for small and medium-sized enterprises (ZIM). ZIM is a funding programme of the Federal Ministry for Economic Affairs and Energy. The project was supervised and administered by AiF Projekt GmbH, acting in a fiduciary role. We would like to express our special thanks to Aspens GmbH , the project partner, for their willingness to cooperate, as well as for providing the necessary materials and their comprehensive expertise.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.227.pdf

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Graebener Maschinentechnik GmbH & Co. KG, Information on .

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 243-252

doi: 10.4028/p-fKT3xg

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-20

Accepted:
2026-02-24

Online:
2026-04-16

Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

The original version of this paper is available on https://www.scientific.net/SSP.389.243.pdf

MAMROS Elizabeth 1,a*, SHAFFER Derek 2, b, RAGAI Ihab 3,c, CLARK Austin 3,4, d

¹Bucknell University, Lewisburg, PA 17837, USA

2 Phoenix Laser Solutions, Meadville, PA 16335, USA

3 The Pennsylvania State University, Erie, PA 16563, USA

4 GROB Systems Inc., Bluffton, OH 45817, USA

a* elizabeth.mamros@bucknell.edu, b  derek.shaffer@phoenixlaser.com, cihab.ragai@psu.edu,  daclark@grobsystems.com

Keywords: incremental forming, laser welding, springback, sheet metal, tailor welded blanks

Abstract

Tailor welded blanks (TWB) are commonly used in the automotive industry to achieve heterogeneous components, particularly for creating high strength, lightweight parts. Laser welding is one method for joining TWB. Laser welding was used to create TWB composed of stainless steel 304L, with varied thicknesses, in a "patchwork quilt" pattern forming quadrants within the sample. The mechanical properties and quality of the weld were evaluated via tensile testing and microscopy. Truncated pyramids were then formed with weld seams along the faces, and springback and mechanical properties after forming were analyzed. Optical microscopy revealed that the weld seams remained intact after forming. The weld seam location in the center of the pyramid walls did not have a significant impact on the geometrical accuracy of the formed parts. The results of this study show promise for the use of SPIF with quilted TWB to achieve optimal formed part properties for the intended part application.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.243.pdf

Since 1992, tailor welded blanks (TWB) have been an integral part of the automotive industry, especially to consolidate parts, reduce tolerances, decrease weight, and increase stiffness [1]. TWB are composed of dissimilar materials or materials with differing thicknesses, which allows for varying material properties across the part. TWB are fabricated using various welding methods, including friction stir, electron beam, tungsten inert gas (TIG), and laser. Common concerns with TWB include reduced formability and displacement of the weld line during forming.

Single Point Incremental Forming (SPIF) is a sheet metal forming process that uses localized deformation, imparted by a typically hemispherical forming tool following a user-defined toolpath, to fabricate thin components. SPIF is commonly used for small production batches or prototyping due to its ability to form custom geometries without requiring dedicated tooling like dies, but it takes longer processing time than stamping. SPIF is also considered a flexible manufacturing process, based on its generic tooling requirement, and can be performed using a computer numerical control (CNC) machining center [2] or an industrial robot [3]. SPIF has been shown to increase material formability [4], which makes it a promising technology to combat the limitations of TWB.

Combining TWB and SPIF, previous work has focused mainly on aluminum and steel alloys. Carlone et al. found that the formability of aluminum alloy (AA) 6082-T6 blanks, fabricated using varying sets of friction stir welding parameters, was similar to the formability of the unwelded blanks [5]. Two studies that used laser welding to produce TWB studied formability along the weld seam for a 'D' shape geometry [6] and dome shaped forms [7]. Silva et al. used friction stir welding to fabricate AA1050-H111 TWB and used a dummy sheet during forming to prevent galling [8]. Recently, Katiyar et al. investigated TWB composed of C-103 refractory alloy sheets to produce critical space components [9]. Although previous work has investigated the formation of TWB using
various metallic materials with subsequent forming via SPIF, the use of a four-component TWB is a relatively unexplored area.

In this paper, stainless steel (SS) 304 blanks with differing initial thicknesses were laser welded in a "patchwork quilt" pattern. The SS304 TWB were then subjected to SPIF to fabricate truncated square pyramids. The geometrical accuracy, material properties, and weld quality were assessed after the forming operation. This work provides promising results for using laser welding to manufacture multi-component TWB that can provide the optimal part properties for the intended application after forming.

Materials and Methodology

The original version of this paper is available on https://www.scientific.net/SSP.389.243.pdf

Materials. SS 304 sheets with initial thicknesses of 0.91 mm and 1.22 mm were purchased from a commercial supplier. The nominal chemical compositions provided are listed in Table 1.

Table 1. Typical SS304 chemical compositions from the supplier [10][11]

Thickness | %C | %Si | %Mn | %P | %S | %Cr | %Mo | %Ni | %N | %Cu | %Fe
0.91 mm | 0.027 | 0.50 | 1.48 | 0.032 | 0.0010 | 18.07 | 0.43 | 8.08 | 0.060 | 0.53 | Bal.
1.22 mm | 0.027 | 0.36 | 1.29 | 0.033 | 0.0025 | 18.22 | 0.43 | 8.03 | 0.063 | 0.49 | Bal.

Laser Welding. An Alpha Laser ALFlak 1200F was used to perform autogenous, full penetration, pulsed laser beam welding. Prior to welding, the SS304 sheets were first cut via a waterjet into 112.5 mm×112.5 mm pieces which were then cleaned and rinsed with acetone. The square blanks were then loaded in the welding fixture which provides ample clamping force near the seam to ensure intimate contact in the interface and avoid distortion along the weld. The fixture is also designed with a gas port that supplies a constant stream of argon gas to the bottom side of the weld. Along with the backing gas, a localized argon cover gas is applied to the weld area, minimizing the risk of oxidation induced defects. The welding was then performed with a peak power of 4000 W , pulse time of 10 ms , frequency of 10 Hz , a spot size of 1.4 mm , and a travel speed of 5 mm/s. The laser is focused via a built in optical focal objective which focusses the laser on the surface of the material 150 mm from the lens. Each blank was added in this fashion to form the "quilt" pattern where each weld interface represents a TWB of dissimilar thicknesses as shown in Fig. 1.

[picture]

Fig. 1. Quilted, laser welded specimen prepared for SPIF. Values indicate the sheet thickness in each quadrant.

Fig. 1. Quilted, laser welded specimen prepared for SPIF. Values indicate the sheet thickness in each quadrant.

Weld Quality. The welds were evaluated during and immediately after processing by the weld operator via the built-in microscope optics used to monitor and control the laser. Upon magnified visual inspection, no cracking was observed in the weld metal or in the heat affected zone (HAZ) adjacent to any of the welds. Further evaluation of the bottom of the welds was performed to ensure full penetration was achieved (Fig. 2). No observable defects were noted on any of the samples. Destructive cross-sections of the welded sheets were used to identify microstructural features and any
internal defects. Cross-sectioning of the welds before and after SPIF also provided perspective on the impact the process has on the weld microstructure. Cross-sections were performed by removing samples using metallographic saws and water jetting to minimize any risk of added deformation or heat input into the samples. Samples were then mounted, ground, polished and etched using Vilella's reagent to expose the microstructure. Microstructural images were taken in brightfield mode on an Olympus DSX 1000 optical microscope.

[picture]

Fig. 2. Weld quality before forming.

Fig. 2. Weld quality before forming.

Single Point Incremental Forming (SPIF). A TorqueCut 22 (Bridgeport) computer numerical control (CNC) machining center with a custom frame, shown in Fig 3a, was used for all SPIF experiments. The 225 mm×225 mm welded blanks were prepared, following laser welding, by drilling the hole pattern shown in Fig. 1. The hole pattern aligns with bolts in the fixture to securely clamp the sheet and creates an unclamped area of approximately 165.1 mm×165.1 mm for forming. An infrared camera (FLIR T640) was included in the experimental setup to capture temperature data during forming. The emissivity value was set to 0.95 for all thermal analysis. A 10 mm diameter hemispherical tool made of hardened A2 tool steel was used with thin layer of multi-purpose synthetic grease (Super Lube NLGI) spread across the blank for lubrication. The toolpath was generated in Mastercam 2024 [12] using a surface finishing contour operation, feed rate of 952.5 mm/min, spindle speed of 60 rpm , climb milling, and a maximum stepdown of 0.25 mm for each layer. The forming time was approximately 22 minutes. It is worth noting that this speed could be improved for eventual industrial applications by optimizing the toolpath parameters. The geometry of interest was a truncated square pyramid (Fig 3b) with a 30∘ wall angle and forming depth of approximately 25.4 mm , as shown in Fig 3c. The overall dimensions were intentionally selected to allow for the geometry to be rotated without modification for future investigations.

[picture]

Fig 3. SPIF (a) experimental setup, (b) TWB and formed part, and (c) truncated cone geometry, dimensions in mm .

Fig 3. SPIF (a) experimental setup, (b) TWB and formed part, and (c) truncated cone geometry, dimensions in mm .

Geometrical Accuracy. A 3D laser handheld scanner (Artec Space Spider), with an accuracy of 0.05 mm , was used to create a 3D point cloud of the formed specimens after removal from the forming fixture. The target computer-aided design (CAD) model was imported into the postprocessing software (Artec Studio 15 [13]) and manually aligned by the user for geometrical accuracy analysis. This manual alignment may induce additional error into the associated results; however, careful considerations were taken during the alignment process to reduce such error.

Tensile Testing. Tensile testing was conducted in two orientations, along the rolling and transverse directions, for the undeformed, raw materials (SS304: 0.91 mm thick and 1.22 mm thick) and undeformed, welded materials. Experiments were repeated three times to ensure statistical relevance for a total of 18 tests. An Instron 3366 with a 10 kN load cell was set to a displacement rate of 0.05 mm/s, corresponding to a 10−3 s−1 (quasistatic) strain rate (verified using two-dimensional Digital Image Correlation). The strain presented in the Results section is calculated using crosshead displacement due to machine incompatibility with the data synchronization system. For the welded specimens, the cross-sectional area of the thinner half is used in calculations. The ASTM E8 subsize geometry was chosen for tensile testing [14], and a gage length of 25 mm was assumed based on the standard. All specimens were waterjet cut from a single quilted blank, and the edges in the gauge section were lightly sanded to debur prior to testing. Fig. 4 shows an example of where the weld seam tensile specimens were extracted from the quilted blank.

[picture]

Fig. 4. Orientation of tensile specimens along weld seams on quilted blank.

Fig. 4. Orientation of tensile specimens along weld seams on quilted blank.

Microhardness Testing. Microhardness evaluations were performed in an effort to elucidate the effect of welding on the local mechanical properties as well as the impact of the strain induced during SPIF. Vickers microhardness evaluations were performed on a Leco LM 248AT with a 500 gf load in accordance with ASTM E384 [15]. Two-dimensional hardness maps were generated over the joints to gain a better understanding of local variations in mechanical properties throughout the crosssectional thickness.

Results

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Weld Response. Fig. 5 shows microscope images of the undeformed bottom and right weld seams. Full penetration welds were achieved using the parameters described in the Materials and Methodology section. Fig. 6 shows images of the weld quality after forming. The bottom wall of the truncated pyramid was extracted by cutting the geometry at 45∘ angles using a vertical band saw. Significant relaxation was observed in the part during cutting, i.e., the truncated pyramid relaxed into a near-flat shape as shown in Fig. 6. Two areas in the formed region, labeled A and B to correspond with the appropriate subfigures, were analyzed at a higher magnification. Both regions show deformation across the weld, compared to Fig. 5, due to forming, but the weld integrity remains intact.

[picture]

Fig. 5. Microscope images of weld quality before forming.

Fig. 5. Microscope images of weld quality before forming.

[picture]

Fig. 6. Bottom wall of truncated cone and microscope images of weld quality at indicated locations after forming.

Fig. 6. Bottom wall of truncated cone and microscope images of weld quality at indicated locations after forming.

The unwelded material appears to flow over the top of the weld which aligns with expected localized surface deformation. As the tool travels transversely across the weld, unwelded material is "smeared" over the top of the weld on the leading edge. As the tool leaves the weld, the edge of the weld metal is also deformed, elongating one side of the top of the weld. Further analysis is needed to understand the implications of the localized deformation combined with bulk strains with respect to phase transformation, grain morphology, and properties of the weld.

SPIF. An example of the formed part is shown in Fig. 7. No signs of failure were detected along the weld seams or elsewhere on the part, indicating a successful forming operation. On the toolside of the part, a rough surface finish and small chips were observed after the first few layers were completed. A possible explanation, based on the noises during forming, is chatter due to the high forces exerted on the cantilever-like tool. Additional work will focus on force and surface roughness measurements.

[picture]

Fig. 7. Example of a formed SS304 truncated pyramid.

Fig. 7. Example of a formed SS304 truncated pyramid.

At the start of forming, the specimen and tool were at room temperature ( 22∘C ). At the end of forming, the maximum temperature recorded by the IR camera was 97.9∘C as shown in Fig. 8. This increase in temperature as forming progresses directly influences the martensitic transformation in the stainless steel formed part [16]. It is worth noting that while this temperature is generally too low to cause significant thermal reversion of existing martensite back to austenite, which usually requires higher temperatures, it strongly influences the transformation during processing. Based on previous results, it is assumed that a heterogenous microstructure is achieved across the part with respect to forming depth. This heterogeneity can be intentionally manipulated to tailor the final part properties for their intended application.

[picture]

Fig. 8. Temperature distribution captured at the end of forming.

Fig. 8. Temperature distribution captured at the end of forming.

The geometrical accuracy of an example part is shown in Fig. 9. The first scan was taken on the toolside, i.e., forming side. The part was then flipped over (left-to-right) and scanned on the nontoolside. The weld lines are clearly visible in the toolside image due to differences in thickness across these locations. In the formed part region, the diagonals show a positive deviation while the walls
shown a nearly equivalent deviation in the opposite direction. This negative deviation in the pyramid walls is likely due to springback, a well-known sheet metal forming defect. This also indicates that the weld seams, centrally located in each pyramid wall, are not significantly reducing the springback with the current part geometry and orientation. A slight asymmetry is shown along the left weld seam (with respect to the toolside image) in the formed region. This could be due to material orientation effects, but further analysis is warranted. The values reported are likely a combination of springback and CAD model alignment effects.

[picture]

Fig. 9. Geometrical accuracy on the toolside and non-toolside of a formed truncated pyramid.

Fig. 9. Geometrical accuracy on the toolside and non-toolside of a formed truncated pyramid.

Material Properties. The results of the tensile tests are shown as true stress-strain curves in Fig. 10a. For the welded samples, all samples broke in the reduced thickness section of the gauge length, i.e., not at the weld location, with the exception of one specimen (Fig. 10b). Further failure analysis on this particular specimen is warranted. For the differing thicknesses of SS304, the curves overlap, as expected (shown by the red solid and black dotted curves). The slight difference in material hardening between the weld curves may be attributed to the anisotropy of the base material. The martensitic transformation of SS304 also has a dependency on material orientation [17]. Overall, the weld specimens resulted in slightly increased material strength ( 6%−10% ), which may be attributed to the use of the thinner's sections cross-sectional area for calculations, but decreased the final strain value by ~28%.

[picture]

Fig. 10. (a) True stress-strain curves for raw and welded SS304 and (b) welded tensile specimens after testing.

Fig. 10. (a) True stress-strain curves for raw and welded SS304 and (b) welded tensile specimens after testing.

Hardness testing across an undeformed weld joint as well as across the weld joint located at the base of the pyramid (location closest to the sheet flange) and the truncated portion of the pyramid (closest to the center of the sheet) provides insight into the reaction of the material to the welding process as well as the forming process. The first observation is that, in the undeformed condition, the thicker sheets have higher hardness ( 238±7HV ) than the thinner sheets ( 220±6HV ), which is a trend that is observed across the joint in all strain conditions. Although there is variation in the hardness values, the location of the weld seam has comparable or only slightly reduced hardness compared to the adjacent blank materials. Investigating further the impact of strain on the joint hardness, the more highly strained material near the truncated portion of the pyramid has higher hardness (280±18HV) due to strain hardening and strain-induced phase transformations. While the hardness correlates well with the area near the truncated portion of the pyramid, the base of the pyramid has lower hardness ( 202±9HV ) on average than the undeformed sample ( 229±11HV ). Lower hardness with minor amounts of plastic strain is likely an effect of local residual stress reduction through phase transformations that requires further investigation to analyze thoroughly. Two-dimensional maps of the deformed material also revealed additional insight about the hardness profiles, e.g., shown in Fig. 11. The hardness along the toolside was significantly higher. The contact stress of the tool causes local plastic deformation increasing the strain and hardness on the toolside of the sheet. This toolside hardness increase was observed at both the base and near the truncated portion of the pyramid even though the average mid-thickness hardness was not as high in the base of the pyramid wall.

[picture]

Fig. 11. Two-dimensional hardness map over the deformed joint in the pyramid wall (thickness cross-section) portraying higher hardness on the toolside of the sheet (top).

Fig. 11. Two-dimensional hardness map over the deformed joint in the pyramid wall (thickness cross-section) portraying higher hardness on the toolside of the sheet (top).

Conclusion

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SS304 blanks of two different thicknesses were laser welded into a quilt pattern. The quilted blanks were subjected to SPIF to form truncated square pyramids. No signs of failure were observed after forming. Deformation across the weld seam, without compromising the integrity of the welds, was observed with optical microscopy. A temperature increase of approximately 76∘C was observed during forming. The geometrical accuracy was not significantly impacted by the weld seam location in the pyramid walls. The welded tensile specimens showed an apparent increase in strength and reduction in elongation in comparison to the raw material. Hardness measurements revealed that the hardness increased at the area near the truncated portion of the pyramid compared to the undeformed weld. Also, the hardness increased on the toolside compared to the non-toolside. Future work will focus on the effects of geometry orientation with respect to the weld location on springback and weld quality and other types of tailor welded blanks, e.g., with different material compositions. Tensile specimens extracted from the formed walls will also be analyzed to determine the effects of forming on material properties in the final part.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.243.pdf

The authors would like to thank Alex Hilliard (Phoenix Laser Solutions) for assistance with laser welding. The authors would also like to thank Mr. Daniel Johnson (Product Development Laboratory, Bucknell University) for assistance with fabrication of the SPIF fixture, specimen preparation, and equipment operation. We acknowledge the partial support of the US National Science Foundation in the form of a Travel Support Grant [CMMI 2511050], which enabled the authors to attend and present at this conference.

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The original version of this paper is available on https://www.scientific.net/SSP.389.243.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 253-266

doi: 10.4028/p-gAD5RR

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-22

Accepted:
2026-02-24

Online:
2026-04-16

Reducing the Uncertainty in Flow Forming of Metastable Austenites

The original version of this paper is available on https://www.scientific.net/SSP.389.253.pdf

Lukas Kersting 1,a,*, Mustafa Koyuncu 1, Bahman Arian 2, b, Julian Rozo Vasquez 3,c, Ansgar Trächtler 1,4, d, Werner Homberg 2,e and Frank Walther 3,f

1 Fraunhofer Institute for Mechatronic Systems Design (IEM), Paderborn, Germany

2 Paderborn University, Forming and Machining Technology (LUF), Germany

3 TU Dortmund University, Chair of Materials Test Engineering (WPT), Germany

4 Heinz Nixdorf Institute (HNI), Paderborn University, Germany

alukas.kersting@iem.fraunhofer.de; b  ba@luf.uni-paderborn.de; cjulian.rozo@tu-dortmund.de; 

d  ansgar.traechtler@hni.uni-paderborn.de; e  wh@luf.uni-paderborn.de; ffrank.walther@tu-dortmund.de

*corresponding author

Keywords: Flow forming, metastable austenites, uncertainty, closed-loop property control

Abstract

Flow forming of metastable austenites is an innovative, incremental metal forming process with special capabilities due to the TRIP effect. However, the TRIP effect during flow forming is significantly affected by disturbances and especially batch fluctuations leading to process uncertainty. This aspect is further analyzed and quantified in this paper to give insights on how to minimize the impact of uncertainty. For this purpose, semifinished parts and resulting flow forming workpieces are systemically characterized concerning their properties and the property uncertainty supported by mathematical methods like correlation analysis and error propagation. A result is that the most influencing impact factor on the strain induced α '-martensite volume fraction as a material property are batch fluctuations, specifically the variations of the chemical composition. Those especially appear from batch to batch, but also within a batch accompanied by e.g. temperature effects. To counter this challenge, different methods from control theory like closed-loop property control and adaptive control can be applied to flow forming. Thus, uncertainty will be reduced to increase process robustness and to enable industrial exploitation of the TRIP effect in flow forming of metastable austenitic steels.

Introduction

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In the automotive, aerospace and railway industry, there is a rising demand on high strength, lightweight and tamper-proof metal forming parts [1]. In context of tubular parts, flow forming of metastable austenites is proposed in academic literature as a suitable, innovative metal forming process for manufacturing [2-4]. Here, locally restricted areas of α '-martensite can be integrated into an austenitic semifinished part that might act as an invisible magnetic or QR code or as wear resistant functional elements since α '-martensite has a higher hardness and is ferromagnetic in contrast to austenite which is paramagnetic. To form the α '-martensite in the austenitic semifinished part, the TRIP effect (Transformation Induced Plasticity) of metastable austenites like AISI 304 / AISI 304L is used. Here, a strain-induced phase transformation from γ-austenite to α '-martensite takes place during plastic deformation. However besides plastic deformation and the effect of factors such as grain size and strain rate, the phase transformation is especially influenced by the forming temperature and the chemical composition of the material [5]. For this reason, the TRIP effect during metal forming is often considered as difficult to reproduce. Distinct applications are primarily found in academic literature e.g. for flow forming, deep drawing or bulk metal forming (c.f. [6-8]). In industrial mass production however, even if AISI 304 is a wide-spread material, the TRIP effect depicts more a challenge than a useful feature [9]. Taking a special regard to the flow forming process,
no industrial application is known where the TRIP effect is specifically used to set the workpiece properties. This might also be due to flow forming's process complexity. That means flow forming has many process parameters that interact in a complex way with the measurable properties of the manufactured workpieces such as the geometry or α '-martensite volume faction. However, some of the input parameters such as the geometry and material properties of the semifinished parts fluctuate, e.g. due to the accuracy and tolerances of upstream manufacturing processes [10]. Additional disturbances are also possible during the manufacturing like temperature effects. Those factors leads to a certain uncertainty in flow forming that affect the product quality [10]. There are generally different types of uncertainty in literature. It can be distinguished between aleatoric uncertainty like stochastic effects and epistemic uncertainty due to a lack of knowledge. The term uncertainty is also connected to the uncertainty of the quality measurement and of prediction models. Fortunately, it is possible to overcome uncertainty if it can be described and evaluated [11]. However, even if there are some publications that mention the uncertainty in flow forming (and also separately for the TRIP effect), there is to our knowledge no quantitative study that describes and evaluates uncertainty in flow forming of metastable austenites. This paper tries to fill the gap by presenting an experimental study about the uncertainty in flow forming of metastable austenites. In the following, uncertainty is characterized and mathematically evaluated based on experimental data from different material batches, accompanying the whole chain from the semifinished part to the final workpiece. When uncertainty is known, it will be shown and discussed how current research from the field of control engineering can help to master the uncertainty in flow forming of metastable austenites and thus improve the manufacturing process.

Process, Setup and Background

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Process setup. In context of this paper, flow forming of metastable austenites especially focusses on backward flow forming with a single roller flow forming machine. Here, a roller tool is axially moved with a defined radial infeed Δr and axial feed rate f=x˙roller  alongside a rotating workpiece (see Fig. 1a). This leads to characteristic plastic deformation of the material below the roller. In consequence, there is a wall thickness reduction Δw of the initial wall thickness w0, a material flow in opposite direction to the roller motion leading an elongation of the initial length L0 by ΔL and also a change of the α '-martensite volume fraction of the metastable austenitic workpiece material due to the strain induced phase transformation. However, the actual amount of martensite formation, elongation and wall thickness reduction also depends on the semifinished parts with its initial properties and uncertainties.

[picture]

Fig. 1. Backward flow forming process (a) and eccentricity of the semifinished parts (b)

Fig. 1. Backward flow forming process (a) and eccentricity of the semifinished parts (b)

Semifinished parts and material. In this paper, tubular semifinished parts from AISI 304L (DIN 1.4307, X2CrNi18-9) are used. The material is a stainless, metastable austenitic Cr -Ni-steel
which is nominally pure austenitic. It contains austenite stabilizing alloying elements like carbon (C), manganese (Mn), or nitrogen (Ni) and elements that support martensite formation during plastic deformation like silicon (Si) or chrome (Cr) [19]. The chemical composition, as defined by DIN EN 10216-5, is given by Table 1.

Table 1. Chemical composition of AISI 304L (1.4307, X2CrNi18-9) according to DIN EN 10216-5 [12] and the manufacturer data sheet for different batches of semifinished parts

| C | Si | Mn | P | S | N | Cr | Ni
DIN 10216-5 | ≤ 0.030 | ≤ 1.00 | ≤ 2.00 | ≤ 0.040 | ≤ 0.015 | ≤ 0.10 | 17.5 – 19.5 | 8.0 – 10.0
Batch A | 0.019 | 0.25 | 1.12 | 0.030 | 0.002 | 0.07 | 18.3 | 8.2
– 0.021 | – 0.27 | – 1.13 | – 0.031 | – 0.006
Batch B | 0.021 | 0.35 | 1.87 | 0.035 | 0.006 | 0.09 | 18.2 | 8.1
– 0.022 | – 0.38 | – 1.89 | – 0.036 | – 0.007
Batch C | 0.018 | 0.31 | 1.26 | 0.032 | 0.003 | 0.03 | 18.2 | 8.1
– 0.022 | – 0.37 | – 1.78 | – 0.036 | – 0.013 | – 0.10 | – 18.4 | – 8.2
Batch D | 0.020 | 0.39 | 1.62 | 0.038 | 0.002 | 0.03 | 18.4 | 9.2
Batch E | 0.020 | 0.26 | 1.35 | 0.032 | 0.006 | 0.06 | 18.3 | 8.2
– 0.021 | – 0.28 | – 1.38 | – 0.036 | – 0.008

However, the norm only defines boundaries for the chemical conditions. Thus, the actual chemical composition might differ from batch to batch due to tolerances. To illustrate this effect, Table 1 also contains the actual composition of five different material batches according to the manufacturer data sheets that were available to the authors of this paper. Except for Batch D, each data sheet contains the results of multiple samples that vary within a batch. It has also to be noted that the amount of some chemical elements such as copper, molybdenum or niobium is not defined in the norm. The fraction of those elements is oftentimes not delivered by the data sheet and remain uncertain since they are not controlled by the manufacturer. The semifinished parts used in this paper are cold drawn, seamless tubes manufactured according to DIN EN 1016-5. The tubes have an external diameter d= 80 mm , initial wall thickness w0=4 mm and initial length L0=150 mm. However, the initial wall thickness w0 can vary up to ±10% and the external diameter up to ±0,75% according to the norm [12]. Thus, those parameters also include uncertainty due to the variation. It has to be noted that the variation can appear from part-to-part and in a single part by the tube eccentricity (see Fig. 1b). This effect is analyzed in Fig. 2. Here, the initial wall thickness w0 was determined for a total of 144 semifinished parts from the five material batches at 24 measuring points axially and angularly distributed alongside the shape. The measurements were manually performed with caliper D4R50 (Kroeplin, Schluechtern). The results show that the mean initial wall thickness of the investigated batches, characterized by the median in the boxplots of Fig. 2, varies from 3.9 mm to 4.26 mm and also within a batch, the mean initial wall thickness w0 of each part vary up to 0.3 mm . Thus, there is a total variation of mean w0 between 3.75 mm (lowest value Batch B) and 4.4 mm (highest value Batch A) with certain overlap between the batches near the nominal value of 4 mm . Each value is within the tolerances given by DIN EN 1016-5, but the permissible range is almost entirely covered due to the variance in the reality.

[picture]

Fig. 2. Uncertainty of the (mean) initial wall thickness w0 from semifinished part to semifinished part for different material batches

Fig. 2. Uncertainty of the (mean) initial wall thickness w 0 from semifinished part to semifinished part for different material batches

In contrast to the tolerated variance of w0, the initial α '-martensite volume fraction α0′ of the semifinished parts from AISI 304L is nominally defined to be zero. However, measurements with Feritscope FMP30 (Fischer, Sindelfingen) have shown that also a slight variation of up to 1 Vol. −% can be detected in reality that might be due to the undesired inclusion of ferromagnetic phases or the presence of conductive elements such as copper. This effect also varies from batch to batch and from part to part as an uncertainty (see Fig. 3).

[picture]

Fig. 3. Uncertainty of the (mean) initial α '-martensite volume fraction α0′

Fig. 3. Uncertainty of the (mean) initial α '-martensite volume fraction α 0 ′

It can be concluded that from the semifinished parts result a certain uncertainty that might affect the flow forming process, as will be investigated in the following of this paper. However, also the measurements have a certain uncertainty due to the limited accuracy of the measurement devices used for characterization.
Measurement devices for materials characterization. In this paper, caliper D4R50 is used for measurement of the wall thickness or the determination of the wall thickness reduction Δw with an accuracy of approx. ±0,05 mm. The α '-martensite volume fraction is determined in this paper by nondestructive material testing. Here, the measurements are performed by Feritscope FMP30, that utilizes the magneto-inductive method as working principle and the correlation for the α '-martensite calculation by Talonen et al. [13]. The overall accuracy for the configuration used in this paper is 3% at maximum according to the manufacturer.

Procedure

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Methodology. The impact of the previously described uncertainty of the semifinished parts on the final flow forming workpiece is further analyzed and quantified in the following, taking the example of two different material batches (Batch A and Batch B). For this purpose, a full factorial series of experimental investigations was performed to characterize Batch B using a single roller flow forming machine Leifeld PLB 400 from Paderborn University (see [14, 15] for further details on the machine). In the experiments, workpieces were manufactured using 9 different process parameter combinations,
i.e. the feed rate f(0.1 mm/s,0.3 mm/s,0.5 mm/s) and the infeed Δr(1 mm,2 mm,3 mm) varied from workpiece to workpiece, while the rotational speed remained constant at 30 rpm . The experiments were conducted under isothermal conditions due to the cooling from the machine. However, insufficient cooling might be a disturbance variable that affects the results. Thus, the ambient and cooling temperature were also monitored among others during the experiments to capture this source of uncertainty. To handle the uncertainty, each experiment was conducted twice, as frequently performed in the flow forming literature for statistical reasons (see e.g. [16]). The results were supplemented by previous experiments that were performed under the same conditions (machine, characterization methods) in the past for Batch A. Those results were already published in [17] and will be compared to the new results for Batch B in the following. At first, the overall transfer behavior of each batch is identified which is characterized by the mean value of wall thickness reduction Δw and α '-martensite volume fraction of each specimen or process parameter combination. Based on this, the uncertainty within a batch is determined and compared to the batch-to-batch variation of the transfer behavior. The results are further discussed in the following.
Analysis of the transfer behavior (Uncertainty from batch to batch). For the analysis of the overall transfer behavior of each batch, the mean wall thickness reduction Δw of each workpiece is plotted against the process parameters f and Δr (see Fig. 4). It can be seen that Δw arise by reducing the feed and increasing the infeed. This effect is in accordance to the literature [18] and should not be further discussed at this point. Here, the focus is quantitively on the batch dependency. According to the figure, the mean wall thickness reduction Δw for both batches is quantitatively in the same range. In the experiments of Batch B, Δw tends to be larger than in Batch A. However, the mean deviation between both batches is only 0.03 mm which is in the range of the measurement accuracy of the caliper and might also result from small differences in the experimental conditions in both experimental series (e.g. operator of the machine and measurement device). Thus, it can be concluded that there is only a minor batch dependency of the resulting wall thickness reduction Δw.

[picture]

Fig. 4. Transfer behavior of the wall thickness reduction Δw for Batch A and B

Fig. 4. Transfer behavior of the wall thickness reduction Δ w for Batch A and B

For the analysis of the overall transfer behavior of the α '-martensite formation, the α '-martensite volume fraction of each workpiece is measured using the Feritscope FMP30. From the literature, it is already known that measurements should correlate in a sigmoidal shape to the strain [19, 20]. In flow forming there is especially a dependency on the radial strain φr, that corresponds to the wall thickness reduction by Eq. 1

φr=lnw0−Δww0,(1)

and the feed rate f as already found by Riepold et al. [21]. Thus, the results are plotted for the batch analysis against f and φr which is calculated by Eq. 1 from the measurements of Δw.

[picture]

Fig. 5. Transfer behavior of the α '-martensite fraction for Batch A (a) and Batch B (b)

Fig. 5. Transfer behavior of the α '-martensite fraction for Batch A (a) and Batch B (b)

It can be seen from Fig. 5 that in both batches the α '-martensite volume fraction arises by reducing feed rate f and increasing φr which is conform to the literature (see [21]). However, the results quantitively deviate from batch to batch. For Batch A, the maximum value is 71 Vol. −%, but in Batch B only 27 Vol. −% of α '-martensite is induced for the same feed rate f and a similar radial strain φr. This also applies to the other measurement results. Thus, a clear dependency on the batches can be stated because both experimental series were performed under the same nominal boundary conditions (machine, cooling temperature). It might be caused by the higher amount of austenite stabilizing manganese ( Mn ) and nitrogen ( N ) in Batch B according to Table 1 and probably by austenite stabilizing elements that are not defined in the data sheet such as copper.

To deeper analyze and to characterize the effect of the different batches on the overall transfer behavior, the measurements were approximated by a material model function (see color and grey surfaces in Fig. 5). Here, an approach from [21] for three roller flow forming has already been adapted to single roller flow forming in previous investigations by the authors. This leads to Eq. 2:

α′=gα(Δw,f)=c1·(1−exp(−abs(φr(Δw)c2)))·(f−c3).(2)

In the equation, the first term represents the dependency on radial strain φr. It resembles the models of Smaga et al. [22] or Olson and Cohen [20] that describe the nucleation and growth of α 'martensite by a sigmoidal function. The first term thus could be interpreted as a phenomenological component of the equation. In the second term, the dependency on feed rate during flow forming is described by an exponential function as an ansatz function to approximate the data. In the equation, the parameters c1,c2 and c3 are regression coefficients that can be determined by nonlinear regression (see [17,21]). The parameters of Batch A were already determined in the previous investigations by the authors and are shown in Table 2.

Table 2. Material model parameters

| C₁ | C₂ | C₃
Batch A | 19.872 | 0.0445 | 0.5169
Batch B | 5.0599 | 0.1041 | 0.7425

The table also includes the parameters for Batch B that are newly identified by nonlinear regression. In both cases, the deviations between Eq. 2 and the measurement data are less than 5 Vol. % with two exceptions at all (see Fig. 6). Thus, it can be concluded that the general functional relationship between the feed rate f, radial strain φr and α '-martensite volume fraction is the same, but the parameters vary depending on the batch. This is an important gain in knowledge given by the
experimental study in this paper. It shows that the previously investigated material model approach for flow forming is transferable to other material batches and that the batch-to-batch variation of the transfer behavior can be characterized as a variation of the model parameters.

[picture]

Fig. 6. Residuals between material model and measurements for Batch A (a) and Batch B (b)

Fig. 6. Residuals between material model and measurements for Batch A (a) and Batch B (b)

This batch-to-batch variation depicts an important uncertainty concerning the α '-martensite formation in flow forming of metastable austenites. However, there are also variations within a batch that are not visible when analyzing only the average α '-martensite volume fraction or the average wall thickness reduction. For this purpose, it is necessary to analyze the wall thickness and the α 'martensite volume fraction of every individual workpiece on its own. Thus, the uncertainty from workpiece to workpiece within the batch can be characterized. The results will be discussed in the following.
Characterization of uncertainty within a batch. To characterize the uncertainty within a batch, the deviation of single measurement values from the average for each process parameter combination, i.e. the deviation from the transfer behavior, is further analyzed. For the wall thickness reduction Δw of Batch A, it can be seen from Fig. 7a that the measurement values deviate between -0.03 mm and 0.04 mm from the average value. However, for most process parameter combinations the deviation is lower. Thus, the mean deviation of all process parameter combinations is 0.014 mm . For Batch B, the results are similar (see Fig. 7b). Here, the deviation lays in a range between -0.05 mm and 0.05 mm , and the mean deviation is 0.02 mm . Hence, there is no batch dependency on the results. Furthermore, there is no clear dependency on process parameters visible for both batches. Thus, the deviation seems to be a stochastic effect. The amount of deviation is in the range of the measurement accuracy of the caliper D4R50 that was utilized for the wall thickness measurement. For this reason, it cannot be clearly stated whether the deviation results from the measurement, from inhomogeneities of the initial wall thickness within a batch or from other random effects.

For the α '-martensite volume fraction of Batch A, the results are shown in Fig. 7c. Here, the measurement values by Feritscope FMP30 deviate −4.36Vol.−% and 3.6Vol.−% from the average value and the mean deviation is 1.96 Vol-%. For Batch B, the deviation is much lower with range of ±1.165Vol.−% and a mean deviation of 0.425Vol.−% (see Fig. 7d). Thus, a clear batch dependency on the uncertainty is obvious that correlates to the amount of α '-martensite. For example, the mean percentage deviation (quotient of deviation and average value) is 7% for Batch A and 5% for Batch B with a maximum deviation of 18% for Batch A and 19% for Batch B. This percentage deviation exceeds the measurement error of the Feritscope that has a trueness error of ≤3% and a repeatability error of ≤1% according to the data sheet of the manufacturer. Thus, other possible reasons are analyzed based on the material model (Eq. 2).

[picture]

Fig. 7. Process deviations of the wall thickness reduction δΔw and α '-martensite volume fraction δα′ from the average values for Batch A(a+c) and Batch B(b+d) during repetitive experiments

Fig. 7. Process deviations of the wall thickness reduction δ Δ w and α '-martensite volume fraction δ α ′ from the average values for Batch A ( a + c ) and Batch B ( b + d ) during repetitive experiments

According to the equation, there are three factors that have an impact on the calculated α′ martensite volume fraction: the feed rate and the wall thickness reduction acting as input quantities, as well as the model parameters c1,c2 and c3 that describe the transfer behavior. However, while the feed rate is the same for each process parameter combination, the wall thickness reduction stochastically varies according to Fig. 7. It is analysed in the following how the uncertainty of wall thickness reduction leads to an uncertainty of the α '-martensite volume fraction by using the mathematical method of error propagation. According to [23], error propagation via a function y=g(x1,…xm) is described by Eq. 3

(δy)2=∑i=1m(∂g(x1,…xm)∂xi)2|0(δxi)2,(3)

where ∂g(x1,…xm)∂xi denotes the partial derivative of function g for an arbitrary operating point, δxi denotes the deviation of the system inputs x1…xm and δy is the deviation of the system output. In most cases, for δx the standard deviation is chosen. However, Eq. 3 can be applied to an arbitrary deviation, if the deviation is sufficiently small. This restriction is caused by the fact that Eq. 3 is built on Taylor series expansion and linearization. In the following, the deviations from Fig. 7 are used that are in the range of the standard deviation. Thus, the equation can be applied.

For the analysis, it is additionally assumed that the model parameters are certain. In this case, the wall thickness reduction Δw is the only uncertain input δxi and Eq. 3 is reduced to Eq. 4

δy=∂g(x1,…xm)∂x1|0δx1.(4)

More specifically, the deviation of the α′-martensite volume fraction δα′ is calculated by the deviation of the wall thickness reduction δΔw and the partial derivative of function g. In this case, function g is given by the material model equation 2 and the partial derivative (Eq. 5) is

∂gα∂Δw|Δw0,f0=c3c1(1−e−[φr(Δw0)]c2)·f0c3−1.(5)

Here, Δw0 and f0 denotes the nominal wall thickness reduction and the feed rate at the operating point, i.e. in case of uncertainty the mean values of Δw and f for multiple repetitions of specific process parameter combinations. This leads to Eq. 6 that describes the deviation of the α '-martensite volume fraction δα′ :

δα′(δΔw,Δw0,f0)=c3c1(1−e−[φr(Δw0)]c2)·f0c3−1·δΔw(6)

This equation can now be applied to the experimental results from Fig. 7a and b to estimate the impact of the wall thickness deviation δΔw on the α '-martensite deviation. For this purpose, the deviation δΔw from Fig. 7, the feed rate f0=f related to those deviations and the measured mean wall thickness reduction Δw0=Δw from Fig. 4 are inserted in Eq. 6 and the α '-martensite deviation δαprop ′=δα′(δΔw,Δw0,f0) is calculated via propagation. The results are shown in Fig. 8 in comparison to the measured values αmeas ′ from the previous figure.

[picture]

Fig. 8. Comparison between the α′-martensite deviations of each experiment δαmeas ′ from Fig. 7, measured via Feritscope, and the propagated α′-martensite deviations δαprop ′, calculated from the wall thickness deviation δΔw, for Batch A (a) and Batch B

Fig. 8. Comparison between the α ′ -martensite deviations of each experiment δ α meas ′ from Fig. 7, measured via Feritscope, and the propagated α ′ -martensite deviations δ α prop ′ , calculated from the wall thickness deviation δ Δ w , for Batch A (a) and Batch B

If all the measured α′-martensite deviations δαmeas ′ result from the uncertainty of the plastic deformation leading to δΔw, the quantities δαprop ′ and δαmeas ′ would be equal. Thus, the data points in Fig. 8 would lay on the diagonal line that represents the equality of δαprop ′ and δαmeas ′. However, it can be seen from Fig. 8 a for Batch A that δαmeas ′ deviates from δαprop ′ for most data points with a wide scatter in vertical direction of the plot. Thus, δαmeas ′ must be caused by another phenomenon. For Batch B, the results are more compact without the large scatter. However, also in this case the data points are not aligned along the diagonal.

It can be concluded that the deviation of the α '-martensite volume fraction does not result from the wall thickness reduction. Thus, there must be an uncertainty of the model parameters c1,c2 and c3. From Table 2, it is already known that the material depicts a parametric uncertainty. In principle, a variation of the temperature may lead to a parametric uncertainty because α '-martensite is significantly influenced by the temperature (see [19, 20]). However, the experiments were performed with the same cooling as confirmed by additional measurement of the ambient and cooling temperature with minor variations of max. 3.5∘C, but those variations do not correlate the deviation of the α '-martensite. Therefore, the most probable explanation for the deviation of the α '-martensite
are inhomogeneities of the material and fluctuations of the chemical composition within a batch. However, those variations within the batch are on a lower scale than the batch-to-batch variations.

Countering the Uncertainty by Closed-Loop Property Control

The original version of this paper is available on https://www.scientific.net/SSP.389.253.pdf

Nevertheless, both inner-batch and batch-to-batch variations are undesirable and should be reduced or minimized to produce workpieces of a specific quality. At this point, the usage of property control approaches from control engineering in context of flow forming could help to improve the flow forming of metastable. One possibility to counter the uncertainty is closed-loop property control. This type of control was proposed in [24] by Allwood et al. as a strategy to control metal forming processes. For the special case of flow forming of metastable austenite, the authors of the present paper already presented and validated a closed-loop property control approach in [25]. It consists of a control for the α '-martensite volume fraction ( α '-martensite control) that is (optionally) extended by a control of the wall thickness reduction (wall thickness control) to ensure desired geometry while controlling the α '-martensite fraction. The general structure is shown in Fig. 9.

[picture]

Fig. 9. Closed-loop property control structure for flow forming of metastable austenites

Fig. 9. Closed-loop property control structure for flow forming of metastable austenites

In the closed-loop control, the infeed Δr is corrected for setting the wall thickness reduction to a desired value and the feed rate f is utilized to achieve the desired α '-martensite volume fraction. For this purpose, the α '-martensite volume fraction is determined with a soft sensor approach since the Feritscope FMP30 is not suitable to detect the α '-martensite volume online during the workpiece production. For the soft sensor, micromagnetic measurements of the magnetic Barkhausen noise (MBN) with a 3MA-II sensor (Fraunhofer IZFP, Saarbruecken) or eddy current (EC) measurement by e.g. Elotest PL600 (Rohmann, Frankenthal) are used. Those sensors are placed at the machine support of the flow forming machine moving with the roller alongside the workpiece and measuring continuously in the already deformed workpiece area. There are also two laser distance sensors OM 70 (Baumer, Frauenfeld) mounted at the machine. One of the laser distance sensors is measuring in the deformed and the other in the undeformed area of the workpiece. From the difference of both sensor signals, the wall thickness reduction Δwmeasured  is determined. Thus, online information about wall thickness reduction and the α '-martensite volume during flow forming is available as a feedback signal for the closed-loop control. Those feedback signals are further processed by a property controller. In the approach from [25], a PI controller is utilized for each control. The PI controller consists of a proportional and an integral gain. Both gains have a constant value that is predetermined by model-based control design methods offline before workpiece production with a real-time model of the flow forming process. The predetermined controller gains are then included
into the flow forming machine control. Thus, they can be used online to calculate the correction signal to the feed rate f or the infeed Δr. This approach has already been successfully validated in [25]. However, it was not analyzed how the controller deals with the uncertainty in flow forming. This is investigated in the following for the α '-martensite control. For this purpose, a simulative study is performed using a real-time simulation model for flow forming of metastable austenites that was already proposed by the authors in [14, 26, 27]. In the study, multiple parts are manufactured closedloop controlled with the same parameter combination while the α '-martensite formation is stochastically varied from part to part within range of the previously identified inner-batch fluctuations. Fig. 10 shows the result of the simulation study for Batch B. The aim was here to set the α '-martensite volume fraction to a desired value of 14Vol.−%. This is achieved by consecutively reducing initial feed rate starting from f=0.25 mm/s.

[picture]

Fig. 10. Simulation result of the α '-martensite control for an uncertain α '-martensite phase transformation behavior (Batch B, Elotest soft sensor)

Fig. 10. Simulation result of the α '-martensite control for an uncertain α '-martensite phase transformation behavior (Batch B, Elotest soft sensor)

It can be seen from the measured α '-martensite volume fraction that the uncertainty leads to different initial values at the beginning that vary between 7.3 Vol. −% and 9.3 Vol. −%. Despite this variation, the desired value of 14Vol.−% is finally reached in any case. This is possible since the controller corrects the feed rate f depending on the measurements to a value between 0.1315 mm/s and 0.1552 mm/s. Thus, the control reacts on the inner-batch variations. It can be stated that the uncertainty in the α '-martensite volume fraction leads to uncertainty in the feed rate f (both marked in grey in the figure), but the uncertainty concerning the α '-martensite formation within a batch is successfully compensated by the control. It is obvious that the control performance, i.e. the dynamics or the speed until reaching the desired value and the damping behavior of the control response, is also slightly affected by the uncertainty of α '-martensite formation. However, the impact of the uncertainty on the control performance is only minor if the uncertainty is within the range of the inner-batch variations. In the figure, there is also a simulation result where α '-martensite volume fraction at the beginning is 5.5 Vol.-%. It means that the deviation is outside of the inner-batch uncertainty, which may occur if the semifinished part belongs to another batch for example. In this case, the control reaction tends to overshoot, and if the deviation would be higher, the control becomes even unstable. Hence, the change to another batch depicts a limit for the constant-gain closed-loop property control.

It can be concluded that closed-loop property control with a constant gain is suitable to reduce the uncertainty within a batch. To handle the variety from batch to batch, it is necessary to retune the controller parameters. This could be done manually by identifying the transfer behavior or the parameters in Eq. 2 and applying the model-based control design methodology from [25] again for the new batch. However, this approach may be time consuming, as some workpieces for model identification must first be manufactured in an open-loop (without property control) before the actual workpieces with defined properties can be produced in the closed-loop control. Another possible solution is to adapt the controller parameters automatically. In this context, the closed-loop property control could be extended to an adaptive property control to automatically adapt the controller parameters concerning the batch-to-batch variations. The term adaptive control means that the controller parameters and / or the model for the determination of the controller parameters are automatically updated depending on the online measurements from the actual system. This type of control already exist in control engineering and the industry since the 1980's, but in the field of metal forming, an application of adaptive control in the sense of a closed-loop control adaption is only investigated in a few examples (see [28,29]) until now. To extent the flow forming closed-loop property control, a suitable adaptation algorithm for PI controller is required. There are different types of adaption algorithms that can be divided in indirect methods, where a model is automatically updated and then the controller is systematically designed, and direct methods such as model reference adaptive control where the controller parameters are directly updated (see [30]). Such an approach could be adapted to flow forming to automatically counter the batch-to-batch uncertainty. In this case, the closed-loop property control would be extended by a closed-loop-controlled model and the measurements from the actual system would be continuously compared to the model. From the deviation between model and the actual system, the new controller parameters could be automatically calculated by a modified extended Kalman filter (MEKF, see [31]). However, this approach is not state of the art for flow forming and should be further investigated in future.

Summary

The original version of this paper is available on https://www.scientific.net/SSP.389.253.pdf

This paper focused on the uncertainty in flow forming of metastable austenites. Besides disturbance variables such as the temperature, this uncertainty especially results from the chemical composition and the initial wall thickness of the semifinished parts which differ from batch-to-batch and within a batch. It was found out that the uncertainty of the mean initial wall thickness leads to a small deviation of the resulting wall thickness reduction from part to part and does not significantly differ from batch to batch. However, it was evidenced that the α '-martensite formation shows a strong dependency on the material batch leading quantitively to a totally different transfer behavior. This effect could be interpreted as a parametric uncertainty. Additionally, there are also fluctuations in the experimental results within a batch that are directly related to the α '-martensite formation because they do not result from the uncertainty in plastic deformation as shown in the error propagation analysis. Thus, solutions are necessary to reduce the uncertainty from batch to batch and within a batch. It was shown that for the inner-batch fluctuations closed-loop property control is a suitable solution to reduce the uncertainty. To automatically counter batch-to-batch fluctuations, current research of the authors focuses on extending the existing closed-loop property control to an adaptive control that can adapt the controller parameters to an unknown material batch without additional experiments. Thus, the uncertainty in flow forming of metastable austenites could be reduced fully automatically in any case.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.253.pdf

The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for their support of the depicted research within the priority program SPP 2183 "Property-controlled metal forming processes", through project no. 424335026 "Property control during spinning of metastable austenites".

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The original version of this paper is available on https://www.scientific.net/SSP.389.253.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 267-275

doi: 10.4028/p-OGKr4i

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-22

Accepted:
2026-02-24

Online:
2026-04-16

Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

Ali Beigzadeh 1,a, Enrico Simonetto 1, b, Andrea Ghiotti 1,c and Stefania Bruschi 1, d

¹Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131, Padova, Italy

a* ali.beigzadeh@phd.unipd.it, b enrico.simonetto.1@unipd.it, c andrea.ghiotti@unipd.it, d  stefania.bruschi@unipd.it

*Corresponding author

Keywords: tubes, roll forming, incremental forming.

Abstract

Thick-walled longitudinally arc-welded tubes are indispensable in modern infrastructure owing to their exceptional load-bearing capacity and structural integrity. Nevertheless, their fabrication remains highly challenging, as the conventional forming forces demand the use of largescale industrial presses. To address this limitation, this research introduces a novel process architecture that integrates agile tube roll forming process for tube manufacturing, thereby enabling the production of such tubes using significantly smaller and more flexible manufacturing systems. To this end, three tube support configurations-namely, support-less, dynamic roller support, and static support-were systematically investigated in this study on 7,9,11, and 15 mm thick 304 stainless steel. While the supportless condition represents the most economical option, the incorporation of dynamic or static support significantly improves geometric accuracy, yielding near-net cross-sections combined with reductions in tube ovality of approximately 75 and 79%, respectively, compared to support-less configuration. Considering the straightness of the weld line as a quality indice, the dynamic support provides the highest quality. Using the static/dynamic support strategies, the deformation forces arise between 2 and 3 times compared to support-less strategy.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

The longitudinally welded Tubes are indispensable components in modern engineering, serving two principal roles. Structurally, they are widely employed in construction, infrastructure, and automotive systems, where durability, high strength-to-weight ratio, precision, and cost efficiency are critical. In fluid transport, they ensure the continuous and reliable conveyance of oil, gas, and water. Stainless steel welded tubes, in particular, are vital in the food, chemical, pharmaceutical, and all other industries, where superior corrosion resistance and hygienic performance are required.

Longitudinally welded tubes are commonly manufactured using the processes: I) Continuous roll forming (tube mill), II) UOE forming (U-press, O-press, expansion), and III) JCOE forming (J-press, C-press, O-press, expansion). Fig. 1 illustrates approximate thickness-diameter applicability ranges according to the industrial catalogues from Japan, China, the UK, the USA, and Türkiye (Turkey).

[picture]

Fig. 1. Approximate thickness-diameter applicability ranges for tube roll forming, UOE forming, and JCOE forming processes.

Fig. 1. Approximate thickness-diameter applicability ranges for tube roll forming, UOE forming, and JCOE forming processes.

Roll forming is a continuous process in which a (commonly coiled) metal strip passes through successive, precisely aligned roll stands that incrementally shape it into a constant open and closed cross-section [1], resulting in comparatively low forming forces. While the process is highly economical for large-scale production, it is generally uneconomical for small batches [2] due to the high initial expense of manufacturing the roll tools and providing the motors needed to drive the rollers.

To address this gap, agile roll forming process has been introduced. Agile roll forming process [3] is the new concept of roll forming processes in which a blank-holder constrains the blank while a (pair of) roller(s) move(s) both along and perpendicular to [4,5] the length of the profile and incrementally shape(s) the blank into the desired profile. This concept minimizes the number of the rollers, minimizing the initial manufacturing cost and time, resulting in agility. While this concept has been successfully fulfilled manufacturing of uniform [ 3,4 ] and non-uniform [ 5,6 ] open profiles, the manufacturing of closed profiles hasn't been investigated yet. To enable tube manufacturing using the agile roll forming machine, it is necessary to redesign the roller system and the blank-holder section based on the forming strategy.

This study introduces a novel process concept for the production of longitudinally welded tubes, roller design, and integration of various process configurations. The target geometry is a tube with an outer diameter of 200 mm and a length of 500 mm .

Design and Numerical Modeling of Agile Tube Roll Forming Process concepts.

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

Agile Tube Roll Forming configurations

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

Fig. 2 presents three configurations of the agile tube roll forming process: (a) support-less, (b) dynamic support-assisted, and (c) static support-assisted. The support-less configuration represents the simplest setup, aiming to minimize initial cost and system complexity, thereby achieving the highest level of process agility. The static support-assisted configuration provides internal surface referencing of the tube to enhance dimensional accuracy while maintaining a relatively simple dynamic process. This configuration is more suitable for shorter tubes, whereas the dynamic supportassisted configuration is preferable for longer tubes when higher dimensional accuracy is required.

[picture]

Fig. 2. Schematic of the agile tube roll forming process for production of longitudinal welded tubes; (a) Support-less, (b) Static support, and (c) Dynamic support. (d) Dimensions and lateral view of the Forming roller and support.

Fig. 2. Schematic of the agile tube roll forming process for production of longitudinal welded tubes; (a) Support-less, (b) Static support, and (c) Dynamic support. (d) Dimensions and lateral view of the Forming roller and support.

Forming strategy

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

Several forming strategies-namely the W (reverse) forming, Double Radius (DR) forming, Single Radius (SR), and edge forming strategies-are available in conventional tube roll forming technology [7,8]. Among these, the edge forming approach enables the use of one roller (set), making it particularly suitable for the proposed process. Accordingly, this strategy and its corresponding flower pattern are adopted in the present research.

Stripe feed and toolpath

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To achieve the final tube shape, a coordinated combination of stripe feeding and repetitive roller movements is essential. Fig. 3 illustrates the toolpath and stripe feed in the agile tube roll forming process. During the forming stage, the roller(s) move along the y -direction (longitudinal axis of the
tube), transferring the roller profile into the stripe. After completing each forming step, the stripe is fed along the x -direction. The repeated sequence of these motions ultimately results in the formation of the desired tube shape.

Schematic illustration of the coordinated roller and stripe feed motions in the agile tube roll forming process. The diagram depicts 18 representative forming steps. The red dashed line represents the roller position along the y -direction, and the blue dashed line denotes the stripe feed along the x direction. The accompanying schematic shows the progressive formation of the half-tube profile in the x−z plane corresponding to each forming step.

[picture]

Fig. 3. Toolpath and feed movement in agile flexible roll forming process.

Fig. 3. Toolpath and feed movement in agile flexible roll forming process.

Material

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In this study, AISI 304 steel was selected as the reference material. Test specimens were prepared from strips with an initial width of 200 mm . Using laser cutting, tensile samples were fabricated with a gauge length of 8 mm and a gauge width of 3 mm , as illustrated in Fig. 4-(a). The specimens were oriented at 0∘,45∘, and 90∘ relative to the rolling direction. Tensile experiments were carried out at room temperature on an MTS 322TM  hydraulic dynamometer equipped with a Zeiss Gom Aramis DIC system, which was employed to capture the true strain paths of the samples. All tests were performed at a strain rate of 0.1 s−1, corresponding to the strain rates typically observed in roll forming operations. The resulting true stress-strain curves (Fig. 4-(b)) were subsequently incorporated into the numerical roll forming model.

[picture]

Fig. 4. Tensile test results of the reference material.

Fig. 4. Tensile test results of the reference material.

Modeling

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The forming process was simulated using the LS-Dyna TM software environment and solved using an implicit solver for the tube roll forming process following by implicit calculation of the elastic recovery (springback). The 7,9,11, and 15 mm thick stripes with a length of 325.1,328.1,331.3, and 337.6 mm , respectively, and a width of 500 mm were modeled as a deformable part discretized using rectangular meshes, using fully integrated shell elements, having an average size of 1 mm along xdirection and 5 mm along y -direction and 7 integration points through thickness (z-direction).

The interaction between rollers and strips was modeled using a Coulomb friction model with both static and dynamic friction coefficients set to 0.2 . To achieve the desired geometry along the length of the tube, rollers move along the y-direction to copy the shape of the rollers' contact to the sheet. After the rollers pass completely along the tube length, the blank holder releases the strip, and the strip advances incrementally along the x -direction. This loop repeats multiple times till reaching the ideal geometry of the tube.

To determine the optimal setup design, the process was modeled under three different conditions (see Fig. 2): (a) support-less, (b) dynamic support-assisted, and (c) static support-assisted agile roll forming. The forming rollers and the dynamic/static supports were represented using fully integrated rigid shell elements, with mesh sizes ranging from 0.5 mm to 1 mm depending on geometric complexity. The interaction between rollers and strips was modeled using a Coulomb friction model with both static and dynamic friction coefficients set to 0.2 . To achieve the desired geometry along the length of the tube, the toolpath method described in Fig. 3 has been implemented.

The blank holder was modeled using fully integrated rigid shell elements with a size of 2.5 mm . Similar to the roller/support-stripe interaction, static and dynamic friction coefficients set to 0.2 for the blank holder-stripe interaction. The cyclic load between the blank holders and stripe set to 200 MPa during the forming and 0 in the stripe feed stage.

Results and Discussion

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Cross-sectional view

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Fig. 5 illustrates the cross-sectional views of the tubes produced by agile roll forming, with the corresponding strain distribution along the circumference, obtained using a cutting plane normal to the y -axis at y=250 mm. The results highlight the influence of thickness and support technology on both the geometry and strain localization. At smaller thicknesses, the sections deviate more significantly from the ideal circular shape, resulting in higher ovality. As the tube thickness increases, the proportion of the elastically deformed region relative to the plastically deformed region through the thickness of the tube decreases, resulting in a lower elastic recovery level. Generally, the results demonstrate that not only the ovality is minimized in thicker tubes, but also the strain distribution is more homogeneous, leading to improved geometric accuracy.

[picture]

Fig. 5. Cross-sectional view of the tubes modelled using agile tube roll forming technology.

Fig. 5. Cross-sectional view of the tubes modelled using agile tube roll forming technology.

On the other hand, in the support-assisted agile tube roll forming setups, the dynamic/static support part acts as a reference for the inner surface of the tube, it leads to better cross-sectional accuracy by decreasing the ovality, showing the importance of using a support in agile tube roll forming. As the static support provides a more global support for inner surface of the tube, it improves the strain distribution in static support assisted agile roll forming compared to the dynamic-assisted condition.

The effective plastic strain maps reveal that deformation is concentrated at specific angular positions, particularly near the forming closure regions ( ζ=0∘ ), where localized peaks in strain appear. On the other hand, around ζ=90∘, especially when using the dynamic support, there is strain nonhomogeneity, referring to the Roller(s)-stripe separation point. Around ζ=180∘ which is the end of the stripe, there is not enough material flow because of the boundary condition applied and when the thickness is maximum, another peak is observed.

Ovality

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As shown in Fig. 6, tube ovality is significantly influenced by both thickness and the applied support condition. The support-less case exhibited the highest ovality, ranging between 13.5% and
22.6%, which reflects considerable geometric distortion caused by springback and non-uniform deformation. With the application of dynamic support, ovality values were reduced to a lower level, starting at approximately 8.3% for the thinnest tube and steadily decreasing to 0.4% as thickness increased. The static support condition provided the most favorable results, maintaining ovality 4.9% for the thinnest tube and approaching below 2.5% in the 9,11 , and 15 mm thick tubes.

Two clear trends can be identified from these results. First, increasing tube thickness enhances circularity, as the higher elastic-to-plastic ratio through the wall reduces distortion. Second, the introduction of support systems-especially static support-improves process stability by decreasing the sensitivity of the process to thickness change. From a manufacturing perspective, these findings demonstrate that support-assisted strategies are highly effective in reducing cross-sectional distortion and ensuring improved geometric accuracy in agile roll forming.

[picture]

Fig. 6. (a) Ovality index results. (b) Schematic of tube cross-section showing the dmin and dmax.

Fig. 6. (a) Ovality index results. (b) Schematic of tube cross-section showing the d min and d max .

Straightness of the weld line

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Fig. 7 represents the straightness of the formed weld line as a factor to investigate the quality of the manufactured tube. Considering the thickness, the maximum deviation of the weld line-excluding the support condition effect-decreases from 22 to 12 mm , where the thickness increases from 7 to 15 mm . The dynamic assisted support condition shows its success in reaching the best weld line quality, by reaching to a deviation of around 2 mm in the case of the 9 mm thick tube. On average, the support-less configuration leads to higher deviations along the weld line, which shows the importance of support to avoid deviations. On the other hand, the use of dynamic support prevents unnecessary stripe-support contact, resulting in lower deviations along the weld line.

[picture]

Fig. 7. Straightness of weld line; (a) 7 mm , (b) 9 mm , (c) 11 mm , and (d) 15 mm tubes.

Fig. 7. Straightness of weld line; (a) 7 mm , (b) 9 mm , (c) 11 mm , and (d) 15 mm tubes.

Forming Forces

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Fig. 8 shows the deformation forces along the x,y, and z directions, as well as the total force, for tubes produced under different support conditions and thicknesses. While in the case of the supportless and dynamic support configurations, Fx is the dominant component of the deformation force, Fz is the dominating force in the case of the static support. The Fy which represents the force along the tube axis, remained the smallest contribution of the deformation force components. The values of the Fy remains constant when the thickness is the same and the support configuration changes.

In the support-less condition, the forces rise steadily with thickness, with the total force in the range of 48 kN for the thinnest to 198 kN for the thickest tube. Using the dynamic/static support, the overall force level rises between 2 and 3 times compared to the support-less case, revealing that dynamic/static support redistributes the deformation more uniformly but requires greater load.

From a manufacturing standpoint, these results highlight that support strategies not only influence the geometric quality of the tube but also affect the forming load requirements, similar to the comparison of die-less and die-assisted forging processes.

[picture]

Fig. 8. Force diagrams; (a) 7 mm , (b) 9 mm , (c) 11 mm , and (d) 15 mm tubes.

Fig. 8. Force diagrams; (a) 7 mm , (b) 9 mm , (c) 11 mm , and (d) 15 mm tubes.

Conclusion

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This paper depicts the potential of the novel agile tube roll forming process to manufacture thick tubes with three different strategies. This process decreases the initial costs of the manufacturing setup compared to the conventional tube roll forming processes by decreasing the number of the roll stands and tube pressing (UOE and JCOE) by using the smaller presses.

From manufacturing standpoint, while the support-less condition represents the most economic condition combined with the less complexity of the machine design and lower forming forces, the
support assisted processes represent better cross section by decreasing the ovality of the tube and better strain distribution.

In summary:

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Using a dynamic support results in localized plastic strain around ζ=0∘ and ζ=90∘.

Ovality decreases from 18% (support-less) to 4.5% (dynamic) and 3.6% (static), representing reductions of 75% and 79%, respectively.

Dynamic support yields the highest weld line straightness.

Deformation forces increase 2−3 times with support compared to support-less condition, reflecting a trade-off between precision and deformation force.

Acknowledgment

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

This study was carried out within the PNRR research activities of the consortium iNEST (Interconnected North-Est Innovation Ecosystem) funded by the European Union NextGenerationEU (Piano Nazionale di Ripresa e Resilienza (PNRR) - Missione 4 Componente 2, Investimento 1.5 D.D. 1058 23/06/2022, ECS_00000043). This manuscript reflects only the Authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.267.pdf

Hofmann J, Becker M, Kubik C, Groche P. Machine learning based operator assistance in roll forming. Production Engineering 2025;19:283-94. https://doi.org/10.1007/s11740-024-01311-0.

Suckow T, Schroeder J, Groche P. Roll forming of a high strength AA7075 aluminum tube. Production Engineering 2021;15:573-86. .

Simonetto E, Ghiotti A, Bruschi S. Agile manufacturing of complex shaped bent profiles by incremental deformation. Manuf Lett 2023;36:40-3. .

Simonetto E, Beigzadeh A, Ghiotti A, Bruschi S. Manufacturing Letters Evaluation of the effect of forming strategy in newly introduced flexible roll forming process. vol. 41. 2024.

Beigzadeh A, Simonetto E, Ghiotti A, Bruschi S. Tool path effects on wrinkling in metal sheet incremental roll profiling. Materials Research Proceedings, vol. 41, Association of American Publishers; 2024, p. 1446-55. .

Essa A, Abeyrathna B, Rolfe B, Weiss M. Incremental shape rolling of a variable depth profile. J Mater Process Technol 2023;316. .

Simonetto E, Wang Q, Ghiotti A, Bruschi S. Forming Quality Indices for Tube Roll Forming: Definition and Modelling. Lecture Notes in Mechanical Engineering, Springer Science and Business Media Deutschland GmbH; 2024, p. 569-76. .

Emami Satellou AA, Sedighi M. Effect of different roll-forming flower patterns on coiled tubing ovality and pressure performance. Geoenergy Science and Engineering 2023;225. .

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 277-284

doi: 10.4028/p-I1ojoL

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-21

Accepted:
2026-02-24

Online:
2026-04-16

Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

The original version of this paper is available on https://www.scientific.net/SSP.389.277.pdf

Mehmet Okan Görtan 1,a*, Ümit Türkmen 2,b, İlker Kuzucu 2,c, Elif Çivisöker 2,d Rahman Ehvan 2,e

1 Hacettepe University, Mechanical Engineering Department, Ankara/Türkiye

2 Rokeron Otomotiv A.S., Kocaeli/Türkiye

a okangortan@hacettepe.edu.tr, b umitturkmen@rokeron.com, cilkerkuzucu@rokeron.com,

Keywords: Flexible roll forming, advanced high strength steels, height-variable profiles, finite element analysis.

Abstract

In the present study, the technical feasibility of manufacturing a height-variable profile from an advanced high-strength steel (AHSS) sheet using the roll forming process was investigated through finite element analysis (FEA). The study focused on the production of a cross member used in a B-segment passenger vehicle. For this purpose, the kinematics of the forming rolls in both the height and longitudinal directions were derived and integrated into the finite element model. The sheet metal was modeled using both shell and solid (3D) elements. These two different modeling strategies were evaluated in terms of the formed profile geometry. The results demonstrated that the manufacturing of the selected cross member is feasible with the derived roll kinematics. Additionally, it was observed that the use of shell elements led to higher deviations from the desired geometry compared to solid elements. The analyses are planned to be validated experimentally in the next phase of the study.

Introduction

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In the automotive industry, two major trends that have defined the past decade are vehicle lightweighting efforts aimed at reducing exhaust emissions and initiatives to lower production costs. The roll forming process is particularly suitable for the economical manufacturing of profile-shaped components made from high-strength steel sheets. However, this method inherently produces profiles with a constant cross-section [1]. Nevertheless, in automotive applications, the use of straight profiles is often inefficient in terms of load-bearing capacity. Therefore, it becomes necessary to produce profiles with variable height along their length.

In recent years, flexible roll forming (FRF) has emerged as a promising manufacturing technique to overcome this limitation by enabling the production of profiles with a variable cross-section along their length. In contrast to conventional roll forming, FRF allows the roll stands to move laterally, enabling the gradual variation of profile height and thus improving structural efficiency and loadbearing performance. Owing to these advantages, flexible roll forming has attracted increasing attention, particularly for lightweight structural applications in the automotive industry [2-5].

However, the majority of previous studies on flexible roll forming have focused on low- to medium-strength steels, primarily due to their higher formability and lower risk of process instabilities. The application of FRF to advanced high-strength steels (AHSS), such as DP980, remains limited in the literature. This is mainly attributed to the increased forming forces, higher springback, and elevated risk of edge cracking associated with these materials. As a result, the forming behavior and geometrical accuracy of height-variable profiles made from AHSS are not yet sufficiently understood.

In this study, a finite element analysis of the flexible roll forming process applied to height-variable profiles made of DP980 advanced high-strength steel is presented. The numerical model aims to capture the deformation behavior, and final geometry of the formed profiles. Particular emphasis is
placed on evaluating the capability of different element formulations, namely solid and shell elements, to accurately predict the profile geometry and deformation characteristics.

Material and Methodology

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The finite element model of the height-variable profile was developed using MSC.Marc 2022.4. A schematic side view of the investigated profile geometry is shown in Fig. 1. The profile has a total length of 900 mm and corresponds to a hat-shaped cross-section, which is commonly used in automotive structural applications. The maximum profile height is 21 mm , while the minimum height is 13 mm . Between these two regions, the profile geometry transitions through three different radii, whereas the remaining sections are designed with linear height variation. The sheet thickness of the profile is constant and equal to 1.0 mm .

[picture]

Fig. 1. Geometrical properties of the investigated profile.

Fig. 1. Geometrical properties of the investigated profile.

The roll geometries were modeled as rigid bodies. The arrangement and dimensions of the forming, support, and feeding rolls are schematically illustrated in Fig. 2. The feeding rolls, highlighted in yellow and orange, rotate only about their own axes and do not perform any additional translational motion during the process. The support rolls, shown in green, also rotate during forming; however, their positions in the X-direction are adjusted at each forming step to match the local profile geometry.

The forming rolls, depicted in blue, perform both rotational and translational motions during the forming process. The lower forming roll is designed to be movable only in the height direction (Ydirection), whereas the upper forming roll is movable in both the Y - and Z -directions. This kinematic configuration enables the gradual variation of profile height along the longitudinal direction and represents the key mechanism of the flexible roll forming process.

[picture]

Fig. 2. Schematic view of the roll configuration (a) side view and (b) front view of forming rolls.

Fig. 2. Schematic view of the roll configuration (a) side view and (b) front view of forming rolls.

The motions of the top and bottom forming rolls in the Y - and Z -directions were defined based on the target profile geometry shown in Fig. 1. The roll trajectories at the final forming step are presented as representative examples in Fig. 3 and Fig. 4. During the derivation of these kinematics, particular attention was given to ensuring that the forming rolls accurately follow the cross-section of the height-
variable profile and remain in continuous tangential contact with the sheet throughout the forming process.

The investigated hat-shaped profile was designed to be bent by 10 degrees at each forming step, resulting in a total of nine forming steps to achieve the final geometry. This stepwise forming strategy enables a gradual deformation of the sheet and reduces the risk of excessive local strains, which is particularly important when forming advanced high-strength steels such as DP980.

[picture]

Fig. 3. Displacement in Y-direction of the top and bottom forming rolls in the last forming station.

Fig. 3. Displacement in Y-direction of the top and bottom forming rolls in the last forming station.

[picture]

Fig. 4. Displacement in Z -direction of the top forming roll in the last forming station.

Fig. 4. Displacement in Z -direction of the top forming roll in the last forming station.

In the developed finite element model, the sheet material was defined as deformable, while the rolls were modeled as rigid bodies. An example of the numerical model is shown in Fig. 6. Owing to the symmetric geometry of the hat-shaped profile, only half of the sheet was modeled to reduce computational cost. The sheet was constrained by applying displacement boundary conditions in the directions indicated by the green arrows in Fig. 5. In addition, the sheet motion was restricted in the direction shown by the black arrows. The rigid rolls were driven over the sheet according to the prescribed kinematics described in the previous section.

To investigate the influence of element type on the prediction of the profile geometry, two different finite element models were established. In the first model, three-dimensional solid elements (7-type, linear integrated) were employed. In the second model, two-dimensional shell elements with three integration points in thickness direction (139-type, linear integrated) were used. For both employed element types, a fully integrated formulation was selected. In addition, an assumed strain formulation together with constant dilatation was activated to control hourglass effects.

Both models consisted of 9,000 elements, ensuring a direct comparison between the two modeling approaches. Both models have a single element over thickness. However, in order to have same integration points on the surface of the sheet metal, shell model had three integration points over the thickness. A refined mesh was applied in the regions where forming takes place, while coarser elements were used in the less deformed zones to maintain computational efficiency. The width of the elements in bending regions was 0.8 mm . On the flat sections of the profile, an element width of 2.8 mm was selected. Element size in length direction was constant and was equal to 4 mm in al regions.

[picture]

Fig. 5. Finite element model of the flexible roll forming process (green arrows indicate fixed boundary condition in X-direction, black arrows indicate fixed boundary condition in Z-direction).

Fig. 5. Finite element model of the flexible roll forming process (green arrows indicate fixed boundary condition in X-direction, black arrows indicate fixed boundary condition in Z-direction).

The mechanical behavior of the DP980 steel used in the finite element analysis was determined using tensile tests in three directions, namely 0∘,45∘, and 90∘. The tensile test results in the 0∘ direction and the corresponding material model predictions are exemplarily shown in Fig. 6. During the development of the material model, the constitutive equation given in the figure was employed up to a true plastic strain of 0.20 . For true plastic strain values exceeding 0.20 , the mechanical strength of the material was assumed to remain constant at 1230 MPa . In addition, the Young's modulus and Poisson's ratio of the DP980 steel were assumed to be 203 GPa and 0.3 , respectively. Furthermore, the anisotropy coefficients of the material measured in the 0∘,45∘, and 90∘ directions were 1.02,0.91, and 1.22, respectively. All these parameters were used to describe the material behavior using the Hill anisotropic material model.

[picture]

Fig. 6. Tensile test results and corresponding material model of the DP980 steel.

Fig. 6. Tensile test results and corresponding material model of the DP980 steel.

In the roll-forming process, sheet materials are bent progressively through successive forming stages. Consequently, the material becomes unloaded between individual forming stations, which may lead to springback. This behavior may give the impression that regions of the material initially subjected to tensile loading during forming are subsequently deformed under compressive loading. However, for the roll-forming process, all deformation occurring during springback remains within the elastic regime. Therefore, the Bauschinger effect is not considered to be significant under these conditions. Accordingly, kinematic hardening effects are typically neglected in relevant studies reported in the literature [6-11]

In metal forming processes, friction generally plays a significant role. However, during the rollforming process, rolling contact predominantly occurs between the sheet material and the rolls, and
it is commonly assumed that no significant relative sliding takes place at the sheet-roll interface. This aspect has been specifically investigated in previous studies. The reported results indicate that, for the roll-forming process, friction does not have a pronounced influence on the forming behavior [12, 13]. Accordingly, friction effects have generally been neglected in earlier studies [6-11]. In line with this approach, friction between the sheet and the rolls is also neglected in the present study.

Results and Discussion

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The results of the finite element analyses focused primarily on the final profile geometry. The displacement of the profile edge in the X - and Y -directions is presented in Fig. 7, where the X -axis represents the total length of the profile. As shown in Fig. 7(a), a larger displacement in the Xdirection is expected in the regions where the profile depth reaches 21 mm compared to the shallower sections. In contrast, in the regions with a depth of 13 mm , the profile edge is expected to exhibit a total displacement of approximately 6 mm in the X-direction due to the imposed geometry variation.

The initial evaluation of the simulation results indicates that the solid element model predicts Xdirection displacements closer to the expected 6 mm value. Moreover, in the deeper regions of the profile, the movement of the profile edge in the X-direction remains more restricted, which is consistent with the higher bending stiffness associated with increased profile depth.

As illustrated in Fig. 7(b), the use of solid elements also results in significantly lower fluctuations of the profile edge in the Y-direction compared to the shell element model. This behavior can be attributed to the higher stiffness inherent to the solid element formulation, which suppresses local oscillations and stabilizes the deformation during forming. Consequently, the solid element approach provides a more stable prediction of the height-variable profile in flexible roll forming simulations.

[picture]

Fig. 7. Displacement in (a) X-direction and (b) Y-direction of the profile edge in finite element models generated with solid and shell elements.

Fig. 7. Displacement in (a) X-direction and (b) Y-direction of the profile edge in finite element models generated with solid and shell elements.

In addition to the displacement of the profile edge, the cross-section of the profile after the final forming step was also examined. The profile cross-sections obtained using shell elements are shown in Fig. 8(a) and (c), whereas the geometries predicted by the solid element model are presented in Fig. 8(b) and (d). The cross-sections extracted at a distance of 200 mm from the profile start correspond to the region with the maximum profile depth.

When shell elements are used, excessive bending is predicted in the central region of the hat profile compared to the expected geometry. Furthermore, as illustrated in Fig. 8(a), pronounced local bending is observed near the profile edge, indicating an overestimation of local deformation. In contrast, the use of solid elements results in a more regular and stable profile geometry after the forming steps. The solid element formulation therefore provides a more reliable representation of the final crosssection for height-variable profiles produced by flexible roll forming.

[picture]

Fig. 8. Profile geometries after forming (a) 100 mm away from the end of shell model, (b) 100 mm away from the end of solid model, (c) 200 mm away from the end of shell model, and (d) 200 mm away from the end of solid model.

Fig. 8. Profile geometries after forming (a) 100 mm away from the end of shell model, (b) 100 mm away from the end of solid model, (c) 200 mm away from the end of shell model, and (d) 200 mm away from the end of solid model.

One of the important limitations of metal forming processes is the formation of cracks, particularly in edge regions, which is closely related to the limited ductility of the materials. Such cracks generally occur when the material reaches its deformation limits under plastic forming conditions. However, one of the key design principles of the roll-forming process is to avoid plastic deformation in the region commonly referred to as the strip edge during forming. If plastic deformation occurs in these regions, roll-forming-specific geometric defects, such as edge waviness or twist, may develop. For this reason, in the present study, a low bending-angle design was adopted to prevent the occurrence of plastic deformation in the edge region of the formed profile. As a result, no plastic deformation was observed at the profile edges during the forming process in either the shell- or solid-elementbased models. Accordingly, it was concluded that there is no risk of crack formation in the process.

Both simulations were performed on the same computer using a single CPU core. The system was equipped with a 20-core processor operating at 5.6 GHz and 64 GB of RAM. The model constructed with solid elements required 5.2 hours to complete. In contrast, the model based on shell elements was completed in 5.6 hours. Although shell elements are generally known to be more computationally efficient than solid elements, three integration points were defined through the thickness direction of the shell elements in order to ensure the presence of integration points on the sheet surface, similar to the solid element formulation. As a result, the computational time of the shell element model was marginally higher.

In the present study, the use of solid elements was found to be more advantageous compared to shell elements. Although shell elements are generally known to be more computationally efficient than solid elements, their stiffness is lower than that of solid elements. As a consequence, the simulation results obtained using shell elements exhibited larger deviations from the expected profile geometry when compared to the solid element model. Furthermore, due to the use of three integration points through the thickness direction in the shell element formulation, the computational time of the shell element model was higher than that of the model based on solid elements.

Summary

The original version of this paper is available on https://www.scientific.net/SSP.389.277.pdf

In this study, a finite element analysis of the flexible roll forming process for height-variable hatshaped profiles made of DP980 advanced high-strength steel was presented. A three-dimensional numerical model was developed using MSC.Marc to simulate the forming of a 900 mm long profile with variable depth along its length. The forming kinematics of the top and bottom rolls were derived directly from the target geometry, ensuring continuous tangential contact between the rolls and the sheet throughout the process.

Two different modeling strategies were investigated to evaluate their capability to predict the final profile geometry: a shell element model and a solid element model with identical mesh density. The simulation results showed that the solid element formulation provides more stable predictions of the profile edge displacement and final cross-section geometry. In particular, solid elements were found to better capture the expected X-direction displacement of the profile edge and significantly reduce unwanted fluctuations in the Y -direction. Furthermore, the cross-sectional analysis revealed that shell elements tend to overestimate local bending, especially near the profile edges and in regions with maximum profile depth.

The results clearly demonstrate that element formulation plays a critical role in the numerical simulation of flexible roll forming, especially when advanced high-strength steels are used. Solid elements provide superior geometric accuracy and stability for height-variable profiles.

However, the outcomes of the present study need to be validated through experimental investigations. For this purpose, a roll-forming machine capable of manufacturing height-variable profiles is currently in the design phase. Using this machine, the geometry of the profile at the central region will be measured after each forming step by means of a coordinate measuring machine (CMM). In addition, the deformation of the profile edges in the X-direction will be measured as a function of the forming angle and compared with the simulation results. Although no pronounced edge waviness was observed in the simulation results, this observation also requires experimental validation.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.277.pdf

This research was funded by Scientific and Technological Research Council of Türkiye (TÜBİTAK), grant number 9229502.

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T. Traub, X. Chen, P. Groche, Experimental and numerical investigation of the bending zone in roll forming, Int. J. Mech. Sci. 131-132 (2017) 956-970.

T. Wang, P. Groche, An analytical model for designing defect-free sheet metal profiles with height-variable cross sections manufactured by Flexible Roller Beading, Int. J. Mater. Form. 15 (2022) 49.

H. Wen, X. Liu, H. Li, Y. Cui, B. Yan, S. Huang, G. Wang, Research on cutting end flaring of C-shaped steel roll forming process, J. Mech. Sci. Technol. 39 (3) 2025 1365-1376.

A. Gehring, Beurteilung der Eignung von metallischem Band und Blech zum Walzprofilieren. Dissertation, Karlsruhe, 2006.

J. L. Amilibia, Geometrical accuracy improvement in flexible roll forming process by means of local heating, Tesis Doctoral, Arrasate-Mondrago'n Unibertsitatea 2011.

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 285-294

doi: 10.4028/p-3JjsnF

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-19

Revised:
2026-02-18

Accepted:
2026-02-24

Online:
2026-04-16

Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

Böhm, Viktor 1,a*, Spörer, Thomas 1, b, Ott, Michael 1,c, Fuchs, Georg 1, d, Richter, Paul 1,e, Tschannerl, Jeremias 1,f, Kong, Linghao 2, g, Ismail, Ahmed 3, h, Münstermann, Sebastian 2,i, Lohmann, Boris 3,j, Volk, Wolfram 1,k

1 Chair of Metal Forming and Casting, Technical University of Munich, Walther-Meißner-Straße 4,85748 Garching, Germany

2 Chair of Material Modelling in Forming Technology, RWTH Aachen University, Intzestraße 10, 52072 Aachen, Germany

3 Chair of Automatic Control, Technical University of Munich, Boltzmannstraße 15, 85748 Garching, Germany

e  paul.friedrich.richter@tum.de, fjeremias.tschannerl@tum.de, glinghao.kong@ibf.rwth-aachen.de, h  a.ismail@tum.de, isebastian.muenstermann@ibf.rwth-aachen.de, jlohmann@tum.de, kwolfram.volk@tum.de

Keywords: free-form bending, overbending and underbending, residual stresses

Abstract

The six independent axes available for free-form bending enable the production of complex three-dimensional bent tube and profile geometries. In industrial environments, only tangential bending strategies are currently used, which means that the bending head is always positioned parallel to the cross-section of the tube in the current bending section. Therefore, the individually controllable axes make it possible to apply other, non-tangential bending strategies. In so-called overbending, the bending head is rotated more in comparison to tangential bending. However, in order to ensure that the bending radius does not change compared to tangential bending, the translational deflection of the bending head must be reduced at the same time. In contrast, the bending head is rotated less during underbending and the translational deflection is increased. Overbending and underbending offer the possibility of improving the mechanical properties while maintaining the same bending geometry. These strategies allow the components to be optimized for individual load cases. As part of this work, a structural component was produced multiple times using free-form bending. Both conventional tangential bending strategies as well as innovative overbending and underbending strategies were applied. The mechanical stiffness of the bent components was then examined on a test bench. The influence of the bending strategy on the cross-sectional change in the bent area was investigated by using a tactile coordinate measuring machine. Furthermore, residual stress measurements were performed on the bent tubes, which allowed the different mechanical behavior of the tangentially bent, overbent and underbent tubes to be explained.

Introduction and State of the Art

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

Most industrial bending processes, such as three-roll push bending or rotary draw bending, can only produce a limited range of individual bending geometries. In rotary draw bending [8, 10], for example, the bendable radius is limited to the shape of the bending template, whereas in three-roll push bending [2, 3], different radii can be produced by varying the position of the work roller. By rotating the tube in the tool, three-dimensional bending geometries can also be achieved with threeroll push bending. However, a short, straight section of tube is needed between each bend to allow the work roller to be reattached to the tube. This means that only 2D-spline geometries or 3D-arc geometries, but no 3D-spine geometries can be produced with this method. Free-form bending provides the greatest freedom in the constructive design of bent profiles and tubes. The six
independently controllable axes of a free-form bending machine allow the production of threedimensional spline geometries [4, 9].

For industrial free-form bending machines it is usual to use a tangential bending strategy. In this process, the bending head is deflected in a translational and rotational manner so that bending head remains parallel to the cross-section of the resulting bent tube in the bending zone, see Fig. 1 (c). Independently controllable axes make it possible to either rotate the bending head to a higher (overbending) or a lower (underbending) degree while the translational deflection is kept constant [6]. However, these bending head kinematics would produce different bending radii. Thus, to produce the same bending radius for all three bending strategies, the bending head must be rotated less but deflected more translationally when underbending than during tangential bending. When overbending, the bending head must be rotated more than during tangential bending, but a smaller translational deflection must be applied.

Free-form bending with a movable die has been extensively studied. The majority of existing research concentrates on enhancing the geometrical accuracy of free-form bent components, while comparatively little attention has been given to the evolution of mechanical properties during the bending process. As demonstrated in [1], the manufacturing strategy used for roll-formed tubes significantly affects the material properties and, consequently, the subsequent bending behavior.

Furthermore, a Barkhausen sensor was used to investigate how the residual stresses of bent steel tubes develop when different bending strategies are applied [6, 7].

This experimental work examines how different bending strategies affect the mechanical behavior of bent components. To explain these differences, the analysis focuses on how the tube cross-section changes for each bending strategy and examines the residual stresses in the bent component resulting from each bending strategy.

Experimental Setup and Procedure

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

All bending experiments for this investigation were carried out on a 6 -axis bending machine NSB090-S from Jörg Neu GmbH. Circular tubes made of P235TR1 with an outer diameter of 42.4 mm and a wall thickness of 2.6 mm were used as semi-finished products for all subsequent bending tests. The tubes were then bent on the bending machine into a specified geometry designed to resemble the most highly stressed arch at the bottom of a rocking chair, see Fig. 2. In addition to the conventional tangential bending strategy, other non-tangential bending strategies such as overbending and underbending were also used in the manufacture of these tube bends.

Following the bending process, the tubes were digitized, and the resulting bending radii and apex angles were evaluated with respect to the bending strategy. For this purpose, a hand-held T-SCAN laser scanner combined with the T-TRACK 10 optical tracking system from CARL ZEISS AG were used to digitize the bent tubes. The subsequent quantitative determination of the bending radius and apex angle of the bent tubes was carried out using the GOM Inspect software.

The bent tube specimens produced using different bending strategies were then tested for their stiffness under load. To do this, they were clamped into an AllRound Line Z 150 tensile testing machine from ZwickRoell GmbH & Co. KG and subjected to a continuously increasing compressive load.

To determine the cause of the differences in stiffness behavior, the area moments of inertia of the deformed tube cross-sections were empirically determined and the residual stresses on the tensile side of the bent tubes were measured. To determine the area moments of inertia, the bent tubes were cut in half (cutting plane was parallel to the plane of the cross-section), and the inner and outer contours of the cross-sections were then measured using an LH 87 coordinate measuring system from WENZEL Group GmbH & Co. KG. Based on this data, the area moments of inertia were then calculated in Matlab. Furthermore, the remaining residual stresses in the bent tubes were measured using the hole drilling method. Therefore, the hole drilling system MTS3000 - Restan from SINT Technology and strain gauges from Hottinger Brüel & Kjaer GmbH were used.

Experimental Results

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

Influence of the Bending Strategy on the Bending Geometry Produced. A feed rate of 75 mm/s was selected for all bending experiments. A bent tube with a radius of 220 mm and an apex angle of 190∘ was defined as the target geometry for the rocking chair, see Fig. 2. To achieve this geometry with the specific material P235TR1 and its profile cross-section of the semi-finished product, a combination of deflection and rotation of 16.79 mm and 24.62∘ for the bending head was necessary for the tangential bending strategy. In order to produce the same bending radius with non-tangential bending strategies, the bending head parameters had to be 18.29 mm and 18.5∘ for underbending and 15.29 mm and 30.5∘ for overbending, see Fig. 2. After bending, the bent tubes were digitized and evaluated in terms of the bending geometry produced. The results are summarized in Fig. 1 (a) and (b). The radii produced with the tangential ( 217.91 mm ) and underbent ( 218.31 mm ) bending strategies are very similar; only the overbent tubes are slightly smaller with an average radius of 214.14 mm . Since the arc length of the tubes was kept constant for all bends, this is also reflected in a slightly higher apex angle of 192.6∘ for the overbent bending strategy compared to the tangential ( 188.44∘ ) and underbent ( 188.39∘ ) bending strategies. It should also be noted that the relative error, erel , in both the radii, R, and, in particular, the apex angles, α, are always the smallest in the underbent strategy. It is assumed that the reduced rotation of the bending head during underbending is the reason for this, as the tool marks at the start of the bend are much less prominent for this bending strategy.

[picture]

Fig. 1. Resulting bending radii for different bending strategies (a), the corresponding apex angles (b) and a schematic explanation of tangential and non-tangential bending strategies (c).

Fig. 1. Resulting bending radii for different bending strategies (a), the corresponding apex angles (b) and a schematic explanation of tangential and non-tangential bending strategies (c).

Tube Compressive Tests. To evaluate the influence of the bending strategy on the mechanical behavior of components, the bent tubes were clamped in a specially designed clamping device on a tensile testing machine and subjected to a compressive load, whereby the force was applied at the highest point of the bent tubes. The traverse speed was set at 0.25 mm/s and the force resistance of the bent tubes to the compressive load of the tensile testing machine was recorded. Reaching 7.2 kN was set as the termination criterion for the compressive tests. The force curves of the tangentially, over- and underbent tubes depicted over the vertical displacement of the traverse are shown in Fig. 2. Each curve contains the mean values and standard deviations of five compression tests. The underbent tubes exhibited the highest force resistance to the translational traverse movement, followed by the tangentially bent tube bends. The lowest force resistance to traverse movement was found in the overbent tubes. There are two possible explanations for this difference in mechanical
behavior when using different bending strategies. On the one hand, [5] have found that non-tangential bending leads to a changed residual stress profile in the bent tubes compared to tangential bending. Another hypothesis for the different mechanical behavior is that the different bending strategies produce differently deformed profile cross-sections, which leads to different area moments of inertia and thus to altered bending stiffnesses. In order to validate Maier's explanatory approach [5] and to test the validity of the hypothesis regarding the altered area moments of inertia, the cross-sections of the individual bends were analyzed and residual stress measurements were carried out.

[picture]

Fig. 2. Results of the tube compressive tests for tubes with the same geometry but bent using different bending strategies.

Fig. 2. Results of the tube compressive tests for tubes with the same geometry but bent using different bending strategies.

Analysis of Cross-Sectional Changes. To analyze the cross-sections, the bent tube segments were cut in half lengthwise. They were then placed on a coordinate measuring machine so that the cut cross-sectional area was parallel to the base of the coordinate measuring machine. Then, both the inner and outer contours were scanned in three horizontal planes ( 1 mm distance from each other) with a ruby touch probe with a diameter of 3 mm , and the corresponding x and y coordinates were recorded. The measurements taken from the cross-section of an unbent reference tube can be seen in Fig. 3. As part of the post-processing of the data using Matlab, the major and minor axes were first defined and their lengths were determined. In the case of the unbent reference tube, there is hardly any difference in the length of the major ( Dmax  ) and minor ( Dmin  ) axes ( ΔD=0.12 mm ). In the case of bent tubes, however, the tube cross-section deforms so that the major axis and minor axis are more pronounced. The ovality, O

O=Dmax−DminDmax=ΔDDmax(1)

can be determined from the ratio between the difference in length between the two axes, ΔD, and the length of the major axis.

Based on the measurement data, an ovality of 0.29% was calculated for the unbent reference tube. Figure 3 also shows the calculated wall thickness over the circumferential angle, φ, with the origin defined on the minor axis at the top point of the cross-section. The unbent reference tube has a relatively constant wall thickness of approx. 2.45 mm . Only in the area of the weld seam, the wall thickness is 0.2 mm lower. During the bending tests, all tubes were placed in the bending machine so that the weld seams were located on the neutral axis of the bends in order to have as little influence on the bends as possible. The cross-sectional area was also calculated, which is 304.53 mm2 in the case of the unbent reference tube.

[picture]

Fig. 3. Cross-section (a) and wall thickness over the circumference (b) of an unbent reference tube.

Fig. 3. Cross-section (a) and wall thickness over the circumference (b) of an unbent reference tube.

Fig. 4 shows the cross-section and wall thickness around the circumference of the tangentially bent tube. Compared to the unbent tube, the ovality of the cross-sectional profile is much more pronounced here ( O=2.76% ). Furthermore, the bending process, which is characterized by superimposed compressive stresses, causes a moderate thickening of the tube, so that the calculated cross-sectional area for the tangentially bent tube is 311.27 mm2. A sine-shaped curve can now be seen in the wall thickness distribution over the circumference, with significant material thickening on the compression side of the bend and moderate material thinning on the tension side compared to the unbent reference tube.

[picture]

Fig. 4. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R=220 mm using a conventional tangential bending strategy.

Fig. 4. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R = 220 m m using a conventional tangential bending strategy.

Similarly, the cross-section and wall thickness for the overbent tube are shown in Fig. 5. In this experimental study, overbending resulted in the greatest thickening of the material, with a measured cross-sectional area of 314.77 mm2. The ovality of the tube cross-section is also higher using this bending strategy (O=2.97% mm) than compared to tangentially bent tubes.

[picture]

Fig. 5. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R=220 mm using an overbending strategy.

Fig. 5. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R = 220 m m using an overbending strategy.

For the underbent tubes, see Fig. 6, the measurements yielded an ovality of 3.17% and a thickening of the cross-section to 313.46 mm2.

[picture]

Fig. 6. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R=220 mm using an underbending strategy.

Fig. 6. Cross-section (a) and wall thickness over the circumference (b) of a bent tube with a radius of R = 220 m m using an underbending strategy.

The bending stiffness, EI, is defined as the product of the modulus of elasticity, E, and the area moment of inertia, I. Since all tubes used for this investigation came from the same batch of material, it can be assumed that the modulus of elasticity E was identical, or at least very similar, in all experiments, regardless of which bending strategy was used. The difference in mechanical behavior during the tube compressive tests can therefore be attributed to the differences in the area moments of inertia, which result from varying degrees of cross-sectional deformation during bending induced by the different bending strategies. The axial moment of inertia about the x -axis, Ixx, is defined as

Ixx=∬Ay2dA(2)

and about the y -axis, Iyy, is defined as

Iyy=∬Ax2dA(3)

Green's theorem was applied, which allows the integral over a flat surface

∬Af(x,y)dA=∯∂Ag(x,y)dx+h(x,y)dy(4)

to be expressed as a curve integral. The measured points of the outer and inner cross-sectional contours served as the data basis for the line integration.

The area moments of inertia, Ixx and Iyy, calculated using this method are summarized in Table 1 for all unbent and bent configurations. The cross-sectional areas as well as the corresponding ovality of all cross-sections examined are also listed.

Since the weld seam was located in the neutral axis of the bend in all tests (see Fig. 4 to Fig. 6), the area moment of inertia relevant for the compressive tests performed on the tensile testing machine is that abound the major axis, corresponding to Ixx. The unbent reference profile has the largest area moment of inertia of 60566.6 mm4. Regardless of the bending strategy, Ixx decreases for all bent crosssections, whereas Iyy tends to increase. Among the bent tubes, the highest area moment of inertia Ixx was calculated for the overbent tubes, and the lowest for the tangentially bent tubes. This finding contradicts the bending stiffness behavior observed in Fig. 2 during the tube pressure tests. The hypothesis that the superior mechanical performance of components manufactured using an underbending strategy is due to more optimal cross-sectional deformation could thus be falsified. To test the explanatory approach proposed in [5], residual stress measurements were carried out on the components manufactured using different bending strategies.

Table 1. Summary of the results of the cross-sectional evaluation, considering the various bending strategies as well as the unbent reference tube.

bending strategy | cross-sectional area A [mm²] | moment of inertia about the x-axis Ixx [mm⁴] | moment of inertia about the y-axis Iyy [mm⁴] | ovality O [%]
unbent | 304.5 | 60566.6 | 60790.9 | 0.29
tangential | 311.3 | 59312.5 | 61399.2 | 2.76
overbent | 314.8 | 59993.9 | 62188.7 | 2.97
underbent | 313.5 | 59635.7 | 61815.3 | 3.17

Residual Stress Measurements using the Hole Drilling Method. As part of the residual stress measurement using the hole drilling method, a 400 mm long tube segment was first cut from the bent tubes. This length is sufficient to ensure that the residual stress measurement is not influenced by the cutting operation on the bent tube due to the release of residual stresses. The tension side of the tube segment was then ground and polished. A triple strain gauge from Hottinger Brüel & Kjaer GmbH was then glued to the prepared area, see Fig. 7. The three individual strain gauges are oriented at 0∘, 45∘ and 90∘. This allows the major and minor stresses to then be calculated retrospectively. A highspeed milling cutter with a diameter of 2 mm was used during the residual stress measurements. The holes were drilled in 0.05 mm increments to a final drilling depth of 1.0 mm , with the strains being recorded between the individual drilling operations. The final evaluation was carried out after the hole drilling was completed. The strains were converted into stresses using the Schwarz-Kockelmann method, which is based on the strain gradient through the wall thickness. The measured axial residual stresses, σzz, along the tube's longitudinal axis for the tangential, over- and underbent tubes are plotted in Fig. 7. The axial residual stress curves for the tangential and overbent tubes show a similar progression through the wall thickness, except that the residual stresses in the overbent tubes are higher in absolute terms. The stress peak forms in both variants at a drilling depth of approx. 0.3 mm . The axial residual stress curve of the underbent tube differs significantly from the others. Here, the peak only forms at a drilling depth of approx. 0.8 mm . Furthermore, the stress values in the outer edge area are significantly lower than for the other two bending strategies, and even compressive stresses were recorded in the outermost edge layer.

[picture]

Fig. 7. Results of the residual stress measurements (a) using the hole drilling method on the tension side of tangentially bent, overbent and underbent tubes, depicted in (b).

Fig. 7. Results of the residual stress measurements (a) using the hole drilling method on the tension side of tangentially bent, overbent and underbent tubes, depicted in (b).

These measured residual stress curves provide a plausible explanation for the differences observed in the tube compressive tests. During the tube compressive test on the tensile testing machine, tensile stresses are generated in the area where the residual stress measurement was performed. These tensile stresses increase as the distance to the outermost edge layer decreases. Since the overbent tubes in this area already have the highest tensile residual stresses due to the manufacturing process, they can only withstand the lowest external compressive force in the tube compressive test. The tangentially bent tubes can withstand a slightly higher load, as the tensile residual stresses in these tubes due to the manufacturing process are significantly lower. The underbent tubes, on the other hand, have the lowest stored tensile stresses in the outer edge layer and even compressive stresses in the outermost edge layer. Based on logic, these tubes can withstand the highest externally applied load, as the stored compressive stresses counteract the externally applied tensile stresses.

The question remains as to why the bending strategy has such a significant influence on the process-related residual stresses. To explain this, it is worth taking a look at the bending strategies shown schematically in Fig. 1 (c). In tangential bending, the bending head is deflected in a translational manner and rotated in such a way that the tube can be pushed through the bending head with as little force as possible. This is also reflected in relatively low tensile residual stresses in the bent tube. In comparison, during overbending, the bending head is rotated more strongly while maintaining the same deflection. The tube is therefore stretched more on the outside and higher tensile stresses are stored. In underbending, on the other hand, the bending head is rotated significantly less and the tube is effectively bent back again, so that compressive stresses tend to be stored on the outer side of the bend.

Conclusion and Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

This work has shown that the mechanical performance of bent components can be improved by applying non-tangential bending strategies in free-form bending. Tube compressive tests were carried out on bent tubes produced using different bending strategies, and it was shown that the underbent components had the highest resistance to externally applied compressive forces. Although this was not investigated any further, it is plausible that the overbent tubes would have performed best under a counteracting external tension load. It is therefore conceivable that overbending and underbending can be used to optimize the mechanical performance of the bent components for individual load cases. In addition, investigations were carried out to determine the influence of the bending strategy on the deformation of the tube cross-section and, consequently, on the area moment of inertia and bending
stiffness. It was found that the cross-section of the tubes increases slightly with all bending strategies and that differently shaped ovals form depending on the bending strategy. The final explanation for the difference in mechanical behavior during the tube compressive tests was provided by investigations into the stored residual stresses on the tension side of the bent tubes using the hole drilling method. Here, compressive stresses were detected in the underbent tubes, which actively counteract the externally applied tensile stresses in the tube compressive test. The hypothesis put forward in [5] could thus be proven.

The most important findings of this work can be summarized as follows:

Non-tangential bending strategies such as overbending and underbending influence the mechanical behavior of free-form bent components.

By selectively choosing the bending strategy, the mechanical performance of the components can be improved and optimized for individual load cases.

The bending strategy influences the deformation of the cross-section during bending and thus the subsequent bending stiffness of the component.

Overbending leads to particularly high axial tensile stresses on the tension side of bends, while underbending leads to significantly lower axial tensile stresses and even to the formation of compressive stresses in the outermost edge layer.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

This paper is based on the results obtained within the research project "Property-controlled process design of freeform bending considering material properties of the semi-finished product", which was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 424334318.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.285.pdf

Beulich, N., Mertens, R., Spoerer, J., Volk, W.: Influence of tube rollforming on material properties and subsequent bending processes. Forming Technology Forum (2019)

Cornelissen, R., Maljaars, J., Hofmeyer, H.: Buckling and wrinkling of rectangular hollow sections curved in three-point-roll bending. Int J Adv Manuf Technol 112(7-8), 2091-2107 (2021). doi: 10.1007/s00170-020-06443-y

Groth, S., Frohn, P., Engel, B.: Product planning system for manufacture-oriented modeling of freeform bend tubes produced by three-roll-push-bending. Procedia Manufacturing 34, 10-18 (2019). doi: 10.1016/j.promfg.2019.06.107

Ismail, A., Maier, D., Stebner, S., Volk, W., Münstermann, S., Lohmann, B.: A Structure for the Control of Geometry and Properties of a Freeform Bending Process. IFAC-PapersOnLine 54(11), 115-120 (2021). doi: 10.1016/j.ifacol.2021.10.060

Maier, D.: Eigenschaftsflexibles Freiformbiegen mit bewegter Matrize. Dissertation, Technical University of Munich (2024)

Maier, D., Stebner, S., Ismail, A., Dölz, M., Lohmann, B., Münstermann, S., Volk, W.: The influence of freeform bending process parameters on residual stresses for steel tubes. Advances in Industrial and Manufacturing Engineering (2021). doi: 10.1016/j.aime.2021.100047

MAIER, D.: Experimental analysis on the influence of freeform bending on Barkhausen noise for steel tubes. In: MAIER, D. (ed.) Experimental analysis on the influence of freeform bending on Barkhausen noise for steel tubes. Material Forming, 2023/04/19, pp. 2091-2100. Materials Research Forum LLC (2023). doi: 10.21741/9781644902479-224

Safdarian, R.: Investigation of tube fracture in the rotary draw bending process using experimental and numerical methods. Int J Mater Form 13(4), 493-516 (2020). doi: 10.1007/s12289-019-01484-5

Scandola, L., Erber, M., Hagenlocher, P., Steinlehner, F., Volk, W.: Reconstruction of the bending line for free-form bent components extracting the centroids and exploiting NURBS curves. Graphical Models 135, 101227 (2024). doi: 10.1016/j.gmod.2024.101227

Strano, M.: Automatic tooling design for rotary draw bending of tubes. Int J Adv Manuf Technol 26(7-8), 733-740 (2005). doi: 10.1007/s00170-003-2055-6

This ePub file was created using machine-generated methods and automated software to convert the source text into an ePub format and may contain formatting inconsistencies from the original version. Formatting may vary depending on the device used.

The original version of this eBook is available on https://www.scientific.net/book/incremental-and-sheet-metal-forming/978-3-0364-1991-6

Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 295-303

doi: 10.4028/p-vWwaU4

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-23

Revised:
2026-02-24

Accepted:
2026-02-27

Online:
2026-04-16

Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

Ecem Ozden 1,a*, Oleksandr Kurtov 2,b, Hans Vanhove 1,c and Joost Duflou 1, d

1 KU Leuven, Department of Mechanical Engineering / Flanders Make, Celestijnenlaan 300B, B-3001 Leuven, Belgium

2 KU Leuven, Jan Pieter De Nayerlaan 5, B-2860 Sint-Katelijne-Waver, Belgium

a*ecem.ozden@kuleuven.be, b  oleksandr.kurtov@kuleuven.be, chans.vanhove@kuleuven.be,  djoost.duflou@kuleuven.be

Keywords: Single point incremental forming, Hybrid manufacturing, TIG welding, Magnesium.

Abstract

This study investigates a hybrid manufacturing route combining heat-assisted Single Point Incremental Sheet Forming (SPIF) with Tungsten Inert Gas welding (TIG)-based material deposition for the local reinforcement of Mg−Zn−Zr (ZK61) alloy thin sheets. Flat and curved substrates extracted from SPIF-formed geometries were used to examine the influence of substrate thickness, forming temperature, and geometry on TIG deposition morphology and thermal distortion. The results indicate that heat input and substrate thickness strongly affect deposition morphology and dimensional stability, while SPIF sheet forming temperature influences the repeatability of the deposition process. In addition, deposition behavior exhibited limited sensitivity to substrate curvature for single depositions, whereas successive depositions resulted in increased thermal distortion due to cumulative residual stresses. Overall, this work identifies key process sensitivities and constraints associated with TIG deposition on SPIF-formed magnesium alloy sheets, providing a basis for the development of hybrid forming-deposition process chains for localized reinforcement applications.

Introduction

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

Single Point Incremental Sheet Forming (SPIF) is a dieless sheet metal forming process in which a clamped sheet is progressively deformed by a numerically controlled tool following a predefined toolpath [1]. Owing to its localized deformation mechanism, SPIF offers high geometric flexibility with low tooling requirements and relatively low forming forces. These characteristics make the process particularly attractive for rapid manufacturing and small-batch production of thin-shell components with complex geometries [1,2].

Despite these advantages, certain applications impose additional functional requirements, such as local thickening and reinforcement, to ensure sufficient structural performance. Such requirements extend beyond the capabilities of incremental sheet forming (ISF) as a stand-alone process, which has motivated growing interest in hybrid manufacturing strategies [3]. In this context, integrating ISF with additive manufacturing (AM) has been proposed as a promising route for local reinforcement and functional tailoring, while maintaining geometric flexibility and limiting additional manufacturing time and cost [3]. Accordingly, integrated hybrid concepts combining SPIF and AM within a single clamping setup have been introduced, including the patented approach reported by Hölker-Jäger et al. [4]. In addition, alternative process sequences, in which SPIF and AM are performed in separate stages, have also been investigated [5,6]. Among these strategies, AM applied after forming is generally considered more compatible with industrial implementation, given the strong dependence of AM-induced material properties on processing strategy and thermal history [3]. Nevertheless, AM on pre-formed sheets introduces challenges related to thermal distortion, interfacial bonding, and toolpath alignment, requiring careful control of the process parameters to maintain dimensional accuracy and structural integrity [3].

For magnesium and its alloys in particular, these challenges are further exacerbated by their low melting point, high susceptibility to oxidation, and rapid solidification rate [7]. These characteristics render magnesium alloys highly sensitive to heat input, increasing the risk of thermal distortion and solidification cracking. This sensitivity, in turn, limits the high-temperature processing window [7,8]. Prior work into the heat-assisted SPIF of Mg−Zn−Zr alloy sheets defined a critical forming temperature range and characterized the effects of forming temperatures and toolpath strategies on the resulting product geometry and material properties [9]. Additionally, a process window for Tungsten Inert Gas (TIG) welding, also known as Gas Tungsten Arc Welding (GTAW), on rolled and annealed Mg−Zn−Zr alloy sheets has been explored, representing an initial step toward post-ISF AM deposition strategies [10]. However, the application of TIG-based material deposition to SPIFformed components and the influence of SPIF-induced geometrical and thermal history on subsequent deposition behavior remain largely unexplored.

The present study addresses this gap through a preliminary investigation of a hybrid manufacturing route combining heat-assisted SPIF with TIG welding-based material deposition for the local reinforcement of Mg−Zn−Zr alloy thin shells. In particular, the effects of selected SPIF process parameters, namely forming temperature and wall angle, on TIG weld deposition morphology and the resulting thermal distortion of the formed sheets are examined.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

In this study, ZK61 magnesium alloy sheets in an annealed, hot- and warm-rolled condition were investigated. The chemical composition was Mg−5.3Zn−0.5Zr (wt.%). The sheets had initial dimensions of 225×225 mm and a thickness of 1.6 mm .

Heat-Assisted SPIF setup and forming parameters. Heat-assisted SPIF was conducted using a KUKA KR500MT robotic arm equipped with a non-rotating hemispherical tool (Fig. 1a). Sheet heating was provided by a Nabertherm N210E chamber kiln ( 11 kW ). The sheet-fixture assembly was mounted on a clampable door system using bolted connections, ensuring stable and uniform thermal conditions prior to forming while enabling immediate air cooling upon completion. Details of the temperature monitoring and control strategy are reported in [9].

[picture]

Fig. 1. Experimental setups used in this study: (a) heat-assisted SPIF [9] and (b) TIG welding deposition [10].

Fig. 1. Experimental setups used in this study: (a) heat-assisted SPIF [9] and (b) TIG welding deposition [10].

Two representative geometries were formed by heat-assisted SPIF using a single-stage toolpath with a constant vertical step size (Fig. 2). Pyramid geometries with varying wall angles were produced at selected forming temperatures to investigate thickness evolution and its influence on subsequent TIG welding when SPIF-formed sheets are used as thin substrates. In addition, cone geometries were produced to enable a direct comparison between flat and curved formed surfaces as substrates for TIG welding.

Two main forming parameters were investigated: sheet temperature and wall angle (Table 1). Based on prior work conducted using the same heat-assisted SPIF setup [9], a forming temperature window of 250−325∘C was selected, as it represents a compromise between enhanced formability, controlled surface oxidation, and acceptable surface quality for Mg−Zn−Zr alloy sheets. Within this temperature range, variations in hardness distribution and grain morphology have been reported, reflecting differences in deformation and recrystallization behavior [9]. Accordingly, forming temperatures were chosen in the present work to introduce controlled differences in the microstructural state of the SPIF-formed substrates. In parallel, the wall angle was varied to produce distinct thickness conditions, which are directly relevant for evaluating thermal distortion during subsequent TIG welding deposition.

All SPIF experiments were performed at a constant feed rate of 2000 mm/min, with a vertical step size of 0.5 mm and a tool diameter of 10 mm , selected to balance surface quality and forming time. No lubricants were applied during forming. Both the pyramid and the cone geometries were formed to a length of 70 mm . The pyramid geometry had an initial width of 184 mm , while the cone geometry had an initial diameter of 180 mm . Prior to forming, the sheets were held at the target temperature for 50 min to ensure steady-state thermal conditions [9]. With the selected parameters, the forming process took approximately 40 minutes, followed by immediate air cooling.

Table 1. Process parameters investigated in the heat-assisted SPIF experiments.

Process parameter | Applied variable
Sheet forming temperature [°C] | 250, 325
Wall angle [°] | 40, 60

Following forming, flat and curved thin sheets were extracted from the pyramid and cone geometries, respectively, using wire electrical discharge machining (wire EDM). Extractions were performed from a defined region extending from the apex to 55 mm below the apex along the Z direction, corresponding to Zone A in Fig. 2. Regions near the pyramid edges and the step size transition zones were excluded. All extracted sheets had dimensions of 25×20 mm to ensure consistency in subsequent experiments.

Microstructural characterization. Microstructural analysis was performed by optical microscopy on cross-sections of the formed and extracted sheets using a Leica Leitz Laborlux microscope equipped with a Zeiss Axiocam MRC-5 camera. Specimens were prepared using standard grinding and polishing procedures, followed by etching with an acetic-glycol solution to reveal the microstructural features.

TIG welding deposition on SPIF-formed substrates. TIG welding was selected due to its arc stability, flexible heat input control, and inert shielding atmosphere, which effectively suppresses oxidation of molten magnesium [7]. The welding setup (Fig. 1b) consisted of a MacGregor arc power source operating up to 99 A with a current resolution of 0.1 A . Pulsed arc parameters, including peak duration as well as upslope and downslope times, were controlled with a temporal resolution of 1 ms . High-purity argon shielding gas was supplied through a gas lens at the torch, while backing gas was applied at a flow rate of 2ℓ/min.

[picture]

Fig. 2. SPIF-formed geometries used for substrate extraction: (a) pyramid geometry and (b) cone geometry.

Fig. 2. SPIF-formed geometries used for substrate extraction: (a) pyramid geometry and (b) cone geometry.

Instead of continuous wire feeding, the filler material was positioned centrally on the substrate surface prior to welding. Deposition was carried out at a constant arc length, resulting in dome-shaped weld deposits. The filler material was prepared from the as-received ZK61 sheets with a thickness of 1.6 mm and machined into cylindrical specimens with a diameter of 5 mm using wire EDM.

Prior to welding, both the substrates and filler material samples were sequentially ground using 600, 1200 and 4000 grit abrasive papers and subsequently cleaned with isopropanol to reduce surface oxides and minimize roughness-related effects. Surface preparation removed approximately 0.1 mm of material from each substrate, eliminating surface features such as the orange-peel effect and toolpath marks. As a result, final substrate thicknesses of approximately 1.1 mm and 0.7 mm were obtained for wall angles of 40∘ and 60∘, respectively.

Substrate thickness varied as a function of the SPIF wall angle; therefore, the TIG welding parameters were adjusted accordingly. Substrates formed at a wall angle of 60∘ were welded using currents of 55 A and welding times of 300-500 ms, whereas substrates formed at 40∘ required higher currents of 70 A and welding times of 500−800 ms. All other parameters were kept constant: the argon flow rate at the torch was 8ℓ/min, the upslope and downslope times were 10 ms and 400 ms , respectively, and a tungsten electrode with a 60∘ tip angle was used at a fixed arc length of 2.4 mm . The electrode condition was inspected after each weld, and at least three repetitions were performed for each parameter set.

The electrode was positioned at a defined distance from the heating contact surface of the sheets, i.e., the surface that was in contact with the heat source during heat-assisted SPIF. The tool contact surface, which was exposed to ambient air and subjected to tool-induced shear during heat-assisted SPIF, was positioned on the back side.

Geometric characterization. To characterize the deposition geometry and thermal distortion, crosssectional profiles of the substrates were measured before and after TIG welding using a Coord3 MC16 coordinate measuring machine equipped with an LC60Dx laser line scanner. Measurements were performed along the X-Z plane, defined by the TIG welding coordinate system (Fig. 1b), passing through the center of each specimen. Prior to deposition, the extracted and ground thin sheets were scanned to define the initial substrate geometry. Post-deposition scans were conducted after cleaning with isopropanol. Finally, the acquired point clouds were analyzed using GOM Inspect 2019 software.

Results and Discussion

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Effect of heat input on cross-sectional deposition geometry. Fig. 3 presents the evolution of the cross-sectional deposition morphology with increasing heat input, controlled by the welding time, on flat substrates extracted from SPIF-formed pyramids with wall angles of 40∘ (Fig. 3a) and 60∘ (Fig. 3b). All substrates were produced at a sheet forming temperature of 325∘C. Here, the deposition morphology is characterized in terms of deposition height, deposition diameter, and contact angle. All reported values represent the average of three repeated experiments conducted under identical conditions.

Increasing heat input led to an increase in deposition diameter, accompanied by a reduction in deposition height and contact angle. Specifically, for substrates formed at a wall angle of 40∘, increasing the welding time from 500 ms to 800 ms reduced the deposition height from 1.3 mm to 0.4 mm , while the deposition diameter increased from 7 mm to 11 mm . A similar trend was observed for substrates formed at a wall angle of 60∘, where increasing the welding time from 350 ms to 450 ms led to a decrease in deposition height from 1.4 mm to 0.7 mm and an increase in deposition diameter from 6 mm to 8 mm .

Additionally, for substrates formed at a wall angle of 60∘, no material deposition was obtained at a welding time of 300 ms , indicating insufficient heat input for stable melt pool formation. Conversely, at a welding time of 500 ms , excessive heat input resulted in a pronounced burst formation without the development of a stable dome-shaped deposit. This behavior is consistent with characteristic trends reported for TIG welding, where higher heat input promotes enhanced spreading and penetration of the molten material [11].

[picture]

Fig. 3. Cross-sectional deposition profiles at increasing heat input, controlled by the welding time, for flat substrates extracted from SPIF-formed pyramids with varying wall angles.

Fig. 3. Cross-sectional deposition profiles at increasing heat input, controlled by the welding time, for flat substrates extracted from SPIF-formed pyramids with varying wall angles.

Influence of substrate thickness and wall angle on thermal distortion. Substrate thickness, governed primarily by the SPIF wall angle, had a pronounced influence on thermal distortion during TIG welding. For substrates formed at a wall angle of 40∘, the as-formed thickness after surface
preparation was approximately 1.1 mm . Fig. 3a shows the effect of increasing the welding time from 500 ms to 800 ms at a constant current of 70 A . Within this parameter range, stable dome-shaped deposits were obtained, exhibiting contact angles below 90∘ and no visible contamination or burst formation. Moreover, the thermal distortion along the X direction remained limited, with the average deviation increasing from ±0.01 mm at a welding time of 500 ms to ±0.02 mm at 800 ms .

In contrast, substrates formed at a wall angle of 60∘ had a thickness of approximately 0.7 mm , which corresponds to a reduced thermal capacity during TIG welding. As thinner substrates have a reduced ability to absorb and dissipate heat, the heat input must be proportionally reduced to prevent excessive melting, thermal distortion, or burn-through [13]. Accordingly, both the welding current and the welding time were decreased, leading to a markedly narrower process window confined to welding times between 350 ms and 450 ms at a current of 55 A (Fig. 3b).

At welding times of 350 ms and 400 ms , average out-of-plane thermal distortions with deflections of approximately ±0.01 mm and ±0.02 mm, respectively, were observed. When the welding time was increased to 450 ms , the average out-of-plane thermal distortion with a deflection increased to approximately ±0.14 mm was observed over a distance of 12.5 mm from the center of the deposition, relative to the pre-deposition geometry (Fig. 3b). The substrate bent upward toward the deposited region, with the magnitude of deformation increasing with welding time. These observations indicate a loss of dimensional stability, showing that an increase in heat input beyond the narrow process window leads to significant deviation along the Z axis in SPIF-formed thin ZK61 alloy sheets during TIG welding.

Effect of sheet forming temperature on deposition repeatability. Substrates formed at a wall angle of 40∘ and sheet forming temperatures of 250∘C and 325∘C were subjected to TIG welding deposition using identical process parameters, namely welding times between 500 ms and 800 ms at a constant current of 70 A . For substrates formed at 325∘C, both wall angles of 40∘ and 60∘ exhibited reproducible deposition morphology across repeated experiments, with the maximum variations below 0.2 mm in deposition height and 0.3 mm in deposition diameter.

In contrast, substrates formed at 250∘C showed pronounced variability in deposition morphology between repetitions. Variations reached up to 0.7 mm in deposition height and 1.2 mm in deposition diameter, and no consistent weld pool geometry or penetration profile was observed across the experiments. These results indicate a reduced repeatability of the TIG deposition process when applied to substrates formed at the lower forming temperature.

This reduced repeatability in welding morphology for substrates formed at 250∘C can be attributed to the relatively heterogeneous microstructure through the sheet thickness. Forming at 325∘C promotes dynamic recrystallization (DRX), resulting in an equiaxed fine-grain structure with a weakened texture across the thickness (Fig. 4b). In contrast, forming at 250∘C leads to pronounced forming texture characterized by forming stripes with DRX grains (Fig. 4a). This interpretation is consistent with previously reported hardness distributions [9]. Sheets formed at 250∘C had a more pronounced hardness increase near the tool contact surface, where shear deformation dominates during forming. Conversely, samples formed at 325∘C show a more homogeneous hardness distribution through the thickness, consistent with a more homogeneous DRX. Such variations in grain size, crystallographic orientation, and microstructural uniformity have been reported to influence weld pool dynamics, wetting behavior, and solidification characteristics [8], which is consistent with the observed differences in deposition morphology and repeatability in this study.

Nevertheless, the impact of post-forming surface preparation should also be taken into consideration. The grinding steps employed to remove the orange-peel effect and toolpath marks may lead to asymmetric material removal between the heating-contact and tool-contact surfaces, potentially modifying the near-surface microstructural properties. This asymmetry can introduce differences in the near-surface strain state, which may locally affect heat transfer and melting behavior during TIG deposition. A more controlled and symmetric surface preparation strategy on
both sides of the substrate could therefore be considered as an optimization route to further improve the uniformity and repeatability of the deposition morphology within the current TIG welding setup.

[picture]

Fig. 4. Optical micrographs of SPIF-formed pyramid geometries with a wall angle of 40∘ at different sheet forming temperatures.

Fig. 4. Optical micrographs of SPIF-formed pyramid geometries with a wall angle of 40 ∘ at different sheet forming temperatures.

Influence of substrate geometry on deposition and distortion. To assess the influence of substrate geometry on deposition behavior and thermal distortion, substrates with curved geometries extracted from SPIF-formed cones were investigated in addition to the thin flat sheets obtained from pyramid geometries. All experiments were conducted within the same TIG welding parameter range to enable a direct comparison between flat and curved substrates. Fig. 5a shows the cross-sectional deposition profiles of cone-derived substrates formed at a wall angle of 40∘ and a sheet forming temperature of 325∘C.

[picture]

Fig. 5. Cross-sectional deposition profiles of SPIF-formed cone-derived substrates with a wall angle of 40∘ at a sheet forming temperature of 325∘C.

Fig. 5. Cross-sectional deposition profiles of SPIF-formed cone-derived substrates with a wall angle of 40 ∘ at a sheet forming temperature of 325 ∘ C .

Under identical welding conditions, the cone-derived substrates had deposition morphologies and distortion levels comparable to those observed for the pyramid-derived flat substrates. As the welding time increased from 600 ms to 800 ms , the average deposition height decreased from 0.8 mm to 0.4 mm , while the deposition diameter increased from 8 mm to 11 mm . Moreover, distortion along the X direction remained within a maximum range of approximately ±0.02 mm at 800 ms . These values are consistent with those measured for flat substrates, indicating that the introduction of moderate curvature alone does not significantly alter deposition geometry or thermal distortion under the investigated conditions.

To further evaluate the effect of cumulative residual stresses on the curved substrates, successive depositions were applied on the same cone-derived curve substrate along the Y direction, defined by the TIG welding coordinate system (Fig. 1b). Substrate distortion was evaluated at the same reference position used for the single-deposition case, corresponding to a central dome deposited along the X direction (Fig. 5b). At a welding current of 70 A and a welding time of 700 ms , the successive deposition condition resulted in a noticeably larger out-of-plane displacement exceeding 0.1 mm (Fig. 5b). This result indicates that residual stresses in the workpiece lead to larger deformations when the stress fields from multiple welding spots are combined, resulting in a progressive loss of dimensional stability as the number of deposited domes increases. Consequently, reducing the heat input and/or pre-defining the SPIF geometry to compensate for thermal distortion appear to be potential strategies for continuous or multi-step deposition processes.

Conclusions and Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

This study investigated a hybrid manufacturing approach combining heat-assisted SPIF with TIG welding-based material deposition for the local reinforcement of Mg−Zn−Zr (ZK61) alloy thin sheets. The effects of SPIF-induced substrate thickness and forming temperature on TIG deposition morphology and thermal distortion were examined.

The results show that TIG heat input strongly influences deposition geometry, with increasing heat input leading to wider and flatter deposits for all investigated substrate conditions. Substrate thickness, controlled by SPIF wall angle, was identified as a critical parameter governing thermal distortion. Substrates formed at lower wall angles exhibited a comparatively wide and stable TIG welding process window, whereas substrates formed at higher wall angles showed a narrower window beyond which significant out-of-plane distortion occurred.

Forming temperature during SPIF was found to influence the repeatability of TIG welding deposition morphology. Substrates formed at higher temperatures showed consistent deposition morphologies across repeated experiments, while substrates formed at lower temperatures showed pronounced variability, primarily attributed to differences in the microstructural properties of the SPIF-formed sheets across thickness. Within the investigated range, substrate curvature did not significantly affect deposition geometry or distortion for single depositions; however, successive depositions resulted in increased thermal distortion due to the accumulation of residual stresses.

Overall, the findings demonstrate the feasibility of integrating heat-assisted SPIF with TIG-based material deposition for localized reinforcement of magnesium alloy thin sheets. The results highlight the importance of jointly considering deposition morphology and thermally induced distortion when defining a suitable processing window for hybrid SPIF-TIG approaches. While the present study focuses on geometric stability and deposition behavior, further investigation of microstructural and mechanical aspects will be required to fully assess process robustness. Ultimately, the work provides a foundation for future studies addressing continuous deposition strategies and toolpath design for SPIF-formed substrates.

Acknowledgment

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

This research was conducted within the framework of the STIFF project, facilitated by the KU Leuven C2 research fund.

References

The original version of this paper is available on https://www.scientific.net/SSP.389.295.pdf

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Solid State Phenomena, ISSN: 1662-9779, Vol. 389, pp 305-318

doi: 10.4028/p-k95d4N

© 2026 The Author(s). Published by Trans Tech Publications Ltd, Switzerland.

Submitted:
2026-01-17

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-16

Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

The original version of this paper is available on https://www.scientific.net/SSP.389.305.pdf

Daria Gelbich 1,a*, Frank Schweinshaupt 1, b, Thomas Stoel 1,c, Philipp Niemietz 1, d, Tim Herrig 1,e and Thomas Bergs 1,2,f

1 Manufacturing Technology Institute (MTI) of RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen

2 Fraunhofer Institute for Production Technology IPT, Steinbachstr. 17, 52074 Aachen

a  d.gelbich@mti.rwth-aachen.de, b  f.schweinshaupt@mti.rwth-aachen.de,

c t.stoel@mti.rwth-aachen.de, d p.niemietz@mti.rwth-aachen.de, e t.herrig@mti.rwth-aachen.de, f  t.bergs@mti.rwth-aachen.de

Keywords: Fine Blanking, FEM Simulation, Process Noise, Tool Geometry

Abstract

In fine blanking, a mass production process for safety-critical components, a discrepancy exists between deterministic modeling approaches and the stochastic nature of real-world measurements, often termed process noise. This work combines Finite Element Method simulations with data from industrial-scale fine blanking experiments, featuring long stroke series across multiple coils with systematically varied die clearances. The analysis shows a strong correlation between force curve characteristics and the formation of tears, a relationship that holds across all tested geometries. In contrast, only weak and inconsistent correlations were found between the force signal and the resulting die roll. This weakness is explained by the finding that multiple physical effects, such as material strength and friction, have competing influences on die roll that are not separable in the single force signal. These results demonstrate that the utility of the force signal for quality prediction is highly dependent on the tool geometry, providing a basis for more reliable tool design strategies in fine blanking.

Introduction

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In the domain of sheet metal processing, fine blanking stands out as a highly productive precision shearing process that enables the economical manufacture of sheet metal parts with strict quality requirements. It is characterized by three independently acting process forces: blank holder, counter, and blanking force, along with a small die clearance and a chamfered shearing edge on a die, which collectively contribute to the formation of compressive stresses and controlled material flow [1]. However, in industrial practice, addressing stochastic process fluctuations, referred to as process noise [2], remains a significant challenge, as its underlying causalities from a complex interplay of material variations, tool wear, and thermomechanical drift are difficult to disentangle from macroscopic process signals.

The inability of Finite Element Method (FEM) simulations to capture this real-world process noise highlights the need for a more data-driven, hybrid approach. While simulations offer valuable insights into the mechanical behavior of materials under idealized conditions, the simplifying assumptions and abstractions inherent to the method fundamentally limit their ability to capture the real-world variability that occurs during manufacturing. These unpredictable factors show as deviations between simulated and measured behaviors, which can significantly impact the quality and consistency of the final product. Rather than being treated as errors, these deviations can be systematically analyzed in research as a source of information on unmodeled physical phenomena.

Several studies have demonstrated the potential of data-driven signal analysis in fine blanking. For example, works by Baer et al. [3] and Unterberg et al. [4] have explored the mechanical punch loads and used force signals for wear monitoring, respectively, highlighting the importance of realtime data in understanding the process. However, a systematic investigation into how key tool design
parameters, such as die clearance and chamfer geometry, influence the stochastic characteristics of the punch force signal in large stroke series (several coils) itself remains largely unexplored.

This paper contributes to the methodological discourse by presenting a hybrid analysis framework that interrogates the deviations between FEM simulations and experimental data. The methodology is centered on a systematic comparison of simulated and measured force curves resulting from variations in die clearance for a long stroke series ( 1 coil per parameter). The key contribution is therefore a framework for analyzing how tool geometry modulates the characteristics of the process noise, and how this modulation affects the signal's ability to predict distinct types of quality metrics, namely large-scale geometric features (die roll) and localized defects (tears).

The paper is structured as follows: Section 2 reviews the state of the art regarding the sources and impact of process noise in fine blanking. Section 3 details the integrated methodology, encompassing the experimental approach, the data analysis methods, and the setup of the numerical model. Section 4 presents and discusses the results from the hybrid analysis, establishing the link between tool geometry, process signatures, and final part quality. Finally, Section 5 concludes the work and outlines directions for future research.

State of the Art - Sources and Impact of Process Noise in Fine Blanking

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In forming and sheet metal separation processes, such as fine blanking, the interactions between the sheet metal material and tool active elements are influenced by unavoidable process noise. Process noise in fine blanking can be attributed to several key factors, including material inhomogeneities, machine behavior, tool wear, reaching steady-state process heating, and environmental factors. The methodological approach proposed in this work focuses on understanding and the explainability of causalities of process noise, aiming to identify and analyze the underlying factors that drive these variations.

Material inhomogeneities along the length of a fine blanked coil, such as variations in thickness, mechanical strength, and microstructure, are a source of real-world stochastic variations in process outcomes. While certain material-related effects, such as non-metallic inclusions affecting ductility and increasing susceptibility to tearing, are known, these microstructural variations and their precise impacts are not yet incorporated into current simulation models [2]. These inhomogeneities, often caused by fluctuations in the rolling process or variations in heat treatment of sheet metal strip, lead to inconsistent blanking forces and sheared surface quality [5,1]. For example, variations in material properties can cause locally uneven stress distribution during the shearing process, resulting in defects such as tears. Tool wear introduces a slow shift in process conditions, which can be difficult to detect and compensate for in real-time [ 3,8 ]. For example, worn tools may require higher blanking forces, leading to increased loads on the machine and potential defects like burr or tears in the final product. Thermal expansion of the tool due to process heating during a stroke series can alter the die clearance, leading to variations in part quality [9, 2]. Additionally, fluctuations in the ambient temperature can affect the material properties, further increasing process instability.

The impact of process noise on fine blanking is multifaceted. Variations in sheared surface quality, such as inconsistent smoothness and flatness, are direct consequences of process noise [5]. Furthermore, process noise can destabilize the fine blanking process, leading to higher reject rates and thus reduced production efficiency [6].

Methodology

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Experimental setup. The experimental setup was designed to systematically investigate the effects of tool design parameters on the fine blanking process under conditions reflective of industrial mass production. The machine setup consisted of a state-of-the-art fine blanking line, centered around a

Feintool XFT 2500 Speed press equipped with a servomechanical main drive system. The line included a decoiler and a leveler, as depicted in Fig. 1, as well as an automatic lubrication system.

[picture]

Fig. 1: Schematic of the fine blanking line used for data acquisition.

Fig. 1. Schematic of the fine blanking line used for data acquisition.

The sheet metal material used was cold rolled 58CrV4+AC (DIN EN material number 1.8161), a high-carbon steel known for its challenging shearing properties. This material was chosen for its industrial relevance and its ability to produce high-quality sheared surfaces under optimal conditions. The experiments utilized cold rolled strips with a thickness (s) of 6 , representative of industrial applications. The material was supplied in an annealed state ( +AC ) to achieve spheroidized carbides. A custom single-cavity fine blanking tool was utilized. The tooling components, including the punch, die, guide, and counter punch, were manufactured from tool steels (Böhler S390 and X155CrVMo12-1). The sheared part geometry was designed to produce a component with different difficulties, featuring varied radii and angles analogous to the functional features of gear teeth, as shown in Fig. 2.

[picture]

Fig. 2: Schematic representation of a fine blanking part with the tool design parameter variations.

Fig. 2. Schematic representation of a fine blanking part with the tool design parameter variations.

To systematically generate a dataset encompassing a wide range of process states, a variation of the die clearance ( u ) was conducted to evaluate its impact on blanking forces and part quality. Three distinct die clearance levels were investigated, as detailed in Table 1. For each of the three die clearances, a new blanking punch was installed to minimize the influence of tool wear on the process results. Each die clearance parameter was run across two separate sub-coils, which correspond to the total length of the cold rolling process. This resulted in a total of six processed sub-coils and approximately 16,200 strokes for a comprehensive evaluation.

Data acquisition and quality evaluation. To create a digital representation of the process, the fine blanking tool was equipped with sensors to measure blanking forces and tool displacement. Piezoelectric force sensors (Kistler 9041A and 9021A) were used to measure the punch and counter forces, providing insights into the load distribution and material resistance. The force and displacement signals were sampled at a frequency of 20 to capture the detailed dynamics of the fine blanking process. The tool displacement was measured using a laser triangulation sensor (Micro-Epsilon optoNCDT 1900).

The quality of the sheared parts was evaluated using a 3D optical profilometer (KEYENCE VR6200). Key quality metrics included the clean-shear area, die roll height, and the presence of tears,

Table 1: Overview of the experiments. Three distinct die clearance levels were investigated, with each die clearance run on two separate sub-coils.

Description
Sub-Coil ID

Die Clearance

Chamfer Angle

Chamfer Height

Ref | R1C6 | 0.03 | 35 | 0.5
| R1C3 | 0.03 | 35 | 0.5
U040 | R1C2 | 0.04 | 35 | 0.5
| R1C5 | 0.04 | 35 | 0.5
U020 | R1C1 | 0.02 | 35 | 0.5
| R1C4 | 0.02 | 35 | 0.5

1Each of the three die clearances was initiated with a new blanking punch.
tear-off, or burr. The analysis in this work focuses on two of these metrics: tear formation and die roll height. Samples were taken at regular intervals (every 200 strokes) for quality analysis.

For the analysis of tear formation, a sample of 20 consecutive parts was collected. Each part was visually inspected, and the total number of tears across twelve predefined corners was recorded. To quantify the die roll height, a systematic sampling strategy was employed. From each collected sample, the 1st, 6th, 11th, and 16th parts were selected. The profiles of three specific corners on these parts (corresponding to workpiece angles of 60,75 , and 90 ) were digitized. The die roll height was then determined algorithmically for each corner individually. This comprehensive dataset forms the basis for the subsequent analysis.

Feature extraction from force signals. To quantitatively analyze the stroke-to-stroke variations in the force signals and to establish a basis for correlation with part quality, a set of physically meaningful features was extracted from each individual blanking force curve. The selection of these features was guided by their ability to represent distinct phases and characteristics of the shearing process, as visualized in Fig. 3. The primary extracted features are detailed below and summarized in Table 2.

[picture]

Fig. 3: Visualization of the key features extracted from a blanking force curve.

Fig. 3. Visualization of the key features extracted from a blanking force curve.

Maximum force (max_force): This feature represents the peak blanking force. It serves as a primary indicator of the material's resistance to deformation and is known to be highly sensitive to variations in material properties and tool condition [3].

Relative position of maximum force (idx_max_rel): This feature is the normalized index at which the maximum force occurs, ranging from 0 to 1 . It provides a standardized measure of the timing of the peak force, allowing for the comparison of strokes with different lengths. Shifts in this value can indicate changes in the onset of fracture or variations in the elastic-plastic transition due to factors like tool wear or lubrication state [8].

Area under force curve (area_force): This feature is the integral of the force curve, representing the total mechanical work required to blank the part. As an indicator of the total energy dissipated, it is highly informative for tracking long-term process drifts [8] that may be caused by changes in material flow stress, friction, or tool condition.

Rise slope (rise_slope): This feature quantifies the slope of the force curve on the rising portion, calculated between 10% and 90% of the maximum force. It characterizes the initial elasticplastic response of the material and is sensitive to tool sharpness and the resulting stress concentrations [10].

Fall slope (fall_slope): This feature quantifies the slope of the force curve's descending portion after the peak force has been reached, calculated between 90% and 10% of the maximum force. It characterizes the plastic flow as well as the fracture behavior of the material. A steep, negative slope typically indicates a more abrupt fracture, whereas a shallower slope suggests a more ductile shearing process [11].

Table 2: Summary of extracted force curve features and their physical significance.

Feature | Description | Primary Physical Significance
max_force | Peak value of the force curve | Material resistance, hardness, friction [3]
idx_max_rel | Normalized position of the peak force | Timing of fracture initiation [8]
area_force | Integral of the force curve | Blanking work, shearing energy [8]
rise_slope | Slope of the initial rising force | Elastic-plastic material response [10]
fall_slope | Slope of the descending force after peak | Fracture behavior (brittle vs. ductile) [11]

Numerical modeling. To provide a physics-based interpretation of the data-driven findings, a Finite Element (FE) model was developed, replicating the experimental geometry and boundary conditions. The modeling approach was adapted from the framework for fine blanking simulation presented by Schweinshaupt et al. [12] and implemented in the commercial software Forge NxT 4.1. The primary purpose of the model is to serve as a tool for a sensitivity analysis designed to decompose and understand the deterministic components of process noise. By systematically varying key physical input parameters, such as the material's flow curve and friction coefficients, the model is used to investigate how these changes deterministically influence the shape of the simulated force curve. These simulated force signatures are then used to explain the physical origins of the correlations observed between the experimental force features and the measured part quality.

To ensure computational tractability, a quarter model was implemented to approximate a geometric symmetry of the component. All active tool components and the workpiece were discretized using 3D tetrahedral elements. Following a mesh convergence analysis, the workpiece in the immediate shear zone was meshed with a minimum edge length of 0.35 . The tool components were modeled as elastic
bodies, the physical and thermophysical parameters used for die and blanking punch (Böhler S390) as well as blank holder and counter punch (cold work tool steel X155CrVMo12-1 or 1.2379), and all specific mechanical and thermophysical parameters for both the tool and workpiece materials were adapted directly from the validated simulation framework presented by Schweinshaupt et al. [12], where they are detailed in full.

The sheet metal material was modeled using a thermoviscoplastic material law with an integrated remeshing algorithm to handle the large deformations inherent to the process. While the model is thermomechanically coupled, the analysis in this work focuses on the mechanical results at constant initial temperature of 20. The material's flow stress was described by the Hensel-Spittel constitutive law [13]. As the experimental material was 58CrV4+AC, and a validated model for this specific steel was not available, the parameters for the chemically similar steel 51 CrV 4 in a soft annealed state were sourced. The constitutive model describes the true stress ( σf ) as a function of temperature ( θ ), true strain ( φ ), and strain rate ( φ˙ ) according to Eq. (1):

σf(θ,φ,φ˙)=A·em1θ·φm2·em4/φ·φ˙m3(1)

The specific coefficients used in the simulation are detailed in Table 3. Material separation was governed by the normalized Cockcroft-Latham ductile fracture criterion, modified by Oh et al. [14], with a critical threshold value of Ccrit =1.44 as determined by Wai Myint et al. [15]. Frictional conditions at the tool-workpiece interface were described using a hybrid law combining a Coulomb model ( μ=0.1 ) with a shear friction limit ( m=0.2 ).

Table 3: Coefficients for the Hensel-Spittel flow curve model for 51 CrV 4 (soft annealed state) [16].

A | m₁ | m₂ | m₃ | m₄
997.51 | -0.00080 | 0.17008 | 0.01324 | -0.00818

To investigate the sensitivity of the force signal to key physical parameters and to provide a basis for interpreting the experimental findings, a systematic parameter variation study was conducted. A reference simulation was established using the parameters of the Ref experimental configuration (see Table 1). Subsequently, a series of simulations was performed where individual parameters were varied while all others were held at their reference values. The variations, detailed in Table 4, were chosen to represent plausible sources of process noise. Specifically, the flow curve was scaled by ±10% to simulate the effect of material property fluctuations inherent in sheet metal coils, while friction and temperature were varied to assess their influence on the process mechanics.

Table 4: Parameters varied in the FEM sensitivity analysis.

Parameter | Low | Reference | High
Factor of flow curve coefficient A [-] | 0.9 (897.76) | 1.0 (997.51) | 1.1 (1097.26)
Friction μ [-] / m [-] | 0.05 / 0.1 | 0.1 / 0.2 | 0.2 / 0.3
Tool Temperature [] | — | 20 | 50

Results and Discussion

The original version of this paper is available on https://www.scientific.net/SSP.389.305.pdf

This section presents the results of the hybrid analysis. The analysis is structured in three parts. First, the experimental process data is analyzed to characterize both the deterministic and stochastic components of the blanking force signal. Second, these signal characteristics are correlated with the measured part quality metrics to establish data-driven process-quality linkages. Finally, the experimental findings are compared with results from the FEM parameter study to provide a physics-based interpretation of the observed phenomena.

Characterization of experimental process signatures. To characterize the evolution of the process signatures, the experimental data was binned into stroke index ranges. For each bin, the mean and standard deviation of the key process and quality metrics were calculated to visualize their temporal trends and variability.

Fig. 4 presents the evolution of the mean maximum blanking force for the three die clearance configurations. The plot reveals a clear deterministic influence of the tool design, with the Ref ( 0.03 mm ) and U040(0.04 mm) geometries consistently requiring a higher blanking force than the U020(0.02 mm) geometry. Furthermore, a temporal drift is evident across all configurations, where the mean force increases over the first ~1500 strokes before stabilizing. This trend can be attributed to long-term phenomena such as the thermal equalization of the tool-press system [17]. The error bars, representing the standard deviation within each bin, quantify the magnitude of the process noise, showing the stochastic variability around the mean trend.

[picture]

Fig. 4: Evolution of the mean maximum blanking force for each die clearance configuration. The points represent the mean value within each bin, and the error bars indicate ± one standard deviation.

Fig. 4. Evolution of the mean maximum blanking force for each die clearance configuration. The points represent the mean value within each bin, and the error bars indicate ± one standard deviation.

The resulting distributions of the two primary quality metrics, die roll and tear count, were then analyzed. Fig. 5 summarizes the die roll height for the three different corner angles across all measured strokes. A clear, non-linear relationship with die clearance is visible. The U020 geometry consistently produced the smallest die roll, while the U040 geometry produced the largest. This is physically consistent with the understanding that a larger clearance allows for more extensive plastic flow before fracture, resulting in a larger radius of curvature at the die edge [18]. The individual data points overlaid on the boxes visualize the stochastic variability inherent to each configuration.

[picture]

Fig. 5: Distribution of die roll height for each tool geometry at the three measured corner angles.

Fig. 5. Distribution of die roll height for each tool geometry at the three measured corner angles.

A similar analysis was performed for the total tear count, with the results presented in the boxplot in Fig. 6. The evolution of tear count reveals a strong, non-linear relationship with die clearance. The U020 geometry, with the smallest die clearance, consistently produced the lowest number of tears, suggesting it represents an optimal parameter set for this material. In contrast, the U040 geometry, with the largest die clearance, exhibited a significantly higher tear count. This is physically consistent with the understanding that an excessive die clearance can induce high tensile stresses as the material is pulled over the die edge, promoting crack initiation and a larger fracture zone [18]. Conversely, a die clearance that is too small can lead to high stress concentration [1]. The U020 configuration appears to achieve the optimal balance between these two competing failure mechanisms.

[picture]

Fig. 6: Evolution of the total tear count distribution for each die clearance configuration. The box represents the interquartile range (IQR), the line inside is the median, and the whiskers show the data range. The connected line represents the evolution of the mean value.

Fig. 6. Evolution of the total tear count distribution for each die clearance configuration. The box represents the interquartile range (IQR), the line inside is the median, and the whiskers show the data range. The connected line represents the evolution of the mean value.

Correlation of process signatures with part quality. To quantify the relationship between force curve characteristics and sheared part quality, a correlation analysis was performed, first on the aggregated dataset and subsequently on each experimental condition individually.

The die roll is a geometric feature formed by the plastic flow of material at clean-shear. The overall correlation analysis, combining all die clearance configurations, is presented in Fig. 7. The heatmap reveals only weak to moderate positive correlations between force magnitude features (max_force, area_force) and the die roll. This suggests that when all process conditions are aggregated, a clear linear relationship is not apparent.

[picture]

Fig. 7: Die roll as a quality metric: the three corners selected for analysis (left), an example of die roll on a sheared surface (center), and the overall correlation matrix between force features and die roll height at these corners (right).

Fig. 7. Die roll as a quality metric: the three corners selected for analysis (left), an example of die roll on a sheared surface (center), and the overall correlation matrix between force features and die roll height at these corners (right).

However, a geometry-specific analysis (Fig. 8) reveals that the weak overall correlation is primarily driven by a single, specific process condition. A notable correlation only emerges for the U040
configuration at the 90∘ corner, where force magnitude features show a moderate positive correlation with die roll (r=0.41). For all other configurations and corners, the correlations are weak to non-existent.

This localized correlation can be explained by examining the die roll distributions (Fig. 5). The U040 geometry at the 90∘ corner exhibits not only the largest absolute die roll but also the highest variability. A linear correlation can only be reliably detected when there is sufficient variation in the data; the lower variability of the other configurations may be insufficient to reveal an underlying relationship. The observed positive correlation in this specific high-variability case is physically consistent with established principles: a larger die clearance allows for more extensive plastic flow, which requires more blanking work (area_force) and results in a larger die roll [1]. Given that this analysis is based on only three of the twelve component corners, however, drawing a definitive conclusion about a universal relationship is not yet possible.

[picture]

Fig. 8: Geometry-dependent correlation matrices between force features and die roll for each die clearance configuration.

Fig. 8. Geometry-dependent correlation matrices between force features and die roll for each die clearance configuration.

A similar analysis was performed for tear count, a localized defect shown in Fig. 9 (left). The overall correlation analysis (Fig. 9 (right)) is again misleading, showing a very strong negative correlation for idx_max_rel (r=−0.11) that is a statistical artifact that arises from combining experiments where the underlying physical mechanics are fundamentally different.

[picture]

Fig. 9: Example of a tear on a sheared surface (left) and the overall correlation matrix between force features and tear count across all experiments (right).

Fig. 9. Example of a tear on a sheared surface (left) and the overall correlation matrix between force features and tear count across all experiments (right).

The geometry-specific analysis in Fig. 10 reveals the true underlying trend. A consistent positive correlation is exhibited by the rise_slope across all three die clearance configurations, suggesting that a more rapid initial loading rate is a key driver of the micro-fracture events, a finding consistent with studies on damage evolution in shearing [19]. However, it is only within the stable, fracturedominated regime of the U020 configuration that other force features, such as idx_max_rel ( r=− 0.87 ), also become strong predictors. This is a critical finding: it demonstrates that while certain force characteristics have a consistent relationship with defects, the overall predictive utility of the force signal is maximized when the process is operating in a stable regime as dictated by the tool geometry. The physical origins of these complex, geometry-dependent relationships will be investigated in the subsequent chapter.

[picture]

Fig. 10: Geometry-dependent correlation matrices between force features and tear count for each die clearance configuration.

Fig. 10. Geometry-dependent correlation matrices between force features and tear count for each die clearance configuration.

Hybrid analysis: simulation-based interpretation. To provide a physics-based interpretation for the experimentally observed phenomena, the results from the FE model were compared with the experimental data.

The first step of the hybrid analysis is the validation of the reference FE model. The simulated force-displacement curve from the reference configuration was compared to the mean experimental force curve (see Fig. 3) from the corresponding Ref experiments. The model demonstrates a good overall agreement, with the simulated maximum force showing a relative deviation of only 3.92% compared to the mean experimental value.

However, discrepancies in the curve shape are apparent. The simulated curve exhibits a steeper elastic rise and a more pronounced drop after the peak force. These differences can be attributed to factors not fully captured in the idealized simulation, most notably the elastic compliance of the press frame and tool system, which is known to affect the force progression in real-world blanking operations [20]. Despite these deviations, the close agreement in peak force confirms that the model serves as a valid baseline for the subsequent sensitivity analysis.

The validated model was then used to conduct the parameter sensitivity study to explain the complex, geometry-dependent correlations found in the experimental data. Fig. 11 presents the simulated blanking force curves for each parameter variation. The analysis demonstrates that variations in the material's flow stress have a global and dominant effect on the magnitude of the force curve. In contrast, parameters like friction primarily influence the shape of the curve during the fracture phase. The effect of an elevated initial tool temperature is shown to be minimal, resulting in only a minor,
localized force reduction at the peak. This indicates that under the simulated conditions, a moderate increase in the tool's starting temperature does not significantly alter the overall process mechanics.

[picture]

Fig. 11: Results of the FEM parameter sensitivity study.

Fig. 11. Results of the FEM parameter sensitivity study.

These simulated signatures provide a direct physical basis for interpreting the experimental correlations. The experimental analysis revealed that the rise_slope was a robust predictor of tear count across all die clearances. The simulation results in Fig. 11 explain this by confirming that the rise_slope is a direct indicator of the material's initial resistance to deformation (the flow curve). A steeper rise_slope signifies a more rapid pressure buildup at the shearing zone. This rapid loading can lead to higher local stress concentrations, which accelerate the initiation of micro-fractures at material inhomogeneities, thereby increasing the likelihood of tear formation [19].

Conversely, the experimental analysis for die roll did not reveal any clear, universal predictor, with the correlations being generally weak. The simulation provides a direct physical explanation for this weakness by revealing conflicting physical mechanisms. An analysis of the simulated die roll shows that a higher material strength flow curve leads to a higher max_force but a smaller die roll ( 0.9 mm vs. 1.5 mm for the lower strength case). This confirms the foundational principle that a stronger material exhibits lower formability [1]. This creates a conflict: an increase in max_force due to higher material strength would suggest a negative correlation with die roll. However, other process variations, such as an increase in friction, could also increase the max_force while potentially increasing the die roll. Since the macroscopic force signal is an integrated measurement that is unable to distinguish between these opposing effects, it is an inherently unreliable predictor for die roll.

A further observation concerns the thermomechanical component of process noise. The U040 configuration did not show the expected decrease in average blanking force relative to Ref, despite the larger die clearance. This can be attributed to competing thermal effects: while a larger clearance reduces shearing resistance, the associated increase in plastic deformation volume generates more heat, leading to thermal softening of the workpiece material [20]. These thermomechanical couplings, which accumulate over a long stroke series, are not captured by the single-stroke FE model used in this study.

The hybrid analysis therefore, leads to a key takeaway: the measurable process signature is not a universal sensor. The force signal is a robust predictor of localized defects (tears) because this quality metric is strongly linked to a single, dominant feature (rise_slope). In contrast, the signal is an unreliable predictor of large-scale geometric features (die roll) because the final die roll is the result of multiple, competing physical phenomena (such as material strength and friction), which have opposing effects and cannot be distinguished from the single, integrated force signal.

Summary and Outlook

The original version of this paper is available on https://www.scientific.net/SSP.389.305.pdf

This study presented a hybrid analysis framework to decompose and understand process noise in fine blanking by systematically interrogating the deviations between experimental data and numerical simulations. The primary objective was to investigate how tool geometry, specifically die clearance, modulates the information content of the macroscopic force signal and its ability to predict distinct quality metrics.

The experimental analysis revealed a complex, geometry-dependent relationship between process signatures and sheared part quality. For large-scale geometric features like die roll, the correlations were found to be generally weak and inconsistent, indicating that the force signal is an unreliable predictor for this metric. A likely reason for this weak correlation is the comparison of a global force signal, integrated over all twelve corners, with local die roll measurements taken from only three of those corners. In contrast, the analysis for localized defects like tears yielded a more nuanced and significant finding. A consistent trend was identified for the rising force during the shearing progress rise_slope, which exhibited a positive correlation with tear count across all three die clearance configurations.

One finding remained unexplained within the current framework: the reference die clearance with 0.03 mm (Ref) required a higher average blanking force than the smaller die clearance with 0.02 mm(U020). This finding contradicts the general physical expectation that a smaller die clearance should increase shearing resistance, a relationship that has previously been studied primarily for single strokes. This discrepancy points to the influence of unmodeled sources of process noise, potentially arising from minor manufacturing deviations in the tool components or slight misalignments between the punch and die, which are known to have a significant impact on measured process mechanics [21].

Future investigations should aim to bridge this fundamental gap between single-stroke simulation and industrial stroke-series reality. This would require the development of more sophisticated thermomechanical FE models capable of accounting for the cumulative heat transfer and thermal stabilization over thousands of cycles, which remains a significant computational challenge. Such a model, validated by the integration of high-resolution temperature measurements, would allow for a direct investigation of the thermal softening effects hypothesized in this work. Second, a systematic study incorporating controlled variations in tool alignment and manufacturing tolerances could be conducted to quantify their contribution to the observed process noise. Finally, these findings form a crucial groundwork for the development of more advanced, physics-informed machine learning models, where the insights into the geometry-dependent nature of process information can be used to create more robust and explainable tool design strategies [2].

Acknowledgements

The original version of this paper is available on https://www.scientific.net/SSP.389.305.pdf

The authors would like to thank the German Research Foundation (DFG) for funding this research under the project number 520460745 within the priority program SPP 2422.

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The original version of this paper is available on https://www.scientific.net/SSP.389.305.pdf

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Keywords Index

A

Aa6061 Experimental and Numerical Investigation of AA6061 Tube Flowformability

Advanced High Strength Steels Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

B

Bending Moments Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Bending Sequence Influence of Process Parameter Variations on Stamping-Bending Component Quality

Biocompatible Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Bipolar Plates Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling; Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing; Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Bipolar Plates; 3D Printed Tool; Micro-roller Embossing; Fuel Cell; Multi Stage Forming Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Blank-holder Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Bulge Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

C

Closed-loop Property Control Reducing the Uncertainty in Flow Forming of Metastable Austenites

Composite Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Cranioplasty Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Curvilinear Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

D

Deep Drawing Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Design Of Experiments Influence of Process Parameter Variations on Stamping-Bending Component Quality

Die Material Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

Disturbances Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Drop Tower Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

E

Electric Motor Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Electrohydraulic Forming Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Electromagnetic Forming Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

F

Fem Simulation Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Ferrofluid Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Fiber Reinforced Plastic Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Fine Blanking Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Finite Element Analysis Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

Finite Element Modeling Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Finite Element Simulation Experimental and Numerical Investigation of AA6061 Tube Flowformability

Flexible Roll Forming Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

Flow Forming Reducing the Uncertainty in Flow Forming of Metastable Austenites

Flowforming Experimental and Numerical Investigation of AA6061 Tube Flowformability

Forming Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Free Forming Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges

Free-form Bending Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Fuel Cell Systems Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

G

Gas-based Hot Forming Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Geometry Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

H

Hairpin Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Hardness On the Surface Quality of Incrementally Formed Niobium Sheets

Height-variable Profiles Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

Hollow Embossing Rolling Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Hot Forming Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Hot Metal Gas Forming Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets

Hybrid Manufacturing Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

I

Impact Testing Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Implants Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Incremental Forming Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF); Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks; Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Incremental Sheet Forming Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers; On the Surface Quality of Incrementally Formed Niobium Sheets

Incremental Sheet Forming (isf) Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

L

Laser Heat Treatment Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Laser Welding Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Leveling Influence of Process Parameter Variations on Stamping-Bending Component Quality

M

Magnesium Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Magnetorheologic Actuator Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Metastable Austenites Reducing the Uncertainty in Flow Forming of Metastable Austenites

Micro-channels Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets

Multivariate Analysis Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

N

Niobium On the Surface Quality of Incrementally Formed Niobium Sheets

Numerical Simulations Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

O

Overbending And Underbending Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

P

Parameter Study Influence of Process Parameter Variations on Stamping-Bending Component Quality

Peek Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Pillow Effect Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Plasma Arc Welding; Controlled Tube Expansion; Aisi 316 Stainless Steel; Multi-step Expansion; Finite Element Modeling Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

Pmma Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Precipitation Hardening Aluminum Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Pressure Distribution Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Pressure Wave Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Process Noise Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Profilometry-based Indentation Plastometry;experimentation Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Punch Wear Assessment Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

R

Residual Stresses Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Resistance Heating; Hot Stamping; Coating Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Robot Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges

Roll Forming Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Rubber Forming Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

S

Schlieren Imaging Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Sheet Injection Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment

Sheet Metal Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Sheet Metal Forming Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives; Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties; Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Sheet-bulk Forming Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Sheet-metal Forming Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

Shockwave Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Simulation Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Single Point Incremental Forming Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA; Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Springback Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath; Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Stamping Influence of Process Parameter Variations on Stamping-Bending Component Quality

Surface Quality On the Surface Quality of Incrementally Formed Niobium Sheets

T

Tailor Welded Blanks Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Tailored Blanks Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Thermoplastic Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Thinning Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Tig Welding Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Titanium Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Tool Geometry Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Toolpath Strategies Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Tube Flowformability Experimental and Numerical Investigation of AA6061 Tube Flowformability

Tubes Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Twisting Process Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

U

Uhmwpe Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Ultra-thin Sheets Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets

Uncertainty Reducing the Uncertainty in Flow Forming of Metastable Austenites

Authors Index

A

Abell, J. Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Albracht, L. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Althoff, M. Influence of Process Parameter Variations on Stamping-Bending Component Quality

Ambrogio, G. Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

An, S. Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Arian, B. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Astarita, A. On the Surface Quality of Incrementally Formed Niobium Sheets

B

Banu, M. Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Barnett, P. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Behrens, B. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating; Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Beigzadeh, A. Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Bergs, T. Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing; Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming; Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Borda, F. Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

Bouchard, P. Experimental and Numerical Investigation of AA6061 Tube Flowformability

Bruschi, S. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives; Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Buchner, M. Influence of Process Parameter Variations on Stamping-Bending Component Quality

Böhm, V. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

C

Caruso, S. Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

Cho, D. Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Clark, A. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF); Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Conte, R. Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Cusanno, A. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

D

Damaškovič, M. Influence of Process Parameter Variations on Stamping-Bending Component Quality

Depke, H. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Derek, S. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

Duflou, J. Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Durante, M. On the Surface Quality of Incrementally Formed Niobium Sheets

E

Ervan, R. Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

F

Filice, L. Numerical Modeling of Controlled Multi-Step Expansion in Plasma Arc Welded AISI 316 Stainless-Steel Tubes

Filippi, S. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Fink, D. Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Fleischer, L. Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

Formisano, A. On the Surface Quality of Incrementally Formed Niobium Sheets

Frigge, A. Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

Fuchs, G. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

G

Gagliardi, F. Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Garlaschè, M. On the Surface Quality of Incrementally Formed Niobium Sheets

Gelbich, D. Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Ghiotti, A. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives; Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Gröbel, M. Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Guglielmi, P. Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Görtan, M. Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

H

Han, D. Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Hartmann, C. Influence of Process Parameter Variations on Stamping-Bending Component Quality

Hauser, L. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Herrig, T. Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing; Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming; Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Holländer, U. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Homberg, W. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Hübner, S. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating; Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

I

Ismail, A. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

J

Jesus, M. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment

Jr, K. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF)

K

Kauta, N. Experimental and Numerical Investigation of AA6061 Tube Flowformability

Kersting, L. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Khademi, M. Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Kimmina, S. Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Kipping, J. Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Koller, L. Influence of Process Parameter Variations on Stamping-Bending Component Quality

Kong, L. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Koyuncu, M. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Kräusel, V. Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes; Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Kurtov, O. Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Kuzucu, I. Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

L

Langohr, A. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Langstädtler, L. Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Lee, Y. Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Lian, J. Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets; Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Liewald, M. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Linnemann, M. Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

Lohmann, B. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

M

Magrinho, J. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Mamros, E. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF); Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Maso, M. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives

Meerkamp, M. Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Mocellin, K. Experimental and Numerical Investigation of AA6061 Tube Flowformability

Moon, J. Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming

Mu, Z. Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Münstermann, S. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

N

Napoli, L. Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Nettig, D. Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Niemietz, P. Multivariate Analysis of Scrap Web Sheared Surface Roughness for Punch Wear Indicators in Sheet-Metal Forming; Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

O

Ott, M. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Ozden, E. Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

P

Palumbo, G. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Pauli, S. Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Pereira, M. Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Piccininni, A. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Prisco, U. On the Surface Quality of Incrementally Formed Niobium Sheets

Psyk, V. Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes; Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

R

Ragai, I. Comparison of PEEK and UHMWPE Cranial Implants Fabricated at Room Temperature Using Single Point Incremental Forming (SPIF); Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Rath, J. Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Reuther, F. Numerical Study of Process-Specific Disturbances in Hollow Embossing Rolling

Richter, P. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Rüschkamp, H. Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

S

Scharifi, E. Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets; Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Schenck, C. Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Scherillo, F. On the Surface Quality of Incrementally Formed Niobium Sheets

Schnettger, A. Resistance Heating in an Atmosphere Suitable for XHV with thin Aluminium Film Coating

Schweinshaupt, F. Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

Schüppstuhl, T. Hot Double-Sided Incremental Forming of Fiber-Reinforced Thermoplastics: Process Capabilities and Challenges; Classifying Parameters and Target Variables in Incremental Sheet Forming of Fiber Reinforced Polymers

Shaffer, D. Single Point Incremental Forming (SPIF) of Stainless Steel 304 Quilted, Laser Welded Blanks

Silva, M. Extending the Process Window of Sheet Injection in AW6082-T6 Aluminium via Localised Laser Heat Treatment; Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Simonetto, E. Numerical Investigation and Optimization of Blank-Holder and Magnetorheological Actuators Configurations for Deep Drawing Objectives; Agile Tube Roll Forming, a New Process Architecture for Manufacturing of Longitudinally Welded Tubes

Sommer, J. Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

Sorgente, D. Mechanical Characterization by Profilometry-Based Indentation Plastometry of Locally Heat-Treated Blanks for Sheet Injection Applications

Spörer, T. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Stoel, T. Hybrid Analysis of Tool Geometry and Process Noise in Fine Blanking Through Simulation and Experiment

T

Taub, A. Mitigation of Geometric Inaccuracy in Closed-Contour Incremental Sheet Forming via Curvilinear Toolpath

Tausendfreund, A. Pressure Wave Analysis in Electrohydraulic Forming - A Multiple Sensor Approach

Tilly, K. Gas Based Hot Forming of Micro-Channels for High Strength Aluminum Alloy Sheets; Hybrid Hot Forming of High-Strength Aluminum Alloys: Influence of Local Deformation on Post-Aging Mechanical Properties

Trimarchi, S. Design and Development of a Hydrostatic Support Device for Hot Incremental Sheet Forming of PMMA

Trächtler, A. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Tschannerl, J. Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

Türkmen, Ü. Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel

U

Uhlmann, L. Feature Based Investigation of the Forming Behavior of Titanium Grade 1 for Bipolar Plate Manufacturing

V

Vanhove, H. Local Reinforcement of SPIF-Formed Mg-Zn-Zr Alloy Thin Sheets by TIG Welding

Vasquez, J. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Volk, W. Influence of Process Parameter Variations on Stamping-Bending Component Quality; Innovative Bending Strategies - Optimization of Bent Components to Suit Individual Load Cases Using Overbending and Underbending Strategies for the Free-Form Bending Process

W

Walther, F. Reducing the Uncertainty in Flow Forming of Metastable Austenites

Walther, R. Comparative Analysis of Die Materials for Reducing the Rebound-Effect in Electromagnetic Forming Processes

Weiss, M. Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Y

Yaaalimadad, B. Rubber Forming as a Novel Manufacturing Approach for Bipolar Plates in Fuel Cell Systems

Yoon, J. Combined Finite Element Simulation and Regression Modeling for Predicting Final Protrusion Length of Twisted Hairpin Legs in Stators

Z

Zhang, P. Multi-Stage Roller Embossing of Bipolar Plate Microchannels Using 3D-Printed Tooling

Ç

Çivisöker, E. Finite Element Analysis of Flexible Roll Forming of Height Variable Profiles Made of Advanced High Strength DP980 Steel