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ISBN print: 978-3-0364-0994-8
ISBN eBook: 978-3-0364-1994-7
DOI book: 10.4028/b-kq07R8
© 2026 Trans Tech Publications Ltd, All Rights Reserved

Forging and Rolling

Edited by
Bernd-Arno Behrens

Forging and Rolling

Special topic volume with invited peer-reviewed papers only

Edited by
Bernd-Arno Behrens

Scientific.Net

Copyright © 2026 Trans Tech Publications Ltd, Switzerland

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Volume 1183 of
Materials Science Forum
ISSN print 0255-5476
ISSN web 1662-9752

Full text available online at https://www.scientific.net/book/forging-and-rolling/978-3-0364-1994-7

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Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp -1-0

© 2026 Trans Tech Publications Ltd, All Rights Reserved

Accepted:
2026-04-08

Online:
2026-04-13

Preface

The original version of this paper is available on https://www.scientific.net/MSF.1183.-1.pdf

Topics covered by this issue include but are not limited to: Development of new and optimization of existing Forging and Rolling; Mathematical description and parameterisation of flow, damage and fracture behaviour of new workpiece and tool materials; Mathematical description and parameterisation of friction, heat transfer and wear in forging and rolling; Development of numerical methods, formulations and algorithms for simulation of forging and rolling processes; Validation of simulation models on industrial examples; Computer-aided process control. Furthermore, the results of the Collaborative Research Center 1153 on Tailored Forming are presented.

Main Editor

The original version of this paper is available on https://www.scientific.net/MSF.1183.-1.pdf

Prof. Dr.-Ing. Behrens, Bernd-Arno
Leibniz Universität Hannover, IFUM

Co-editors

The original version of this paper is available on https://www.scientific.net/MSF.1183.-1.pdf

BTU Cottbus-Senftenberg, Fachgebiet Hybride Fertigung
FAU Erlangen-Nürnberg, Lehrstuhl für Fertigungstechnologie
TU Dresden, Institut für Fertigungstechnik
Universität Stuttgart, Institut für Umformtechnik
TU München, Lehrstuhl für Umformtechnik und Gießereiwesen
Institut für Integrierte Produktion Hannover gGmbH

Table of Contents

Preface

Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Niklas Gerke, Hendrik Amend, Julius Peddinghaus, Kai Brunotte, Bernd Arno Behrens

Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Matthias Hammes, Armin Piwek, Norman Mohnfeld, Julius Peddinghaus, Johanna Uhe, Bernd Arno Behrens

Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Kishan Rahul Prajapati, René Laeger, Norman Mohnfeld, Julius Peddinghaus, Johanna Uhe, Bernd Arno Behrens

A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Cristian Cappellini, Claudio Giardini, Gabriele Locatelli, Mariangela Quarto

Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

Kenji Fuchiwaki, Tatsuhiko Aizawa

Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

Christian Overhagen, Robert Martin

A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Shaheryar Younas, Jos Havinga, Camile Hol, Ton van den Boogaard

Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Moritz Gouverneur, David Bailly, Junhe Lian

Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Aratz Barandiaran, Lander Galdos, David Abedul, Julen Agirre

Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Alexandros Prospathopoulos, Apostolos Argyros, Maria Pappa, Nikolaos Michailidis

Keywords Index

Authors Index

The original version of this eBook is available on https://www.scientific.net/book/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 1-11

doi: 10.4028/p-veE4uC

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

Submitted:
2026-01-19

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-13

Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

Gerke Niklas 1,a*, Amend Hendrik 1, b, Peddinghaus Julius 1,c, Brunotte Kai 1, d and Behrens Bernd-Arno 1,e

1 Leibniz University Hannover, Institute of Forming Technology and Forming Machines, An der Universität 2, 30823 Garbsen, Germany

a * gerke@ifum.uni-hannover.de, b  hendrik.amend @stud.uni-hannover.de, c  peddinghaus@ifum.uni-hannover.de, d  brunotte@ifum.uni-hannover.de, ebehrens@ifum.uni-hannover.de 

Keywords: tailored forming, thermal management (process control), hybrid components, spray cooling, induction heating, multi-stage forming.

Abstract

Adaptive thermal management is a prerequisite for multi-stage tailored forming of hybrid steel-aluminium blocks, as each section of material must remain within its forming temperature window and the joining zone must be protected from excessive thermal stress. This study defines a control-oriented process space for a combined induction heating and dual-fluid spray cooling concept developed in the Collaborative Research Center (SFB) 1153 "Tailored Forming." A three-phase test program is applied: Phase A quantifies and evaluates the influence of air pressure pair, water pressure pw, and nozzle distance d on the cooling performance and the formation of an axial gradient using standardized regression coefficients. In phases B and C, a reference setting is applied to rotationally friction-welded 20MnCr5/ENAW−6082 blocks in a cold-start and preheated state, which are representative of multi-stage forming processes. The results show that pair  and pw dominate both the cooling capacity and the formation of gradients, while d plays a subordinate role in the range investigated. The relationships remain qualitatively consistent for hybrid blanks and preheated conditions when the heating program is adapted to the aluminium and joining zone boundaries. The derived actuator ranking forms the basis for closed-loop temperature control in volatile, multi-stage tailored forming chains.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

The increasing demand for lightweight, high-performance components is driving interest in hybrid material systems that combine complementary properties within a single bulk part. In the Tailored Forming approach, a joined hybrid semi-finished workpiece is locally thermally conditioned prior to forming so that each material region reaches a material-specific forming temperature window, enabling function-integrated, weight-optimized components to be manufactured. [1,2]
Moving from single-step studies to multi-stage Tailored Forming chains narrows permissible thermal windows and increases volatility (e.g., varying transfer times and residual heat). Therefore, temperature profiles must be not only achievable but also controllable and reproducible. Defining a control-oriented process space and reliable actuators for process-integrated thermal management is a prerequisite for robust multi-stage chains. [3]
The Collaborative Research Centre (CRC) 1153 "Tailored Forming" process chain starts from joined, semi-finished billets and combines induction heating with localized two-fluid spray cooling to establish axial gradients, followed by transfer/handling and forming steps. Because induction power and spray cooling have their own parameter space, the overall system should be well suited for adaptive control. [1,3,4,5,6]
CRC 1153 studies by Piwek et al. [3, 4, 5, 6] and Ince et al. [7] have demonstrated the feasibility and potential of tailored temperature gradients for hybrid steel-aluminium billets and linked thermal histories to joint properties and process outcomes. However, these works typically employed one selected spray setting. Thus, a transferable, control-oriented characterization of the spray parameter space-needed for multi-stage operation with higher volatility-remains missing. [3,4,5,6,7]

In this paper, the focus is on a control-oriented process-space definition for induction-spray thermal management as an enabling step for subsequent forging-stage validation within the CRC 1153 process chain. The goal is to create a high temperature gradient in order to keep the steel area as hot as possible within its forming window, thereby improving formability and reducing the yield stress discrepancy with aluminium. At the same time, the aluminium segment and the joining-zone set hard upper limits, making thermal management a selective, spatially resolved control problem rather than a global cooling task. For steel-aluminium hybrids, thermal management is particularly critical. Mismatched allowable temperatures can cause inhomogeneous softening and unstable forming conditions [8], while the joining-zone must be protected against excessive thermal exposure and brittle Fe−Al intermetallic growth [9]. In addition, the aluminium segment must stay safely below incipient melting, making allowable aluminium temperatures and exposure times hard constraints for any adaptive strategy.

Induction heating offers production-relevant cycle times and adjustable penetration depth [10,11], but in hybrid geometries contrasts in electromagnetic and thermal properties can distort power deposition near the material transition and limit the reproducibility of heating-only gradient generation [7]. In this study, the induction setup and frequency are kept constant (penetration depth is not actively tuned). Therefore, surface heat extraction via spray cooling (air/water pressure and nozzle distance) is treated as the main adjustable actuator.

Localized two-fluid spray cooling provides flexible, tunable heat extraction to increase and maintain gradients after heating. Depending on surface temperature and heat-flux density, regimes range from single-phase convection to nucleate/transition boiling and high-temperature regimes with reduced effective heat transfer [12, 13]. In air-water systems, pressure levels shape droplet size, momentum and mass flow [14], while nozzle distance affects jet spreading and impingement distribution and thus local heat-flux density [15]. Spray cooling does not eliminate heat conduction, but counteracts heat conduction-driven homogenization by selectively removing heat where high temperatures are undesired, enabling higher and more reproducible gradients over process-relevant cycle times.

Despite this qualitative understanding, evidence remains limited on how adjustable spray parameters, together with application-oriented induction profiles, affect cooling power and axial gradients-especially under transfer conditions with different initial thermal states [16]. Systematic monomaterial reference studies and explicit transferability assessments to hybrid billets are rare, and sensitivity measures that prioritize dominant control variables for robust design and subsequent control are insufficiently reported for combined induction-heating/spray-cooling strategies [17].

The goal of this paper is to define a process space for adaptive thermal management in multi-stage Tailored Forming process chains. Phase A screens and ranks relevant adjustable spray parameters as potential control variables. Phases B and C then assess transferability across billet type and multistage thermal history (preheated transfer states), which is essential for process-chain implementation. This control-oriented process-space definition is intended to enable subsequent correlation with joining-zone geometry, intermetallic evolution and bond properties, as demonstrated in earlier Tailored Forming studies on steel-aluminium hybrids. [3, 4, 5, 6]

Accordingly, the research questions are structured along phases A−C to ensure a direct link between variable screening, transferability and process-chain relevance.

From this analysis, three research questions arise. First, which spray parameters (air pressure, water pressure and nozzle distance) dominate cooling power and the resulting axial temperature gradient under non-preheated initial conditions. Second, how does a preheated initial state affect the achievable gradients and the incremental cooling effect of the parameters in a multi-stage cycle. Third, can the experimental data be used to derive a robust, interpretable ranking of control variables for process design, enabling key variables to be prioritized for subsequent process control?

Materials and Methods

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

A three-stage experimental concept was used to identify and validate control-relevant spray-cooling actuators for process-integrated thermal management. Phase A employs monomaterial 20 MnCr 5 reference specimens to quantify the isolated influence of air pressure ( pair  ), water pressure ( pw ) and nozzle distance (d) on cooling power and axial temperature gradients. Phase B applies the Phase-A insights to rotary-friction-welded 20MnCr5/ENAW−6082 hybrid billets starting from ambient temperature to assess transferability and the additional heat-sink effect of the aluminium segment. Phase C reproduces preheated transfer conditions of a multi-stage process chain using residual heat from a preceding heating-transfer-cooling cycle. Therefore, the induction profile is adapted to keep the aluminium segment within its allowable window and to limit joining-zone thermal exposure. Intermetallic layer growth in the Al-steel joining zone becomes critical once joining-region temperatures exceed roughly >350∘C ( FeAl ) and >500∘C ( Fe2Al5-type), therefore the process window is defined to keep Tc2/Tc3 below these thresholds during cycling. [18]
All tests were conducted on cylindrical specimens ( ∅40 mm×126 mm ). Monomaterial reference specimens were manufactured from the case-hardening steel 20 MnCr 5 ( 1.7147 ). After rotary-friction-welding of the hybrid billets, the flash formed during the upset stage was removed using an integrated turning unit. In the hybrid sample, the length of the steel part was 100 mm and that of the aluminium part is 26 mm .

Experiments were performed on a dedicated test bench combining induction heating and active two-fluid (air-water) spray cooling. The monomaterial Phase-A design enables an interpretable actuator-response mapping without confounding effects from the dissimilar material pair, while Phases B/C evaluate qualitative transferability to hybrid billets and to preheated transfer states.

The specimen was positioned concentrically in a water-cooled copper coil which was flush with the upper edge of the sample and fixed at the top of the sample by a spring clamping system. The clamping device was insulated by a ceramic spacer. No insulation was provided at the lower mount. Induction power was applied according to defined time-power profiles, followed by a transfer/handling segment (no heating, no spray cooling) and a subsequent spray-cooling segment. Induction heating was activated at t=0−60 s (phases A/B) and at t=175−210 s (phase C), while spray cooling was activated in parallel. A medium-frequency generator (TruHeat MF 3010 G3 from TRUMPF Hüttinger) was operated in constant-power mode. For the main experiments, a baseline heating program of 11.3 kW for 60 s was applied. To benchmark energy-equivalent settings and identify process limits, additional power-time pairs were used ( 9.3 kW/80 s,10 kW/70 s,12.5 kW/53 s), where 12.5 kW/53 s was classified as near-critical due to incipient surface melting. For hybrid billets, the induction power was kept constant ( 11.3 kW ) while the first heating phase was shortened to 60 s ( 65 s caused local melting). For multi-stage process simulation, the billet was reheated after cooling in air to 650∘C at Tc1, and a transfer time of 15 s was considered between stages. The coil geometry (turns: 6, inner diameter: 52 mm , high: 40 mm ) and positioning were kept constant for all tests to ensure repeatable coupling.

The vertical offset between the nozzle plane and the induction-coil mid-plane was kept constant for all experiments to decouple geometric alignment effects from the investigated spray parameters. A splash guard was installed below the coil to shield rising spray mist and minimise negative effects on heating. The schematic of the experimental setup can be seen in Fig. 1.

The nozzle spacing d was examined at discrete levels (Tab. 1) in order to compare the spacingrelated changes in impact and wetting.

Four two-fluid nozzles (Type: Z-R4) were arranged around the sample body, each offset by 90∘. These nozzles are round jet air nozzles with an internal mixing pressure principle and an outlet angle of 20∘. Air and water pressures control droplet momentum, mass flow and atomisation quality, while nozzle distance controls the local impingement distribution.

The spray parameter range investigated and the reference setting used for the transfer tests are summarized in Tab. 1.

The parameter bounds were derived from preliminary trials [18] as stable operating limits of the spray system (no flooding/pulsation) while still producing clearly distinguishable cooling responses.

Although two-fluid nozzles allow wider nominal operating ranges, the investigated window was restricted by application-specific constraints (coil proximity, splash shielding to avoid mist-induced disturbances of inductive coupling, and hybrid thermal limits). In addition, a significant increase in pressure meant that temperatures above 1000∘C could not be achieved. To compensate for this, the heating power was increased, which led to melting of the sample. Cooling power was evaluated over a fixed 90 s interval to ensure direct comparability between settings.

Table 1. Investigated spray-parameter space and reference setting.

The thermal response was measured using four thermocouples ( Tc 1 to Tc 4 ) positioned along the specimen axis. Thermocouples Tc1 to Tc3 are type K elements. The thermocouples Tc2 and Tc3 were attached by spot welding 5 mm above and below the joining zone. Tc1 and Tc4 (type J) were positioned on the end faces by spring force. The measurement positions can be found in Fig. 1. Induction heating can generate radial temperature gradients because the induced power density is concentrated near the surface (skin effect), while the bulk temperature equalizes only by heat conduction. In this work, the thermal state is therefore evaluated primarily along the surface using Tc1 to Tc4 (Fig. 1) rather than assuming a uniform cross-sectional temperature. During the spray segment, heat extraction is predominantly surface-effective, which can reduce internal gradients over time. This effect is considered when interpreting gradient evolution and phase transferability. The axial gradient indicator is defined as ΔT(Tc1−Tc4), i.e., the temperature difference between the top and bottom positions at identical time stamps of the cycle. This definition is used consistently to compare gradient magnitudes across phases and boundary conditions.

[picture]

Fig. 1. Schematic of the experimental setup for induction heating and air-water spray cooling with thermocouple positions Tc1 to Tc4 and nozzle distance d.

Fig. 1. Schematic of the experimental setup for induction heating and air-water spray cooling with thermocouple positions Tc1 to Tc4 and nozzle distance d.

Cooling power was quantified using a weighted temperature indicator T― that represents the specimen's global thermal state while emphasizing the hotter end. Following Amend [18], T― is defined as a weighted mean of Tc 1 to Tc 4 , and the extracted heat ΔQ (Eq. 2) is calculated from the change of T― over a fixed evaluation interval Δt using the specimen mass and a temperature-dependent heat capacity. The temperature-dependent specific heat capacity cp(T) used in Eq. 2 is given in Tab. 2. The values between the tabulated nodes were determined by linear interpolation. The effective cooling power is then obtained as Pcool=ΔQ/Δt (Eq. 3). This metric is used as an effective, comparative energy-balance indicator derived from the thermocouple signals for screening parameter effects and ranking actuators [10]. It is not interpreted as a strict lumped-capacitance model (Biotnumber requirement) nor as a direct wall heat-flux measurement.

T―=(2*Tc1+Tc2+Tc3+Tc4)/5(1)

ΔQ=m∫T―(t0+Δt)T―(t1)cp( T)dT(2)

Pcool=ΔQ/t(3)

Table 2. Temperature-dependent specific heat capacity cp(T) used in the energy-balance evaluation.

T (°C) | cp, 20MnCr5 (J/(kg K)) | cp, EN AW-6082 (J/(kg K))
20 | 439.8 | 911.2
100 | 487.6 | 944.0
200 | 529.8 | 985.0
300 | 564.7 | 1026.0
400 | 605.9 | 1067.0
500 | 666.5 | 1108.0
600 | 760.2 | n/a
700 | 1008.2 | n/a
800 | 803.3 | n/a
900 | 650.0 | n/a
1000 | 650.0 | n/a
1100 | 650.0 | n/a

Here, Tc1−Tc4 denote the thermocouple temperatures, ΔQ is the extracted heat and t is the evaluation time. The weighting factor of 2 for Tc 1 was taken from Amend [18] in order to increase the contribution of the hotter end of the sample in the indicator and thus improve sensitivity to gradient-related changes (Eq. 1).

To assess the combined influence of the spray parameters, data from the structured parameter study were evaluated using multiple linear regression with air pressure, water pressure and nozzle distance as predictors and cooling power as the response. Standardized regression coefficients (SRCs), obtained from z-standardized inputs, were used as the effect measure to rank the dominant actuators [19]. Each parameter setting was repeated three times ( n=3 ) under identical conditions. The timeresolved temperature signals were averaged at each time step.

For Phase C, preheated transfer conditions were reproduced by a multi-stage test-bench cycle rather than separate furnace preheating. After an initial heating-transfer-cooling step, the specimen was not cooled to room temperature but reheated after a defined intermediate period, yielding a preheated initial state representative of residual heat from a preceding stage (approximately Tc2 ≈360∘C,Tc3≈312∘C and Tc4≈130∘C at t=175 s in the cycle: see Fig. 4). The same induction power profile was used for Phases A and B to compare monomaterial and hybrid effects under identical heating boundary conditions. In Phase C, power level and/or heating time were adjusted because the elevated initial level would otherwise overheat the aluminium segment and increase joining-zone exposure.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

Phase A quantifies the isolated effects of the adjustable spray parameters (air pressure, water pressure and nozzle distance d) on cooling power and axial temperature gradients and provides a factor ranking. Phase B transfers the Phase-A setting to hybrid 20MnCr5/ENAW−6082 billets under coldstart conditions, and Phase C evaluates the influence of multi-stage thermal history by reproducing preheated transfer states.

Phase A (monomaterial20MnCr5)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

Increasing the air pressure increases cooling power markedly from 720.8 W at 0.6 bar to 973.5 W at 1.2 bar and 1475.5 W at 1.4 bar (Fig. 2a) consistent with stronger atomisation and higher droplet momentum in two-fluid sprays. Although 1.4 bar yielded a higher calculated Pcool in the screening, this setting showed insufficient reproducibility in the underlying preliminary study, and was therefore not used as the reference operating point. In Amend [18], 1.2 bar is reported as the highest reproducible cooling power within the investigated range, while the 1.4 bar value was deemed not robust due to measurement deviations. In addition to the mean trend, the data indicate increasing scatter at the upper air-pressure range, which is plausible given the transition between spray states and the sensitivity of multi-droplet impingement to local wetting dynamics. [20]

For water pressure, cooling power increases from 780.3 W(0.2 bar ) to a maximum of 1030.7 W ( 0.6 bar) and then decreases at 0.7 bar ( 954.3 W ), indicating a non-monotonic response within the investigated operating window (Fig. 2b). The decrease in cooling capacity at pw=0.7 bar despite increased liquid supply is consistent with a change in state in two-fluid spray cooling. At higher water pressure, the air-liquid ratio decreases, the droplet size may increase, and local flooding or a thicker liquid film may occur. This can reduce effective heat transfer, for example by shifting the surface towards stable film boiling conditions or by reducing atomisation quality and impact efficiency. Such non-monotonic trends with increasing liquid flow are reported for spray cooling at high surface temperatures and during quenching. [12, 13, 15, 20, 21]

For nozzle distance, the maximum occurs at d=60 mm(780.3 W), whereas at 20 mm(721.2 W) and 80 mm(712.7 W) lower values are observed (Fig. 2c), consistent with distance-driven changes in jet spreading, droplet deceleration and impingement distribution. [15]

Based on Phase A, a robust reference setting for the subsequent transfer checks is defined as air pressure 1.2 bar, water pressure 0.6 bar and nozzle distance d=60 mm. This setting lies within the stable operating region and yields high cooling power without relying on extreme parameter limits, which is beneficial for reproducibility and later closed-loop implementation.

[picture]

Fig. 2. Cooling power after 90 s as a function of (a) air pressure, (b) water pressure and (c) nozzle distance.

Fig. 2. Cooling power after 90 s as a function of (a) air pressure, (b) water pressure and (c) nozzle distance.

Regression-based sensitivity assessment (Fig. 3)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

To quantify factor effects beyond the local trends in Fig. 2, a linear main-effects multiple linear regression (MLR) model was fitted using air pressure, water pressure and nozzle distance as predictors and cooling power as the response. Standardized regression coefficients (SRCs), obtained from z -standardized inputs, were used as a screening measure to rank the dominant, controllable actuators. [19] The SRC ranking confirms that the spray pressures are the primary control variables, while nozzle distance is secondary within the investigated range.

For robust process-chain operation, the most effective lever is the reproducible control of air and water pressure (and thus droplet momentum and mass flow), whereas nozzle distance mainly acts as a geometric tuning parameter that should be kept constant once aligned.

[picture]

Fig. 3. Global parameter sensitivities quantified by standardized regression coefficients (SRC).

Fig. 3. Global parameter sensitivities quantified by standardized regression coefficients (SRC).

Phase B (hybrid, cold-start initial state)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

Fig. 4 combines the cold-start cycle (phase B) and the subsequent reheating cycle (phase C) on a timeline. Phase B refers to the first heating and subsequent cooling segment starting from room temperature. It is important to note that the temperatures do not return to room temperature within the time window shown; the term "cooling to ambient conditions" is therefore not applicable. The second heating segment from t=175 s belongs to phase C and represents the reheating from a preheating state generated by residual heat (see Materials and Methods).

Under identical heating and cooling conditions, the hybrid sample systematically reaches lower temperatures than the reference sample made of a single material. This is consistent with the assumption that the aluminium segment acts as an additional cooling path and changes the effective heat flow distribution. The resulting temperature values at the most important points in time (end of heating at t=60 s and maximum temperature after heating at t=75 s ) are summarized in Tab. 3, and the complete temperature curves are shown in Fig. 4.

[picture]

Fig. 4. a) measured temperatures ( Tc 1 to Tc 4 ), b) the axial gradient indicator t=175 s for monomaterial 20 MnCr 5 and hybrid t=175 s.

Fig. 4. a) measured temperatures ( Tc 1 to Tc 4 ), b) the axial gradient indicator t = 175 s for monomaterial 20 MnCr 5 and hybrid t = 175 s .

For easier comparison, Tab. 3 summarizes the thermocouple temperatures and the axial gradient indicator at the key points in time used in Fig. 4.

Table 3. Key data points from the initial heating phase and subsequent response (Fig. 4).

t in s | Tc1 mono in °C | Tc2 mono in °C | Tc3 mono in °C | Tc4 mono in °C | ΔT mono in °C | Tc1 hyb in °C | Tc2 hyb in °C | Tc3 hyb in °C | Tc4 hyb in °C | ΔT hyb in °C
0 | 20 | 20 | 20 | 20 | 0 | 20 | 20 | 20 | 20 | 0
60 | 900.3 | 66.7 | 28.7 | 28.5 | 871.8 | 731.7 | 61.2 | 31.6 | 28.8 | 702.9
75 | 1021.5 | 160.4 | 85.7 | 32.1 | 989.4 | 939.5 | 148.5 | 90.3 | 49.2 | 890.3
175 | 658.4 | 275.1 | 260.7 | 100.7 | 557.7 | 562.7 | 362 | 311.9 | 129.6 | 433.1
210 | 977.9 | 78.2 | 32.5 | 55.1 | 922.8 | 794.6 | 69.7 | 32.9 | 35.5 | 759.1
225 | 1074.9 | 179.5 | 87.9 | 45.1 | 1029.8 | 975.5 | 160.1 | 94.8 | 55.7 | 919.8

Comparison Phase A vs. B (qualitative transferability)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

The dominant control variables identified in Phase A (air and water pressure) remain effective for shaping the thermal trajectory of the hybrid billet. The absolute temperature levels and gradient magnitudes shift because the aluminium segment introduces an additional heat-sink pathway and changes the boundary conditions. Consequently, adaptive process strategies must combine spray control with appropriate heating control (e.g., power/time adaptation) for hybrid process-chain states. [1,2]

Phase C (hybrid, preheated initial state, Fig. 4)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

The preheated state is generated by a reproduced multi-stage cycle (see Materials and methods). After an initial heating-transfer-cooling step, the billet is not cooled to room temperature but subsequently reheated after a defined intermediate period, yielding elevated initial temperatures representative of residual heat from a preceding stage. Compared with the cold-start case, the preheated cycle reaches comparable or moderately higher peaks after subsequent reheating, while the
inner measurement locations start from elevated levels. Therefore, heating parameters were adapted to avoid overheating the aluminium segment and to limit joining-zone thermal exposure.

During reheating in phase C (from t=60 s ), the initial temperatures are elevated due to residual heat from the previous cycle. The corresponding preheated initial state at t= is listed in Tab. 3, and the subsequent trajectories are shown in Fig. 4. These values define the deviation of the thermal history from phase B and explain the upward shift in the subsequent temperature curves. The heating parameters are therefore adjusted to prevent overheating of the aluminium segment and to limit the exposure time of the joining zone.

Comparison Phase B vs. C (thermal-history transferability)

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

For a better overview, Tab. 4 compares Phase B and Phase C at key points in time in Fig. 4 using directly readable values. Comparing the hybrid states at the end of the heating step ( t=75 s vs. t=225 s 210 s ) and at the at the end of the transfer segment (corresponding to the maximum temperature after heating, immediately before spray cooling) ( 731∘C→794∘C vs. 939∘C→975∘C ) shows qualitatively similar trajectories, with an upward shift due to the preheated initial condition. For example, Tcl increases from 28∘C→35∘C and 49∘C→55∘C (Fig. 4), while Tc4 increases from superscript number and mathematical formula. These results support the conclusion that the identified control relationships remain qualitatively consistent across multi-stage initial states, provided that the allowable aluminium temperature window and the joining-zone exposure time are deliberately limited. [8,22]

Table 4. Phase B vs. Phase C comparison for the hybrid billet at the end of heating and cooling segments.

Phase B

Tc 1 B

Tc 4 _B

mathematical formula _B

Phase C

Tc 1 _C

Tc 4 _C

mathematical formula _C

End

Heating

60 s
731
28
703
210 s
794
35
759

End

Cooling

75 s
939
49
890
225 s
975
55
920

Summary and Outlook

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

This contribution targets the definition of a process space for adaptive thermal management in multistage Tailored Forming process chains. A combined strategy of induction heating and localized airwater two-fluid spray cooling is investigated to generate and maintain axial temperature gradients under process-relevant constraints (aluminium temperature window and joining-zone exposure) and under varying initial states representative of multi-stage routes. [3, 4, 5, 6] The phase-based evaluation provides a consistent storyline. In Phase A, air pressure and water pressure are identified as the dominant, controllable actuators for cooling power and gradient shaping, while nozzle distance is secondary within the investigated range. Fig. 2 and 3 jointly provide the trend-based interpretation and the global actuator ranking (SRC screening). In Phase B and Phase C, the qualitative relationships remain valid for hybrid billets and for preheated transfer states (Fig. 4), supporting transferability to multi-stage process-chain operation. Relative to prior CRC 1153 demonstrations that employed one selected spray setting, the present work contributes a control-oriented characterization and prioritization of the available spray actuators. That is an essential step toward making induction-spray thermal management regulatable in volatile multi-stage environments. Phases B/C are intentionally transfer checks (single reference setting) rather than additional full process-window explorations. Quantitative prediction across the entire hybrid parameter space therefore requires further calibration. From an implementation perspective, adaptive control should prioritize reproducible regulation of air and water pressure (fast, high leverage) and treat nozzle distance as an aligned setup parameter. The observed non-monotonic response at high water pressure also indicates that purely linear models are suitable for screening, while more detailed nonlinear mappings may be beneficial for predictive control in an extended parameter space.

Future work should expand the parameter space on hybrid billets, include systematic variations of transfer time and residual heat, and validate the identified process window in real multi-stage forming sequences. In addition, thermal states should be linked to forming-relevant quality metrics (e.g., flow behavior, bond strength and intermetallic-layer evolution) to connect thermal control to component performance. Finally, the actuator ranking and transferability evidence provided here can be used to design closed-loop temperature profiling strategies (e.g., using pyrometric feedback and pressure control) for CRC 1153-style multi-stage Tailored Forming routes, where maintaining the aluminium window and limiting joining-zone exposure are decisive constraints.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

The authors thank the German Research Foundation (DFG) for financial support within the Collaborative Research Center SFB 1153, in particular subproject B02. (DFG Project number 252662854).

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.1.pdf

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B.-A. Behrens, A. Chugreeva, J. Diefenbach, C. Kahra, S. E. Thürer, J. Uhe, Microstructural characterization of steel-aluminum hybrid components manufactured by friction welding and die forging, Metals, 10 (2020) 1365. .

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Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 13-23

doi: 10.4028/p-LDA6yf

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

Submitted:
2026-01-19

Revised:
2026-02-16

Accepted:
2026-02-24

Online:
2026-04-13

Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

Hammes Matthias 1,a*, Piwek Armin 1, b, Mohnfeld Norman 1,c, Peddinghaus Julius 1, d, Uhe Johanna 1,e and Behrens Bernd-Arno 1,f

1 Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

a*hammes@ifum.uni-hannover.de, b  piwek@ifum.uni-hannover.de, c  mohnfeld@ifum.uni-hannover.de, d  peddinghaus@ifum.uni-hannover.de, e uhe@ifum.uni-hannover.de, f behrens@ifum.uni-hannover.de

*corresponding author: hammes@ifum.uni-hannover.de

Keywords: hot forming, finite element method, heat treatment, residual stresses.

Abstract

In order to achieve a long service life for highly stressed parts such as shafts for drivetrains, a combination of a bainitic microstructure with compressive surface residual stresses is beneficial. While a bainitic microstructure offers a good balance between strength and toughness, compressive residual stresses especially near the surface have a positive impact on service life. Research has shown that this is due to a shift of the crack initiation towards the core and a reduced crack growth. These properties can be achieved by hot forming as an established method for manufacturing highly stressed parts followed by an adapted cooling strategy. As this general approach was demonstrated for a simplified process in a prior study, the present article is dedicated to the functionalisation for hot forming processes. In detail, a customised spray cooling is presented for a hot impact extrusion process whereby shafts made of AISI 4140 are cooled down from the forming heat in a single step with adjusted cooling rates. In a finite element-based process design, different cooling strategies were investigated and adequate heat treatments to achieve the combined properties were identified. Following this process design, shafts are formed via hot impact extrusion and spray cooled according to the cooling strategy for experimental validation of the numerical model. Additionally, shafts with air cooling are produced as a reference. During forming, force-displacement curves are measured, which are used for the validation of the numerical hot impact extrusion simulation. The resulting plastic strain and temperature distribution significantly influence the following cooling simulation. The final microstructure as well as hardness values of the produced shafts are determined and compared for the varying cooling strategies.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

Parts manufactured via hot forming offer beneficial properties such as a finer microstructure as well as load adjusted grain orientations, leading to highly durable components [1]. In addition, a bainitic microstructure is favoured due to a good balance between strength and toughness [2], which is crucial for highly stressed parts. In order to obtain the desired mechanical properties, heat treatments are used after forming. However, these treatments influence the residual stresses on the surface, where often tensile stresses remain which have a negative impact on service life. On the other hand, compressive residual stresses positively influence crack initiation and propagation leading to later component failure and longer service life [3].

Residual stresses form due to different reasons: plastic deformation, local unequal thermal contraction of the surface and the core or changes in the microstructure [4]. Furthermore, these stresses are present while no external loads are applied. In this context, the formation of martensite is relevant, since due to the diffusionless transformation of martensite, a highly strained tetragonal crystal structure forms leading to an increase in volume. In turn, this increase in volume leads to compressive residual stresses [4]. Therefore, martensite formation is linked with compressive residual
stresses, and a combination of martensite near the surface and bainite in the core is desired, which is the aim of this process design through numerical studies.

When modelling the behaviour of the different microstructures of steel, phase-specific properties are required. In most cases, it is difficult to generate experimental material data for pure microstructural phases. However, these properties can also be calculated based on the chemical composition and empirical equations founded on physical principles as an estimation, which can be used instead [5].

The benefit of heat treatments directly from the forming heat are shown in [6, 7], where tailormade cooling strategies involving spray cooling led to adapted component properties. In order to implement the spray cooling process in simulations, heat transfer coefficients (HTC) are needed. These are determined with an experimental-numerical approach, where cooling curves are measured and the experimental setup subsequently simulated, adjusting the HTC values until the cooling curves of the simulation and the experiment match [8]. Through spray cooling, different cooling rates can be realised between the surface and the core, leading to an adapted microstructure.

When combining heat treatment and surface residual stress modification in one step, energy and resources can be saved compared to the conventional production route consisting of separate production steps since no reheating is necessary. Previous studies with simple cylindrical specimens showed that compressive residual stresses can be induced directly after hot upsetting with an adapted cooling strategy. The investigated steel was AISI 52100, with the focus on the formation of pearlite and martensite regarding the microstructure [9]. However, this research is dedicated to the manufacturing of shafts made of AISI 4140 via hot impact extrusion. The shafts are immediately cooled from the forming heat in order to achieve different microstructures consisting of bainite and martensite. The focus of this paper lies on the experimental validation of the implemented material models used for the process design with numerical simulations. A validated simulation model, especially regarding the prediction of the microstructure after forming and cooling, is essential for the prediction and further optimisation of residual stresses.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

The semi-finished products in this study were cylindrical steel bars made of AISI 4140 with a diameter of 30 mm and a length of 130 mm . The general process route is shown in Fig. 1, which consists of three major steps: Heating and homogenous austenitisation of the semi-finished product at 1,150∘C, followed by a hot impact extrusion operation and a subsequent adapted cooling from the forming heat.

[picture]

Fig. 1. General process route of the hot formed shafts with subsequent cooling.

Fig. 1. General process route of the hot formed shafts with subsequent cooling.

At first, the influence of different cooling strategies on the resulting surface residual stresses were investigated in pre-studies with finite element (FE) simulations in Simufact forming v2025.2. For the hot impact extrusion, both punch and die are modelled as rigid heat-conducting dies made of tool steel AISI M2. The values for the specific heat capacity and the thermal conductivity were taken from
the Simufact forming material library. Friction was modelled by a combined Coulomb-Tresca model with a friction coefficient of 0.3 [10] and a friction shear factor of 0.4 [11]. In addition, a constant HTC of 20 kW/(m2· K) between the workpiece and the dies was implemented [12]. For the calculation of flow curves of AISI 4140, the GMT model specified in Eq. 1 was calibrated with experimental cylinder compression tests [13].

kf=c1·ec2· T·εn1· T+n2·el1· T+l2φ·ε˙m1· T+m2(1)

The flow stress kf is calculated as a function of the true strain ε, the true strain rate ε˙ and temperature T with the material specific coefficients given in Table 1.

Table 1. Fitted GMT model parameters [13].

superscript number in

superscript number in superscript number

superscript number in

superscript number in -

superscript number in

superscript number in -

superscript number in

superscript number in -

6054.21 | -0.0039 | -3.0846 | 0.3000 | 1.8926 | -0.03548 | -9.4422 | 0.2484

In addition, time-temperature-transformation diagrams are implemented for AISI 4140, which were experimentally determined in [14], as the final phase distribution is of high interest. Furthermore, phase changes play an important role in the evolution of residual stresses. The transformation induced plasticity (TRIP) effect is also taken into account by implementing phasespecific TRIP-coefficients, evaluated with an experimental-numerical approach in [14]. The remaining material parameters for each phase were calculated with the software JMatPro, which uses the chemical composition of the alloy and empirical equations. Therefore, temperature-dependent and phase specific values were obtained for the specific heat capacity, thermal conductivity, thermal expansion coefficient, density, Young's modulus, Poisson's ratio, latent heat and hardness of AISI 4140. In addition, the flow curves were revaluated for each phase. The total strain is calculated with the additive strain decomposition method from the implicit MSC.Marc solver, where the total strain is calculated as the sum of the elastic and plastic strain increments as well as the thermal, transformation-induced and transformation-plasticity strain increments [14].

For both the forming and cooling simulations, a 2D-FE model was developed due to the rotational symmetry of the process, as shown in Fig. 2.

[picture]

Fig. 2. FE model of hot impact extrusion, top: before forming, bottom: after forming.

Fig. 2. FE model of hot impact extrusion, top: before forming, bottom: after forming.

An element edge length of 0.5 mm was chosen for the workpiece following a mesh sensitivity study, offering a good trade-off between result accuracy and computation time. The initial condition implemented for the forming simulation consists of a numerically calculated thermally expanded cylindrical billet with a temperature of 1,150∘C and a 100% austenitic microstructure for the initial process design. In addition, an impact velocity of 500 mm/s was defined, in accordance with the experimental setup. The workpiece is extruded to a diameter of 22 mm with a stroke of 51 mm . Subsequently, the geometry as well as the stress and temperature field were transferred to a cooling simulation. A combination of air and spray cooling is investigated by implementing temperaturedependent surface HTC. The HTC were determined with an experimental-numerical approach, as detailed in [15]. The spray was mixed in the nozzle with a water pressure of 0.04 MPa and an air pressure of 0.1 MPa . Fig. 3 shows the implemented HTC curves.

[picture]

Fig. 3. HTC depending on the temperature between air or spray and AISI 4140 steel based on [15].

Fig. 3. HTC depending on the temperature between air or spray and AISI 4140 steel based on [15].

The plot shows high HTC values for the spray, with a peak of approximately 37 kW/m2 K at 100∘C, whereas the values for air are in a much lower range, with a maximum of 60 W/m2 K at 750∘C. Overall, the spray cooling behaviour can be separated in three different stages, starting with film boiling at high temperatures and lower HTC, leading to nucleate boiling at lower temperatures with very high HTC, which drop rapidly due to the change to convection with falling temperature. In contrast, air cooling exhibits only free convection. In order to precisely assign the specific HTC for spray cooling to a defined surface, the near-field contact function of Simufact Forming was used. For the remaining surfaces not exposed to the spray, the HTC between steel and air was assigned.

For the experimental validation, the workpiece was heated to 1,150∘C and held for 15 min for full austenitisation under argon gas atmosphere in order to reduce scaling. Afterwards, the workpiece was manually transferred in approximately 9 s to the spindle press Lasco SPR 500 for impact extrusion. Before each extrusion, the die was manually lubricated with an oil-based lubricant (Berulit 722, Bechem). The punch was fitted with strain gauges, allowing for direct force measurements without the influence of the machine stiffness. The corresponding displacement was given by the machine control. Fig. 4.a) shows the experimental setup.

[picture]

Fig. 4. a) Press space of the Lasco SPR 500 spindle press with installed tools and b) spray cooling station.

Fig. 4. a) Press space of the Lasco SPR 500 spindle press with installed tools and b) spray cooling station.

Following the ejection of the formed shaft, it was transferred manually in approximately 9 s to the cooling station. It was mounted near the top of the greater diameter with the smaller diameter pointing downwards. This allows only the smaller section and the shoulder area to be cooled by the spray. The cooling station and the mounting setup for the extruded shaft are shown in Fig. 4.b). Six nozzles were placed in a circular pattern in order to ensure uniform cooling from all sides.
During initial testing of the experimental setup, it was found that the temperature loss after transfer to the cooling station was higher compared to the initial simulation due to the clamping setup. In order to measure the differing cooling behaviour, a near-surface temperature-time measurement was conducted with an already formed shaft, which was reheated in the oven for 15 min for full austenitisation and then mounted in the cooling station where no spray cooling was used. Direct surface measurements by contacting the surface with a type K thermocouple proved unsuccessful, since the measured temperature was too low due to scaling.

Consequently, in order to generate different ratios of martensite, two cooling routes were experimentally investigated with five extruded shafts each, differing in starting times of the spray cooling as well as spray cooling durations, based on the near-surface temperature-time measurement and numerical pre-studies. Table 2 gives an overview of the different cooling sequences.

Table 2. Cooling sequences for different strategies.

| Strategy 1 | Strategy 2
1. Air cooling for | 380 s | 340 s
2. Spray cooling for | 4 s | 9 s
3. Air cooling for | 136 s | 140 s
4. Spray cooling for | 120 s | 150 s
5. Air cooling | until the whole shaft reaches room temperature

All the aforementioned parameters were also used for the simulation of the whole experimental process chain including transfers.

For the analysis of the microstructure and the hardness measurements, the shafts were cut in half lengthwise and samples were taken from the transition area. The etchant used was 2% alcoholic nitric acid (nital), and for the micro hardness measurement Vickers-indents (HV0.1) were utilised.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

For a validation of the forming step, the numerical force-displacement curves were compared to the experimental results, shown in Fig. 5.

[picture]

Fig. 5. Experimentally and numerically determined force-displacement curves of hot impact extrusion.

Fig. 5. Experimentally and numerically determined force-displacement curves of hot impact extrusion.

The numerical results show a good agreement with the experimental data, with only minor differences in the increase of force. During experiments, a smoother increase can be seen due to a higher contact area between the workpiece and the slightly greater forming die. This results from an eccentrical insertion leading to unsymmetrical bulging, which in turn increases the contact area steadily, whereas in the simulation, a perfect centred position is implemented. Here, the deformation occurs mainly in the tapered zone of the forming die, leading to a steady increase in force at first. At the same time, the initial cylinder outside the main forming zone increases until the surface comes into contact with the slightly greater forming die resulting in instant additional friction, which is seen in a sharp force increase. Starting from the maximum force, which is around 400 kN in both curves, is the relevant part for the forming process, where a good agreement is desired. The slope following the force peak is slightly steeper in the simulation compared to the experimental results, since during experiments the friction conditions change with decreasing friction surface, while in the simulation the conditions do not change, but the surface decreases resulting in lower forces. Overall, the maximum difference between experimental and numerical results after the initial force peak does not exceed 10%, which indicates an adequate model with suitable assumed boundary conditions such as friction [16].

For the cooling simulation, a numerical pre-study was conducted in order to identify suitable cooling strategies leading to significant compressive surface residual stresses as well as a mainly bainitic microstructure (see Fig. 6).

[picture]

Fig. 6. Residual tangential stress and martensite distribution after initial process design.

Fig. 6. Residual tangential stress and martensite distribution after initial process design.

The results show that a small formation of martensite can lead to compressive surface residual stresses, formed at the transition section between the smaller diameter and the shoulder, where the highest stresses are present in later usage due to the geometric discontinuity. The corresponding cooling strategy involved air cooling for approximately 11 min , followed by spray cooling for 3 s and
a spray cooling pause for 110 s until spray cooling is resumed. The spray cooling pause was set in order to allow bainite transformation in the core, resulting in martensite formation only near the surface. Further numerical pre-studies were conducted for different amounts of martensite. Based on these pre-studies and the temperature-time measurement of the reheated shaft, the cooling sequences shown in Table 2 were adapted.

For the simulation of the whole experimental process chain, the HTC of the mounting setup was determined similar to the air and spray behaviour and implemented in the model. The resulting microstructure of the numerical calculation is compared to the experiments using micrographs as well as hardness measurements for validation. Strategy 1, where spray cooling starts after 380 s , shows a mixed microstructure in the numerical simulation consisting of bainite with a maximum volume fraction of 68% near the surface and martensite with a maximum volume fraction of 39% near the core (see Fig. 7).

[picture]

Fig. 7. Mixed microstructure from numerical simulation of strategy 1.

Fig. 7. Mixed microstructure from numerical simulation of strategy 1.

The results show that the mounting setup has a major influence on the whole thermal behaviour of the system, which leads to a significant amount of martensite near the core. In the corresponding micrograph shown in Fig. 8.a), a mixed microstructure of bainite and martensite is also present.

[picture]

Fig. 8. a) Comparison between numerical (left) and experimental microstructure with hardness values of the individual phases (right) and b) location of hardness profile measurements and c) hardness profiles for both rows for strategy 1 .

Fig. 8. a) Comparison between numerical (left) and experimental microstructure with hardness values of the individual phases (right) and b) location of hardness profile measurements and c) hardness profiles for both rows for strategy 1 .

The harder phase of 541 HV0.1 corresponds to martensite, while the softer of 289 HV0.1 is bainite. These individual measurements were taken from hardness profiles, where only a single phase was indented, and the hardness profiles were measured in two rows approximately 4 mm apart (see Fig. 8.b)). Regarding the measurements shown in Fig. 8.c), the hardness profile shows fluctuations through the core, indicating a finely distributed microstructure with an increasing amount of martensite. The first indents close to the surface have a lower hardness due to a slightly lower martensite fraction as well as a coarser grained bainitic ferrite which is mostly indented. Following the rule of mixtures, the measured mixed hardness can be interpreted as the sum of the hardness of the individual phases taken from single-phase indentations, weighted with their respective volume fraction [17]. Therefore, the average hardness of 356 HV0.1 for row 1 and 364 HV0.1 for row 2 indicate a ratio of approximately 70% bainite and 30% martensite, which also agrees with [18], where Vickers hardness values were determined for different microstructures of bainite and martensite of the same AISI 4140 steel. Compared to the simulation, the calculated ratios are in a similar range, but with small deviations.

Starting the spray cooling earlier as in strategy 1 results in an increase of martensite formation as seen in Fig. 9.a).

[picture]

Fig. 9. a) Comparison between numerical (left) and experimental microstructure with hardness values of the individual phases (right) and b) hardness profiles for both rows for strategy 2.

Fig. 9. a) Comparison between numerical (left) and experimental microstructure with hardness values of the individual phases (right) and b) hardness profiles for both rows for strategy 2.

The micrograph shows a fine microstructure with a higher amount of martensite compared to strategy 1, which is also seen in the high fluctuations of the hardness measurements in Fig. 9.b). An average hardness of 450 HV0.1 for row 1 and 432 HV0.1 for row 2 corresponds to around 58% bainite and 42% martensite. The simulation yields values of up to 45% martensite.

Overall, it can be seen in both strategies that due to the mounting setup, the thermal behaviour of the system was greatly changed, leading to the formation of significant amounts of martensite near the core. This also results in different residual stresses on the surface of the shaft predicted by the adjusted simulation considering the thermal influence of the mounting. Fig. 10 shows the comparison of the final microstructures between experiment and simulation for the two strategies.

[picture]

Fig. 10. Comparison of final microstructures between experiment (derived from hardness values) and simulation for the two strategies.

Fig. 10. Comparison of final microstructures between experiment (derived from hardness values) and simulation for the two strategies.

Generally, the simulation shows a slight overestimation of the martensite fraction. For the characterisation of the spray cooling behaviour, the resulting HTC implemented in the simulation were determined with small cylindrical specimens, where the whole cylinder surface was directly sprayed on. In contrast, the surface of the shafts is only partially sprayed, where excess water drips down towards the tip leading to a slightly different cooling performance, thus resulting in the aforementioned difference.

Summary and Outlook

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

For the validation of the numerical models regarding forming and cooling, the process chain was experimentally realised. By comparing the force-displacement curves of the numerical model and the experiment, a good agreement was found, validating the forming simulation. In addition, two different cooling routes were investigated and the resulting microstructures of simulation and experiment were compared. Here, also a good agreement was found for both strategies. In strategy 1,30% martensite forms, while the simulation predicts 37%. When comparing strategy 2,42% martensite was determined in the experimental microstructure, where the simulation shows 45%. However, it can be seen that the martensite formation was not only close to the surface but also in the core in both strategies due to the change of heat transfer caused by the mounting setup. Therefore, the mounting setup for the shafts in the cooling station has to be modified in future work, so that the contact between specimen and mount is reduced to a minimum. In addition, the HTC of the spray should be determined where the surface is only partially sprayed and compared to the initial results with full surface spray. Furthermore, the cooling strategy has to be optimised by numerical process design in order to find the optimal cooling parameters so that a predominantly bainitic microstructure forms in the core. Additionally, the induced surface residual stresses of the experimentally formed shafts are to be measured and compared to the numerical results.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 530125423.

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The original version of this paper is available on https://www.scientific.net/MSF.1183.13.pdf

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I. Serebriakov, E. S. Puchi-Cabrera, L. Dubar, P. Moreau, D. Meresse, J. G. La Barbera-Sosa, Friction analysis during deformation of steels under hot-working conditions, Tribology International 158 (2021) 106928, doi: 10.1016/j.triboint.2021.106928.

D. Jeong, D. Kim, J. Kim, B. Kim, T. Dean, Effects of surface treatments and lubricants for warm forging die life, Journal of Materials Processing Technology 113-1-3 (2001) 544-550, doi: 10.1016/S0924-0136(01)00693-8.

P. R. Burte, Y.-T. Im, T. Altan, S. L. Semiatin, Measurement and Analysis of Heat Transfer and Friction During Hot Forging, Journal of Engineering for Industry 112-4 (1990) 332-339, 1990, doi: 10.1115/1.2899596.

B.-A. Behrens, J. Schröder, H. Wester, D. Brands, S. Uebing, C. Kock, Experimental and Numerical Investigations on the Development and Stability of Residual Stresses Arising from Hot Forming Processes, in: G. Daehn, J. Cao, B. Kinsey, E. Tekkaya, A. Vivek, and Y. Yoshida (Eds.), Forming the Future (The Minerals, Metals & Materials Series), Springer International Publishing, Cham, 2021, pp. 2289-2301.

B.-A. Behrens, A. Chugreev, C. Kock, Macroscopic FE-Simulation of residual stresses in thermo-mechanically processed steels considering phase transformation effects, in: E. Oñate, D.R.J. Owen, D. Peric M. Chiumenti, and E. de Souza Neto, (Eds.), XIV International Conference on Computational Plasticity: Fundamentals and Applications (COMPLAS 2019), Barcelona, 2019.

B.-A. Behrens, J. Schröder, D. Brands, L. Scheunemann, R. Niekamp, A. Chugreev, M. Sarhil, S. Uebing, C. Kock, Experimental and Numerical Investigations of the Development of Residual Stresses in Thermo-Mechanically Processed Cr-Alloyed Steel 1.3505, Metals 9-4 (2019) 480, doi: 10.3390/met9040480.

Z. Keran, M. Math, P. Piljek, FEM Analyses of Friction Coefficient in Open Die Coining Process of Different Grain Sizes, Journal Material Sci. & Eng. 1-1 (2012) 5, doi: 10.4172/21690022.1000105.

M. Alibeyki, H. Mirzadeh, M. Najafi, A. Kalhor, Modification of Rule of Mixtures for Estimation of the Mechanical Properties of Dual-Phase Steels, Journal of Material Eng. and Perform. 26-6 (2017) 2683-2688, doi: 10.1007/s11665-017-2687-6.

F. Nürnberger, O. Grydin, M. Schaper, F.-W. Bach, B. Koczurkiewicz, A. Milenin, Microstructure Transformations in Tempering Steels during Continuous Cooling from Hot Forging Temperatures, Steel research int. 81-4 (2010) 224-233, doi: 10.1002/srin.200900132.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 25-33

doi: 10.4028/p-IZfbh8

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

Submitted:
2026-01-16

Revised:
2026-02-17

Accepted:
2026-02-24

Online:
2026-04-13

Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

Prajapati Kishan Rahul 1,a*, Laeger René 1, b, Mohnfeld Norman 1,c, Peddinghaus Julius 1, d, Uhe Johanna 1,e and Behrens Bernd-Arno 1,f

1 Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

a*prajapati@ifum.uni-hannover.de, b laeger@ifum.uni-hannover.de, c  mohnfeld@ifum.uni-hannover.de, dpeddinghaus@ifum.uni-hannover.de, e  uhe@ifum.uni-hannover.de, f  behrens@ifum.uni-hannover.de

*corresponding author: prajapati@ifum.uni-hannover.de

Keywords: powder metallurgy, characterisation, flow behaviour, porosity.

Abstract

In cold bulk metal forming, coatings based on zinc phosphate are commonly used for lubrication. This has a negative impact on the environment, negatively affects human health, and requires significant pre- and post-surface treatments. Powder metallurgical (PM) components are a promising alternative to zinc phosphate coatings due to the process related porosity of the workpiece which acts as lubricant reservoir. During the forming process, the lubricant stored in the pores is released and lubricates the tool and workpiece surfaces. For an efficient process design of such components, finite element method (FEM) is an effective tool to analyse forming and friction behaviour. To this end, a realistic material model is essential for accurate simulation results. Hence, in this work, the flow behaviour of PM semi-finished products is characterised by means of compression and tensile tests. The results indicate that the material exhibits different behaviour under compression and tension. In compression, the material demonstrates higher yield strength and flow stresses compared to tension. Additionally, inhomogeneity of the material distribution can be observed, characterised by a denser core and more porous outer regions. The porous outer regions make it suitable for storing lubricant for application in forming processes.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

The growing concern regarding industrial application of hazardous lubricants is highlighted by new legislations such as Registration, Evaluation, Authorisation and Restriction of Chemicals [1]. Due to these legislations, there has been an increased focus on environmental and human health from the risk posed by these chemicals. In cold forming, lubrication is essential to increase the tool life and reduce forming forces [2]. In cold bulk metal forming, the surface expansion can reach values up to 3,000%, leading to a need for conversion layers as lubricant carrier [3]. Coatings based on zinc phosphate are commonly used for this application. The coating procedure has several environmental drawbacks such as sludge of heavy metal phosphates that needs to be reclaimed or buried, large amount of water requirement in rinse baths and high quantities of waste water typically containing grease, oil, acid, and soap [4]. Furthermore, the coating process requires significant pre-surface treatments such as shot blasting and pickling to prepare surface for adhesion of coatings [3,5]. This leads to higher costs and energy requirements for the lubrication process.

As an alternative to zinc phosphate coatings, several options have been developed. Electrolytic phosphating developed by Bjerrum et al. does not produce heavy metal sludge in baths and avoids the use of acid by electrochemical pickling compared to the chemical phosphating process [6]. Replacing chemical zinc phosphating with electrolytic calcium phosphating also eliminates heavy metal sludge in phosphating bath resulting in coatings free of heavy metals such as Zn and Ni [4]. Another alternative to zinc phosphate coatings are microporous coatings. Utsunomiya et al. used artificial oxidation in air followed by reduction of oxides in hydrogen atmosphere to create porous
surfaces on steels [7]. Similarly, Arentoft et al. used selective etching to remove one of the two metals in two phase alloy of Sn and Zn , which was electrochemically deposited on surface to develop porous coatings [8]. These small pores act as reservoirs to carry and distribute lubricant during the forming process. Additionally, dry-in-place lubricating systems have been developed to replace phosphate coatings. Hu et al. evaluated three different dry-in-place lubricants and compared it with conventional phosphating lubricant. The study showed mica-type lubricant had comparable friction characteristics to those of the conventional phosphating lubricant at temperature of 210∘C [9].

On the tool side, different hard coatings are used to decrease the friction during the forming process. Development of newer coatings has enabled dry forming without any lubricants. Bobzin et al. developed a new coating system of CrAlN+MoS, where the hard CrAlN matrix is enhanced with Mo and S to provide friction reduction by the formation of a MoS2 layer under tribological conditions [10]. The developed coating was tested for dry full forward impact extrusion tests and showed no wear and 15% lower punch forces compared to uncoated dies. Likewise, Prieske and Vollersten investigated the use of Chemical Vapour Deposition (CVD) diamond coatings for dry forming of aluminium and showed its suitability for wire drawing [11]. Although these new coatings offer great potential for dry forming, they have not been tested at an industrial scale and might not be effective for PM components due to increased friction conditions due to open pores.

PM processes are well known for high material utilisation and ability to produce near-net shape components [12]. Similar to the porous coatings, the process-induced porosity of PM components can be used as lubricant storage [13]. This eliminates the need for conversion layer coatings and their negative impacts. During the forming process, the lubricant stored in the pores is released, effectively lubricating the surfaces of the tool and the workpiece. Besides, the forming process also compacts the material improving its mechanical properties. Preliminary investigations by Behrens et al. showed that 20% higher forces were required during compression tests of dry PM components compared to the PM components impregnated with lubricant [14]. Furthermore, no cracks were observed in the PM components impregnated with the lubricant in contrast to the dry ones. The compression test also resulted in the reduction of the porosity of the component. Similar investigations on forming behaviour of PM components using compression tests also reported densification of material due to closing of pores [15-17]. The combination of the self-lubrication behaviour of lubricant infiltrated PM products and the compaction of the material during cold forming processes presents a high potential for more ecological manufacturing.

To manufacture defect-free PM components using cold forming processes, it is crucial to design the process taking into consideration the brittleness of the PM components due to its pores. FEM is an efficient tool to reduce time and costs associated with process design. However, detailed knowledge of material behaviour is essential to obtain reliable simulation results. The flow behaviour of the material is a key input for modelling the plastic behaviour during forming. In this paper, the flow behaviour of the PM components is characterised by means of local compression and local tensile tests.

Material and Methods

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

Steel powder mixture Atomet 1001 (Rio Tinto Metal Powders) was used in this study. Table 1 contains the chemical composition of the powder [18]. The compaction was carried out from both sides (top and bottom) using a multi-axial powder press HPM 200 E2 from SMS Meer. A 130.7 g of powder mixture was used to create a green body by applying a compacting pressure of 353.7 MPa . The green body was then sintered in Gero HTK 8 sintering furnace from Carbolite Gero GmbH & Co. KG under vacuum condition ( 10−3 bar) at 1,000∘C for 60 min . The process resulted in a cylindrical specimen with a diameter of 30 mm and a height of 26.74 mm . The resulting specimen has an absolute geometrical density of 6.839 g/cm3 with a standard deviation of 0.128% and a relative density of 0.9 . The relative density was determined using a spark plasma sintered specimen with a density of 7.6 g/cm3 as a reference. The resulting density is sufficient to allow lubricant infiltration but not so low that the formability is reduced significantly.

Table 1. Chemical composition of Atomet 1001 in wt% [18].

C | O | S | Mn | Fe
0.004 | 0.09 | 0.01 | 0.18 | ≥ 99.4

The powder pressing results in inhomogeneous distribution of pores in the specimen due to the effects of friction during pressing [19]. To evaluate the effect of inhomogeneity on flow behaviour due to the porosity distribution, compression and tensile specimens were extracted from various regions of the specimen by wire erosion. The extraction regions of compression and tensile specimens is shown in Fig. 1. To analyse the effect of inhomogeneity in axial direction, the specimens were extracted from three different heights (top, middle, and bottom). For analysing the effect of inhomogeneity in radial direction, specimens were extracted from different radii. For compression tests, specimens were extracted from three radial positions: centre (D0), diameter of 14 mm (D14) and 23 mm (D23). The compression specimens had a diameter of 5 mm and height of 10 mm . For tensile tests, specimens were continuously extracted from one end to another with a thickness of 2 mm .

[picture]

Fig. 1. Extraction regions of a) compression and b) tensile specimens.

Fig. 1. Extraction regions of a) compression and b) tensile specimens.

The compression tests were carried out in a servo-hydraulic forming simulator DYNSJ5590 from Instron GmbH. The experimental setup and a schematic cross-sectional view are shown in Fig. 2. For testing, the specimen was placed between two punches and then compressed at the velocity of 10 mm/s by moving the lower punch at room temperature to half the initial height. This results in initial strain rate of 1 s−1. The chosen velocity corresponds to the forming process being analysed. The tests were repeated at least three times (three times for D0 and twelve times for D14 and D23). The force F was measured using a strain gauge-based force measuring cell and the length change Δl using inductive path sensor. Since the displacement was measured using the position of the punch rather than directly on the specimen, empty test runs were performed to remove the elastic deformations of the machine from the data.

[picture]

Fig. 2. Test setup for compression test.

Fig. 2. Test setup for compression test.

The tensile tests were carried out in a quenching and forming dilatometer DIL 805A/D/T from TA Instruments. The tests were performed according to Mohnfeld et al. [20]. A schematic illustration of the test setup is shown in Fig. 3. For testing, the specimen was placed between two specimen holders and tested with a strain rate of 1 s−1 at room temperature until fracture. The tests were repeated three times. During the experiments, the force F was measured using force cell and length change Δl was measured using two push rods.

[picture]

Fig. 3. Schematic of tensile test setup.

Fig. 3. Schematic of tensile test setup.

The force and length change measured during the experiments were then used to calculate true stress σ and true plastic strain εpl using Eq. 1 and 2, where Ai is the instantaneous cross-sectional area, 10 is the initial length of the specimen, and E is the Young's modulus of elasticity.

σ=F Aiεpl=ln(1+Δll0)−σE

(1)(2)

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

The engineering stress strain curves for compression and tensile test are shown in Fig. 4. For compression, specimen D0 from middle section and D23 from top section were used to represent central and outer region respectively. For comparison of engineering stress, the tensile specimens were selected from similar extraction positions as the compression specimens. For this purpose, a tensile specimen with a radial distance of 0.9 mm was selected from the middle section and taken from the upper section with a radius of 13.08 mm .

[picture]

Fig. 4. Engineering stress strain curves for compression and tensile test.

Fig. 4. Engineering stress strain curves for compression and tensile test.

With the compression test, significantly higher deformations up to an engineering strain of 0.5 can be reached compared tensile test for both central and outer region. This can be explained by the different behaviour of the pores present in the specimen during compression and tension [21]. During compression, the pores are closed resulting in the densification of the material that allows material to accommodate high strains. On the contrary, during the tensile test, the pores grow larger severely limiting the ability of material to undergo plastic deformation. Ultimately, the pores act as a source for crack initiation leading to premature fracture of the material. The material also fractures at the maximum engineering stress indicating the brittle nature of material under tension. To evaluate the flow behaviour of the material, flow curves were calculated using Eq. 1 and 2 for the specimens from the different positions of the cylinder. The resulting median flow curves from the compression tests are shown in Fig. 5. The median flow curve is chosen to avoid the influence of outliers for D14 and D23 specimens and to accurately reflect the actual material behaviour. The range of scattering is also plotted for specimens from the middle section. It is determined by subtracting the minimum flow stress from the maximum flow stress and then dividing the result by the median flow stress. Similar ranges of scattering were also obtained for specimen from top and bottom sections. These are not shown to maintain readability of the figure.

In Fig. 5a, flow curves for different radial positions from the middle section of the cylinder are plotted. When comparing the flow behaviour from the different radial positions, slightly lower flow stresses are observed with increasing radial distance from the centre. An explanation could be that during powder compaction, friction at the die wall causes the powder to be loosely packed at the outer region compared to the core [22,23]. This results in a density gradient along the radius of the cylinder with the highest density in the core. This density gradient causes the higher flow stresses in the specimen from the core compared to the outer regions. Upon closer examination, the disparity in flow stresses between specimens from radial positions D0 and D14 is less pronounced than that between D14 and D23. This suggest that D0 and D14 exhibit similar level of homogeneity, but it decreases between D14 and D23.

[picture]

Fig. 5. Flow curves from compression tests for different specimen positions: a) middle, b) top and bottom.

Fig. 5. Flow curves from compression tests for different specimen positions: a) middle, b) top and bottom.

In Fig. 5b, flow curves for different radial positions from the top and bottom sections of the cylinder are shown. Here, a similar behaviour along the radial direction can be seen. A negligible difference in flow stresses is observed when comparing the flow curves from same radial position for top and bottom section. As the powder is pressed from both sides with equal forces, a symmetric specimen is obtained lengthwise. Furthermore, lower flow stresses are observed when comparing with the specimen from the middle section. At a plastic strain of 0.2 , deviations of 21.55 MPa ( 3.62 %) for D0, 29.65 MPa ( 5 %) for D14, and 42.1 MPa ( 7.24 %) for D23 can be observed between specimens from middle and top/bottom sections. These discrepancies in flow stresses also align with the porosity measurements reported by Behrens et al., where the porosity at the centre of the cylinder was 4.84% compared to over 10% at the outer regions [13]. To compare the flow behaviour under tension and compression, flow curves of specimen from central position of the cylinder are plotted in Fig. 6.

[picture]

Fig. 6. Material flow behaviour at central position of cylinder under compression and tension.

Fig. 6. Material flow behaviour at central position of cylinder under compression and tension.

Under tension, the material yields at a lower flow stress of 232.2 MPa compared to 258.8 MPa under compression. A deviation of above 10% can be seen in flow stress even for a relatively low plastic strain of 0.02 . During tension, pores act as a region for stress concentrations, resulting in
localised yielding of the material at lower stress. In addition, tensile force causes the pores to grow reducing the effective cross-sectional area that withstands the forming force. This causes the material to deform at lower forces resulting in lower flow stresses. On the contrary, compressive forces cause the material to densify through closure of pores resulting in higher yield strength and flow stresses. In Fig. 7, the radial distribution of the tensile strengths and failure strains at different extraction positions are shown. The effect of the inhomogeneous distribution of the pores can be seen here.

[picture]

Fig. 7. Tensile strength and failure strain of material at different specimen positions.

Fig. 7. Tensile strength and failure strain of material at different specimen positions.

The specimen from the outermost radial position of the cylinder shows the lowest tensile strength for specimens from all three axial positions. The remaining specimens from the different radial positions show a similar level of tensile strength at approx. 300 MPa . This shows that the material is homogeneous within a diameter of 20 mm and is increasingly porous between 20 mm and 30 mm . The flow behaviour from the compression tests also demonstrated similar result (compare D23 and D14 in Fig. 5). The porous outer region makes it well-suited for lubricant impregnation. Furthermore, tensile tests also exhibit lower failure strains at the outer region of the cylinder. For the top and bottom sections, the lowest failure strain is observed at the outermost radial position. For the middle section, outermost radial position shows the second lowest failure strain with a value of 0.169 with radius of 8.4 mm showing lowest with a value of 0.163 . This brittle behaviour of material especially at the outer region of cylinder needs to be taken into account for designing subsequent forming process.

Summary and Outlook

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

PM semi-finished products offer great potential for self-lubrication application due to the process related porosity in the material. The inhomogeneity present in the PM components due to the pores results in different material behaviour depending on the region of the workpiece. Higher flow stresses and tensile strength were observed for the specimens from the core as compared to the outer region indicating higher porosity in the outer region. Furthermore, different material behaviour under tension and compression was found, with higher yield strength and flow stresses observed during compression.

In future work, porosity measurements will be performed to validate the differences in mechanical behaviour attributable to local porosity differences. Additionally, the behaviour of pores during compression and tension will be studied using microstructural images. In parallel, the flow behaviour of the PM components will be modelled taking into account the inhomogeneity in porosity. Flow behaviour will also be characterised at different strain rates. Furthermore, for design of defect-free forming process of PM-components, Gurson Tvergaard Needleman (GTN) damage model [24] will be parametrised based on the tensile tests in order to take damage into account during simulation of the forward rod extrusion.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 264818458.

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The original version of this paper is available on https://www.scientific.net/MSF.1183.25.pdf

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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/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 35-44

doi: 10.4028/p-Sau95E

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

Submitted:
2025-12-18

Revised:
2026-02-12

Accepted:
2026-02-24

Online:
2026-04-13

A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

The original version of this paper is available on https://www.scientific.net/MSF.1183.35.pdf

Cristian Cappellini 1,a*, Claudio Giardini 1, b, Gabriele Locatelli 1,c and Mariangela Quarto 1, d

¹Department of Management, Information and Production Engineering, University of Bergamo, Via Pasubio 7/b, 24044, Dalmine, Italy

a* cristian.cappellini@unibg.it, b claudio.giardini@unibg.it, c gabriele.locatelli@unibg.it, d  mariangela.quarto@unibg.it

*corresponding author: cristian.cappellini@unibg.it

Keywords: ring rolling, fishtail effect, FEM, slab method.

Abstract

Ring rolling (RR) is a widely used process for producing seamless rings, but its complex thermo-mechanical behavior often requires costly experiments or FEM simulations. This study presents a novel analytical method for predicting torque and energy in RR that explicitly accounts for the fishtail effect, a lateral deformation of the ring cross-section. The approach combines a slab-based mechanistic model with a regression linking fishtail deformation to the kinematic ratio between mandrel feed and ring rotation. Validation was performed via FEM simulations on an industrial AISI 1045 steel case, covering thirty conditions with varying feed rates and rotational speeds. Results show that conventional models ignoring fishtail can overestimate errors by over 60% for torque and 50% for energy, whereas the proposed method reduces errors below 15% in most cases. These findings highlight the importance of including fishtail effects, offering a fast, reliable, and efficient tool for early-stage RR process design and optimization.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1183.35.pdf

Ring rolling (RR) is a rotary forming process widely used for manufacturing seamless rings. Compared with conventional roll-bending techniques, RR eliminates welding operations and enables the processing of a broad range of materials, including steels and alloys that are difficult to weld [1,2]. For these reasons, it is extensively applied in aerospace, automotive, energy, and bearing industries to produce components such as turbine rings, gear blanks, and bearing races [3]. RR is performed using specialized equipment consisting of a driving roll, which provides torque and rotation, a radial mandrel that compresses the workpiece, and a pair of conical axial rolls. The coordinated motion of these tools increases the ring diameter while simultaneously reducing its height and thickness until the desired geometry is achieved [4]. Despite its industrial relevance, RR process analysis remains challenging due to the strong coupling of thermo-mechanical phenomena, complex material flow, and continuously evolving contact conditions [5]. As a result, reliable estimation of loads, torque, and energy consumption typically relies on experimental trials or finite element method (FEM) simulations, which are costly and time-consuming [6]. This represents a major limitation in industrial practice, where rapid and accurate predictions are required during process design. To address these challenges, several analytical models have been proposed to describe RR mechanics. Slip-line-based approaches adapted from shape rolling theory have been used to estimate forces and torque under the small instantaneous reductions typical of RR [7]. Other analytical frameworks focus on contact interface estimation and rolling force prediction for kinematic optimization of mandrel and axial rolls [8]. In addition, the slab method has demonstrated good accuracy in predicting the evolution of rolling loads and torques [9]. However, most existing analytical approaches neglect the fishtail effect, which arises from non-uniform deformation along the ring height and causes localized bulging at the axial ends. Previous studies have identified mandrel feed rate, roll geometry, lubrication conditions, and the kinematic ratio between mandrel feed and ring rotational speed as the main factors influencing
fishtail formation [10]. Nevertheless, analytical models that explicitly incorporate this effect are still lacking.

In this context, the present work proposes a novel analytical methodology for predicting torque and energy consumption in RR. The approach extends the classical slab formulation by introducing a regression-based correction that accounts for fishtail-induced lateral deformation as a function of the kinematic ratio. The methodology is implemented in a dedicated computational framework and validated through FEM simulations on an industrial RR case [11], demonstrating improved accuracy and reliability in predicting key process parameters.

The Proposed Methodology

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The RR setup (Fig. 1a) consists of a driving roll, a mandrel, and a pair of conical axial rolls, each governed by independently programmed kinematics. During the RR process, the ring is rotated at an angular velocity ωr[rad/s] by the driving roll, which operates at an angular speed ωDR[rad/s]. Concurrently, the mandrel is radially fed toward the driving roll at a rate f[ mm/s], thereby reducing the initial ring width wi[ mm]. The initial ring height hi[ mm] is controlled by axially feeding the upper axial roll toward the lower one at a rate fAR[ mm/s]. As a result of these combined motions, both the initial internal diameter di[ mm] and the external diameter Di[ mm] of the ring progressively increase until the target geometry is achieved, defined by the final width wf[ mm], height hf[ mm], and internal and external diameters df[ mm] and Df[ mm], respectively (Fig. 1b).

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Fig. 1. Ring rolling setup (a) and ring cross-section evolution (b).

Fig. 1. Ring rolling setup (a) and ring cross-section evolution (b).

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Fig. 2. Ring cross-section deformation due to the fishtail effect.

Fig. 2. Ring cross-section deformation due to the fishtail effect.

Owing to the closing motion of the rolls during RR, the ring cross-section undergoes increasing lateral spreading, commonly referred to as the fishtail defect [12], rather than maintaining an ideal rectangular shape. Fig. 2 compares the ring cross-sections obtained with (solid line) and without (dashed line) the fishtail effect and illustrates the parameters adopted for its quantification. These include the central cross-section width w[ mm], the enlarged widths at the top and bottom w*[ mm],
and their difference, defined as the spread difference Δw*[ mm]. This lateral deformation of the crosssection leads to an increase in rolling torque and energy consumption, which are systematically underestimated by the classical slab method, as it neglects fishtail-induced spreading [13]. To overcome this limitation, an analytical formulation that explicitly accounts for lateral spread is proposed in the present work.

Classical Slab Approach Not Considering Fishtail Defect.

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Fig. 3 represents the cross-sectional view of the rolling gap (Fig. 3a) and the generated driving roll normal pressure (Fig. 3b). The ring enters with a width win[ mm], corresponding to a contact angle αin [rad], and exits from it with a reduced width wout [mm]. As demonstrated in [13], at the angular position αn[rad], defined as the neutral angle, the normal pressure is maximum, and the driving roll and the ring surface have the same tangential velocity. From αin to αn− entering area - a friction action τ+(α) forcing the ring toward the roll gap, and increasing the required torque is generated. The friction action τ−(α) from αn to exit - exiting area - is instead opposed to the material flow, reducing the total amount of required torque.

[picture]

Fig. 3. Roll gap cross-section.

Fig. 3. Roll gap cross-section.

The application of slab method allows to determine αn with Eq. 1 [13]:

αn=12wout RDR·tan[tan−1(RDRwout ·αin )−12wout RDR·ln(win wout )μ](1)

where RDR[ mm] is the driving roll radius, μ is the friction coefficient at the ring-driving roll interface, and αin is calculated with Eq. 2 [13].

αin =cos−1(1−win −wout 2·RDR)(2)

Considering then the mean normal pressure in the roll gap p¯[MPa] (Eq. 3), instantaneous driving roll torque T[Nm] and total energy E[ J] are assessed by Eq. 4 and Eq. 5 respectively, where h is the instantaneous ring height, σeq is the material equivalent stress [MPa], and tRR is the process time [s] (Eq. 6).

p¯≅23σeq(3)

T=μ·p¯·h·RDR2·αin·(1−2·αnαin)(4)

E=∫0tT·ωDR·dt(5)

tRR=wi−wff(6)

Modified Slab Approach Considering Fishtail Defect.

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When the fishtail effect develops, the ring cross-section no longer remains uniform along its height. Instead, the central width w increases progressively toward the axial ends, reaching a maximum value w* at the interface with the axial rolls (Fig. 2). After half a revolution, this deformed cross-section enters the mandrel-driving roll gap, where it produces a non-uniform contact angle along the ring height. The largest contact angle, denoted as αin*, occurs at the upper and lower edges of the ring at the onset of contact (section A-A in Fig. 4), where the local ring width equals win*, corresponding to the w* measured half a rotation earlier. As the material advances toward the exit of the roll gap (section B-B in Fig. 4), both the ring width and the associated contact angle gradually decrease. When the roll gap width matches the central ring width win-equal to the w value measured half a revolution before - the entire lateral surface of the ring comes into contact with the driving roll. This condition corresponds to the minimum contact angle αin (section C-C of Fig. 4).

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Fig. 4. Variability of contact angle along ring height due to the fishtail effect.

Fig. 4. Variability of contact angle along ring height due to the fishtail effect.

The value of αin* is calculated by substituting win with win* in Eq. 2. The complex shape of the cross-section makes it difficult to evaluate the contact length along ring height. To overcome this limitation, a mean value of αin* and αin, defined as αin―, between, is employed as contact angle. Substituting it in Eq. 1, it is then possible to evaluate the mean values of the neutral angle αn―. Defining then thr[ s] as the time required for threading half revolution of the ring, the estimation of torque T* and energy E*, considering the fishtail effect, can be finally carried out by Eq. 7 and Eq. 8, respectively.

T*={μ·p¯·h·RDR2·αin·(1−2·αnαin) for t<thrμ·p¯·h·RDR2·αin―·(1−2·αn―αin―) for t≥thrE=∫0tT*·ωDR·dt=∫0thrμ·p¯·h·RDR2·αin·(1−2·αnαin)·ωDR·dt+∫thrtμ·p¯·h·RDR2·αin―·(1−2·αn―αin―)·ωDR·dt

(7)(8)

Material and Methods

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To validate the proposed model, its results were compared with the ones obtained from a RR FEM simulations campaign previously verified by the authors [11]. The FEM campaign was performed by means of Deform 3D software (SFTC, Ohio, US) and concerned the ring rolling process of an industrial bearing component made of AISI 1045 carbon steel. The driving roll had a radius RDR of 350 mm , the mandrel radius RM was 55 mm , and the conical axial rolls were 400 mm height with a taper angle of 15.7∘. Table 1 reports initial and final dimensions of the ring.

Table 1. Main dimensions of the ring.

Geometric parameter | Initial dimensions | Target/final dimensions
External diameter | Di = 258 [mm] | Df = 387.39 [mm]
Internal diameter | di = 120 [mm] | df = 279.79 [mm]
Width | wi = 69 [mm] | wf = 53.8 [mm]
Height | hi = 75 [mm] | hf = 54.5 [mm]

A total number of 15 simulations were performed by combining three levels of f(1.00;1.25;1.50[mm/s]) and five levels of ωr(5;10;15;20;25[rad/s]), maintained constant during each test. The axial roll motion law fAR was defined by Eq. 9, allowing the determination of instantaneous width w and height h of the ring with Eq. 10 and Eq. 11, respectively:

fAR=f2·hi−hfwi−wf+f2·hi−hf(wi−wf)2·t(9)

w=wi−∫0tfdt=wi−f·t(10)

h=hi−∫0tfARdt=hi−f·hi−hfwi−wf·t·(1+fwi−wf·t)(11)

The value of ωDR required for maintaining the ring at a constant speed ωr, was then calculated by considering ring volume constancy (Eq. 12).

ωDR=ωrRDR·D2=ωr2·RDR[w+hi·wi·(Di−wi)h·w](12)

A zero-resistance torque condition was imposed on both the mandrel and the axial rolls. All machine components were modeled as perfectly rigid, whereas the ring was assigned the viscousplastic material model for AISI 1045 steel available in the software database. Interactions between the ring and the forming tools were defined using a limiting shear stress friction model. The simulations were conducted under isothermal conditions, with the ring temperature set to 1150∘C. Further details regarding the FEM configuration are reported in [11].

Torque peaks and energy associated with the driving roll were extracted from the simulations and compared with the predictions of both the classical and the modified analytical models. In addition, the final spread difference Δwf* obtained at the end of each simulation was measured and subsequently used to estimate the evolution of Δw* throughout the RR process, as further described.

Implementation of the Proposed Methodology

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The mechanistic model accounting for the fishtail effect emphasizes the need to determine the instantaneous spread difference Δw*. Considering that Δw* increases during the RR process [12], as a first approximation, this work hypothesizes a linear growth of Δw* during time. Therefore, once the spread difference at the end of process Δwf* is known, its evolution can be assessed with Eq. 13:

Δw*=w+Δwf*·ttRR(13)

Considering the significance of the kinematic ratio kr, - the ratio between f and ωr-on the lateral spread [10], the behavior of Δwf* from FEM simulations was plotted as a function of kr (Fig. 5). The strong influence of kr on the fishtail effect is observable. As kr increases, the lateral spread also increases, exhibiting a parabolic trend. Consequently, a quadratic regression was employed to determine Δwf*, resulting in Eq. 14 with a R2 equal to 0.9911 , confirming the model's good fitting capability.

Δw*=132.29·kr2+9.2815·kr(14)

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Fig. 5. Final lateral spread difference Δwf* vs. kr and quadratic fitting regression curve.

Fig. 5. Final lateral spread difference Δ w f * vs. k r and quadratic fitting regression curve.

The governing equations of the previously introduced models were implemented in a custom Matlab®-based software to compute the evolution of torque and energy. The overall computational workflow, illustrated in Fig. 6, includes calculations performed both with and without accounting for the fishtail effect. In accordance with [14] for hot rolling conditions, the friction coefficient μ was set to 0.6 . All time-dependent variables were evaluated at each time increment Δt. To ensure an adequate temporal discretization of the process, Δt was selected as the time required for the ring to complete one fifteenth of a full revolution. During the initial computation stage, the variables w,h,fAR,ωDR, and the number of ring revolutions Nrev [rev] (Eq. 15) were updated iteratively until the total rolling time tRR was reached. Simultaneously, the radial εy, axial εz, and circumferential εx strain components were calculated assuming perfectly plastic and incompressible material behavior (Eq. 16). These strain components were then used to determine the equivalent strain εeq (Eq. 17) and the corresponding equivalent strain rate ε˙eq (Eq. 18).

Nrev=ωr2π·t(15)

{εx=−(εy+εz)εy=lnwiwεz=lnhih(16)

εeq=23(εx2+εy2+εz2)(17)

εeq˙=23(εx2˙+εy2˙+εz2˙)ωr2π·t(18)

This permits to determine σeq and p¯, employing the material flow stress of Eq. 19 [15] with a temperature θ equal to 1150[∘C].

σeq=(64.36+499.9εeq−940.3εeq2)(1+0.1061lnεeq·)e[(−0.00359+8.73×10−5lnεeq)·(θ−1223)](19)

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Fig. 6. Adopted workflow for ring rolling torques and energies calculation.

Fig. 6. Adopted workflow for ring rolling torques and energies calculation.

Subsequently, the algorithm computes torque and energy using either the classical or the modified slab formulation. When the classical slab method is adopted, the instantaneous ring width at the entry of the mandrel-driving roll gap, win(t), remains equal to the initial width wi until the ring completes one full revolution ( Nrev =1 ). After this point, the entry width win(t) is updated as the exit width from the preceding revolution win (t−Δt1 rev ), where Δt1 rev  denotes the time required for a single ring revolution. In all cases, the instantaneous exit width is equal to the current ring width w(t). When the modified slab method is employed, the instantaneous entry width win*(t) remains equal to wi until half a ring revolution is completed, corresponding to the moment when the deformed cross-section first reaches the roll gap. From that instant onward, win*(t) is defined as the sum of the initial width wi and the instantaneous spread difference Δw*(t), since Nrev (t)=1. After one full revolution, the entry width is updated as the sum of the instantaneous spread difference Δw*(t) and the exit width from the previous revolution win (t−Δt1rev ). As in the classical formulation, the exit width in the modified approach remains equal to w(t). Once the temporal evolutions of the entry and exit ring widths have been determined for both formulations, the instantaneous contact angle, neutral angle, and contact length are evaluated, allowing the corresponding torque to be calculated. Owing to the
discrete implementation of the model, the evolution of energy, E(t) or E*(t), is obtained by a Riemann summation of the product of torque, T(t) or T*(t), and the driving roll angular velocity over time, as expressed in Eq. (20).

E(t)=∑Δt=0t[T(t)+T(t−Δt)]·[ωDR(t)+ωDR(t−Δt)]2·Δt(20)

Results and Discussion

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Fig. 7a shows the maximum values of torques TMAX  resulting from simulations ( Δ ), slab approach (X), and the proposed modified slab method (O). Accordingly, Fig. 7b plots the values E. The good superposition of torques and energies when the proposed methodology is applied is observable.

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Fig. 7. Summary of (a) torque maximum values and (b) energy.

Fig. 7. Summary of (a) torque maximum values and (b) energy.

The percentage errors e%, correlated to the two analytical models respect to the FEM results, in the calculation of torque and energy peaks, are reported in figure 8 a and figure 8 b respectively.

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Fig. 8. Percentage errors in torque and energy analytical calculations for all the tests.

Fig. 8. Percentage errors in torque and energy analytical calculations for all the tests.

The errors of the analytical model not considering the fishtail effect underline its inadequacy, showing unacceptable errors reaching values greater than the 60% and the 50% for torque peaks and energy respectively. On the contrary, when the model concerning the fishtail effect is applied, the errors are lower than 15%, with only some exceptions. These are mainly related to tests characterized by low values of kr−f=1.25 mm/s and ωr=25rad/s with kr=0.050;f=1.00 mm/s and ωr=15rad/s with kr=0.067− where a high dispersion of the values around the curve of Fig. 5 is observable. This causes a bad approximation of Δwf*, resulting in a wrong calculation of the mean contact angle that, in turn, reduces the accuracy of torque and energy assessment. To overcome the limitations related to the employment of Eq. 14 for estimating Δwf*, further studies on lateral spread behavior will be performed.

Fig. 9 shows torque and energy evolutions for the tests giving the lowest percentage errors namely f=1.50 mm/s,ωr=25rad/s for torque (Fig. 9a) and f=1.50 mm/s,ωr=10rad/s for energy (Fig. 9b). The good match along the process time is detectable, underlining the capability of the proposed modified slab approach in forecasting torque and energy behavior.

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Fig. 9. Torque (a) and energy (b) evolution for the lowest percentage error tests.

Fig. 9. Torque (a) and energy (b) evolution for the lowest percentage error tests.

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1183.35.pdf

This study proposed and validated a new analytical methodology for torque and energy estimation in ring rolling processes, considering the fishtail effect. The model combines the classical slab approach with a regression-based evaluation of lateral spread as a function of the kinematic ratio, thereby extending the predictive capability of analytical formulations.

The methodology was benchmarked against an industrial FEM simulation campaign, showing that neglecting the fishtail effect leads to severe inaccuracies, with torque and energy prediction errors exceeding 60% and 50%, respectively. In contrast, the proposed model drastically reduced such deviations, achieving errors below 15% in the majority of tests. Cases with higher discrepancies were associated with limitations in the regression approximation or FEM fluctuations rather than intrinsic weaknesses of the model.

Overall, the proposed framework enables accurate, efficient, and robust prediction of ring rolling mechanics without the need for computationally intensive FEM analyses. Its integration into process design tools can support industrial applications by providing quick and reliable estimations of torque and energy.

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.35.pdf

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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/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 45-53

doi: 10.4028/p-OB0yef

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

Submitted:
2026-01-17

Revised:
2026-02-23

Accepted:
2026-02-24

Online:
2026-04-13

Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

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Kenji Fuchiwaki 1,a* and Tatsuhiko Aizawa 2, b

¹183-7 Hirasawa Hadano, Kanagawa, 257-0015, Japan

21-29-1 Nishi-Rokugo, Ota-City, Tokyo 144-0056, Japan

a* kenji-fuchiwaki@hatanoseimitsu.co.jp, b taizawa@sic.shibaura-it.ac.jp 

Keywords: fine blanking, punch edge shape control, plasma nitriding, less punch edge distortion.

Abstract

A fine blanking (FB) has grown up as a manufacturing means to fabricate the precise automotive parts from the thick sheet metals. During this net-shaping process, each part product had fully burnished surfaces through a single stroke. The punch for this FB, were highly loaded enough to distort the punch edge and to deteriorate the cost competitiveness and sustainability. A chamfered SKH51 tool steel punch was designed by controlling the chamfer widths and angles. A massively nitrogen supersaturated SKH51 punch was also prepared to investigate its effect on the suppression of punch edge distortion. AISI304 stainless steel work was used to describe the variation of punch distortion and blank qualities with increasing the number of strokes.

Introduction

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Fine blanking (FB) has been growing up as a key metal forming means to fabricate the precise automotive parts from the thick sheet metals [1]. During this net-shaping process, each part product is formed to have fully burnished surfaces through a single stroke under the narrow clearance between the outer diameter of FB-punch and the inner diameter of FB-die [2]. In addition, as depicted in Fig. 1 , the work sheet metal is fixed by the FB-punch against the counter punch (CP), and, by the FB-die against the blank-holder (BH). Under this situation, the punch and die edges are subjected to severe loading. As stated in [3, 4], the normal and shear stresses concentrate at the FB-punch edges and surfaces due to the singular points in the metal flow around the edge corners. To be free from this severe FB conditions, the clearance is possible to be widened; then, the dimensional accuracy as well as the sheared surface quality deteriorate by themselves, without any treatment, the FB-punch tool life can be shortened to worse the cost-competitiveness [5,6]. This trade-off-balancing is only saved by a new FB-punch design.

[picture]

Fig. 1. A typical fine blanking process where the blank is fixed by the punch against counter punch (CP) and by the die against the blank-holder (BH), and, the blank holding load (Fv), the counter load (Fc), and, blanking load (Fs) are applied at the same time.

Fig. 1. A typical fine blanking process where the blank is fixed by the punch against counter punch ( C P ) and by the die against the blank-holder ( B H ) , and, the blank holding load ( F v ) , the counter load (Fc), and, blanking load (Fs) are applied at the same time.

In the present paper, the punch-edge chamfering and the punch surface hardening are proposed as a new FB-punch design to reduce the stress concentration at the vicinity of punch edges by controlling
the local metal flow along the chamfered punch edges and to reduce the geometric distortion of FBpunch by strengthening and hardening. In the former, the FB-punch edge profile is controlled by precise machining to have the tailored chamfer width ( w ) and skew angle ( θ ). In the latter, the plasma immersion nitriding process is employed to make massive nitriding supersaturation (MNS) of FBpunch surfaces at 673 K for 14.4 ks [7, 8]. No nitride precipitates are synthesized by this MNS as stated in [8, 9]; then, no risks are embedded in the MNSed punches to initiate the fatigue cracking from the inside of punch. The homogeneous MNSed layer is formed around the FB-punch surfaces. A bare SKH51 FB-punch is employed as a reference to describe the fine blanking behavior with less geometric distortion by these two approaches and to demonstrate the FB-punch life extension without reduction of product qualities by experiments.

Methods and Materials

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FB-Punch Design.

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A new FB-punch was designed to chamfer its edges and edge-corners by controlling the chamfer width and skew angle and to make surface treatment of its head and surfaces by MNS.
In fine blanking, the punch edge geometry strongly affects burr formation and assembly accuracy. A sharp edge promotes smooth shearing and minimizes burr height, since the punch edge crosssection is directly transferred to the burr. When a rounded edge is used, the burr in the thickness direction becomes thinner and is more likely to detach and remain on the die surface, which may cause appearance defects or functional problems. Therefore, a chamfered edge was adopted instead of a rounded edge to maintain a sharp cutting interface while controlling edge deformation and suppressing burr growth in the thickness direction.

[picture]

Fig. 2. A newly designed FB-punch. a) Geometric configuration of SKD51 FB-punch, and b) punch edge chamfering design.

Fig. 2. A newly designed FB-punch. a) Geometric configuration of SKD51 FB-punch, and b) punch edge chamfering design.

Chamfering.

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A SKH51 high-speed steel punch with the hardness of 62 HRC , was commonly utilized in the following experiments with and without chamfers. As depicted in Fig. 2a, it had a square head by 8.00 mm×8.00 mm. Its edge was chamfered to have its width of 0.25 and 0.50 mm and its skewed angle of 2.5∘ and 5.0∘, as shown in Fig. 2b. The die was also made of SKH51. The clearance was held constant by 0.01 mm .

Massive Nitrogen Supersaturation (MNS) Treatment.

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A plasma immersion nitriding system was utilized to make MNS treatment of SKH51 high-speed steel punch. As schematically depicted in Fig. 3, the punch was placed in the hollow cathode to intensify the nitrogen ion and NH-radical densities for efficient MNS. After evacuation to the base pressure of 0.1 Pa , the nitrogen gas was introduced to the chamber; the punch was heated up in the nitrogen atmosphere at 100 Pa up to 673 K . After pre-sputtering at 673 K for 1.8 ks under the DC (Direct Current) plasma by -500 V at 60 Pa under the nitrogen gas flow, the punch was MNSed at 673 K for 16.0 ks at 60 Pa . Together with the DC-bias, RF (Radio-Frequency) voltage was applied by +250 V . The nitrogen to hydrogen gas flow rate was selected to be 100 mL/min to 20 mL/min after the plasma diagnosis through OES (Optical Emission Spectroscopy). This MNS treatment was followed by cooling down to RT under the nitrogen atmosphere.

[picture]

Fig. 3. A schematic view on the plasma immersion nitriding system for MNS treatment of SKH51 punches at 673 K .

Fig. 3. A schematic view on the plasma immersion nitriding system for MNS treatment of SKH51 punches at 673 K .

Measurement.

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The punch edge profile at the R 0.5 corner was measured by using the contact type contour profilometer at the specified number of strokes by N=1,2,5,10,20 and 50 , respectively. The dieroll and burr heights of blank were also measured at each N in the above.

[picture]

Fig. 4. Fine blanking experimental setup. a) Overview on the fine blanking press machine, b) die setup including the FB-punch and core-die.

Fig. 4. Fine blanking experimental setup. a) Overview on the fine blanking press machine, b) die setup including the FB-punch and core-die.

FB system.

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A hydraulic press machine (FB-160FD manufactured by Mori Iron Works, Co., Ltd., Saga, Japan) was utilized in the following fine blanking experiments, as shown in Fig. 4a. The blank holding load was 80 kN , the counter load was 40 kN , and, the blanking speed was 10 mm/s. The lubricant (FBH9HMC, Nihon Kohsakuyu Co., Ltd., Tokyo, Japan) with the viscosity of 101 mm2/s was pasted onto the work sheet material.

Materials.

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Work Materials.

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AISI304 austenitic stainless steel plate with the yield stress of 352 MPa and the tensile strength of 638 MPa was used as work material. Its thickness was 3.0 mm .

FB punch and die Materials.

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SKH51 high-speed steel with the hardness of 62 HRC were commonly used in every case.

Results

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Fine Blanking Behavior.

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Fine blanking experiments were performed to investigate the effect of chamfering and MNS treatment of FB-punches on the abrasive wear at the punch edges with increasing the number of strokes ( N ).

Bare Punch.

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A bare FB punch in Fig. 2a was used as the normal punch. As shown in Figs. 5a and 5b, the edges and edge-corners were worn out in abrasive to deteriorate the punch edge profiles only at N=10. Figure 5c depicts the variation of edge cross-section with N. The bulging displacement or the lateral displacement advances even in the early stage of N together with the vertical displacement. This geometric distortion at N=10 exceeds the tolerance for continuous fine blanking operations. In particular, the axial displacement, Dz , reaches Dz=20μ m at N=1, and, Dz=30μ m at N=10.

[picture]

Fig. 5. Evolution of the wear damage at the punches with N when using the normal punch. a) Punch configuration at N=0, b ) punch configuration at N=10, and c ) variation of the edge cross-sections with N .

Fig. 5. Evolution of the wear damage at the punches with N when using the normal punch. a) Punch configuration at N = 0 , b ) punch configuration at N = 10 , and c ) variation of the edge cross-sections with N .

In application of chamfering to the edges, this Dz for the bare punch was employed as a reference to investigate the effect of chamfering width and skew angle on the geometric distortion.

Chamfer Width Effect.

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The chamfer width was varied to be 0.25 mm and 0.5 mm . Figure 6. depicts the variation of axial displacement, Dz, at the edge-corner when the skew angle was constant by 2.5∘. When w=0.50 mm, Dz monotonically increased with N and becomes 10μ m at N=50. On the other hand, Dz increased with N and approaches to 15μ m at N=5. It saturates to 18μ m even increasing N to 50 when w=
0.25 mm . This revealed that the geometric distortion is controllable within the engineering tolerance when reducing the chamfer width was set to be 0.25 mm .

[picture]

Fig. 6. Variation of the axial displacement at the edge corner with N for w=0.25 and 0.50 mm when the skew angle is constant by 2.5∘. And bare punch surface.

Fig. 6. Variation of the axial displacement at the edge corner with N for w = 0.25 and 0.50 mm when the skew angle is constant by 2.5 ∘ . And bare punch surface.

Chamfer Skewed Angle Effect.

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The chamfer skew angle θ, also has a possibility to influence on the geometric distortion at the edges and edge-corners in the similar manner to w. Figure 7 shows the variation of Dz with N for θ=2.5∘ and 5.0∘ when w is constant by 0.25 mm . At the beginning, Dz at θ=2.5∘ is more than Dz at θ=5.0∘. After N=5, both are nearly the same; Dz at θ=5.0∘ turns to exceed Dz at θ=2.5∘ when N =50. This reveals that smaller chamfer skew angle reduces the geometric distortion at the edge corner when the chamfer width is selected to be 0.25 mm .

Through this parametric survey, w=0.25 mm and θ=2.5∘ must be optimum to reduce the geometric distortion at the edges and edge-corners with reference to the bare punch with w=0.0 mm and θ=0.0∘.

[picture]

Fig. 7. Variation of the axial displacement at the edge-corner with N for θ=2.5∘ and 5.0∘ when w is constant by 0.25 mm . And bare punch surface.

Fig. 7. Variation of the axial displacement at the edge-corner with N for θ = 2.5 ∘ and 5.0 ∘ when w is constant by 0.25 mm . And bare punch surface.

Hardening by MNS.

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Reduction of punch edge displacements proves that stress concentration at the edges and edgecorners was relaxed by chamfering the edges in width and skew angle. Because of no change in the constitutive punch materials, the risk of abrasive and adhesive wears is still left as an engineering issue.

The plasma immersion nitriding system was utilized to form a massively nitrogen supersaturated layer from the punch surface to the depth of 40μ m. As shown in Fig. 8, the punch head and side surface were surrounded by this layer with higher nitrogen content than 1 mass %. Its average hardness reached 1400 HV . By this pretreatment, the original SKH51 punch with 62 HRC or 750 HV has a surface hardened layer with +650 HV . This surface hardening provided a way to promote the abrasive wear resistance. Nitrogen supersaturation with high nitrogen solute content also played a role to promote the adhesive wear resistance. In particular, when fine-blanking the difficult-toforging work materials, such as austenitic stainless steels and titanium, this adhesive wear or galling exaggerate the shortage of punch life as well as the low quality of products.

[picture]

Fig. 8. SEM image and nitrogen mapping on the cross-section of SKH51 tool materials after massive nitrogen supersaturation.

Fig. 8. SEM image and nitrogen mapping on the cross-section of SKH51 tool materials after massive nitrogen supersaturation.

Fine Blanking by Optimum-Chamfered and MNSed Punch

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The chamfer width and angle were optimized to be 0.25 mm and 2.5∘. This chamfered punch was MNSed to cover the punch by hardened layer.

Fine Blanking Behavior.

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The punch configuration was shown in N=0 and N=50, Figs. 9a and 9b. Although the normal and chamfered punches suffered from severe abrasive and adhesive wears, no significant weardamages were detected at the edges and edge-corners of chamfered and MNSed punches. Figure 9c describes the variation of edge cross-sections with N. No bulging or lateral displacements were detected while the vertical displacement was suppressed to 5μ m. As compared to Fig. 5c, this no lateral displacement at the edges and edge-corners preserves the initial clearance between the punch outer diameter and the punch-guide inner diameter even after increasing the number of strokes. In addition, the axial displacement was less than 5μ m in Fig, 9c becomes much smaller than those in Figs. 6 and 7.

[picture]

Fig. 9. Evolution of the wear damage at the punches with N when using the chamfered and MNSed punch. a) Punch configuration at N=0, b ) punch configuration at N=10, and c ) variation of the edge cross-sections with N.

Fig. 9. Evolution of the wear damage at the punches with N when using the chamfered and MNSed punch. a) Punch configuration at N = 0 , b ) punch configuration at N = 10 , and c ) variation of the edge cross-sections with N.

This significant reduction of lateral and axial displacement at the punch edge cross-section proved that abrasive and adhesive wear resistance was promoted by MNS treatment.

Quality of Blanks.

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The punch displacements in the X - and Z -directions reflects on the burr and die-roll heights of sheared blanks as suggested in [10]. The die roll of blank is pushed back by shearing to leave the die-roll height at the edge corners of sheared blank. The burr of blank is also formed by local metal flow into the clearance around the edge corner. These two dimensional inaccuracies of product were measured at the specified number of strokes. Figure 10 compares the variation of the burr and dieroll heights, or Zb and Zd , with increasing N among three punches.

[picture]

Fig. 10. Evolution of the burr and die-roll heights, or, Zb and Zd with increasing N when using the optimum chamfered and MNSed punches with comparison to other two punches. a) Variation of Zb with N, and, b ) variation of Zd with N .

Fig. 10. Evolution of the burr and die-roll heights, or, Zb and Zd with increasing N when using the optimum chamfered and MNSed punches with comparison to other two punches. a) Variation of Zb with N, and, b ) variation of Zd with N .

Figure 10a compared the burr height (Zb) evolution with N. Since the edges and edge-corners were worn out at N~10,Zb abruptly enhanced itself for N>5 when using the normal punch. When using the chamfered punch, Zb fluctuated between 45 to 50μ m irrespectively of N . On the other hand, when using the chamfered and MNSed punch, Zb increased to 70μ m at N=2; this Zb monotonously decreased with N and Zb<50μ m at N=50. This revealed that the burr height was suppressed in the early stage of strokes by the chamfered and MNSed punch to preserve the blank quality.
The evolution of die-roll height ( Zd ) with N was compared among three punches in Fig. 10b. No significant difference was detected, and Zd ranged from 420 to 480μ m for three punches.

Discussion

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In literature, many studies have been performed toward tool life extension during FB. As stated in [11-12], importance on the advanced heat treatment and coating was stressed in addition to tool-steel high qualification. Numerical simulation was utilized to make parametric survey on the effect of clearance on the metal flow during FB [13]. A very few directions to suppress the abrasive wear in FB were pointed out. In particular, no policies were proposed on the punch edge profile control and its synergetic rule with surface treatment.

After parametric survey in the present study, the chamfering width ( w ) and skewed angle ( θ ) had much influence on the geometric distortion. With narrowing w and θ, the local metal flow approaches to a stream pattern with singular points at the edges and edge-corners [3], and then w and θ must be w>0.1 mm or clearance and θ>1∘. On the other hand, more w than 0.5 mm , and θ>5∘ deteriorate the dimensional accuracy of products. Hence, w and θ had optimum ranges to balance the trade-off between the tool-life shortage by geometric distortion of punch edges and the dimensional accuracy of products.

Without local metal flow control around the edges and edge-corners, the hardened punch surface layer was inevitably subjected to abrasive wear by normal and shear stress concentration [3]. In order
to make full use of synergetic effect in the present method, the punch edges must be first chamfered and then MNSed to constraint the punch surface layers by hardening. Under the reduced stress conditions, MNS works to suppress the geometric distortion of fine blanking punches.

Let us consider the relationship between the tool steel punch matrix and the surface treatment. When using the PVD coating, its coated punch is subjected to high stress concentration by metal flow with the singularity at the punch edges. Even if the coating layer had sufficient stiffness not to initial the cracks, the substrate could plastically deform and induce the onset of failure. The coating thickness is still lower than the affected zone thickness by stress concentration. On the other hand, the heat treated layer has enough thickness more than this affected zone depth, but its hardness is insufficient to preserve the integrity against the abrasive wear. MNSed layer thickness reached 40 μm, more than the affected zone thickness. Its average hardness reached 1400 HV against the abrasive wear.

In the ordinary nitriding process [14], the punch surface layer is hardened by fine nitride precipitates. The plasma nitrided tools at relatively high holding temperature have a risk of punch edge embrittlement. The coarsened nitride precipitates have a risk to trigger the fatigue cracking under the high stress transients with increasing N. In the MNS, no nitrided are synthesized as a precipitate to drive the punch-edge embrittlement and fatigue cracking. As reported in [15], MNSed punch surface has chemical inertness enough to be from adhesive wear from the work materials.

Different from the coating method [11], the initial clearance and punch edge profile were preserved after MNS treatment. As shown in Fig. 8, the hardened layer was formed from the original surface to the depth of punch. Although the surface roughness might be induced by crystalline lattice expansion of SKH51 via the MNS process [7, 8, 16], the initial punch surface remains as it was. In its hardness depth profile, the homogeneous hardness plateau with the average of 1400 HV gradually decreases to the matrix hardness of SKH51 with the depth. There was no risk of inner fatigue crack initiation and failure damage. The inner SKH51 matrix was constrained by this hardened surface layer against the applied stresses and displacements.

Summary

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The optimum chamfering technique with massive nitrogen supersaturation treatment plays a synergetic role to reduce the geometric distortion of punch profiles, to improve the blank quality and to make tool life extension. In particular, the lateral and axial displacements of edges and edgecorners were suppressed and saturated to several micro-meters or less than 10% of clearance even until N=50. This results promises that this punch design should be applicable to practical fine blanking processes to yield the net-shaped parts and mechanical elements.

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.45.pdf

K. Lange, F. Birzer, P. Hofel, A. Munkhoty, H. Singer, Cold Forming and Fineblanking, (1997) 5.

Q. Zheng, X. Zhuang, Z. Zhao, State-of-the-art and future challenge in fine-blanking technology. Production Engineering. 13 (2018) 61-70.

R. G. Balijepalli, M. R. Begley, N. A. Fleck, R. M. McMeeking, E. Arzt, Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates. Int. J. Solid Structures. 85-86 (2016) 160-171.

K. Fuchiwaki, M. Takeshita, Y. Matsumoto, T. Aizawa, Fine blanking punch edge control for life extension. Proc. JSTP (2021) 602.

K. Fuchiwaki, T. Aizawa, Enhancement of punch tool life in fine blanking by massive nitrogen supersaturation treatment. Proc. AWMFT and APSTP 2025 (2025, November; Kaohsiung, Taiwan) 211-212.

K. Fuchiwaki, T. Aizawa, Punch edge control for tool life extension and finer blanking. Mater. Trans. (2026) (in press).

A-R. Farghali, T. Aizawa, Nitrogen supersaturation process in the AISI420 martensitic stainless steels by low temperature plasma nitriding. ISIJ International 58 (3) (2018) 401-407.

T. Aizawa, Low temperature plasma nitriding of austenitic stainless steels. Chapter 3 in Stainless steels and alloys. IntechOpen, London, UK (2019) 31-50.

T. Aizawa, Micro-/meso-structure control of multi-hostmetal alloys by massive nitrogen supersaturation. Materials 17, 1294 (2024) 1-13.

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T. Kashi, N. Horikawa, T. Miyajima, A. Ueno, A. Sakaida, Y. Kawano, Y. Yamamoto, Fatigue strength of high-speed tool steel, JIS SKH51 with TiAlN/DLC nano-multilayered hard coating film. J. Jpn. Soc. Design Eng. 53 (1) (2018) 43-56.

G. Claus, M. Weber, M. Demmler, Increase of lifetime for fine blanking tools. Procedia Eng. 183 (2017) 45-52.

M. Sahli, X. Roizard, G. Colas, M. Assoul, L. Carpentier, P-H. Cornuault, S. Giampiccolo, J. P. Barbe, Modelling and numerical simulation of steel sheet fine blanking process. Procedia Manufacturing 50 (2020) 395-400.

A. G. F. Araújo, M. Naeem, L. N. M. Araújo, T. H. C. Costa, K. H. Khan, J. C. Díaz-Guillén, J. Iqbal, M. S. Liborio, R. R. M. Sousa, Design, manufacturing and plasma nitriding of AISIM2 steel forming tool and its performance analysis. J. Mater. Res. Technol. 9 (6) (2020) 1451714527.

K. Dohda, M. Yamamoto, C. Hu, L. Dubar, K. F. Ehmann, Falling phenomena in metal forming. Friction 9 (2021) 665-685.

A-R. Farghali, T. Aizawa, T. Yoshino, Microstructure/mechanical characterization of plasma nitrided fine-grain austenitic stainless steels at low temperature. J. Nitrogen 2 (2) (2021) 244258.

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The original version of this eBook is available on https://www.scientific.net/book/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 55-67

doi: 10.4028/p-y3MapP

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

Submitted:
2026-01-19

Revised:
2026-02-16

Accepted:
2026-02-24

Online:
2026-04-13

Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

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Christian Overhagen 1,a* and Robert Martin 2, b

1 University of Duisburg-Essen, Sustainable Metallurgy, Friedrich-Ebert-Strasse 12, 47119 Duisburg, Germany

2 University of Duisburg-Essen, Mathematics for Engineers, Friedrich-Ebert-Strasse 12, 47119 Duisburg, Germany

a  christian.overhagen@uni-due.de, b  robert.martin@uni-due.de

Keywords: Cold Strip Rolling, Friction in Rolling, Inverse Parameter Identification, Physics-Informed Neural Network

Abstract

Friction plays an important role in flat rolling processes for the force and power demands, kinematics and final product quality. In search for a method of in-situ characterization of the coefficient of friction (COF) denoted by μ by non-contacting measurements, a method for determination of the COF from high-accuracy forward slip measurements, i.e. by laser doppler velocimetry combined with a comprehensive evaluation without simplifications is the method of choice. The evaluation must comprise the volume flux equilibrium at the neutral point and the roll gap exit, as well as the connection of the neutral point and COF by von Karman's ODE. This iterative procedure involves multiple solutions of the ODE as well as the nonlinear volume flux relation. In the present work, this problem is addressed by a physics-informed neural network (PINN), providing a rapid connection between the forward slip and the COF based on the mathematical rolling theory. The contribution shows that we can solve von Karman's ODE inversely by a PINN, enablind detection of the COF and the neutral angle from the measured forward slip.

Introduction

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Friction is an important process parameter in hot and cold rolling, as it determines the force, work and power demands of the process and is of crucial meaning for the neutral point, connecting stress and velocity distributions in the roll gap. Hence, a fast non-contacting method for in-situ characterization of the friction coefficient in rolling is of great interest for process control, especially for interstand tension control in continuous multi-stand rolling mills.

State of the Art

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The importance of the friction on the stress distribution and forward slip was already described by von Karman as well as Dresden in 1925 [19, 2]. Experimental methods of friction characterization can be subdivided in two groups: firstly, methods which attempt to measure the stress distribution in the roll gap directly by mechanical transducers. Secondly, indirect methods which leverage the measurement of process quantities which are influenced by friction, as forward slip. In the first group, Siebel and Lueg carried out rolling experiments using a pin-transducer embedded on the roll surface and were able to measure the stress distribution in the roll gap [15]. Similar experiments were reported by Sylwestrowicz, as well as van Rooyen and Backofen [16, 17] for hot and cold rolling. In 2006, experiments with a newly developed transducer were carried out by Arentoft et al and measured stress distributions were presented [5]. All of these methods have in common that the experimental transducers alter the rolling process in a way that such measurement devices cannot be introduced in a continuous practical rolling process, accompanying everyday industrial production.

A number of works discussed the friction measurement by forward slip, where a summary is given by Lenard, who came to the conclusion that the assessment of friction from forward slip was unreliable when simple formulae are used to relate these quantities [6]. However, Lundberg reports successful friction measurements in hot rolling, estimating the forward slip from billet head interstand times [8]. The fundamentals of the evaluation were laid out by Jarl, who pointed out the difficulties of this method and also used very simplistic relations [4]. For more precise measurement of the forward slip, laser-doppler velocimetry experiments were carried out by Li et al. with an uncertainty analysis [7].

Modeling of the flat rolling process. In flat rolling, a rectangular cross section with the initial height h0 passes through two rotating tools with radius R, while its height is reduced to the exit height h1. The geometry of the roll gap is shown in Figure 1. For the mathematical modeling of the stress distribution in this process, different methods are available. Nowadays, the Finite Element Method (FEM) has become a general-purpose tool for numerical analysis of metal forming processes. However, the process of cold strip rolling as treated in the present analysis has the geometrical nature that much more efficient modeling tools may used, for instance the classical slab method. As already shown by Pawelski, the results of stationary FEM calculations and the slab method are nearly identical for cold strip rolling [12]. Also, rolling models based on the slab method achieve high fidelity in comparison to measured values of roll force and torquein cold strip rolling, as already shown by Hessenberg and Sims [3]. Due to these reasons, FEM calculations are omitted in the current analysis and attention is paid to time-efficient simulations based on the slab method.

In 1925, Theodore von Karman published his contribution to the theory of the rolling process, in which an ordinary differential equation (ODE) was formulated on the basis of a differential force equilibrium on a strip element in the roll gap. Von Karman's ODE describes the gradient of the specific horizontal force σxh (specific: per unit strip width) with respect to the x coordinate as a function of the normal and shear stresses,

d(σxh)dx=2(σN±τFtanα)(1)

The local roll gap inclination angle α is described by the spatial derivative of the strip thickness distribution,

tanα=12dhdx(2)

The strip height distribution is given by the circular shape of the arc of contact,

h(x)=h1+2R(1−1−x2R2).(3)

For smaller contact angles, as in cold strip rolling, we may substitute the circular arc with the parabolic function

h(x)≈h1+x2R(4)

with the derivative

dhdx=2xR.(5)

For the frictional shear stress τF, classical works of the rolling theory assume slipping friction with

τF=μσN(6)

or shearing friction according to

[picture]

Fig. 1: Geometry of the roll gap. xF : neutral point position

Fig. 1. Geometry of the roll gap. x F : neutral point position

τF=mk=mkf3.(7)

After simplified analytical solutions to von Karman's ODE were published by several authors, Alexander presented a numerical solution to the ODE by Runge-Kutte methods [1]. This solution was later extended by Venter and Abd-Rabbo [18] to include Orowan's theory of inhomogeneous deformation in rolling [9]. Their final ODEs are generally of the form

dσNdα=F(σN,α) for slipping friction, and dσNdα=G(α) for sticking friction. 

(8)(9)

These can be solved numerically for the normal stress distributions σN(α). To construct an inverse method for determination of μ from a known neutral angle αN, the whole process of numerical solution of the differential equations must be iterated several times, until a good approximation of μ is found, which satisfies the given αN, increasing evaluation times substantially. If elastic roll flattening is accounted for, even an additional iteration loop enters the evaluation procedure, making the model difficult to use for online process applications.

Kinematical relationship of neutral point and forward slip. The solution of the ODE of the roll gap provides the distribution of the normal stress along the roll gap coordinate x or α. On the kinematics side, the basis is the constancy of the volume flux

V˙= const =A0v0=A1v1=A(α)v(α),(10)

expressing that the product of the cross section and the longitudinal velocity (in the direction normal to the cross sectional surface) is a constant value at any roll gap coordinate. Therefore, we can also apply this equation to the neutral plane at α=αN, giving

A1v1=ANvN=ANvCcosαN(11)

Here, AN is the cross section in the neutral plane, vC is the circumferential velocity of the roll and αN the neutral angle. We may express the circumferential velocity by the angular roll velocity and the roll radius as vC=ωR, giving

cosαN=A1ANv1ωR(12)

The forward slip κ relates the strip exit velocity to the circumferential roll velocity according to

κ=v1−vcvc=v1vc−1=v1ωR−1,(13)

which allows us to express the neutral angle as

cosαN=A1AN(1+κ)(14)

We should note at this stage, that the absolute value of αN (in radians) is strongly connected to the geometrical bite angle α0, as αN∈[0;αN]. Therefore, we may define the dimensionless neutral angle βN as

βN=αNα0(15)

The cross sections A1 (at exit) and AN (at the neutral angle) can be described as the product of height and width at the respective positions,

A1=h1w1(16)

and

AN=hMwN(17)

When we disregard lateral spread, w0=w1=wN, we can write

A1AN=h1hN(18)

and therefore

cosαN=h1hN(1+κ)=h1(1+κ)h1+2R(1−cosαN)(19)

An analytical solution to this transcendental equation will be given later in this paper.
Physics-informed neural networks. Neural networks provide a framework for a wide range of modeling tasks. A set of input information features is passed through a number of hidden layers until it reaches the output layer. The passing through one layer is basically a vector-matrix multiplication followed by addition of a bias vector of the respective layer and application of an activation function to the results, which in turn are fed as inputs into the next layer. The manipulation of the data in each layer is influenced by the bias vectors and weight matrices, which constitute the model parameters. In order to evaluate the network successfully, the model parameters must be adjusted so that the network generates the intended outputs from the given inputs, according to the modeling task at hand. This adjustment procedure is called the training process. During the training, a loss function is evaluated
which assesses the quality of the prediction, based on which the network parameters are updated by an optimizer routine. This process is repeated many times (called the epochs) until the loss of the validation data (a subset of the total data, which is not used to update the model parameters) has reached a desirably low value. In each epoch, the training data is fed into the network in multiple batches. The batch size is the number of training samples processed in one forward and backward pass before the model's internal parameters (weights and biases) are updated [11].
The default method of training a neural network utilizes given input and target output data for the respective inputs. Typical default loss functions are based upon mean squared error losses, comparing the predicted outputs to the target outputs. A physics-informed neural network is a special form of training where the loss function is replaced by a special function which contains information about the physical nature of the problem to be solved, often in the form of (partial) differential equations. To handle differential equations, the loss function makes use of automatic differentiation provided by the machine learning framework used to check the gradients of the predicted outputs against a given differential equation. This opens a wide range of applications to the PINNs (physics informed neural networks), from the data-driven solution of differential equations, combined with data modeling, up to inverse parameter identification of physical models which are based on differential equations [13,14]. PINNs are already used to solve metal forming problems, like roll pass design [10].

Aims of the Present Analysis

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In the present paper, we will construct a physics-informed neural network to solve von Karman's ordinary differential equation of the roll gap. Two versions of the neural network will be presented, with the first being a forward model for predicting the stress distribution in the roll gap from the given friction coefficient. The purpose of the second model (the inverse model) is to accomplish an inverse parameter identification of the friction coefficient and find a physical friction coefficient μ which corresponds to a prescribed neutral angle. The kinematic relationship between the forward slip and neutral point position will be calculated analytically.

Scientific Methodology

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In this section, we will present the models which were built to address the present problem of friction coefficient estimation from measured forward slip, while the results obtained will be presented in the next section.

Methods and tools. To tackle the present problem of the friction coefficient estimation from measured forward slip, a physics-informed neural network was trained using the PyTorch Machine Learning Framework [11] and Python programming language. Especially, PyTorch's automatic differentiation engine is leveraged to find the gradients of the predicted stress values in the form of a PINN as described by Raissi et al. [13]. The PINN solves von Karman's differential equation, and the friction coefficient μ is estimated from alignment of the solution with a normalized neutral angle βN previously calculated from the measured forward slip. In the current state of development, the solution does not take elastic roll flattening into account. As this effect, prevalent in cold strip rolling, affects the length of the contact region and stress distribution, an impact on the results is to be expected. Therefore, we present numerical results accounting for roll flattening in the results section, obtained by classical numerical solution of von Karman's differential equation and Hitchcock's roll flattening model. Another simplification used in the analysis is that the friction coefficient is kept constant in the roll gap, which is owed to the fact that the forward slip measurement only provides a very global means of friction assessment, from which the way in which the friction coefficient changes throughout the roll gap cannot be deduced.
The actual industrial problem of cold rolling is therefore reduced to a mathematical inverse parameter identification problem for von Karman's differential equation, solved by a physics-informed neural network.

Forward solution of von Karman's ODE for rolling using a neural network.

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[picture]

Fig. 2: The forward ANN model for the local stress and neutral point evaluation

Fig. 2. The forward ANN model for the local stress and neutral point evaluation

For the forward solution of the ODE, we prepare a deep neural network with the input parameters normalized friction coefficient μ^ and the normalized x^ coordinate. The physical x coordinate, ranging from x=−ld (entry plane) to x=0 (exit plane) is changed to the normalized x^ so that x^=0 at entry and x^=1 at exit by

x^=1+xld⇔x=ld(x^−1).(20)

The network's structure is sketched in Figure 2. The first hidden layer has 20 neurons, followed by five hidden layers of 50 neurons each and two more hidden layers of 40 and 20 neurons, finally generating two output features, i.e. the nomalized horizontal stress σ^x at x^ and the normalized neutral angle βN. The normalized friction coefficient μ^ ranges from 0 to 1 according to

μ^=μ−μminμmax−μmin.(21)

The network will predict the normalized horizontal stress σ^x and the normalized neutral angle α^N. The network is trained with a set of friction coefficients ranging from μmin  to μmax . In contrast to conventional ANN training where target outputs must be supplied, we leverage a custom loss function to assess the alignment of the derivatives of the predicted stresses with the given differential equation. The boundary conditions on the horizontal stresses for given strip tensions t0 and t1 are enforced by a suitable normalization of the output stress. We require σ^x=t0^ at x^=0 and σ^x=t1^ at x^=1. We do this by transforming σ^x to the physical stress σx using

σx=C(σ^x−s^0−s^1)(22)

with

s^0=(σ^x0−t^0)(1−x^)(23)

and

s^1=(σ^x1−t^1)x^(24)

C is a normalizing factor in the order of magnitude of the maximum physical stress, for cold rolling of steel strips, typically C≈1000.σ^x0 and σ^x1 are the predicted σ^x values at roll gap entry and exit,
respectively. The original form of the physical ODE in Equation 1 is now further elaborated to an expression for dσx/dx and replacing dh/dx by Equation 5,

dσxdx=2h[σN−xR(σx∓τF)](25)

In the loss function, we want to use this ODE in the normalized form dσ^xdx^. Differentiating Equation 22 with respect to x, we get

dσxdx=Cld(dσ^xdx^−ds^0dx^−ds^1dx^)(26)

from which it follows in combination with Equation 25 that

dσ^xdx^=ldC2h[σN−ld(x^−1)R(σx∓τF)]−(σ^x0−t^0)+(σ^x1−t^1)(27)

with σx from Equation 22. For cold rolling, we define the shear stress τF according to slipping friction with τF=μσN. As can be seen from the double sign in the preceding equations, τF must undergo a sign change at the neutral point. When the boundary conditions are automatically satisfied by the above normalization and satisfaction of the ODE is enforced by the loss minimization, the neutral point is the only unknown. We therefore include the neutral point position as an output parameter to make the network select it appropriately. This output has its own output layer and the sigmoid activation function

σ(x)=11+e−x(28)

is applied to ensure α^N∈[0;1]. To retain differentiability, no abrupt change of the direction of shear stresses should be introduced. Instead, a smooth transition will be formulated using a tanh approach based on the neutral point position x^n. Therefore,

τF=−μσNtanh[D(x^−x^N)](29)

where D is a scaling parameter for the smoothness of the transition in the order of magnitude of D≈100. The normal stress σN, required several times in the final ODE, is a function of σx by the yield criterion and the vertical force decomposition. Firstly, we express the physical relation between σx and a vertical stress σz by Tresca's yield criterion

σz−σx=kf(30)

when compressive stresses are defined as positive values. The relation between σz and σN is defined from the vertical force decomposition as

σN=σz1∓μtanα(31)

Finally, the loss is calculated on each training batch using the loss function

ℒ=‖G−dσ^xdx^‖2(32)

where G are the gradients of the predicted stress values calculated by automatic differentiation using PyTorch's autograd engine, and dσ^x/dx^ are the physical gradients given by Equation 27. Note that we do not need to include the satisfaction of the boundary conditions in the loss function as the normalization applied above provides that the network is unable to predict a result which does not satisfy the
boundary conditions. After evaluation of the network, the forward slip resulting from the predicted neutral angle is evaluated based on Equation 19, giving

κ=cosαNh1+2R(1−cosαN)h1−1.(33)

The network was trained for a cold rolling pass of fixed geometry with an initial strip thickness of h0=1.0 mm, exit strip thickness of h1=0.7 mm at a roll diameter of R=400 mm. The network was trained with 40 friction coefficients μ ranging from 0.03 and 0.15 . The hyperparameters used in the training are learning rate 10−5, batch size 768 at 15000 epochs. This model is referred to as the forward model, as it calculates the neutral point position and resulting forward slip from the given friction coefficient.

Inverse model and determination of friction coefficients. The purpose of the inverse model is to to predict the friction coefficient from a given forward slip. This inversion can be performed easily using the present neural network approach without any further iteration necessary. For this purpose, an inverse PINN is trained, taking the normalized neutral point α^N and the normalized coordinate x^ coordinate as input values, yielding the constant normalized friction coefficient μ^ and the horizontal stress at position x,σ^ as outputs. Beforehand, the neutral angle must be calculated from the nonlinear equation Equation 19. Without further simplifications, the solution is

cosαN=2ψ±4ψ−8ψ(κ+1)+4ψ2+1+14ψ(34)

where

ψ=Rh1.(35)

Out of the two mathematical solutions, the second one with the negative double sign can be omitted as it does not provide resonable results. We can however simplify this equation when we disregard one of two cosαN expressions from Equation 19 and arrive at

cosαN≈1−κ2ψ.(36)

For the inverse training of the network, only a slight change to the loss function is necessary compared to the forward version, i.e. the friction coefficient must be taken from the model predictions and the neutral point from the input parameters.

Results

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All calculations are performed for a strip material C15 with the cold flow curve given by kf=850·φ0.23. Figure 3 shows the horizontal stress distributions predicted by the forward neural network for different friction coefficients, together with stress distributions calculated by numerical solution of von Karman's differential equation, resembled by the dotted lines.

As can be seen from these results, the stress distributions produced by the neural network include the typical sign change in the frictional shear stress at the neural point, leading to a peak value of the horizontal stress. Therefore, it is evident that the model is capable of selecting the neutral point position according to the given coefficient of friction. The inverse model predicts the stress distributions as a function of the given neutral point positions. Figure 4 shows the normal stress distributions for nominal forward slips κ between 0.01 and 0.06 . The dotted lines represent the stress distributions, which were recalculated numerically from the friction coefficients predicted by the neural network.

Table 1 shows the results concerning the resulting friction coefficients, along with the predicted normalized neutral point positions. These predicted friction coefficients were then used to recalculate

[picture]

Fig. 3: Horizontal stress distributions predicted by the Forward PINN, compared to results of numerical solution of the ODE (dots)

Fig. 3. Horizontal stress distributions predicted by the Forward PINN, compared to results of numerical solution of the ODE (dots)

Table 1: Nominal forward slip values κ, friction coefficients and neutral points predicted by the neural network, and numerically calculated forward slips from the predicted friction coefficients

Nominal forward slip (%) | Predicted friction coefficient | Predicted normalized neutral point
5 | 0.42 | 0.52
10 | 0.48 | 0.54
15 | 0.52 | 0.55
20 | 0.55 | 0.56
25 | 0.57 | 0.57
30 | 0.59 | 0.58

the forward slip values using the direct numerical solution. These back-predictions are shown as κback  in Table 1.

Figure 5 shows the difference between the neural network and numerical model for a continuous range of forward slips at the cold rolling pass under consideration.

Both models predict higher friction coefficients at higher forward slips, though there are differences in the absolute friction coefficients predicted for higher forward slips and friction coefficients. The red dots indicate the numerical results when roll flattening is accounted for by Hitchcock's equation for steel rolls with the Young's modulus E=210GPa and the Poisson's coefficient ν=0.3,

R′R=1+CFSΔh(37)

with the specific roll force per unit strip width FS, where

C=16π1−ν2E(38)

At this stage, it shall be noted that the numerical iterative technique requires the complete stress distributions to be calculted in order to connect the neutral point to the friction coefficient. For the ANN, this is not needed and the evaluation of a single point of this stress-distribution is sufficient to determine the friction coefficient μ associated to a given normalized neutral angle βN. We will call this technique the single-point ANN evaluation in constrast the full ANN evaluation; the only difference

[picture]

Fig. 4: Normal stress distribution calculated by the inverse network for given forward slips, and the numerically calculated stress distributions for the predicted friction coefficients (dots)

Fig. 4. Normal stress distribution calculated by the inverse network for given forward slips, and the numerically calculated stress distributions for the predicted friction coefficients (dots)

is that the latter technique generates the stress distribution at multiple points as another informative result.

As we expect the single-point evaluation to be faster than the full ANN evaluation, it will be interesting to compare the evaluation times of both inverse ANN in comparison to the inverse classical solution, as the purpose of the present study is to significantly speedup the evaluation by using the ANN. Table 2 shows the evaluation times for the three variants considered (full ANN evaluation with stress distribution tANN,full, single-point ANN evaluation without stress distribution tANN,sp, classical inverse method tclass  ). The mean evaluation times were determined at 1000 equal evaluations of each method.

Table 2: Nominal forward slip values κ, friction coefficients and mean evaluation times

κ | μANN | μclass | tANN,full [ms] | tANN,sp [ms] | tclass [ms]
0.01 | 0.027 | 0.028 | 0.562 | 0.227 | 15.18
0.02 | 0.034 | 0.035 | 0.590 | 0.252 | 16.08
0.03 | 0.045 | 0.044 | 0.474 | 0.225 | 15.89
0.04 | 0.059 | 0.056 | 0.549 | 0.253 | 16.64
0.05 | 0.076 | 0.074 | 0.544 | 0.282 | 20.58
0.06 | 0.092 | 0.104 | 0.563 | 0.272 | 20.49

[picture]

Fig. 5: Relation of friction coefficient and forward slip according to neural network and numerical solution

Fig. 5. Relation of friction coefficient and forward slip according to neural network and numerical solution

Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1183.55.pdf

The present contribution demonstrates the construction of a physics-informed neural network which is capable of solving von Karman's ordinary differential equation of the roll gap in cold strip rolling for both forward and inverse analyses of friction in cold rolling. The forward model is capable of selecting the neutral point position according to the given friction coefficient and implement the sign change of the frictional shear stresses accordingly. The inverse model uses a given neutral point position which may be initially calculated from a measured forward slip and selects the friction coefficient so that the final solution satisfies the underlying differential equation, as well as the boundary conditions and the given neutral point. However, if the classical numerical technique is employed to solve this problem, multiple iterations are required to perform an inverse parameter fit for the friction coefficient. This problem is overcome by the present neural network based solution. It should also be noted that it is not necessary to calculate the total stress distribution throughout the roll gap to achieve the connection between forward slip and friction coefficient; the evaluation of the ANN at one single x-value is sufficient, which provides an additional performance boost to the new model. A similar method of calculating the stress distribution in rolling by a PINN is not yet found elsewhere in the literature. The comparison of evaluation times as seen in Table 2 reveals a substantial speedup of the ANN evaluation in comparison to the classical inverse evaluation method. If only the friction coefficient is of interest, the single-point evaluation method can be employed, achieving a calculation which is more than 60 times faster than the classical method. The full ANN evaluation including the local stress distribution is still about 30 times faster than the classical method. In view of this speedup, the additional training time required to set-up the PINN of about 15-20 minutes even for 15000 training epochs is more than justified.

In the current model, elastic roll flattening is not taken into account, an effect prevalent in cold strip rolling, affecting the length of the contact region and stress distribution. However, the inclusion of roll flattening in the model is possible by adding the satisfaction of Hitchcock's equation to the loss function. This extension would only increase the training effort substantially as the roll force must be calculated for each training epoch, but would not affect the evaluation speed, leading to further tremendous increases of the model performance compared to the classical iterative numerical technique. Therefore, it is planned to extend the model to elastic roll flattening and to address this extension in future publications.

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.55.pdf

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E. Li, A. Tieu, and W. Yuen. Forward slip measurements in cold rolling by laser doppler velocimetry: uncertainty analysis and accuracy improvement. Journal of Materials Processing Technology, 133(3):348-352, 2003-02.

S.-E. Lundberg. Evaluation of friction in the hot rolling of steel bars by means of on line forward slip measurements. Scand J Metallurgy, 33(3):129-145, 2004-06.

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C. Overhagen and R. Martin. Roll pass design for round and square sections using an informed artificial neural network. Materials Research Proceedings, 44:444-455, 2024-09-15.

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H. Pawelski. Interaction between mechanics and tribology for cold rolling of strip with special emphasis on surface evolution. Technische Universität Bergakademie Freiberg, 2004.

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C. Smith, F. Scott, and W. Sylwestrowicz. Pressure distribution between stock and rolls in hot and cold flat rolling. Journal of the Iron and Steel Institute, 170:347-359, 1952.

G. Van Rooyen and W. Backofen. Friction in cold rolling. J. Iron Steel Inst., pages 235-244, 1957.

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The original version of this eBook is available on https://www.scientific.net/book/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 69-79

doi: 10.4028/p-I1nbWq

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

Submitted:
2026-01-19

Revised:
2026-02-14

Accepted:
2026-02-24

Online:
2026-04-13

A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

The original version of this paper is available on https://www.scientific.net/MSF.1183.69.pdf

Shaheryar Younas 1,a*, Jos Havinga 1, b, Camile Hol 2,c, Ton van den Boogaard 1, d

1 Faculty of Engineering Technology, University of Twente, Netherlands

2 Tata Steel Nederland B.V.

a  S.younas@utwente.nl, b  jos.havinga@utwente.nl, c  camile.hol@tatasteeleurope.com, d  a.h.vandenboogaard@utwente.nl

Keywords: Cold Rolling, Roll Force, Friction Hill, Anisotropy, Plane Strain Point

Abstract

Cold rolling forces are strongly affected by lubrication and material properties, and may potentially be used to estimate material property variations along the coil. The 1D slab method is commonly used to estimate rolling forces as it is computationally inexpensive. By model definition, the pressure distribution as modelled in the slab method has a single peak or friction hill in the roll bite. However, it has been observed in several studies that multiple local peaks can appear in the pressure distribution in the roll bite. Additionally, material anisotropy also affects the contact pressure distribution and steady state roll force. In the present work, a 2D plane strain finite element rolling model is used for a detailed sensitivity study of the multitude of parameters that affect the vertical pressure distribution and the steady state roll force. The considered model parameters are material anisotropy, entry sheet thickness, roll radius, tensions, coefficient of friction and roll gap.

Introduction

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Prediction of rolling force has been a topic of research for decades, with models ranging from analytical relations and one-dimensional slab models up to detailed finite element (FE) simulations. Roll force predictions are relevant for controlling the roll gap and ensuring robust production conditions. In addition to that, roll forces and torques are affected by material property variations, and may therefore potentially be used to assess the evolution of material properties over rolling stands [1,2]. For this specific purpose, a precise description of the effect of process conditions and incoming material properties on the rolling force is required.

Friction plays a key role in the sheet rolling process. At the entry zone, the sheet speed is lower than the roll speed, meaning that the relative velocity of the sheet with respect to the roll is backward. The friction force will therefore act in the forward direction and help pull the sheet into the roll bite. In the exit zone, the relative velocity of the sheet with respect to the roll is forward, meaning that the frictional force acts in the backward direction. In between the forward and backward slipping regions, there is a stick zone, where the roll and sheet speeds are equal [3]. In several two-dimensional models, the stick region is represented as a point along the contact arc between the roll and the sheet, which is called the neutral point. When the process conditions are such that the forward and backward slipping region are established, with a neutral zone in between, steady state rolling is achieved. Otherwise, certain combinations of process conditions and material properties may result in only forward or backward slip, meaning that the process conditions are unstable.

Several modeling approaches have been developed to predict sheet rolling forces and deformations. A popular cold rolling model in industry is the slab model due to its computational speed. It divides the sheet into one-dimensional elements called slabs, applies force equilibrium to get the differential equation describing pressure distribution and then integrates over sheet length. It was first developed by Von Karman in 1925 who also gave the concept of neutral point. Later, Orowan improved the model by including strain hardening and roll elastic deformation [4]. An important result from Orowan's model is the vertical pressure distribution along the roll bite, also called as friction hill which helps in understanding the process. The roll contact pressure increases from the entry side, reaches maximum pressure and then decreases towards the exit zone. The point of maximum pressure
represents the neutral point along the sheet length. Another important parameter is the reaction force applied by the roll on the sheet upon contact, which is also called the roll force. As the roll force is commonly measured in industrial rolling processes, it is often used as an indicator of changes in process conditions.

Several extensions of the slab method have been developed to improve prediction accuracy and the applicability of the model, for example for asymmetric rolling, while benefiting of its low computational cost [5]. On the other side, several researchers have used the FE method to obtain a more accurate description of the sheet and roll deformations in the roll bite, at the expense of increased computational cost. While Orowan's model is a one-dimensional representation of the problem that accounts for a single peak of the vertical pressure distribution, several studies have reported multiple pressure peaks when FE models are used [5,6]. These pressure peaks appear as oscillations on top of a pressure distribution that is similar to the one obtained with the slab method. Recently, a semianalytic model that uses multiple-scales asymptotics has been developed, that is able to describe stress and strain oscillations in rolling direction and through thickness under the assumption of rigid plastic material deformation. This model can be used to describe pressure oscillations with a computational cost in the order or seconds [7].

Besides the need to describe pressure oscillations for obtaining a more accurate rolling force prediction, another factor that is commonly not accounted for in two-dimensional rolling models is the effect of material anisotropy [8]. Cold rolling generates anisotropy in the sheet due to texture evolution. As plane strain conditions apply in most of the sheet (expect at the edges) during rolling, it is important to use anisotropic material models to account for the position of the plane strain point in the yield locus correctly, even while modeling the process in 2D.

This study aims to determine qualitative effect of various cold rolling input parameters such as plane strain point, sheet thickness, roll radius, coefficient of friction, tensions and unloaded roll gap fraction on vertical pressure distribution, friction hills and steady state roll force through sensitivity analysis using a FE model of the process. Analysis has been done using both isotropic and anisotropic hardening. The contents of the paper are divided in the following way: in section "Cold Rolling Model", details of the cold rolling model are given. In section "Sensitivity Analysis", strategy of sensitivity analysis of input parameters of cold rolling model is discussed, followed by the sections "Results and Discussion" and "Conclusion".

Cold Rolling Model

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Specifications. This section describes specifications of the cold rolling model developed using commercial Finite Element (FE) software ABAQUS which is used for the sensitivity analysis. In this work, the following coordinate directions are used for stress and strain: the 11-direction represents the sheet length direction, the 22 -direction represents the sheet width direction and the 33 -direction represents the sheet thickness direction.

When the sheet width is significantly larger than the thickness, cold rolling can be considered as a plane strain process, meaning that the strain in width direction is zero ( ε22=0 ). Therefore, the process can be modeled in 2D. An implicit dynamic simulation is used to roll a sheet section until steady state conditions are reached. To reduce the computational time, a single work roll and half the sheet thickness is modeled by assuming symmetry about the 11 -axis. A partial deformable roll is modeled, with high mesh density around the contact zone.

The roll angular velocity has a constant value of almost 42rad·s−1. The sheet position is initialized just in front of the roll bite, with zero initial velocity, and prescribed front and back tensions Tin and Tout . The displacement of the sheet is force controlled: the difference between prescribed front and back tension ΔT will pull the sheet into the roll bite, and will continue to accelerate the sheet until the sheet tensions equilibrate with the roll contact forces and steady state is reached. A mild steel material model is used with tabulated hardening and a Hill yield locus. The nominal hardening curve yields
at 304 MPa and saturates at 0.6 equivalent plastic strain at a value of 566 MPa . A constant Coulomb friction parameter is used for the contact between the roll and the sheet. The values of the different model parameters will be presented in the section "Sensitivity Analysis".

The work roll is meshed with gradually increasing mesh density from its inner region to the outer region that is in contact with the sheet. The total number of elements and nodes in the work roll are 54.448 and 46.051 respectively. The total number of elements and nodes in the sheet are 12.810 and 13.740 respectively, with 15 elements through thickness of the sheet. With this mesh, approximately 105 sheet elements are in contact with the roll in the contact zone in the base simulation. As the model is 2D, the computational time for implicit dynamic analysis still remains reasonable.
Implementation of Anisotropic Effect in the Model. Material anisotropy has a significant effect on the roll force, and must therefore be accounted for in the model [8]. Specifically, it is important to consider that material anisotropy evolves over rolling stands. In this study, the Hill 48 yield criterion is used. It is considered that it is not beneficial to use a more advanced yield criterion, as the plane strain point of the yield locus is the only relevant part of the yield locus when modeling 2D plane strain rolling. The Hill yield locus is a quadratic yield criterion resulting in an ellipsoidal shape in 3D:

F(σ11−σ22)2+G(σ22−σ33)2+H(σ33−σ11)2+2Lσ232+2Mσ312+2Nσ122=σeq2(1)

Where σ11,σ22,σ33 are normal stresses, σ12,σ23 and σ31 are shear stresses and F,G,H,L,M and N are Hill parameters.

In the above-mentioned study where the effect of anistotropy in cold rolling was characterized, planar anisotropy was assumed, and the Lankford parameter in rolling direction was used to parametrize the anisotropy, using a Hill yield locus. In that case, the plane strain stress in rolling direction σ11,PS and in transverse direction σ22,PS are directly defined by the Lankford parameter in rolling direction. Alternatively, in this work it is chosen to decouple the effect of both stress components in the plane strain point, to identify whether these components have an independent effect on the rolling conditions. To do so, the relation between the Hill yield locus parameters F, G and H, the plane strain stress components σ11,PS and σ22,PS, and the yield stress σy has been determined, and used to find the values of the Hill parameters as function of the stress values at the plane strain point:

F=(σ11,PS2−σy2)(σ11,PS−σ22,PS)σ11,PSσ22,PS2G=1−σ11,PS2−σy2σ11,PSσ22,PSH=σ11,PS2−σy2σ11,PSσ22,PS

(2)(3)(4)

In determining these relations, plane stress in thickness direction ( σ33,PS=0 ) and plane strain in width direction (ϵ22=0) were assumed, meaning that the used parametrization of the material properties respresent the plane strain point with in-plane loads only, despite the fact that the actual stress state in rolling is not a plane stress condition. The other parameters L,M and N were taken as constants, equal to 1.5 , being the coefficients from the isotropic case.

Sensitivity Analysis

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A detailed sentitivity study is performed, to characterize the effect of different parameters on the vertical pressure distribution in cold rolling. The set of performed simulations can be categorized in three different groups:

Group I: Sensitivity to stress components of plane strain point. This set of simulations is performed to study the effect of both stress components of the plane strain point on the rolling force. With the plane strain point of an isotropic yield locus being defined as a reference point with stress values σ¯11,PS and σ¯22,PS, both stress components were varied with −5% and +5%. With minimum, nominal and maximum values for σ11,PS and for σ22,PS, a total of 9 positions of the plane strain point have been analyzed, as visualized in Fig. 1.

[picture]

Fig. 1: Hill yield loci used in sensitivity study of stress components of plane strain point.

Fig. 1. Hill yield loci used in sensitivity study of stress components of plane strain point.

Besides the above-mentioned simulations, two sets of Hill yield locus parameters have been identified with exactly the same plane strain points, but with different uniaxial yield stress values, to verify that the results are completely dependent on the plane strain point values and independent of the uniaxial yield stress value.
Group II: Sensitivity to unloaded roll gap fraction. The unloaded roll gap fraction is defined as the unloaded roll gap distance divided by the undeformed sheet thickness. In case of rigid rolls and no elastic springback, the final thickness of the sheet will be equal to the unloaded roll gap. In the simulations, roll deformation and springback is accounted for, meaning that the final sheet thickness will be larger than the unloaded roll gap distance. Simulated roll gap fractions vary from 50% to 90% with steps of 10%.

These simulations are performed for a material model with isotropic properties, and for a material model with anisotropic properties. The plane strain point of the anisotropic model is defined as σ11,PS=1.22·σy and σ22,PS=0.58·σy (such that σ22,PS/σ11,PS=0.475 ) where σ11,PS and σ22,PS are normal stresses in the length and width direction under plane strain condition. Note that the ratio σ22, PS /σ11, PS  equals 0.5 for isotropic materials.
Group III: Sensitivity to other process parameters. Finally, a set of simulations is performed to assess the sensitivity of the roll pressure distribution to different model parameters, by evaluating a one-at-a-time (OAT) design of experiments in which a set of base settings is defined, and one parameter at a time is varied to its minimum and maximum values. The set of analyzed parameters and used ranges are given in Table 1.

The front and back tensions are parametrized using the difference of tensions ΔT=Tout −Tin  and the average tension Tavg =(Tout +Tin )/2, as these parameters better characterize the set of realistic sheet tension values that are used in sheet rolling. ΔT determines the friction force in longitudinal direction that is required to reach steady state conditions. Tavg  determines amount of stretch in the sheet.

Table 1: Base values and deviations of parameters used in the rolling model.

Parameter | Base values | Deviation from the base values
Sheet thickness hi | 1.825 mm | ±10%
Roll radius R | 240 mm | ≈ ±5%
Unloaded roll gap fraction (% of sheet thickness) | 90% | 50% to 90%
Coefficient of friction μ | 0.07 | ±30%
Difference of front and back tensions ΔT | 123.9 kN/m | ±10%
Average tensions Tavg | 280.8 kN/m | ±10%

Results and Discussion

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The results of the different analyses are presented below.

Group I: Sensitivity to stress components of plane strain point.

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The roll pressure distributions for the simulations with varying plane strain points are presented in Fig.2. As expected, the plane strain stress component in length direction σ11,PS has a significant effect on the pressure distribution. On the other hand, it can be observed that the 22 -direction stress component of the plane strain point has minimal effect on the pressure distribution. The roll forces are also shown in the contour plot of Fig. 3, showing that the effect of σ11, PS  is significant while the effect of σ22,PS is negligible.

[picture]

Fig. 2: Vertical Pressure Distribution

Fig. 2. Vertical Pressure Distribution

In this study, it is also verified that only the location of the plane strain point in stress space is relevant for rolling, whereas the actual value of uniaxial yield stress σy does not directly affect the roll force. This was done by defining two material models with equal plane strain point location but distinct yield stress values. The corresponding stress values are given below, and the yield loci are shown in Fig. 4.
Case 1: σy=304MPa,σ11,PS=370.88MPa,σ22,PS=176.32MPa.
Case 2: σy=334.4MPa,σ11,PS=370.88MPa,σ22,PS=176.32MPa.
The only difference between the results that could have been expected is the part of the deformation path when a material point moves from elastic to plastically deforming, as the stress state under elastic

[picture]

Fig. 3: Contour plot of steady state rolling force w.r.t. σ11 and σ22.

Fig. 3. Contour plot of steady state rolling force w.r.t. σ 11 and σ 22 .

[picture]

Fig. 4: Hill yield loci for cases 1 and 2.

Fig. 4. Hill yield loci for cases 1 and 2.

deformation with a Poisson ratio ν of 0.3 does not reach the yield locus at its plane strain point. However, this effect is minimal, and it was observed that the roll force and roll pressure distribution for both cases is identical, with a steady state roll force value of approximately 2600kN/m.

Group II: Sensitivity to unloaded roll gap fraction.

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The steady state roll force computed with the isotropic and anisotropic models is shown in Fig. 5. It increases with unloaded roll gap fraction as the thickness reduction and the length of the arc of contact increase. Note that the force is slightly higher for the anisotropic case, as the 11-direction stress component of the plane strain point is higher than in the isotropic case, being σ11,PS=1.22·σy.

When examining the vertical stress distribution in the roll gap for the isotropic and anisotropic cases in Fig. 6, it can be seen that the contact length increases and that the pressure also increases, leading to a higher roll force. The oscillations in the vertical pressure are apparent, and correspond with the observations in other studies [5,6,7]. The number of oscillations increases with decreasing roll gap, as listed in Table 2. It can also be observed that the amplitude of the oscillations decreases with increasing number of oscillations. Note that it is essential to have a large number of sheet and roll elements in the contact zone to identify these detailed oscillations in the pressure distribution.

[picture]

Fig. 5: Roll force Line Plots for Different Unloaded Roll Gap Fractions (Percent)

Fig. 5. Roll force Line Plots for Different Unloaded Roll Gap Fractions (Percent)

[picture]

Fig. 6: Vertical Roll Pressure Distribution for Varying Unloaded Roll Gap Fractions (Percent)

Fig. 6. Vertical Roll Pressure Distribution for Varying Unloaded Roll Gap Fractions (Percent)

Table 2: Number of oscillations in the vertical pressure for different unloaded roll gap fractions.

Unloaded roll gap fraction | mathematical formula | mathematical formula | mathematical formula | mathematical formula | mathematical formula
Number of oscillations | Isotropic Model | 3 | 5 | 6 | 8 | 7
Anisotropic Model | 3 | 5 | 6 | 7 | 9

Group III: Sensitivity to other process parameters.

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The effects of sheet thickness, roll radius and friction coefficient on the total roll force are presented in Fig. 7. It is observed as expected that the roll force increases with increasing sheet thickness, roll radius and friction coefficient.

[picture]

Fig. 7: Roll force values for different sheet thicknesses, roll radii and coefficients of friction.

Fig. 7. Roll force values for different sheet thicknesses, roll radii and coefficients of friction.

Sheet thickness.

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The increase of steady state roll force with increasing sheet thickness can be understood from the following cold rolling relations [9,10]:

L≈RΔh=R(ho−hi)=Rhi(hohi−1)=Rhi(1r−1)⇒L∝hiFr=bLσf(1+μLhm)

(5)(6)

Where L is the length of the arc of contact, R is the roll radius, hi is the input sheet thickness, ho is the output sheet thickness, r is the thickness reduction, F is the roll force, b is the sheet width, σf is the flow stress, μ is the friction coefficient and hm=(ho+hi)/2 is the average thickness. Equation (5) shows that when the sheet thickness increases, the length of the arc of contact between sheet and the roll also increases. As a result, roll force also increases according to Equation (6), which is known as Sims formula.

The effect of thickness variation on the vertical pressure distribution is shown in Fig.8a. The location of the oscillations shifts with varying thickness, which can be understood from the observation that the ratio between sheet thickness and contact zone length determine the number of oscillations in the pressure distribution [7]. It can even be observed in Fig. 8a that the number of peaks in the pressure distribution is four for the lowest thickness, and three for the other two cases. This also explains why the increase of the roll force in the sensitivity study is not linear, as can be seen in Fig. 7.

The steady state force increases with increasing roll radius, as shown in Fig. 7. The reason is that a larger roll radius increases the length of the arc of contact, and thereby also increases the roll force. However, the effect of roll radius on the pressure distributions is not very significant, as seen in Fig. 8b. The width of the pressure distribution is slightly affected by the roll radius, but the pressure distribution within the contact zone is close to equal in all cases.

Coefficient of friction.

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Like sheet thickness and roll radius, it can be seen in Fig. 7 that steady state force also increases with increasing coefficient of friction. The explanation is that the pressure gradient increases with

[picture]

Fig. 8: Vertical pressure distribution due to variation in roll radius and sheet thickness.

Fig. 8. Vertical pressure distribution due to variation in roll radius and sheet thickness.

coefficient of friction according to the Orowan's model:

dpdx=−2μph+2dkdx(7)

Where p is the vertical pressure, x is the distance along the sheet length, μ is the coefficient of friction, h is the exit thickness and k is the shear strength. As per Equation (7), the pressure increases with increasing friction coefficient, as can be seen in Fig. 9. With varying friction small changes in the position of the oscillations in the pressure distribution can be observed..

[picture]

Fig. 9: Vertical pressure distribution for different friction coefficients.

Fig. 9. Vertical pressure distribution for different friction coefficients.

Front and Back Tensions.

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As mentioned in Section "Sensitivity analysis", front and back tensions have been analyzed by varying the tension difference ΔT and the average tension Tavg . Note that the steady state roll force increases with increase in both ΔT and Tavg . The reason behind influence of ΔT is that it governs the net force which pulls the sheet through the roll bite. Therefore, the roll has to work lesser if ΔT and the net force is higher. The reason behind influence of Tavg  is that it governs the stretch in the sheet along longitudinal direction due to the tensions applied in the opposite directions. This makes rolling relatively easier and we see decrease in rolling force. the effect of Tavg  is more significant. Further, it can be seen that the steady state roll force remains the highest for the base cases. Vertical pressure distribution also follows a similar pattern (fig. 11) where the upward shift of pressure is more noticeable for variation in Tavg .

[picture]

Fig. 10: Roll force values for different values of tension difference ΔT and of average tension Tavg .

Fig. 10. Roll force values for different values of tension difference Δ T and of average tension T avg .

[picture]

Fig. 11: Vertical pressure distributions for for different values of tension difference ΔT and of average tension Tavg .

Fig. 11. Vertical pressure distributions for for different values of tension difference Δ T and of average tension T avg .

Conclusions

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In this research, the effect of different cold rolling parameters on steady state roll force and vertical pressure distribution for isotropic and anisotropic models were studied qualitatively through sensitivity analysis. Based on the results, the following conclusions can be made:

1 The roll force is sensitive towards the longitudinal stress component of the plane strain point σ11,PS, and not sensitive to the transverse stress component of the plane strain point σ22,PS.

2 There can be several combinations of uniaxial yield point and plane strain point for which the roll force will be the same.

3 As known from literature, it is verfied that steady state roll force increases with increasing sheet thickness, roll radius and roll gap closure.

4 It has been observed that the steady state roll force increases with increase in ΔT and Tavg . However, the effect of Tavg  is more prominent.

5 By modelling the contact zone in the FE model with a large number of elements on the roll and on the sheet, oscillations in the vertical pressure distribution in the roll gap could be observed in all simulations. The number of oscillations is strongly affected by the unloaded roll gap fraction, weakly affected by the sheet thickness, and not significantly affected by the other parameters that were varied in this study. Also, the amplitude of the oscillations decrease with the increasing number of oscillations in the roll gap.

Acknowledgements

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This research was carried out under project number N21022d in the framework of the Partnership Program of the Materials innovation institute M2i (www.m2i.nl) and the Netherlands Organization for Scientific Research (www.nwo.nl).

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.69.pdf

A. Del Prete and T. Primo: Inverse flow stress model validation in hot rolling with different thermal conditions, Int. J. Adv. Manuf. Technol. (2025), pp. 1-17

D. Szeliga, M. Graf, R. Kawalla and M. Pietrzyk: Identification of material properties based on rolling process at 4-stand laboratory mill, AIP Conf. Proc. Vol. 1353 (2011), pp. 391-397

Y. Shigaki, R. Nakhoul and P. Montmitonnet: Numerical treatments of slipping/no-slip zones in cold rolling of thin sheets with heavy roll deformation, Lubricants 3(2) (2015), pp. 113-131

E. Orowan: The calculation of roll pressure in hot and cold flat rolling, Proc. Inst. Mech. Eng. 150(1) (1943), pp. 140-167

P. Montmitonnet: Hot and cold strip rolling processes, Comput. Methods Appl. Mech. Eng. 195(48-49) (2006), pp. 6604-6625

A.C.M. Miranda, C.L. Neto, W. da S. Labiapari, P.H.R. Pereira, P.R. Cetlin and A.R. Arias: Study of the coefficient of friction and forward slip in cold rolling of stainless steel AISI 430 in sendzimir mills, J. Mater. Res. Technol. 34 (2025), pp. 4912-923

M. Erfanian, E.J. Brambley, F. Flanagan, D. O'Kiely and A.N. O'Connor: Through-thickness modelling of metal rolling using multiple-scales asymptotics, Eur. J. Mech. A/Solids (2025), p. 105712

L.J.M. Jacobs, E.H. Atzema, J. Moerman and M.B. de Rooij: Quantification of the influence of anisotropic plastic yielding on cold rolling force, J. Mater. Process. Technol. 319 (2023), p. 118055

R.B. Sims: The calculation of roll force and torque in hot rolling mills, Proc. Inst. Mech. Eng. 168(1) (1954), pp. 191-200

W.L. Roberts: Cold rolling of steel, Routledge (2017)

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Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 81-92

doi: 10.4028/p-5wea0U

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

Submitted:
2026-01-19

Revised:
2026-02-24

Accepted:
2026-02-25

Online:
2026-04-13

Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

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Moritz Gouverneur 1,a*, David Bailly 1, b and Junhe Lian 1,c

1 Institut of Metal Forming, RWTH Aachen University; Intzestraße 10, 52072 Aachen, Germany

a* moritz.gouverneur@ibf.rwth-aachen.de, b david.bailly@ibf.rwth-aachen.de, cjunhe.lian@ibf.rwth-aachen.de

Keywords: forging, damage, modelling, simulation.

Abstract

Open-die forging is an incremental bulk metal forming process for producing large, safetyrelevant components such as turbine and generator shafts. Besides achieving the target geometry, the process improves mechanical properties through grain refinement and the elimination of castingrelated defects. With the increasing use of high-alloy steels, precise process control is required to prevent surface and internal cracking caused by material damage. However, predictive models for damage evolution under the thermo-mechanical conditions of open-die forging remain limited, particularly with respect to high-temperature recrystallization and the incremental process character with inherent pause times. In this work, a recrystallization-sensitive damage model was developed and validated for open-die forging. The parameters of the Lemaitre damage formulation were determined for the cold work tool steel D2 (1.2379, X155CrVMo12-1) using hot tensile tests over the relevant forging temperature range. Dynamic recrystallization kinetics were characterized by hot compression tests and described using an Avrami-type JMAK formulation, while static recrystallization behavior was analyzed by stress relaxation experiments and also modeled with JMAK kinetics. These results enabled the quantification of recrystallized fractions as functions of strain, temperature, strain rate, and dwell time. To link microstructural evolution with damage development, tailored recrystallization states were generated in dilatometer experiments and examined metallographically with respect to void formation and healing. The extended model was implemented in a finite element framework and validated through open-die forging experiments on demonstrator geometries, showing its capability to predict damage initiation under industrially relevant conditions.

Introduction

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Open-die forging is an incremental bulk metal forming process that enables the manufacturing of longitudinally oriented components with various cross-sections like shafts as well as more complex shaped components like bushings.

In this process, the workpiece is heated to forging temperature, positioned beneath the press by a manipulator, and plastically deformed in a stroke-wise manner using tools of simple geometry, such as flat or slightly contoured dies. By the targeted execution of often several hundred individual strokes over multiple passes and forging heats, the final component geometry is achieved. While forging, the goal is not only to achieve a specific geometry, but also to achieve excellent material properties. This is possible due to the ability to close casting related voids and to convert coarse microstructure resulting from casting in a fine homogeneous one [1].

The increasing demand for open-die forged components made from highly developed and alloyed steels necessitates increasingly precise and reproducible process control, in particular with respect to narrow allowable temperature and forming windows. In industrial practice, however, open-die forging operations are still frequently performed under manual control. This leads to unavoidable process fluctuations, for example in temperature management, positioning accuracy, and height reduction per pass, which significantly increase the risk of exceeding critical process limits and promote the formation of surface and internal cracks.

To compensate for these uncertainties, forged components are often produced with increased oversize. While this approach improves process robustness, it results in substantially higher material consumption. Given that the starting material can account for more than 50% of the total manufacturing cost of forged components [2], oversizing leads to increased production costs, higher energy demand, and elevated CO2 emissions [3,4]. This contradicts the efforts to minimize material usage and machining through near-net-shape production. Furthermore, approaches known to reduce the risk of cracking, such as applying smaller height reductions per pass or introducing additional reheating steps, are also commonly employed in practice. Although these measures reduce local strain accumulation and thermal gradients, they significantly increase forging time, energy consumption, and overall production costs. Consequently, such approaches are not economically viable for the efficient production of large or complex forged components.

To analyze the risk of cracking and to assess the suitability of alternative process routes, various damage models were developed in the past. However, application in open-die forging is usually difficult because most approaches were originally developed for other types of loading, e.g. sheet metal forming [5], or they do not account to changing load directions like in incremental forming processes [6]. In addition, the approaches are often designed for cold forming, meaning that they do not consider softening mechanisms such as recovery and recrystallisation [7].

Based on these considerations, this work focuses on the calibration and extension of the damage model of effective stresses originally proposed by Lemaitre [8]. Building upon the approach introduced by Rüf et al. [9], the model is adapted for application in open-die forging, as the stress states encountered in warm upsetting processes show strong similarities to those occurring during incremental forging operations. In a first step, the damage model is calibrated using hot tensile tests conducted up to material failure. To enhance the predictive capability of the model under hot forging conditions, the formulation is subsequently extended to incorporate the influence of dynamic recrystallization, which is known to reduce damage during high-temperature deformation [10]. Furthermore, to account for the incremental nature of open-die forging and the associated dwell times between forming steps, the behavior and impact of static recrystallization are experimentally characterized and integrated into the damage formulation. Finally, the extended model is applied within a finite element framework to analyze damage evolution in a representative open-die forging process.

Damage Modeling

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In metal forming processes, material formability is fundamentally limited by the initiation and evolution of damage, ultimately leading to failure. In this context, damage is defined as the nucleation of microvoids and microcracks, as well as their subsequent growth and coalescence during deformation. Progressive damage accumulation eventually results in the formation of macroscopic cracks, which corresponds to the failure of the formed component [11].

For the damage-minimized design and assessment of open-die forging processes, it is essential to reliably predict the evolution of material damage as a function of process parameters. This includes not only the spatial distribution and magnitude of damage but also the initiation of macroscopic cracking with sufficient accuracy. To do so, numerous approaches for describing damage and failure are available in the literature. Most of these approaches are based on stress- and strain-dependent functions, which can be obtained from continuum mechanical descriptions but cannot be directly measured during the forming process. Here, damage models can generally be classified into historyindependent and history-dependent formulations. History-independent approaches evaluate damage solely based on the current stress or strain state and are therefore mainly suitable for simplified limit assessments [12,13]. In contrast, history-dependent approaches consider the forming history and thus enable a more accurate description of damage evolution [14,15]. A further distinction can be made between macromechanical and micromechanical damage models, depending on the type of variables used to describe material damage. Macromechanical models rely on global variables, whereas micromechanical models consider local stress and strain states.

Due to the incremental character of open-die forging, the complex thermo-mechanical boundary conditions, and frequently changing loading directions, the local stress and strain states can vary significantly throughout the workpiece volume. Consequently, history-dependent, micromechanically motivated damage models are particularly well suited for the simulation of opendie forging processes, as they inherently consider both the complete forming history and the local stress state in the evaluation of material damage. Recent publications on damage modeling in metal forming emphasize the importance of such approaches, especially when aiming at predictive simulations under hot forming conditions and in combination with microstructure evolution [7,11,1417].

Model of effective stresses.

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To describe ductile material damage, Lemaitre introduced the forming history-dependent and micromechanically motivated Model of Effective Stresses (MES) [2]. The MES represents a compromise between computational efficiency, practical applicability in terms of parameter calibration, and the number of required input variables. By considering a representative volume element (RVE), the model assumes that, in the presence of material damage D, only the undamaged surface fraction (1−D) of a sectional plane within the RVE is capable of transmitting forces.
For the one-dimensional case, the effective stress σ~eff is defined as:
σ~eff=FA=FA0−AD=σ1−D.

Here F denotes the normal force, A0 the total cross-sectional area, and AD the area fraction occupied by voids due to damage. Accordingly, the damage variable is defined as D=AD/A0 where D=0 describes an undamaged and D=1 describes a failed material state. Assuming isotropic damage, the effective Cauchy stress tensor σ~ij is given by:
σ~ij=σij1−D.

The evolution of damage is described by Lemaitre through the dissipation potential ψ, resulting in a scalar, convex damage evolution law:
D˙=∂ψ∂Y=(YS0)S0·ε¯˙.

In this law S0 is a material parameter, ε¯˙ is the equivalent plastic strain rate, and Y denotes the damage energy release rate. The parameter s0 is a material-specific calibration factor controlling damage sensitivity. As no significant influence of s0 on the model calibration was observed, it was set to s0= 1. To distinguish between tensile and compressive stress states, the stress tensor is decomposed into positive and negative components, yielding in the following description for the energy release rate:
Y=1+v2·E·[⟨σ¯⟩:⟨σ¯⟩(1−D)2+h·⟨−σ¯⟩:⟨−σ¯⟩(1−h·D)2]−vE·[(tr(⟨σ¯⟩)1−D)2+h·(tr(⟨−σ¯⟩)1−h·D)2].

Here v is the Poisson's ratio, E the Young's modulus, σ¯ the true stress tensor, and h a void-closure parameter accounting for the potential reduction of damage under compressive loading. For an accurate representation of damage evolution, h should be close to zero. By comparing simulations with tensile and compression tests, Rüf [9] showed that h should therefore be set to 0.001 .
According to Lemaitre, the material parameter S0 can be approximated by

S0=σ22·E·(1−D)2·dDdε≈σr22·E·(1−D)2·D1cεr(5)

where σeq  is the equivalent stress, D1c the critical damage under uniaxial tension, and εr the elongation at rupture under uniaxial tension. The one-dimensional critical damage and the general rupture criterion Dc are defined as:

D1c=1−σrσu.Dc=D1c·σu2σeq2·τx(6)

Here σu is the ultimate tensile strength, σr the failure stress, and τx the stress triaxiality function [18]. To describe the damage evolution over time (time increment Δt ) the incremental description in Eq. 7 is used:
Di=Di−1+D˙·ΔtDc.

To identify the material parameters required for the MES damage model, hot tensile tests were conducted at IBF using a TA DIL805 quenching and forming dilatometer. Flat tensile specimens of tool steel X155CrVMo12-1 with a thickness of 2.2 mm and a width of 3 mm in the formed section were used. The specimens were inductively heated to the forming temperature and deformed at a constant strain rate of 0.1 s−1 until fracture. The quenching and forming dilatometer enables experiments under vacuum conditions while providing highly precise and reproducible temperature control throughout the test. The experiments were carried out for typical forging temperatures in a temperature range from 800 to 1200∘C. To ensure reproducibility, each test was performed twice. The resulting mean values of ultimate tensile strength σu, failure stress σr, and rupture elongation εr, together with the corresponding damage resistance parameter S0 evaluated for each temperature according to Eq. 5 and 6, are summarized in Table 1. Based on these experimentally determined material properties and the derived S0-values, the MES damage model is fully calibrated for the tool steel X155CrVMo12-1. Within the investigated temperature range, the temperature-dependent parameters are obtained by interpolation between the tabulated values.

Table 1. Results of the warm tensile tests of the tool steel X155CrVMo12-1.

Temperature

Ult. tensile strength

Failure stress

Rupture elongation

Parameter

800 | 170.9 | 67.9 | 38.5 | 0.071
900 | 121.6 | 132.3 | 30.8 | 0.060
1000 | 143.1 | 66.2 | 34.4 | 0.076
1100 | 98.5 | 32.8 | 35.7 | 0.041
1200 | 62.0 | 16.5 | 36.0 | 0.021

Modeling of DRX Kinetics.

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In materials exhibiting low stacking fault energy, such as the cold work tool steel X155CrVMo12-1 investigated in this study, microstructural softening during hot deformation is governed predominantly by recrystallization mechanisms rather than by recovery effects [19]. Recrystallization processes occurring concurrently with plastic deformation are referred as (meta) dynamic recrystallization (DRX), in contrast to static recrystallization (SRX), which takes place during postdeformation holding periods. At the same time, previous investigations have demonstrated that recrystallization contributes to a reduction in material damage during hot forming by effectively resetting critical strain levels and promoting the closure of small voids [10]. Consequently, the incorporation of DRX effects is of particular importance for physically motivated damage modeling in hot forming processes such as open-die forging.

As the MES was originally formulated for cold forming applications and does not account for microstructural softening phenomena, it was extended to incorporate the influence of DRX, following the general approach proposed in [9]. For this purpose, the kinetics of dynamic recrystallization were experimentally determined for the tool steel X155CrVMo12-1 using cylindrical Rastegaev specimens with an initial diameter of 10 mm and a height of 15 mm . The tests were carried out on a Servotest TMTS servo-hydraulic testing machine at strain rates of 0.1 s−1 and 1 s−1 for temperatures of 800∘C, 900∘C,1000∘C,1100∘C, and 1200∘C, with each thermo-mechanical condition being tested twice. Based on the resulting flow curves, the evolution of the dynamically recrystallized fraction was evaluated in accordance with the methodology proposed by Sun et al. [20] and Brüggemann et al.
[21]. For this purpose, the flow curves determined are divided into a portion subject only to recovery (DRV) and a portion softened due to dynamic recrystallization (DRX). Fig. 1 exemplarily illustrates the procedure for a flow curve at 900∘C and a strain rate of 0.1 s−1.

[picture]

Fig. 1. Exemplary determination of the dynamically recrystallized fraction (DRX) according to Sun et al. [20] at a temperature of 900∘C and a strain rate of 0.1 s−1.

Fig. 1. Exemplary determination of the dynamically recrystallized fraction (DRX) according to Sun et al. [20] at a temperature of 900 ∘ C and a strain rate of 0.1 s − 1 .

For each test, the peak stress σp and the corresponding strain εp were first determined from the experimental flow curve. The critical strain for the onset of DRX εc was then estimated by assuming εc=0.8·εp, as indicated in Fig. 1. The dependence of εc on temperature and strain rate over the investigated range was subsequently described as a function of the Zener-Hollomon parameter Z in accordance with Eq. 8.
εc=c1·Zc2 with Z=ε˙·exp(QwR·T)

The DRV portion of the flow curve was obtained by extrapolating the work-hardening behavior of the experimental flow curve beyond the critical strain εc. The DRX portion was then evaluated from the difference between the measured flow curve and the DRV curve, yielding the strain-dependent dynamic recrystallized fraction XDRX (ε). The DRX fractions from all tests, covering all investigated temperatures and strain rates, were finally analyzed in conjunction. The fraction of dynamically recrystallized material XDRX is described by Eq. 9, where the material specific parameters n and k were identified by non-linear least-squares fitting of XDRX.

XDRX=1−exp(−k·(ε−εcεc)n)(9)

The material-specific parameters describing the DRX kinetics of X155CrVMo12−1 within the investigated temperature and strain rate range are summarized in Table 2.

Table 2. Determined material parameters of DRX kinetics for the tool steel X155CrVMo12-1.

Activation energy mathematical formula

Parameter mathematical formula

Parameter mathematical formula

Parameter superscript number

Parameter superscript number

232.212 | 0.47077 | 2.094 | 0.179 | 0.0093

Modeling of SRX Kinetics.

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Due to the incremental nature of open-die forging and the associated frequent dwell times between the forming steps at elevated temperatures during every pass, the microstructure kinetics of the process are also strongly driven by static effects. To account for the influence of those static recrystallization effects during these pause times, the SRX kinetics were determined by means of stress relaxation experiment.

Therefore, additional hot compression tests were carried out on cylindrical specimens of X155CrVMo12-1 with an initial diameter of 5 mm and a height of 10 mm using the IBF quenching
and forming dilatometer TA DIL 805. The compression tests were conducted at 800∘C,900∘C,1000∘C,1100∘C and 1200∘C with different height reductions representing true strains of 0.10,0.125, and 0.15 in the sample. The applied height reduction was selected for each temperature such that the imposed strain remained below the previously determined critical strain, ensuring that no dynamic recrystallization effects occurred. After reaching the desired deformation, the compression stroke was held constant and the resulting stress relaxation was measured. Based on the obtained stress relaxation curves, the SRX kinetics were subsequently determined as a function of temperature and applied strain according to Karjalainen [22]. For this purpose, the stress relaxation curves were divided into three distinct regions (see Fig. 2): In region 1, creep processes initially dominate the stress relaxation behavior. This is followed by region 2, in which SRX takes place. After completion of SRX, recovery processes are observed in region 3.

[picture]

Fig. 2. Stress relaxation curve with three characteristic regions and static recrystallized fraction at 1000∘C.

Fig. 2. Stress relaxation curve with three characteristic regions and static recrystallized fraction at 1000 ∘ C .

By fitting linear functions to regions 1 and 3 in the log(t)-stress representation the stresses of the purely unrecrystallized and fully recrystallized states are obtained. The respective parameters describing the linear functions are given by the y-axis intercept σ0 and the slope α with indices 1 for the first and 2 for the third region of stress relaxation. The statically recrystallized fraction X at any time within region 2 is then determined individually for each temperature and forming condition using a linear mixture rule based on the measured stress σ :

X=(σ01−α1·log(t))−σ(σ01−σ02)−(α1−α2)·log(t)(10)

For each temperature and strain level, the resulting statically recrystallized fraction X were subsequently fitted with the JMAK-type relation given in Eq. 11, providing an individual description of the SRX kinetics in terms of the Avrami exponent n and the half-life time t50, which is defined as the time required for 50% static recrystallization.

XSRX=1−exp(ln(0.5)·(tt50)n)(11)

To enable a generalized description of SRX kinetics over a broad range of thermo-mechanical conditions, the experimentally determined Avrami exponents were averaged. The temperature and strain dependence of the half-life time t50 was described using Eq. 12 [23]:

t50=A·εq·exp(QR·T)(12)

The activation energy Q and the material-specific parameters A and q in Eq. 12 were obtained from logarithmic plots of the half-life time as a function of temperature and strain by linear fitting using a non-linear least-squares procedure. The corresponding parameter values are summarized in Table 3.

Table 3. Determined material parameters of SRX kinetics for the tool steel X155CrVMo12-1.

Activation energy mathematical formula

Avrami exponent mathematical formula

Parameter mathematical formula

Parameter mathematical formula

114.010 | 0.5553 | 0.00002335 | -0.7228

Damage development due to recrystallization effects.

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Using the model parameters identified in the previous sections, the fractions of dynamically and statically recrystallized microstructure during open-die forging can be predicted for the tool steel X155CrVMo12-1. Nevertheless, a constitutive link between microstructural evolution and the development of material damage must be established.

The effect of dynamic recrystallization on damage evolution is incorporated using the formulation proposed by Abu Al-Rub et al. [24], which has also been employed in the work of Rüf et al. [9]. Unlike the original formulation, the present approach was extended to account for the dynamically recrystallized fraction in an incremental manner. As a result, the damage parameter defined in Eq. 7 is reformulated as a function of the dynamically recrystallized fraction ΔXDRX :

Di=Di−1+D˙·ΔtDc·(1−ΔXDRX).(13)

In contrast to dynamic recrystallization, no general constitutive approaches are available to describe the influence of static recrystallization on damage evolution. Consequently, an experimental strategy, based on the work of Heiser et al. [25], was employed. The objective of this methodology is to describe the evolution of material damage by means of the void area fraction as a function of the statically recrystallized fraction.

To this end, cylindrical tensile specimens of X155CrVMo12−1 with an initial diameter of 10 mm and a measure length of 50 mm were manufactured and tested at room temperature in accordance with DIN EN ISO 6892-1 [26] on a Zwick Z100 tensile testing machine up to uniform elongation. This procedure ensures that a sufficient and homogeneous pre-damage state is introduced into the specimens under tensile loading, enabling microscopic investigation of damage evolution. From the deformed sections of the tensile specimen, cylindrical compression samples with an initial diameter of 5 mm and a height of 10 mm were subsequently extracted. These specimens were subjected to single-step compression tests using the quenching and forming dilatometer TA DIL 805. The deformation parameters were selected according to the SRX kinetics determined in the previous section to achieve statically recrystallized fractions of 0%,50%, and 95%. Table 4 provides an overview of the specific process parameters.

Table 4. Determined process parameters to archive defined statically recrystallized fractions.

Temperature [°C] | Holding time [s]
| 0% SRX | 50% SRX | 95% SRX
800 | 0 | 2.3 | 28.1
900 | 0 | 3.5 | 42
1000 | 0 | 4.9 | 59
1100 | 0 | 6.5 | 78.9

After deformation, the samples were sectioned in height, prepared metallographically and analyzed using a Keyence VHX-7000 digital microscope. High-resolution 4 K imaging combined with advanced image processing enabled automated detection and quantification of voids based on brightness threshold. Fig. 3 shows an exemplary microscopic image of a dilatometer specimen with no statically recrystallized fraction.

[picture]

Fig. 3. Microscopic image of a formed sample. Left: Automatic void detection. Right: Close-up of a void.

Fig. 3. Microscopic image of a formed sample. Left: Automatic void detection. Right: Close-up of a void.

Fig. 3, right shows that the voids are clearly visible as dark features in the microstructure. By applying a brightness threshold, voids can be automatically identified, marked, counted, and measured (see Fig. 3, left). For each specimen, a square evaluation area with an edge length of approx. 2500μ m was analyzed. The selection of a sufficiently large measurement area ensures that the determined void area fraction reflects the overall damage state of the material rather than local microstructural variations. Based on these analyses, the void area fraction was determined for all experiments. Fig. 4 summarizes the averaged void area fractions as a function of the statically recrystallized fraction, revealing a clear decrease in void area fraction with increasing static recrystallization.

[picture]

Fig. 4. Void area fraction as a function of the static recrystallized fraction.

Fig. 4. Void area fraction as a function of the static recrystallized fraction.

Fig. 4 shows that the average void area fraction of approximately 0.048% was reduced by mSRX=25.6% to about 0.035% at near-complete static recrystallization.

These results confirm a direct relationship between the statically recrystallized microstructural fraction and the void area fraction, and thus material damage. With increasing statically recrystallized fraction, a significant healing of voids occurs, leading to a substantial decrease in the overall damage level. To account for this effect in the damage model, the damage variable Di in Eq. 13 is reduced in the presence of static recrystallization according to the statically recrystallized fraction and the experimentally determined void reduction factor mSRX. The resulting damage formulation including static recrystallization is given by:

DSRX, corr =Di+(1−ΔXSRX·mSRX)(14)

Experimental Validation

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The conducted forging trials served to experimentally validate the calibrated and extended damage model. The objective was to forge a demonstrator component in which different damage states could be deliberately induced, including regions exhibiting pronounced cracking as well as regions showing no or only incipient cracks. In parallel, the identical forging process was simulated using the calibrated and extended damage model, enabling a direct comparison between experimental observations and numerical predictions.

The initial workpiece geometry was a rectangular block measuring 150×150×800 mm3, which was forged into a stepped rectangular shape with final cross-sections of 115×115 mm2 and 95×95mm2. Forging was performed at 1200∘C using a relative height reduction of 15% and a bite ratio of 0.5 . All strokes were applied without bite offset and in a purely feeding manner. The resulting forging plan is shown in Table 5.

Table 5. Forging plan for experimental validation.

Pass [-] | Height reduction [%] | Initial height [mm] | Final height [mm] | Bite length [mm] | Bite ratio [-] | Strokes [-]
1 | 15 | 150 | 128 | 75 | 0.5 | 7
2 | 14.5 | 157 | 135 | 79 | 0.5 | 7
3 | 15 | 135 | 114 | 67 | 0.5 | 9
4 | 14.5 | 141 | 121 | 71 | 0.5 | 10
5 | 7 | 121 | 112 | 60 | 0.5 | 13
6 | 6.8 | 123 | 115 | 62 | 0.5 | 13
7 | 15 | 115 | 98 | 58 | 0.5 | 5
8 | 14.5 | 121 | 103 | 60 | 0.5 | 6
9 | 11.6 | 103 | 91 | 52 | 0.5 | 7
10 | 11.3 | 107 | 95 | 54 | 0.5 | 8

The forging plan consists of ten passes executed within a single heat, with the first six passes applied over the full length of the block and the remaining four passes used to form the step over half the block length (see Fig. 5).

The experimental trials were conducted at the IBF forging facility, which combines a 630-ton hydraulic forging press with a six-axis hydraulic heavy-duty robot. This setup enables industrially relevant forming conditions as well as highly reproducible workpiece positioning. Ultrasonically tested blocks free of reportable defects according to EN 10228-4 [27] were used as starting material to exclude significant pre-damage. Prior to forging, the blocks were heated to forging temperature at 1200∘C in a gas furnace and held for 1.5 hours to ensure temperature homogeneity before being forged according to the defined forging plan. The forging was carried out using two flat dies with a width of 200 mm and a radius of 20 mm . During forging, the heavy-duty robot and the forging press operated in automatic mode, ensuring high repeat accuracy of the strokes, as only initial positioning was necessary at the start of each pass.

The corresponding numerical simulations were performed using QForm UK 11.0.2 in explicit mode. The simulation model included the forging block, two flat dies identical to the real forging press, and a virtual manipulator for workpiece positioning. Tetrahedral finite elements were used in combination with an adaptive meshing strategy, resulting in up to 117,000 elements in highly deformed regions. The plastic material behavior was described using the experimentally determined flow curves obtained from the DRX investigations, while additional temperature-dependent material properties were taken from literature [28]. This includes thermal conductivity, density, elastic modulus and specific heat capacity. The dies were modeled as rigid bodies at 400∘C, with a dieworkpiece heat transfer coefficient of 30,000 W/m2 K and a Coulomb friction coefficient of 0.3 . Heat exchange with the environment was considered using an ambient temperature of 20∘C and an airworkpiece heat transfer coefficient of 30 W/m2 K. Adaptive meshing was employed to ensure sufficient resolution in highly deformed regions. The extended damage model, as described by Eq. 3-

14, was implemented via a Lua-based user subroutine, which received stress, temperature, and damage-related state variables from the FE simulation at each time increment and computed the corresponding damage evolution.

Fig. 5 presents the results of the validation forging experiments. In addition to the experimental forging results, the figure also includes the corresponding simulation results obtained using the extended damage model (Fig. 5, bottom).

[picture]

Fig. 5. Experimental and simulation validation. Top: Result of the forging experiment with crack visualization. Bottom: Simulation result with damage model.

Fig. 5. Experimental and simulation validation. Top: Result of the forging experiment with crack visualization. Bottom: Simulation result with damage model.

The demonstrator component exhibits two clearly distinguishable damage regions in which pronounced cracking was intentionally induced. In the first forged region with the larger cross-section (115×115 mm2), clear edge cracks and locally initiated surface cracks are observed. In contrast, the second forged region with the smaller cross-section ( 95×95 mm2 ) shows extensive surface and edge cracking with significantly greater crack depth.

The numerical results demonstrate that the extended damage model is capable of reproducing the dominant damage mechanisms observed during the forging process. In the first step region, the simulation predicts distinct damage maxima at the workpiece edges, which correspond to the experimentally observed crack locations (Fig. 5, marking 1). However, the model does not fully capture the initiation of isolated surface cracks in this region, as the calculated damage values remain below the critical threshold of D=1 (Fig. 5, marking 2). This deviation is likely caused by small variations in the manual positioning of the initial forging stroke, which may result in an unintended overlap of die edges in subsequent strokes and thereby promote localized damage accumulation not represented in the idealized simulation setup. In the second forged region, the damage model predicts critical damage values of D=1 over large areas of the side surfaces and edges of the workpiece, which is confirmed by the occurrence of cracks in the experimental trials (Fig. 5, marking 3). Furthermore, the simulation reveals a damage zone extending from the transition between the second and first step toward the workpiece center and head. This arrow-shaped damage zone is reflected in the experimental forging results by diagonally oriented surface cracks (Fig. 5, marking 4).

Conclusion and Outlook

The original version of this paper is available on https://www.scientific.net/MSF.1183.81.pdf

This work presented an extended damage modeling framework tailored to the specific conditions of open-die forging. Building on the Lemaitre damage model, the formulation was enhanced to include the effects of dynamic and static recrystallization, thereby capturing essential microstructural
mechanisms influencing damage accumulation and healing at elevated temperatures. The incremental nature of the process and the presence of dwell times were explicitly addressed.

The required material parameters were identified through a comprehensive experimental program. Hot tensile tests conducted at multiple temperatures were used to determine the parameters of the base Lemaitre damage model. The dynamic recrystallization behavior was characterized by hot compression tests performed at different temperatures and strain rates, while static recrystallization kinetics were derived from stress relaxation experiments carried out over a relevant temperature range. The effect of static recrystallization on damage evolution was further investigated by combining tensile and compression tests with detailed metallographic analyses. These investigations demonstrated that static recrystallization has a pronounced healing effect on existing damage: a nearly complete static recrystallization resulted in a reduction of the void area fraction by approximately 25.6 %, clearly confirming the damage-mitigating capability of recrystallization processes.

The damage model was implemented into a finite element framework and validated by open-die forging experiments on a demonstrator component. The simulations showed good agreement with experimentally observed damage and crack locations, confirming the model's ability to capture critical damage zones and characteristic damage patterns under industrially relevant conditions.

Future work will focus on examining the constitutive description of SRX-induced damage healing in more detail by means of dedicated numerical case studies and corresponding experiments, in order to explicitly validate the proposed SRX-damage coupling. Furthermore, the influence of individual process parameters on material damage during open-die forging will be systematically investigated. By analyzing the effects of parameters such as forging temperature, height reduction, bite ratio, dwell time, and tool geometry, critical process conditions can be identified. This will enable the development of damage-minimized forging strategies and support the reliable processing of demanding alloys, ultimately contributing to improved component quality and reduced scrap rates.

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The original version of this paper is available on https://www.scientific.net/MSF.1183.81.pdf

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The original version of this eBook is available on https://www.scientific.net/book/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 93-105

doi: 10.4028/p-K6OYoi

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

Submitted:
2026-01-20

Revised:
2026-02-17

Accepted:
2026-02-25

Online:
2026-04-13

Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

The original version of this paper is available on https://www.scientific.net/MSF.1183.93.pdf

Aratz Barandiaran 1,a*, Lander Galdos 1, b, David Abedul 1,c and Julen Agirre 1, d

¹Mechanics and Industrial Production Department, Mondragon Unibertsitatea, Loramendi 4, 20500 Mondragon, Spain

a*aratz.barandiaran@alumni.mondragon.edu, b  lgaldos@mondragon.edu, c  dabedul@mondragon.edu, djagirreb@mondragon.edu

Keywords: cold forging, 42 CrMoS 4 , constitutive modelling, ductile fracture.

Abstract

This work analyses the influence of batch-to-batch variability on both strain hardening and ductile fracture behaviour of a 42 CrMoS 4 steel under cold forging conditions. Mechanical testing combined with full-field strain measurements and finite element simulations is used to characterise material response and fracture under different stress states. Batch-dependent hardening laws are identified, and ductile fracture initiation is described using the Hosford-Coulomb criterion, calibrated independently for each material batch. The identified fracture strains and fracture response exhibit a measurable variability between batches, even for similar stress-state conditions. The results provide quantitative evidence of batch-dependent material behaviour relevant for forming simulations.

Introduction

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Cold forging is widely used for the production of high-performance mechanical components, where reliable prediction of material flow, forming forces and failure is essential. Finite Element Method (FEM) simulations are routinely employed to support process design and optimization; however, their accuracy strongly depends on the proper calibration of constitutive models describing the mechanical response of the material.

Under cold forging conditions, the mechanical response of metallic materials is governed by strain hardening, while ductile fracture represents a critical failure mode that must be avoided to ensure process robustness. Plastic flow is commonly described using constitutive laws calibrated from mechanical testing [1], while stress-state dependent fracture criteria have been shown to improve failure prediction under complex loading conditions [2]. The combined effect of stress triaxiality and Lode angle parameter plays a key role in ductile fracture initiation under multiaxial stress states [3]. Consequently, hybrid experimental-numerical approaches combining mechanical testing, full-field strain measurements and FEM simulations are increasingly used to identify both hardening and fracture parameters [4].

Despite these advances, industrial simulations are typically based on a single representative material behaviour for a given steel grade [5]. However, batch-to-batch variability related to differences in chemical composition, microstructure and processing history may lead to measurable variations in mechanical response, even within the same material designation [6]. Such variability affects both the identification of strain hardening behaviour and the calibration and transferability of ductile fracture models, becoming particularly relevant in digital twin and model-based process control applications, where predictive accuracy is required despite inherent material scatter.

Ductile fracture tests generally exhibit non-proportional loading paths, with evolving stress triaxiality and Lode angle parameter during deformation. For modelling simplicity, a proportional loading assumption is commonly adopted, using mean stress-state approaches based on averaged values up to fracture for the identification of fracture initiation criteria.

This work investigates the influence of raw material variability on strain hardening and ductile fracture behaviour of a 42CrMoS4 steel. Five industrial batches were characterised through tensile and compression tests, complemented by metallographic analysis and hardness measurements, to identify batch-dependent strain hardening behaviour. The hardening laws were subsequently refined using experimental-numerical calibration based on fracture tests. Ductile fracture behaviour was
analysed using Notched (NT), Plane Strain (PS) and Shear (SH) specimens, combining experimental testing, Digital Image Correlation (DIC) and FEM simulations. Average stress triaxiality and Lode angle parameter at fracture were used to calibrate a Hosford-Coulomb fracture initiation model based on a proportional mean stress-state approach. The impact of batch-to-batch variability on fracture modelling in cold forging simulations is finally discussed.

Experimental Procedure

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The investigated material was a 42CrMoS4 steel supplied as industrial cylindrical billets for cold forming, with a diameter of ∅25 mm. Five industrial batches (B1-B5), originating from different manufacturers and different heats, were analysed to assess batch-to-batch variability within the same steel grade. All batches were investigated in the as-received condition and characterised in terms of chemical composition, microstructure and hardness. The chemical composition of each batch was obtained from the corresponding material certificates and is reported in Table 1. Minor variations in alloying elements were observed among batches, which may contribute to differences in microstructure and mechanical response and support the batch-to-batch comparison discussed in the following sections.

Table 1. Chemical composition of the investigated 42 CrMoS 4 batches (wt.%).

| C | Mn | Si | Cr | Mo | P | S | Al
B1 | 0.420 | 0.790 | 0.170 | 0.978 | 0.173 | 0.012 | 0.022 | 0.023
B2 | 0.433 | 0.815 | 0.162 | 0.991 | 0.175 | 0.014 | 0.024 | 0.025
B3 | 0.433 | 0.752 | 0.181 | 1.130 | 0.169 | 0.010 | 0.026 | -
B4 | 0.430 | 0.797 | 0.163 | 0.994 | 0.174 | 0.014 | 0.024 | 0.024
B5 | 0.420 | 0.750 | 0.200 | 1.060 | 0.174 | 0.011 | 0.026 | 0.022
42CrMoS4 | 0.427 ± 0.007 | 0.781 ± 0.029 | 0.175 ± 0.016 | 1.031 ± 0.064 | 0.173 ± 0.002 | 0.012 ± 0.002 | 0.025 ± 0.002 | 0.023 ± 0.001

Metallographic analyses were performed on transverse sections of the cylindrical billets to characterise the initial microstructure and identify possible differences between batches. Samples were prepared using standard grinding and polishing procedures up to 1μ m and etched with Nital. Optical microscopy observations were conducted at the same magnification for all batches to allow a consistent comparison of grain morphology and phase distribution. Representative micrographs are shown in Fig. 3.

Vickers micro-hardness measurements were performed on the same transverse sections to evaluate hardness distributions and batch-to-batch variability. Prior to testing, the specimen surfaces were prepared following standard metallographic procedures, with a final polishing step using a 1μ m diamond suspension. Measurements were carried out using a Vickers micro-hardness tester (Qness Q60 A+ EVO) with an applied load of 0.5 kgf (HV0.5) and a dwell time of 12 s . Multiple indentations were performed along a diagonal path across the section, as illustrated in Fig. 4(b).

Mechanical testing was conducted to characterise both strain hardening and fracture behaviour. All specimens were manufactured by wire electro-discharge machining (EDM). Uniaxial tension (Fig. 1 (a)) and uniaxial compression (Fig. 1 (b)) tests were used to identify the hardening response, while NT (Fig. 1 (c)), PS (Fig. 1 (d)) and SH (Fig. 1 (e)) specimens were employed to investigate fracture under different stress states. Uniaxial tension tests were performed on standard flat specimens with a gauge width of 6 mm and a thickness of 1.5 mm , following ASTM E8/E8M-04 recommendations [7], under strain-controlled conditions at a nominal strain rate of 0.002 s−1. Uniaxial compression tests were carried out under comparable quasi-static conditions, following the guidelines of ASTM E9 [8], to extend the hardening characterisation to higher plastic strain levels.

Fracture tests were conducted under displacement control at a constant crosshead speed of 0.015 mm/s. Extensometers with gauge lengths of 60 mm and 15 mm were used to measure global
displacement for the NT and PS/SH specimens, respectively (blue dots in Fig. 1). The geometries of all the tested specimens are shown in Fig. 1. Force and displacement were continuously recorded during the tests. At least three repetitions were performed for each specimen geometry to ensure repeatability, except for the uniaxial tension tests, for which only two repetitions were conducted due to limited material availability.

[picture]

Fig. 1. Specimen geometries used for mechanical testing: (a) Uniaxial tension, (b) Uniaxial compression, (c) NT, (d) PS and (e) SH.

Fig. 1. Specimen geometries used for mechanical testing: (a) Uniaxial tension, (b) Uniaxial compression, (c) NT, (d) PS and (e) SH.

Force measurements were directly acquired from a Universal Testing Machine (UTM) equipped with a 100 kN load cell and recorded through a National Instruments USB-6001 data acquisition system. The force signal was sampled at a frequency six times higher than that used for DIC image acquisition.

Full-field displacement and strain measurements were obtained by DIC. Specimen surfaces were prepared with a random black speckle pattern on a white background. Images were acquired using a JAI GO-5000M-USB CCD camera ( 2560×2048 pixels) and processed with GOM Correlate 2019 to compute displacement and strain fields up to fracture (see Fig. 2(a)). The acquisition frequency was adjusted for each specimen geometry to record approximately 500 images per test, resulting in sampling rates of 2 Hz,5 Hz and 3 Hz for the NT, PS and SH tests, respectively. Local strains were monitored using virtual extensometers (black dots in Fig. 1) with a gauge length of 5 mm for the NT and PS specimens, while three local extensometers with a gauge length of 1 mm were used for the SH specimens to track local deformation and rotation.

For uniaxial tension tests, the extensometer signal was used to determine the macroscopic strain within the gauge length following ASTM E8/E8M-04 recommendations. Experimental data were converted into true stress-true strain curves and used, together with uniaxial compression tests, for the identification of batch-dependent strain hardening behaviour.

Fracture initiation was defined as the onset of the first visible crack, associated with a sudden drop in the recorded force, and was consistently used to define the reference fracture point for all specimen geometries. Post-mortem fractographic analyses were performed on fractured specimens from a representative batch (B1) to qualitatively assess fracture mechanisms associated with the different specimen geometries and stress states. Fracture surfaces were examined using a Scanning Electron Microscope (SEM), FEI Nova NanoSEM 450, following established approaches reported in the literature [9]. These experimental results constitute the basis for the numerical analyses and fracture modelling presented in the following sections.

Experimental Results

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The strain hardening behaviour of the five batches was identified from uniaxial tension and uniaxial compression tests, combined using a plastic work equivalence approach to extend the strain range [10], and fitted with the simplified Hensel-Spittel constitutive law [11]. Fig. 2(b) compares the fitted true stress-true strain curves for each batch, showing a similar overall hardening trend but noticeable differences in flow stress level and hardening response between batches.

To quantify the observed variability, selected mechanical properties were extracted for each batch and are summarised in Table 2. Yield strength (YS), ultimate tensile strength (UTS) and elongation at fracture ( A% ) were obtained from uniaxial tension tests while average hardness values (HV0.5) were derived from micro-hardness measurements. In addition, true stress values at ε=0.4 and ε=0.8 were extracted from the fitted hardening curves as representative points of the medium and high plastic strain regimes relevant for subsequent fracture modelling, as indicated in Fig. 2(b). The last row of Table 2 reports the average value of each property across the five batches. The simplified Hensel-Spittel constitutive law is expressed as Eq. 1:

σ=A1(ε+εb0)m2(1)

where σ is the equivalent flow stress, ε is the equivalent plastic strain, A1 and m2 are material parameters, and εb0 is a reference plastic strain representing the initial hardening state of the material and avoiding singular behaviour at zero plastic strain. The parameters of the hardening law were identified separately for each batch through an inverse fitting procedure based on the combined uniaxial tension and compression data.

[picture]

Fig. 2. (a) Setup for the experimental fracture tests (b) Comparison of fitted true stress-true strain hardening curves for the investigated 42 CrMoS 4 batches.

Fig. 2. (a) Setup for the experimental fracture tests (b) Comparison of fitted true stress-true strain hardening curves for the investigated 42 CrMoS 4 batches.

Metallographic analyses were performed on transverse sections of the five batches to qualitatively assess microstructural differences. Representative optical micrographs are shown in Fig. 3. All batches were supplied in the annealed condition and exhibit a ferritic-pearlitic microstructure at the investigated magnification. Minor variations in pearlite distribution and colony arrangement were observed between batches; however, no pronounced microstructural features were identified that could alone explain the differences in strain hardening behaviour. This indicates that the observed mechanical variability is likely associated with combined effects of microstructure and processing history.

[picture]

Fig. 3. Optical micrographs showing the transversal microstructure of the different 42 CrMoS 4 batches, acquired at the same magnification.

Fig. 3. Optical micrographs showing the transversal microstructure of the different 42 CrMoS 4 batches, acquired at the same magnification.

Vickers micro-hardness measurements (HV0.5) were performed on transverse sections of all batches. Hardness profiles obtained across the section are shown in Fig. 4(a), together with the indentation layout illustrated in Fig. 4(b). For each batch, multiple indentations were carried out along a diagonal path across the section to obtain representative hardness distributions. The measured hardness profiles exhibit a similar overall trend for all batches, with average values close to 200 HV0.5 and limited scatter, indicating a relatively homogeneous material condition at the investigated scale. No pronounced hardness gradients were observed across the section. Average hardness values for each batch are reported in Table 2. Although hardness measurements alone cannot fully explain the differences observed in the fitted strain hardening behaviour, the experimental data show an approximately linear correlation between hardness and the ultimate tensile strength (UTS). This indicates that the base hardness of the material is related to the observed variations in the strain hardening response, although the overall differences remain relatively limited.

[picture]

Fig. 4. (a) Vickers micro-hardness (HV0.5) profiles measured across the transversal section of the investigated batches. (b) Representative indentation layout adopted for the micro-hardness measurements.

Fig. 4. (a) Vickers micro-hardness (HV0.5) profiles measured across the transversal section of the investigated batches. (b) Representative indentation layout adopted for the micro-hardness measurements.

Table 2. Quantification of batch-to-batch variability based on tensile properties, micro-hardness and fitted hardening parameters for 42 CrMoS 4 .

| YS [MPa] | UTS [MPa] | A% [-] | HV 0.5 avg | σ (ε = 0.4) [MPa] | σ (ε = 0.8) [MPa]
B1* | 540 ± 0.0 | 598 ± 0.0 | 22.6 ± 0.0 | 200 ± 7.6 | 831 | 934
B2 | 491 ± 5.6 | 619 ± 0.8 | 26.6 ± 3.7 | 203 ± 7.5 | 842 | 925
B3 | 487 ± 6.2 | 603 ± 1.0 | 25.6 ± 0.8 | 202 ± 8.6 | 834 | 928
B4 | 512 ± 0.9 | 578 ± 1.8 | 23.7 ± 0.2 | 196 ± 8.3 | 802 | 903
B5 | 484 ± 9.9 | 570 ± 3.4 | 26.2 ± 0.0 | 195 ± 8.9 | 784 | 873
42CrMoS4 | 503 ± 24.0 | 593 ± 19.7 | 24.9 ± 1.7 | 199 ± 3.2 | 818.6 ± 23.4 | 912.6 ± 25.9

*Uniaxial tension results are based on a single valid experimental test.
Fractographic analyses were performed on fractured specimens from a representative batch (B1) to qualitatively assess fracture mechanisms under different stress states imposed by the NT, PS and SH geometries. Observations were conducted by SEM at a magnification of 6500×. Representative fractographic images are shown in Fig. 5.

For the NT specimens (Fig. 5(a)), the fracture surface exhibits a ductile morphology dominated by equiaxed dimples, indicating void nucleation, growth and coalescence under a tension-dominated stress state with elevated triaxiality. PS specimens (Fig. 5(b)) show a similar ductile mechanism; however, the dimples appear more elongated and preferentially oriented, reflecting the constrained plastic deformation associated with plane strain conditions.

In contrast, the fracture surface of the SH specimens (Fig. 5(c))) is characterized by flat facets and localized shear features, with limited evidence of void growth. This morphology indicates a sheardominated fracture mechanism, distinctly different from the tension-driven cases. Overall, these observations highlight the strong influence of the stress state on fracture mechanisms and are consistent with the stress-state dependent fracture behaviour identified in the numerical analysis.

[picture]

Fig. 5. SEM images of the fracture surfaces of (a) NT, (b) PS and (c) SH specimens, acquired at a magnification of 6500x.

Fig. 5. SEM images of the fracture surfaces of (a) NT, (b) PS and (c) SH specimens, acquired at a magnification of 6500x.

Numerical Results

The original version of this paper is available on https://www.scientific.net/MSF.1183.93.pdf

Based on the experimental observations, finite element simulations were performed to reproduce the fracture tests and determine the fracture strain under different loading conditions. All experimentally investigated NT, PS and SH specimen geometries were simulated for the different material batches. The simulations served to validate and, where necessary, refine the previously identified hardening model, and to provide a numerical framework for extracting the stress-state variables required for fracture analysis.

The simulations were carried out using the commercial software FORGE NxT 4.1. Geometric symmetries were exploited to reduce computational cost, with one-eighth of the geometry modelled for the NT and PS specimens and one-half for the SH specimens. The meshes consisted of linear tetrahedral elements with an enriched velocity field, using a characteristic element size of 0.1 mm in the region of interest. This mesh density was selected to ensure an adequate description of strain localization prior to fracture (see Fig. 6.).

[picture]

Fig. 6. Finite element meshes used for the numerical simulations of the fracture test geometries: (a) NT specimen, (b) PS specimen, (c) SH specimen and (d) detailed view of the SH specimen showing the locally refined mesh in the fracture region with an element size of 0.1 mm .

Fig. 6. Finite element meshes used for the numerical simulations of the fracture test geometries: (a) NT specimen, (b) PS specimen, (c) SH specimen and (d) detailed view of the SH specimen showing the locally refined mesh in the fracture region with an element size of 0.1 mm .

Material behaviour was described using batch-dependent hardening laws identified from uniaxial tension and uniaxial compression tests and modelled with the simplified Hensel-Spittel constitutive law. The initial parameters were obtained by combining data from both tests through a plastic work equivalence approach and subsequently refined by calibrating numerical simulations against the experimental force-displacement response of the NT specimens.

The NT geometry was selected for this calibration due to its stable fracture behaviour and intermediate stress state. Parameter optimisation was performed independently for each batch by minimising the discrepancy between experimental and simulated force-displacement curves using the objective function defined in Eq. 2. The resulting optimised hardening parameters are summarised in Table 3.

Xh=∑(Fexp−Fsim)2.(2)

where Xh represents the minimized error, Fexp  is the experimentally measured force, and Fsim  is the force predicted by FEM. The optimization procedure was carried out independently for each batch.

Table 3. Optimized parameters of the Hensel-Spittel hardening law identified for the five batches.

A₁ | m₂ | εbo | A₁ | m₂ | εbo
B1 | 864.8 | 0.1848 | 0.05661 | B4 | 837.1 | 0.1877 | 0.05509
B2 | 856.6 | 0.1411 | 0.01842 | B5 | 854.4 | 0.1631 | 0.03187
B3 | 860.9 | 0.1611 | 0.02675 |  |  |  |

To verify the calibration of the batch-dependent material models, numerical simulations of the NT, PS and SH specimens were compared with the corresponding experimental results. Model accuracy was assessed by comparing global force-displacement with the experimental measurements.

Local strain measurements were obtained from DIC by defining two virtual extensometers aligned with the Loading Direction (LD) and the Transverse Direction (TD). In the case of the SH specimens, three local virtual extensometers with a gauge length of 1 mm were used to monitor the rotation and local deformation during the test.

A representative comparison between experimental and numerical force-displacement curves and local strain measurements for the NT, PS and SH specimens is provided in Fig. 7. The comparisons correspond to the NT geometry for batch 3 (NT3), the PS geometry for batch 1 (PS1), and the SH geometry for batch 5 (SH5), selected as representative cases. This verification step ensured that the numerical model reproduces the experimentally observed mechanical response up to fracture for the different specimen geometries and batches.

[picture]

Fig. 7. Comparison of force-displacement curves and local extensometer measurements obtained experimentally (dots) and numerically (lines) for (a) NT3, (b) PS1, (c) SH5 specimens.

Fig. 7. Comparison of force-displacement curves and local extensometer measurements obtained experimentally (dots) and numerically (lines) for (a) NT3, (b) PS1, (c) SH5 specimens.

Fig. 8 presents the true strain fields in the LD, in the TD, as well as the equivalent strain ( εeq=2/3 dp:dp ), obtained from the DIC analysis at the moment of fracture for the NT, PS and SH specimens of the B 2 . These measurements provide valuable information regarding strain localization and the fracture initiation zones. For the NT and PS specimens (see Fig. 8 (a,b,c)), strain localization is observed at the centre of the specimen neck. The corresponding DIC results show that, in the PS specimen, the strain in the TD (see Fig. 8 (c)) is negligible when compared to the strain in the loading direction LD (see Fig. 8 (b)), confirming that the fracture initiation zone is subjected to plane strain conditions. In contrast, the DIC measurements obtained for the SH specimens indicate that strain localization occurs in the region covered by virtual extensometers, leading to peak strain values close to the specimen edge, as shown in Fig. 8 (c).

[picture]

Fig. 8. Digital image correlation (DIC) analysis at the onset of fracture, showing equivalent strain contours for the (a) NT2 and (c) SH2 specimens and (b) LD and (d) TD strain distributions for the PS2 specimen.

Fig. 8. Digital image correlation (DIC) analysis at the onset of fracture, showing equivalent strain contours for the (a) NT2 and (c) SH2 specimens and (b) LD and (d) TD strain distributions for the PS2 specimen.

The initiation of ductile fracture is strongly influenced by the stress state experienced by the material during deformation. For isotropic materials, the stress state can be conveniently described in terms of the stress triaxiality, η, and the Lode angle parameter, θ¯, which account for the effects of hydrostatic stress and the third invariant of the deviatoric stress tensor, respectively.

The stress triaxiality is defined as the ratio between the mean stress and the von Mises equivalent stress (Eq. 3), where σm=13tr(σ) is the mean (hydrostatic) stress and σeq is the von Mises equivalent stress. The influence of the third invariant of the stress tensor is described by the normalized Lode angle parameter θ¯, defined in Eq. 4, where s is the deviatoric stress-tensor.

η=σmσeqθ¯=1−(2π)acos(272det( s)σeq3)

(3)(4)

In the present work, ductile fracture initiation was modelled using the Hosford-Coulomb (HC) fracture criterion, which describes the fracture strain as a function of stress triaxiality and Lode angle parameter. This model was originally proposed by Mohr and Marcadet [4] and has been shown to accurately capture ductile fracture over a wide range of stress states. According to the HC formulation, fracture initiation occurs when the accumulated equivalent plastic strain reaches a critical value εf, given by Eq. 5:

εfHC(η,θ¯)=b(1+c([12(|f1−f2|m+|f2−f3|m+|f3−f1|m)]1 m+c(2η+f1+f3)))1a.(5)

where a,b,c and m are material parameters, and the functions fi depend on the Lode angle parameter according to Eqs. 6-8:

f1(θ¯)=23cos[π6(1−θ¯)]f2(θ¯)=23cos[π6(3+θ¯)]f3(θ¯)=−23cos[π6(1+θ¯)]

(6)(7)(8)

During the fracture tests investigated in this study, the stress state evolves with deformation but remains approximately proportional. For modelling simplicity, fracture modelling was performed using a mean stress-state approach, in which average values of stress triaxiality and Lode angle parameter were computed over the deformation history up to the experimentally observed fracture point. These averaged values were subsequently used for the identification of the HC model parameters.

Fig. 9 shows the evolution of the equivalent plastic strain at fracture as a function of the stress triaxiality η and the Lode angle parameter θ¯ for the different specimen geometries from batch B 1 . The stress triaxiality and Lode angle parameter were evaluated at the material point experiencing the maximum equivalent plastic strain at the instant where fracture takes place, which is assumed to represent the fracture initiation location according to ductile fracture theory. In addition, the fracture strain predicted by the calibrated HC model, εfHC, is reported at the corresponding stress-state values for each geometry. PS specimens exhibit the highest stress triaxiality values, whereas NT specimens show intermediate triaxiality levels, and SH specimens are characterised by near-zero triaxiality, indicative of shear-dominated conditions. Regarding the Lode angle parameter, NT specimens present clearly positive θ¯ values, while PS and SH specimens show θ¯ values close to zero.

[picture]

Fig. 9. Stress-state-dependent fracture strain and Hosford-Coulomb predictions for batch B1: (a) fracture strain vs stress triaxiality; (b) fracture strain vs Lode angle parameter.

Fig. 9. Stress-state-dependent fracture strain and Hosford-Coulomb predictions for batch B1: (a) fracture strain vs stress triaxiality; (b) fracture strain vs Lode angle parameter.

Fig. 10 compares the equivalent plastic strain at fracture as a function of the mean stress triaxiality η and the mean Lode angle parameter θ¯ for the different batches and specimen geometries. For a given geometry, noticeable differences in fracture strain are observed between batches, despite relatively similar mean stress-state parameters. In the NT configuration, the batches exhibit comparable η (Fig. 10 (a))) and θ¯ values (Fig. 10 (d)), while the fracture strain shows a clear batchdependent scatter. A similar trend is observed for the PS specimens, where variations in fracture strain occur at nearly constant η (Fig. 10 (b)) and slightly varying θ¯ (Fig. 10 (e)). In the SH configuration, differences in fracture strain between batches are also evident, even though the mean triaxiality remains close to zero (Fig. 10 (c)) and the Lode angle parameter varies within a narrow range (Fig. 10 (f)).

[picture]

Fig. 10. Comparison between batches in terms of mean stress triaxiality η¯ for (a) NT, (b) PS and (c) SH specimen geometries and in terms of mean Lode angle parameter θ¯ for (d) NT, (e) PS and (f) SH specimen geometries.

Fig. 10. Comparison between batches in terms of mean stress triaxiality η ¯ for (a) NT, (b) PS and (c) SH specimen geometries and in terms of mean Lode angle parameter θ ¯ for (d) NT, (e) PS and (f) SH specimen geometries.

Fig. 11 (a) shows the HC fracture surface obtained for Batch B1, represented in the η,θ¯ space. The surface illustrates the stress-state dependency of the predicted equivalent fracture strain, with higher fracture strains associated with low triaxiality and shear-dominated stress states, and a progressive reduction of ductility with increasing stress triaxiality [12]. The experimentally observed fracture points corresponding to the NT, PS and SH specimen geometries are also indicated, showing a consistent alignment with the predicted fracture surface.

Fig. 11 (b) shows the plane stress fracture loci predicted by the HC model for the five investigated batches, calibrated using NT, PS and SH experimental data. The curves display a consistent qualitative dependence of fracture strain on stress triaxiality, while exhibiting batch-dependent offsets across the investigated range.

Comparable scatter is observed in the regions of triaxiality associated with the stress states employed for model calibration, indicating that batch-to-batch variability is preserved under the stress conditions governing the fitting of the fracture model.

[picture]

Fig. 11. (a) HC fracture surface obtained for the representative Batch B1, with the experimental fracture points corresponding to NT, PS and SH geometries. (b) Batch-dependent plane stress fracture loci predicted by the HC model.

Fig. 11. (a) HC fracture surface obtained for the representative Batch B1, with the experimental fracture points corresponding to NT, PS and SH geometries. (b) Batch-dependent plane stress fracture loci predicted by the HC model.

For completeness, the optimized HC model parameters identified independently for each material batch are summarized in Table 4. The reported parameters correspond to the best-fit values obtained under the assumption of proportional loading. The observed batch-to-batch variability in the parameter values is consistent with the differences in fracture response highlighted by the plane stress fracture loci.

Table 4. Batch-dependent HC model parameters identified under proportional loading.

| a | b | c | n |  | a | b | c | n
B1 | 1.9215 | 1.0506 | 0.000969 | 0.009069 | B4 | 1.8522 | 1.2247 | 0 | 0.011828
B2 | 1.9276 | 0.9785 | 0.001321 | 0.007519 | B5 | 1.7970 | 1.1339 | 0.00274 | 0.013452
B3 | 1.9221 | 0.9220 | 0.001462 | 0.008190 |  |  |  |  |

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1183.93.pdf

Based on the experimental and numerical analyses performed in this study, the main conclusions can be summarised as follows:

Batch-to-batch variability leads to significant differences in both strain hardening and ductile fracture behaviour, even for materials sharing the same nominal steel grade.

The hybrid experimental-numerical approach enabled the identification of batch-dependent material behaviour, which was consistently captured by independently calibrating the simplified Hensel-Spittel constitutive law and the Hosford-Coulomb fracture criterion for each batch.

Although comparable mean stress states were obtained for a given specimen geometry, a noticeable scatter in fracture strain and, therefore, in the resulting fracture response was observed between batches.

This scatter tends to be more pronounced under tension-dominated loading conditions, whereas reduced variability is generally observed for shear-dominated stress states.

The assumption of a single representative material behaviour may therefore introduce nonnegligible uncertainties in fracture predictions.

The proposed methodology provides a practical framework to quantify material variability and supports the development of more reliable numerical simulations and digital twin approaches for cold forging applications.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1183.93.pdf

The authors gratefully acknowledge Jesús Oñate S.A. for providing the material and for his technical support. Financial support from the Gipuzkoako Foru Aldundia within the framework of the FORBIL project is also acknowledged.

Bibliography

The original version of this paper is available on https://www.scientific.net/MSF.1183.93.pdf

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D. Mohr, S.J. Marcadet, Micromechanically motivated phenomenological Hosford-Coulomb model for ductile fracture, International Journal of Solids and Structures 67-68 (2015) 40-55.

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ASTM International, ASTM E9/E9M-09: Standard Test Methods for Compression Testing of Metallic Materials at Room Temperature, ASTM International, West Conshohocken, PA, 2009.

A. Weck, D.S. Wilkinson, E. Maire, H. Toda, Experimental investigation of void coalescence in metallic sheets containing laser drilled holes, Acta Materialia 56 (2008) 2919-2932.

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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/forging-and-rolling/978-3-0364-1994-7

Materials Science Forum, ISSN: 1662-9752, Vol. 1183, pp 107-117

doi: 10.4028/p-rRmI12

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

Submitted:
2026-01-25

Revised:
2026-02-21

Accepted:
2026-02-24

Online:
2026-04-13

Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

The original version of this paper is available on https://www.scientific.net/MSF.1183.107.pdf

Alexandros Prospathopoulos 1,2,a, Apostolos Argyros 1,2, b, Maria Pappa 1,2,c, Nikolaos Michailidis 1,2, d*

¹Physical Metallurgy Laboratory, Dept. of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

2 Centre for Research & Development of Advanced Materials (CERDAM), Center for Interdisciplinary Research and Innovation (CIRI), Balkan Centre, Building B', 10th km ThessalonikiThermi Road, 57001, Thessaloniki, Greece

a  alexpros@meng.auth.gr, b  aargiros@auth.gr, c  pappmari@auth.gr, d * nmichail@meng.auth.gr

*corresponding author

Keywords: AA7075-T6, rolling anisotropy, three-point bending, high-cycle fatigue, intermetallic particles, crack growth.

Abstract

Rolled 7xxx-series Al alloys exhibit pronounced microstructural anisotropy (pancake grains and intermetallic particles) that can strongly affect fatigue initiation and -crack growth. In the current study, an AA7075-T6 plate was examined in three orthogonal machining orientations-L-S (longitudinal), L-T (long-transverse) and T-S (short-transverse)-using high-cycle three-point bending fatigue at room temperature ( R=0,f=25 Hz,σmax=360−400MPa, i.e., ~0.79−0.88σy ). Optical/SEM observations reveal elongated grains and a grain-density gradient through thickness, accompanied by orientation-dependent distributions of intermetallic particles. Despite only small differences in monotonic response, fatigue performance is strongly orientation-dependent: the T-S specimens exhibit the longest lives in the S−N curves. Fractography and striation-based kinetics show the lowest Paris-regime crack-growth rate for T−S(da/dN≈1.85×10−7 m/ cycle at ΔK≈10.5MPam), while L-S shows the fastest growth ( da/dN≈4.3×10−7 m/ cycle at ΔK≈13.0MPam ). The improved T-S fatigue resistance is discussed in terms of crack-path interaction with grain boundaries and particle populations (coherent/penetrable vs non-coherent/coarse particles), which can either deflect/retard cracks or act as initiation sites. The results provide a compact microstructuremechanics map for rolling-induced anisotropy in AA7075-T6 under bending fatigue.

Introduction

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Aluminum alloys are extensively used in aviation thanks to their superior strength-to-density ratio. Over the years, numerous studies have investigated their fatigue behavior. This process involves crack initiation followed by propagation until failure [1]. Aluminum alloy 7075 is a preferred choice for aircraft structural components due to its exceptional strength-to-weight ratio [2].

AA7075 in the peak-aged (T6) condition is widely used in safety-critical lightweight structures because of its high specific strength. The same microstructural features that enable precipitation strengthening-fine η′/ GP precipitates and dispersoids-coexist with coarse constituent particles (often Fe- and Cu-bearing) and rolling-induced pancake grains [3].

Constituent particles in this alloy exhibit wide variations in composition and structure. They are typically classified into two groups: those rich in Al,Cu,Mg, and Zn , and those containing Al,Fe, Cu,Mn, and Zn [4].

Harlow (2010) investigated the role of constituent particles in 7075-T651 aluminum alloy on the evolution of microstructurally small damage. The study concluded that fatigue damage nucleation and propagation in aluminum alloys involve complex stochastic processes. Constituent particles play a dominant role, with Fe-bearing particles being particularly critical due to local stresses, grain orientation, particle geometry, and possibly other material properties [5].

In Al−Zn−Mg−Cu alloys, brittle intermetallic phases-particularly coarse Fe-rich and Cu containing particles such as Al2Cu2Fe,Al7Cu2Fe and Al6(CuFe),Al6(CuFe)-strongly influence fatigue crack propagation by serving as primary crack initiation sites. These particles fracture readily, inducing crack deflection and branching that initially retards growth but can reduce overall fracture toughness [6].

Espezua et. al. (2012) compared three 6xxx-series aluminum alloys to assess how intermetallics and precipitates affect fatigue crack nucleation. They concluded that mechanical stresses from transport vehicle operation induce material fatigue, resulting in crack nucleation primarily at inclusions, constituent particles, or precipitates, followed by propagation to fracture. The study identified intermetallic particles containing Fe,Mn, and Si as key nucleation sites, as both intermetallics and precipitates act as stress concentrators that readily initiate fatigue cracks [7].

Navaee (2021), in a study on asymmetric cold rolling of AA7075 aluminum alloy, demonstrated that brittle Fe-rich intermetallic particles serve as prime sites for crack initiation and propagation via particle fracture or interface decohesion [8].

The effects of aging on the microstructure and properties of 7075 Al sheets has been investigated by (Zhao, 2020). They showed that for 7075 alloy, a large amount of MgZn2(η) second-phase particles break during cold deformation [9].

A model to assess the influence of weak interface layers on the breaking of coarse constituent particles has been developed by Startik (2005). The researchers concluded that PFZs around particles can have an important influence on their failure in the presence of a stress field such as that caused by a loaded crack progressing through the material. The PFZ strengthen the material and thus PFZs around particles can be beneficial to damage tolerance [10].

Zhang et al. (2020) underscored the research challenge, noting that high-strength aluminum alloys suffer from notoriously poor fatigue performance. Engineers must therefore account for this limitation when designing to improve structural fatigue strength [11].

Leng et al. (2018) described two key models for precipitate-dislocation interactions: the dislocation cutting mechanism and the bypassing (Orowan) mechanism. These depend on precipitate size and coherency with the matrix [12].

Mbuya (2017) notes that although crack propagation through fractured particles occurs, it is less frequent and typically limited to thin, favorably oriented particles parallel to the loading direction [13].

Cold working and subsequent aging frequently align particles into stringers and generate three distinct planes ( L−T,L−S and T-S), leading to direction-dependent fatigue initiation and short-crack propagation. While orientation effects have been reported for several Al alloys under bending fatigue, direct comparisons across all three orthogonal planes of a single AA7075-T6 plate under identical three-point bending conditions remain scarce.

The present study investigates the rolling-induced fatigue anisotropy of AA7075-T6 aluminum alloy, a material widely recognized for its exceptional strength-to-weight ratio and extensive applications in aerospace engineering. Despite extensive research on the fatigue behavior of aluminum alloys, a gap remains in comparative analyses that encompass all three orthogonal orientations under identical loading conditions. This study aims to fill that gap by providing a compact dataset that elucidates the anisotropic behavior of AA7075-T6, revealing critical insights into microstructural influences on fatigue performance combining (i) optical/SEM evidence of grain morphology and particle/crack interactions, (ii) basic mechanical metrics (elastic modulus, hardness and tensile response), and (iii) fatigue S−N behavior with striation-based estimates of Paris-regime crack growth. . By systematically comparing the fatigue life and crack growth rates across the longitudinal, long-transverse, and short-transverse orientations, we offer a comprehensive view that enhances both scientific understanding and practical engineering applications.

The goal is not an exhaustive parametric study, but a compact set of results that links orientation to fatigue performance through the most load-bearing microstructural mechanisms.

Materials and Methods

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The material was supplied by the Hellenic Aerospace Industry. The specimens were machined from pieces of material with random dimensions, but these were sufficient to achieve the desired geometry. Processing was performed using shaping tools such as saws, lathes, milling machines, and drills.

For the experimental analysis, a total of 39 specimens were tested, with 13 specimens designated for each of the three orthogonal orientations: longitudinal (L-S), long-transverse (L-T), and shorttransverse (T-S). Each orientation was subjected to different stress levels ( σmax=360−400MPa ) to comprehensively evaluate the fatigue behavior across varying loading conditions. This approach ensures robust statistical significance and enhances the transparency of the results presented.

A commercial rolled AA7075 plate in the T6 condition was examined. The processing sequence corresponds to solution treatment, quenching, cold rolling and artificial aging (Fig. 1).

[picture]

Fig. 1. Schematic heat-treatment sequence for AA7075-T6 (solution treatment → quench → cold rolling → aging).

Fig. 1. Schematic heat-treatment sequence for AA7075-T6 (solution treatment → quench → cold rolling → aging).

Specimens were cut along the three orthogonal directions of the plate: L−S (longitudinal), L−T (long-transverse) and T-S (short-transverse) (Fig. 2).

[picture]

Fig. 2. Specimen geometry and orientation relative to the rolled plate: L-S, L-T, and T-S (threepoint bending).

Fig. 2. Specimen geometry and orientation relative to the rolled plate: L-S, L-T, and T-S (threepoint bending).

The rectangular fatigue coupons were machined to ( 70 mm×10 mm×3 mm ) (L-T-S) dimensions were tested in three-point bending. The tensile surface (maximum tensile stress) was progressively ground using SiC papers ( 120 to 1200 grit) to minimize roughness-induced scatter.

Fatigue tests were performed at room temperature on a DMA ElectroForce 3550 (TA Instruments) at a frequency of 25 Hz and a stress ratio R=0. The nominal maximum bending stress was set to σmax=360−400MPa (approximately 0.79−0.88 of the yield stress reported for this material). For a rectangular section, the applied load was calculated from the standard three-point bending relation (Eq.1):

F=(σ*2 b* d2)/3 L[ N](1)

Where F is the applied force, L the span, and b and d the specimen width and thickness, respectively.

Microstructure and fracture surfaces were examined by optical microscopy and SEM equipped with EDS. Elastic modulus and tensile stress-strain curves were used to check for orientationdependent monotonic response. Microhardness profiles across the thickness of cracked specimens were also measured to assess local work/strain-hardening trends between compression and tension sides.

Results

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Microstructure and orientation-dependent features

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Optical microscopy confirms the expected rolled-plate morphology: grains are elongated along the rolling direction and exhibit a pronounced gradient in grain density and thickness through the plate thickness. Representative views for the L-S and T-S planes are shown in Fig. 3 and Fig. 4.

The methodology for quantitative grain-width analysis entailed the following: Samples from L-S, L−T, and T−S orientations were sectioned and prepared by grinding, polishing and etched with Keller's reagent to reveal grain boundaries. Five representative optical microscope images per orientation (magnification 100× ) were selected via random sampling across the gauge length to minimize bias. Using Image-J software, grain widths were measured as the mean intercept length perpendicular to the rolling direction: at least 20 test lines (spaced 2μ m apart) were overlaid per image, with intercepts counted only at fully traversed grains.

The above quantitative image analysis reveals a markedly larger mean grain width for the L−T plane ( ≈1.34×105 nm) compared to L-S ( ≈4.50×104 nm ) and T-S ( ≈3.54×104 nm ), with the strongest spatial variation observed toward the tensile surface (Fig. 5). Intermetallic particles are frequently observed along subgrain boundaries and in stringers, and SEM fractography reveals both crackdeflection/retardation at certain particles and crack-bridging pathways created by fractured particle fragments (Fig. 9-10).

[picture]

Fig. 3. Representative optical micrograph showing elongated grains and particle distribution in the rolled plate (example: L-S plane).

Fig. 3. Representative optical micrograph showing elongated grains and particle distribution in the rolled plate (example: L-S plane).

[picture]

Fig. 4a. Elongated grains along the L-S plane, b) Non uniform grains density between the interior and the surface of the (L-S) samples.

Fig. 4. a. Elongated grains along the L-S plane, b) Non uniform grains density between the interior and the surface of the (L-S) samples.

[picture]

Fig. 4b. Grain morphology in the T-S plane (two magnifications).

Fig. 4. b. Grain morphology in the T-S plane (two magnifications).

[picture]

Fig. 5. Quantified grain-width variation across orientations (mean values indicated on plots).

Fig. 5. Quantified grain-width variation across orientations (mean values indicated on plots).

Mechanical response (elastic modulus, tensile behavior and hardness trends)

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Elastic modulus exhibits a clear orientation dependence (Fig. 6): T-S shows a lower modulus than L-S and L-T. Consistently, tensile curves indicate slightly higher tensile strength but reduced elongation in T-S compared with the other two directions. Microhardness profiles across cracked specimens increase from the compression side toward the tensile side, consistent with a non-uniform through-thickness deformation state under bending and with the observed grain-thickness gradient.

Elastic Modulus Comparison

Fig. 6. Elastic modulus of AA7075-T6 in the three orientations (lower modulus in T-S).

High-cycle fatigue (S-N curves)

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Fig. 7 illustrates only a representative part of the S-N curve to highlight the differences in fatigue life of the three orientations. A pronounced anisotropy is observed: the short-transverse T-S orientation consistently provides the longest fatigue life, followed by L−T, while L−S shows the shortest life within the investigated stress range. The life scatter is typical for high-strength Al alloys, where crack initiation is highly sensitive to the presence and location of coarse particles, near-surface defects and local surface conditions.

[picture]

Fig. 7. S-N curves for AA7075-T6 in L-S, L-T and T-S orientations under three-point bending fatigue.

Fig. 7. S-N curves for AA7075-T6 in L-S, L-T and T-S orientations under three-point bending fatigue.

The standard deviations for each orientation is: σ(T−S)=234.383 cycles, σ(L−S)=38.048 cycles, σ(L−T)=128.886 cycles. The following example illustrates the calculation of the standard deviation for the L-S orientation using the formulas (2),(3):

μ(L−S)=ΣxiN(2)

Where: xi= individual fatigue life values
μ(L−S)= mean of the values
N= total number of values

σ(L−S)=∑(xi−μ(L−S))2N−1(3)

Where: σ(L−S)= standard deviation
L-S: Mean = 82422 [N], L-T: Mean =109705 [N], T-S: Mean = 188790 [N]
μ(L−S)=[37536+44583+70141+61764+168269+115427+71348+69455+97182+88517]/10=82422.

Crack-growth kinetics from striation measurements

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To rationalize the orientation dependence beyond initiation, crack-growth rates were estimated from SEM striation spacing, assuming one striation per cycle. Table 1 summarizes the corresponding Paris-regime values, together with the stress-intensity factor ranges reported for each orientation. The T-S specimens exhibit the lowest ΔK and the slowest crack growth, consistent with their longer fatigue life. The crack-growth rates presented in this study were derived from striation spacing measurements, assuming a one-to-one relationship where one striation corresponds to one loading cycle. It is essential to frame these rates as semi-quantitative estimates due to several simplifying assumptions inherent in this method. One of them is the uniform distribution of striations along the fracture surface and the exclusion of potential variations in loading conditions during crack propagation.

Table 1. Striation-based crack-growth rates in the Paris regime ( da/dN=C(ΔK)n with C=3×10−11 and n=3.7 ).

Orientation | Striations (count / 10 μm) | da/dN (m/cycle) | ΔK (MPa√m)
L–S | 23 / 10 | 4.3×10⁻⁷ | 13.02
L–T | 39 / 10 | 2.56×10⁻⁷ | 11.5
T–S | 54 / 10 | 1.85×10⁻⁷ | 10.5

The stress intensity factor ΔK was calculated using an equation proposed by Paris and Erdogan for measuring the crack propagation rate, which is based on assumptions regarding the crack lengths that were indirectly measured rather than directly observed. This introduces inherent uncertainties, as the accuracy of ΔK is contingent upon the validity of these assumptions. Variations in crack morphology and the effects of microstructural features on crack propagation can further contribute to discrepancies between calculated and actual ΔK values. Therefore, it is important to interpret the ΔK results with caution, recognizing these limitations in the context of the overall findings [14]. Fig. 8 shows an indicative example of measuring the crack growth rate using ImageJ software.

[picture]

Fig. 8. Example of crack growth rate measurement.

Fig. 8. Example of crack growth rate measurement.

(L−S)dadN=C(Δ K)m⟹Δ K=14.18MPam

Fractography: particle-crack interactions

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SEM observations emphasize the dual role of intermetallic particles. In some cases, particles act as effective obstacles that deflect and retard the crack (Fig. 9). In others, fractured particles and their fragments create local microcracks and bridge across adjacent grains, providing a preferential pathway for crack advance (Fig. 10). This balance between barrier and weak-path behavior depends on particle size, coherency with the matrix, and their orientation relative to the crack plane.

[picture]

Fig. 9. Example of crack retardation/deflection at an intermetallic particle (T-S specimen).

Fig. 9. Example of crack retardation/deflection at an intermetallic particle (T-S specimen).

[picture]

Fig. 10. Intermetallic particle fragments acting as crack bridges/pathways (L-S specimen).

Fig. 10. Intermetallic particle fragments acting as crack bridges/pathways (L-S specimen).

Crack initiation and propagation originate from distinct mechanisms. Initiation generally starts at microstructural defects or stress concentrators-like inclusions, grain boundaries, or intermetallic particles-and depends on factors such as microstructural heterogeneity and applied loading conditions.
Propagation, however, is controlled by the material's fracture toughness and crack growth mechanisms, which are dictated by local microstructure and stress intensity factors at the crack tip.

Discussion

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The present study highlights an important practical point: in a rolled AA7075-T6 plate, the fatigue ranking under three-point bending can differ from the ranking expected from monotonic strength alone. The elastic modulus and tensile strength vary only modestly with orientation, yet fatigue life changes markedly.

A consistent interpretation emerges when considering the crack path relative to (i) the pancakegrain architecture and (ii) the alignment of particle stringers introduced by rolling. In orientations where the crack front intersects a higher density of grain boundaries and particle bands at high angles, local stress concentrations at particles and interfaces promote earlier microcrack coalescence and faster short-crack propagation. Conversely, the improved T-S performance is compatible with a crack path that encounters fewer effective barriers/weak interfaces per unit advance, leading to a lower effective driving force (lower ΔK ) and slower Paris-regime growth (Table 1).

Particle coherency further modulates this behavior. Coherent or semi-coherent precipitates (often termed 'penetrable') can strengthen the matrix and contribute to crack blunting/deflection, whereas coarse non-coherent particles and debonded interfaces can serve as dominant initiation sites. The SEM examples in Fig. 8-9 illustrate both mechanisms in the same alloy. From an engineering perspective, these findings reinforce that fatigue design in 7xxx alloys should treat orientation as a first-order variable and should control near-surface particle populations and surface preparation to reduce initiation sensitivity.

Key contributions of this scientific study:

Direct, side-by-side comparison of all three orthogonal planes of a rolled AA7075-T6 plate under identical three-point bending fatigue loading.

Coupled S-N ranking with striation-derived crack-growth kinetics, showing that the longest-life orientation (T-S) also exhibits the lowest ΔK and slowest Paris-regime growth.

Mechanism-level fractography demonstrating the dual role of intermetallic particles as both crack barriers and weak paths via fracture/debonding and crack bridging.

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1183.107.pdf

Rolled AA7075-T6 exhibits pronounced microstructural anisotropy (pancake grains and intermetallic particles), which translates into strong fatigue anisotropy under three-point bending.

Within σmax=360−400MPa(R=0,f=25 Hz), the fatigue life ranks as T−S( longest )>L−T>L− S (shortest).

Elastic modulus is lowest in T-S, while tensile curves show only small differences in strength/ductility; fatigue performance cannot be inferred from monotonic response alone.

Striation-based kinetics indicate the slowest Paris-regime crack growth for T−S ( da/dN≈1.85×10−7 m/ cycle, ΔK≈10.5MPam ) and the fastest for L−S(da/dN≈4.3×10−7 m/ cycle, ΔK≈13.0MPam ).

Fractography confirms a dual particle role: certain particles deflect/retard cracks, whereas fractured/debonded particles provide initiation sites and crack-bridging pathways. The orientationdependent crack interaction with grain boundaries and particle alignment rationalizes the observed S−N ranking.

Summarizing, we would say that this study presents a comparative analysis of rolling-induced anisotropy in AA7075-T6 aluminum alloy across three orthogonal orientations: longitudinal (L-S), long-transverse (L-T), and short-transverse (T-S).

Unlike previous studies that often focus on isolated orientations or lack direct comparisons, our approach facilitates a comprehensive understanding of how microstructural features influence fatigue performance under identical loading conditions, which constitutes a valuable resource for engineers researching the optimization of aeronautical aluminum alloys.

References

The original version of this paper is available on https://www.scientific.net/MSF.1183.107.pdf

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Keywords Index

#

42 Crmos 4 Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

A

Aa7075-t6 Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Anisotropy A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

C

Characterisation Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Cold Forging Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Cold Rolling A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Cold Strip Rolling Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

Constitutive Modelling Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Crack Growth Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

D

Damage Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Ductile Fracture Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

F

Fem A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Fine Blanking Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

Finite Element Method Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Fishtail Effect A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Flow Behaviour Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Forging Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Friction Hill A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Friction In Rolling Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

H

Heat Treatment Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

High-cycle Fatigue Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Hot Forming Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Hybrid Components Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

I

Induction Heating Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Intermetallic Particles Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Inverse Parameter Identification Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

L

Less Punch Edge Distortion Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

M

Modelling Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Multi-stage Forming Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

P

Physics-informed Neural Network Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

Plane Strain Point A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Plasma Nitriding Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

Porosity Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Powder Metallurgy Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Punch Edge Shape Control Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

R

Residual Stresses Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Ring Rolling A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Roll Force A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Rolling Anisotropy Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

S

Simulation Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Slab Method A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Spray Cooling Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

T

Tailored Forming Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Thermal Management (process Control) Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Three-point Bending Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Authors Index

A

Abedul, D. Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Agirre, J. Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Aizawa, T. Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

Amend, H. Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Argyros, A. Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

B

Bailly, D. Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Barandiaran, A. Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Behrens, B. Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions; Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat; Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Boogaard, T. A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Brunotte, K. Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

C

Cappellini, C. A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

F

Fuchiwaki, K. Fine-Blanking Punch Edge Control by Chamfering and Plasma-Nitriding under Excessive Load Situation

G

Galdos, L. Predicting the Influence of 42C MoS4 Variability on Cold Forming through Constitutive Modelling and Fracture Analysis

Gerke, N. Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions

Giardini, C. A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

Gouverneur, M. Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

H

Hammes, M. Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Havinga, J. A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

Hol, C. A Qualitative Study of the Contact Pressure Distribution in Cold Rolling

L

Laeger, R. Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Lian, J. Extension of the Lemaitre Damage Model to Account for Static and Dynamic Recrystallization Behavior

Locatelli, G. A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

M

Martin, R. Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

Michailidis, N. Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Mohnfeld, N. Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat; Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

O

Overhagen, C. Fast Inverse Identification of the Coefficient of Friction in Cold Strip Rolling Using a Physics-Informed Neural Network

P

Pappa, M. Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Peddinghaus, J. Tailored Temperature Gradients in Hybrid Components: Influence of Variable Process Parameters under Cold and Preheated Conditions; Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat; Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Piwek, A. Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat

Prajapati, K. Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Prospathopoulos, A. Rolling-Induced Anisotropy in High-Cycle Three-Point Bending Fatigue of an AA7075-T6 Plate

Q

Quarto, M. A Novel Modified SLAB Method Approach for Efficient Energy Assessment in Ring Rolling Showing Fishtail Effect

U

Uhe, J. Microstructure Modification of Hot Formed Shafts through Customised Spray Cooling from the Forming Heat; Characterisation of the Flow Behaviour of Powder Metallurgical Semi-Finished Products for Lubricant-Impregnated Cold Forming Concepts

Y

Younas, S. A Qualitative Study of the Contact Pressure Distribution in Cold Rolling