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ISBN print: 978-3-0364-0984-9
ISBN eBook: 978-3-0364-1984-8
DOI book: 10.4028/b-7J5ycP
© 2026 Trans Tech Publications Ltd, All Rights Reserved

Polymer Processing and Thermomechanical Properties

Edited by
Prof. Roberto Spina

Polymer Processing and Thermomechanical Properties

Special topic volume with invited peer-reviewed papers only

Edited by
Prof. Roberto Spina

Scientific.Net

Copyright © 2026 Trans Tech Publications Ltd, Switzerland

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Volumes 451 of
Defect and Diffusion Forum
ISSN print 1012-0386
ISSN web 1662-9507
(Pt. A of Diffusion and Defect Data - Solid State Data ISSN 0377-6883)

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp -1-0

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

Accepted:
2026-04-15

Online:
2026-04-17

Preface

The original version of this paper is available on https://www.scientific.net/DDF.451.-1.pdf

The aim of this issue is to bring together specialists from academia and industry dealing with modelling and experimental analysis of polymer processing and induced properties. This issue extends from thermo-chemo-mechanical characterization of polymers to coupled transfers in processes, in particular heat transfer in moulded parts, tools and interfaces. The main topics of the issue are: Thermomechanical modelling and optimization of polymers processes. New challenges for characterization and modelling of thermo-chemo-physical properties in homogeneous and heterogeneous media; Heat transfer phenomena in moulds/tools associated with polymers processes; Specific thermal metrology applied to polymers processing.

Editor

The original version of this paper is available on https://www.scientific.net/DDF.451.-1.pdf

Prof. Roberto Spina
Politecnico di Bari

Co-editors

The original version of this paper is available on https://www.scientific.net/DDF.451.-1.pdf

Prof. France Chabert
Université de Technologie Tarbes Occitanie Pyrénées (UTTOP)
Dr. Christian Garnier UTTOP
Dr. Adrian Korycki UTTOP
Dr. Raffaele D'Elia
IMT Mines Albi
Prof. Fabrice Schmidt
IMT Mines Albi
Prof. Gary Menary
Queens University

Table of Contents

Preface

Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

Anne Lise Briard, Raffaele D'Elia, Florentin Berthet, Anthony Cheruet, Fabrice Schmidt

Thermoforming as Rapid Prototyping Strategy of Fishing Lures

Andreas Loth, Ralf Förster, Jan Rösler

Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Adrian Korycki, Jean Denis Beguin, France Chabert, Christian Garnier

Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

Katerina Vrettos, Steven Le Corre, Jean Luc Bailleul, Erwan Bertevas

Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

Pascale Müller, Daniel Kehret, Stefan Junk

3D-Printed Pyrography Using PLA/Wood Filaments

Francisco Comino, José A. Martínez-Sánchez, Alessandro Pellegrini, Roberto Spina

Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Evan Gargadennec, Yun Mei Luo, Eric Monteiro, Luc Chevalier

Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks

Wancley O. Pedruzzi, Igor F. Tosi, William Pablo Montes Quiroz, Raffaele D'Elia, Julio Cesar Sampaio Dutra, Wellington B. da Silva

Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Igor F. Tosi, Wancley Pedruzzi, William Pablo Montes Quiroz, Raffaele D'Elia, Julio Cesar Sampaio Dutra, Wellington da Silva

Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process

Hyunsung Choi, Minjae Baek, Yong Nam Kwon, Ducksung Kim, Daeho Jeong, Yoo In Jeong

Analysis of Large Deformation Characteristics and Formability of PMMA

Min Jae Baek, Yong Nam Kwon, Daeho Jeong, Ducksung Kim, Yoo In Jeong, Hyunsung Choi

From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Mario Emanuele Di Nardo, Pietro Russo, Pierpaolo Carlone

Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Francisco Comino, José A. Martínez-Sánchez, Marco Zaza, Sabina Campanelli, Roberto Spina

Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

Keltoum Oubellaouch, Riccardo Pelaccia, Giulia Zaniboni, Vincenzina Siciliani, Barbara Reggiani

Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Michael Wilhelm, Christoph Schelleis, Georg Zeeb, Frank Henning

Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Giulia Zaniboni, Vito Basile, Riccardo Pelaccia, Rossella Surace, Keltoum Oubellaouch, Francesco Modica, Leonardo Orazi, Giovanna Rotella, Luigino Filice, Irene Fassi

Keywords Index

Authors Index

The original version of this eBook is available on https://www.scientific.net/book/polymer-processing-and-thermomechanical-properties/978-3-0364-1984-8

Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 1-10

doi: 10.4028/p-5rElXG

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

Submitted:
2025-12-12

Revised:
2026-02-20

Accepted:
2026-02-25

Online:
2026-04-17

Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

Anne-Lise Briard 1,2,a*, Raffaele D'Elia 1, Florentin Berthet 1, Anthony Cheruet 2 and Fabrice Schmidt 1

1 Institut Clément Ader (ICA)

Univ Toulouse, IMT Mines Albi, INSA Toulouse, ISAE Sup Aero, CNRS, ICA, Albi France

2 Airbus Operations SAS

316 route de Bayonne, 31300 Toulouse, France

a  anne-lise.briard@mines-albi.fr (*corresponding author), b  raffaele.delia@mines-albi.fr, c florentin.berthet@mines-albi.fr, d anthony.cheruet@airbus.com, e fabrice.schmidt@mines-albi.fr

Keywords: Porosity, Thermoset Prepreg, Flow Simulation, Porous Medium.

Abstract

Carbon Fiber Reinforced Polymers (CFRPs) are essential to the aerospace industry, offering superior strength-to-weight ratios. Currently, the manufacturing of primary structures via standard autoclave curing is a robust, mastered process that successfully minimizes defects, keeping porosity levels below critical thresholds (typically <1% ). Consequently, porosity is generally not considered as an issue in standard, optimized production lines.

However, this stability may be affected by emerging industrial paradigms aimed at increasing production rates and reducing costs. The shift toward accelerated manufacturing - characterized by rapid heating rates, shortened cure cycles and by new manufacturing processes - and the introduction of complex material architectures risk re-introducing significant porosity. In parallel, there is currently no numerical model capable of accurately predicting porosity formation and evolution under these complex conditions. Existing simulation approaches are typically macroscopic and rely on homogenized porous media assumptions, failing to capture the essential micro-scale interactions between bubbles and fibres.

To address this gap, this study presents an extended, custom multi-physics Computational Fluid Dynamics (CFD) solver built upon an existing OpenFOAM framework. The goal is to provide the first predictive tool for void evolution within realistic microstructures. The numerical framework couples a two-phase compressible flow model with the complete thermo-chemo-rheological physics of thermoset curing.

The solver is applied to 2D Representative Volume Elements (RVEs) of a prepreg ply. Simulations of a standard autoclave cycle demonstrated the solver's ability to capture micro-scale dynamics, showing how voids are compressed and transported during the resin viscosity drop before being frozen at gelation. A parametric study comparing 3-bars and 7-bars pressures confirmed the model's physical ability in predicting void volume reduction.

While currently focused on mechanical compression, the tool is designed to support the development of future manufacturing cycles. Future work will incorporate moisture diffusion physics and includes experimental validation via X-ray micro-tomography and in-situ synchrotron monitoring.

Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

Carbon Fiber Reinforced Polymers (CFRPs) are indispensable materials in the aerospace industry, offering exceptional strength-to-weight and stiffness-to-weight ratios. For primary structural components, thermosetting prepregs (e.g., carbon fibre reinforced epoxy) processed via autoclave curing remain the benchmark for achieving high performance, excellent consolidation, and minimal defect content [1].

Among all manufacturing defects, porosity (i.e. the presence of voids) is considered one of the most detrimental [1]. Voids, even at low volume fractions ( 1−2% ), act as stress concentrators,
promoting damage initiation and propagation. They significantly degrade matrix-dominated mechanical properties, most notably Interlaminar Shear Strength (ILSS), compressive strength, and fatigue life [1].

For decades, autoclave processing has been refined to mitigate porosity. This is achieved through vacuum application to remove trapped air and the application of high temperature and pressure. The pressure serves to mechanically compress any remaining trapped air, while also increasing the solubility of gases (air, moisture) in the resin, keeping them in solution until the resin polymerises [2].
However, industrial challenges are emerging:

Accelerated Manufacturing: to increase productivity and reduce costs, accelerated manufacturing approach aim to shorten cure cycles. Faster temperature ramps can, however, lead to a rapid viscosity decrease and can also trigger premature gelation, thereby reducing the time available for void removal. In parallel, alternative processes - such as Out-Of-Autoclave (OOA) curing - are also employed to further lower overall manufacturing costs [3]

New Material Systems: advanced material systems are being introduced to meet new performance needs. These include sandwich structures where prepreg composites are assembled with honeycomb cores, or prepregs toughened with thermoplastic nodules. These complex architectures introduce new interfaces and non-uniform flow paths that can trap air, as highlighted by Kermani et al. [4].
These new challenges highlight the primary limitation of existing manufacturing process simulation. Current models are typically macroscopic, treating the composite as a homogenised porous medium and using semi-analytical models to describe bubble evolution. However, these models are simplified models considering bubble as geometry-independent: coalescence and interaction with fibres are not taken into account [5].

To address this gap, a Computational Fluid Dynamics (CFD) approach is used, enabling the modelling and the visualisation of complex fluid flows. This paper presents the extension of a custom, multi-physics solver built in OpenFOAM that couples two-phase compressible flow with the complete thermo-chemo-rheological physics of thermoset curing.

The objective of this work is the development of a predictive tool that can simulate the evolution of bubble populations within realistic microstructures using Representative Volume Elements (RVEs) under classical industrial processing conditions. To achieve this, the paper is divided into two main sections. First, the numerical methodology of the developed solver is presented, with emphasis on the governing equations of the physics involved. Second, the solver is applied to a standard autoclave cycle, demonstrating its capability to capture microscale void dynamics and significantly outperform macro-scale models, which cannot resolve these features.

Numerical Methodology

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

The numerical framework is developed within the open-source software OpenFOAM version 8, based on the Finite Volume Method (FVM). A custom solver has been extended to capture the complex phenomena occurring during the curing process.

Two-Phase Flow Modelling. The fluid mixture composed of resin (liquid) and void (gas) is modelled as a two-phase, compressible flow. The Volume of Fluid (VoF) method is employed to track the evolution of the resin-gas interfaces. This method solves a transport equation for the phase indicator α, defined as the volume fraction of the resin phase in a given cell:

∂(α)∂t+∇·(αU)+∇·(α(1−α)Uc)=0.(1)

Where U is the velocity vector of the fluid mixture, and Uc is the interface compression velocity. Uc is an artificial velocity added numerically to counteract numerical diffusion of the interface and can be expressed as follows:

Uc=Cα|U|∇α|∇α|(2)

With Cα the compression factor. The phase fraction α=1 represents a cell filled with resin (liquid), α=0 represents a cell filled with gas, and the interface lies in cells where 0<α<1. The properties of the fluid in any cell (e.g., density ρ, viscosity μ ) are calculated as a weighted average (mixture law):

ρ=αρresin +(1−α)ρgas .μ=αμresin +(1−α)μgas .(3)

The gas phase ( ρgas  ) is treated as a compressible ideal gas, while the resin phase ( ρresin  ) is treated as an incompressible fluid. The effective compressibility of the mixture Ψm is therefore expressed as:

Ψm=∂ρ∂p=(1−α)∂ρgas∂p=1−αrT(4)

The core innovation of this work consists in the coupling of the VoF solver with the thermo-chemo-rheological evolution of the thermoset resin. This is achieved by solving three additional, coupled transport equations.

Thermo-Chemical Model (Cure Kinetics). The polymerisation of the thermoset epoxy resin is a scalar field, x, representing the degree of cure (where x=0 corresponds to an uncured matrix, while x=1 to a fully cured one). Its evolution is described by Kamal-Sourour kinetic model [6]:

∂x∂t=(k1+k2xm)(1−x)n with ki(T)=Aiexp(−EiRT),i=1;2(5)

Where m and n are the reaction orders, k1 and k2 the rate constants Ai is the Arrhenius preexponential factor, Ei is the Arrhenius activation energy, R is the ideal gas constant, and T is the local temperature. This equation is solved as a transport equation for the scalar x within the resin phase.

Rheological Model (Viscosity). The viscosity of the thermoset resin, μresin , depends on both temperature T and degree of cure x. This behaviour is captured using a modified William-LandelFerry (WLF) Castro-Macosko model [7, 8]:

μ(T)=μ0exp[−C1(T−Tg0(x)C2+T−Tg0(x)][xgelxgel−x]nviscosity(6)

With μ0 being the reference viscosity or initial viscosity before the beginning of cross-linking, Tg0 the glass transition temperature at 0% polymerisation, C1,C2 and nviscosity  material-specific empirical constants, and xgel the degree of polymerisation at the gel point.

Energy Transport and Exotherm. The temperature field T is solved using the energy equation, which accounts for conduction, convection, and the heat source from the exothermic polymerisation reaction:

∂(ρT)∂t+∇.(ρUT)−∇.(αeff∇T)+(∇.(|ϕ|p)+∂(ρK)∂t+∇.(ρUK))(αcvresin+1−αcvgas)=Sexo(7)

Where αeff  is the effective thermal diffusivity, Cv resin  and Cv gas  are the specific heat capacities for the resin phase and the gas phase respectively, ϕ is the volumetric flux, p is the pressure, and K is the kinetic energy. In practice, additional mass- or continuity-related correction terms originating from the pressure equation may also be included to ensure consistency between the pressure-velocity coupling and the energy equation. The source term Sexo  represents the exothermal heat of reaction and is only active in the resin phase:

Sexo=ρHrdxdt.(8)

With Hr the total heat of reaction. This term creates a non-linear feedback loop: the cure reaction releases heat, which increases the temperature, which in turn accelerates the cure rate (dxdt), releasing even more heat.

Solver Implementation and Coupling. The custom solver is based on the PIMPLE algorithm, which is a combination of Semi-Implicit Methods Pressure-Linked Equations (SIMPLE) and Pressure-Implicit Split-Operator (PISO) algorithms. PIMPLE algorithm is used to solve NavierStokes equations. Basically, at each time step, it performs several pressure corrections loops (such as PISO) within external iterations (such as SIMPLE). PIMPLE algorithm advances the solution in time through iterative prediction of the velocity field, solution of the pressure equation, and subsequent velocity correction, ensuring consistent pressure-velocity coupling at each time step [9]. The result is better convergence and greater robustness for transient or weakly compressible flows, without having to reduce the time step excessively. For this extended solver, at each time step, the following sequence is executed:

[picture]

Fig. 1. Algorithm workflow of the extended solver.

Fig. 1. Algorithm workflow of the extended solver.

Simulation Setup. To represent the composite microstructure, 2D RVEs of a prepreg ply are created using the Digimat® software, which provides a multiscale modeling environment for defining material microstructures. Although the subsequent CFD simulations in OpenFOAM employ a threedimensional mesh, only a single cell is used through the thickness, effectively reducing the problem to a quasi-2D representation while retaining a 3D framework for solver compatibility. Fibres are modelled as circles ( 7μ m diameter) with a stochastic distribution, generated to match a specified fibre volume fraction ( Vf ). In the present case, the RVE has a Vf of 60%.The fibres are treated as an
absence of mesh with no-slip boundary conditions. No-slip condition and zero pressure gradient are also imposed on the left and right walls, as presented in Fig. 2. This choice represents a first-order approximation that effectively suppresses any motion along the lateral boundaries. Such an assumption remains acceptable in the present configuration, as the flow is essentially quasi-static and no significant pressure-driven filling or strong pressure gradients are involved. The thermal cycle is implemented using a time-dependent Dirichlet boundary condition applied to all boundaries of the RVE. Given the microscopic dimensions of the RVE, the Biot number is significantly low, ensuring that the thermal diffusion time is negligible compared to the process duration. Consequently, the internal temperature field remains effectively uniform, governed by the boundary conditions, while still accounting for the localised exothermic heat source term Sexo  within the resin phase. The material-specific parameters for the cure kinetics and the rheological model are confidentials and therefore not explicitly reported. However, the framework is designed to be compatible with any standard thermoset system. For reproducibility purposes, representative coefficients for a typical aerospace-grade epoxy resin (such as those for the 8552 or M21 systems available in literature) can be implemented in the simulation case to yield similar qualitative trends in porosity evolution.

[picture]

Fig. 2. Example of a RVE of a prepreg ply with the details of the boundary conditions.

Fig. 2. Example of a RVE of a prepreg ply with the details of the boundary conditions.

An initial population of bubbles (gas phase) is placed in the inter-fibre spaces. To simulate void closure during curing and polymerisation, two types of initial void distribution are implemented, in order to reproduce the initial impregnation on the surface for a prepreg layer, as illustrated in Fig. 3. In the present work, only the band configuration (Fig. 3 (b)) is examined in detail.

[picture]

Fig. 3. Two types of initial void distribution reproducing surface impregnation. (a) Oval configuration (not considered in this study), (b) Banded configuration.

Fig. 3. Two types of initial void distribution reproducing surface impregnation. (a) Oval configuration (not considered in this study), (b) Banded configuration.

Indeed, the fibres at the core are dry before cure and form air evacuation channels, as highlighted by Hu et al. [2]. To simulate an industrial process, time-dependent autoclave cycles are applied. Temperature cycle is applied across the entire domain and a pressure is imposed at the top and bottom of the domain. A typical industrial cure cycle is simulated.

Numerical Verification. A numerical verification was conducted using meshes of up to 140000 cells per RVE to ensure a high-resolution capture of the fluid interfaces. The study utilised a square cross-section ( 0.1 mm×0.1 mm ) containing approximately 170 fibres to validate the mesh independence. Small timesteps were required to maintain numerical stability and precise resolution of the unsteady-state physics during the 48-hour simulation cycles. The solver, based on the MULES algorithm within OpenFOAM, demonstrated that while parallel efficiency reaches 70−75% at 16 cores (due to non-scalable portions such as MPI communication and I/O operations), the trends in void compression remain numerically stable across different CPU counts.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

The developed solver was applied to a RVE with Vf=60% and an initial void content of ε=20.6%. The simulations were conducted on a high-performance workstation using 16 cores. A complete process simulation of 15640 seconds requires a computational runtime of approximately 48 hours, representing a manageable cost for high-fidelity micro-scale analysis. Fig. 4 shows a series of snapshots from the simulation, illustrating the dynamic evolution of the void phase (blue) within the resin (red) as it flows around the fibres (white).

[picture]

Fig. 4. Time-series of porosity evolution in a 2D RVE ( Vf=60% ) during a simulated autoclave cure. (a) Initial state ti=0s, (b) Before viscosity minimum t=1040s, (c) Viscosity minimum t=4490s, (d) Gelation, tgel =9440s, (e) Final cured state, tf=15640s.

Fig. 4. Time-series of porosity evolution in a 2D RVE ( V f = 60 % ) during a simulated autoclave cure. (a) Initial state t i = 0 s , (b) Before viscosity minimum t = 1040 s , (c) Viscosity minimum t = 4490 s , (d) Gelation, t gel = 9440 s , (e) Final cured state, t f = 15640 s .

Initial State (Fig. 4 (a)): at ti=0, the void is in its initial configuration, with a banded shape. The resin is at room temperature and has a high viscosity ( μ=1.3×105 Pa.s for the resin considered here). The autoclave pressure (3 bars) is applied.

Heating and Viscosity Minimum (Fig. 4 (b)): as the temperature ramps up, the resin viscosity decreases, until it reaches its minimum ( μ=100Pa.s ). The simulation captures the resultant resin flow, which squeezes, deforms, and transports the void. The high external pressure compresses the gas, and the void volume fraction (1−α) decreases strongly.

Curing and Gelation (Fig. 4 (c)): as the temperature continues to rise, the cure reaction x accelerates. The viscosity begins to rise exponentially as the cross-linking progresses. Once the gelation is reached (xgel=0.36), the pore structure is frozen by the cross-linking of the resin.

Final State (Fig. 4 (d)): once x→1, the resin becomes a solid and the void does not evolve beyond the gel point. It is frozen in its final, compressed state. The simulation predicts a final porosity ε~9%.
Fig. 5 plots the key process variables against time.

[picture]

Fig. 5. Process variables versus time. (a) Applied temperature cycle Tautoclave , (b) Degree of Cure x, (c) Logarithm of the viscosity log(μ), showing the characteristic V-shaped viscosity profile. (d) Void volume fraction (1−α).

Fig. 5. Process variables versus time. (a) Applied temperature cycle T autoclave , (b) Degree of Cure x , (c) Logarithm of the viscosity log ( μ ) , showing the characteristic V-shaped viscosity profile. (d) Void volume fraction ( 1 − α ) .

The simulation clearly captures:

The viscosity profile: The log(μ) curve shows the characteristic V-shape, dropping due to temperature and then rising sharply due to curing.

Void compression: The void volume fraction (1−α) drops sharply under autoclave pressure, allowing pressure to be transmitted effectively.
Parametric Study: Effect of Pressure. To demonstrate the model's prediction capability, a higher autoclave pressure is applied. Comparison of the gas volume fraction for 3 bars and 7 bars applied pressure is illustrated in Fig. 6. The informed reader will readily identify that the predicted behaviour is governed by the initial assumption concerning the gas volume fraction; accordingly, the ~4% residual gas content obtained at 7 bars arises from this modelling choice and must not be interpreted as an inherent upper bound of autoclave consolidation.

[picture]

Fig. 6. Comparison of the gas volume fraction for two different values of applied pressure: 3 bars (blue line) and 7 bars (dashed red line).

Fig. 6. Comparison of the gas volume fraction for two different values of applied pressure: 3 bars (blue line) and 7 bars (dashed red line).

When a higher pressure is applied, the void phase decreases more significantly, starting from the same initial volume fraction of gas (banded configuration). This shows the importance of autoclave curing: a pressure of 3 bars is typically applied for sandwich panels to prevent crushing the structure, whereas higher pressures of about 7 bars are generally used for laminates.

Conclusions and Future Work

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

This paper has presented the extension and application of a novel, multi-physics CFD solver framework for modelling porosity evolution at the micro-scale in a thermosetting composite laminate. The key achievements are:

A custom, biphasic, transient, compressible solver implemented in OpenFOAM by extending an existing solver and enabling full coupling of two-phase flow with cure kinetics, thermorheological changes, and the reaction exotherm.

The simulation of void closure (compression, transport, deformation) within realistic RVEs under industrial autoclave cycles.

However, the model presented in this paper only considers the mechanical compression of preexisting, trapped air. A major source of porosity, particularly in OOA processing, is the growth of bubbles from dissolved moisture [10]. Therefore, work is underway to incorporate into the solver the phenomenon of moisture diffusion and the physics of mass transport. This involves solving an additional transport equation for the concentration of dissolved moisture in the resin. This additional physics will be introduced coupling the Henry's Law with a Fickian diffusion to model the mass transfer of moisture from the resin into the bubbles. This final feature will allow us to simulate the complete physics of porosity and resin flow in the autoclave-based prepreg manufacturing process at micro-scale.

In order to validate our model, an experimental campaign is planned. This will involve X-ray micro-tomography on semi-cured samples to quantify the 3D void morphology and compare it with simulation predictions. An in-situ monitoring of the cure process on a synchrotron beamline is currently under validation. If successful, the latter will provide 4D dataset on bubble evolution that will be used for direct validation of the solver's predictions.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.1.pdf

M. Mehdikhani, L. Gorbatikh, I. Verpoest, S. V. Lomov, Voids in fiber-reinforced polymer composites: A review on their formation, characteristics, and effects on mechanical performance, J. Compos. Mater. 53 (2018) 1579-1669.

W. Hu, L. Grunenfelder, T. Centea, S. Nutt, In situ monitoring and analysis of void evolution in unidirectional prepreg, J. Compos. Mater. 52 (2018) 1-14.

J.J. Torres, M. Simmons, F. Sket, C. González, An analysis of void formation mechanisms in out-of-autoclave prepregs by means of X-ray computed tomography, Compos. Part A Appl. Sci. Manuf. 117 (2019) 230-242.

N.N. Kermani, P. Simacek, S. G. Advani, Porosity predictions during co-cure of honeycomb core prepreg sandwich structures, Compos. Part A Appl. Sci. Manuf. 132 (2020) 105824.

B. de Parscau du Plessix, S. le Corre, F. Jacquemin, P. Lefebure, V. Sobotka, Improved simplified approach for the prediction of porosity growth during the curing of composite parts, Compos. Part A Appl. Sci. Manuf. 90 (2016) 549-558.

S. Sourour, M. R. Kamal, Differential scanning calorimetry of epoxy cure: isothermal cure kinetics, Thermochim. Acta 14 (1-2) (1976) 41-59.

M.L. Williams, R. F. Landel, J. D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, J. Am. Chem. Soc. 77 (1955) 3701-3707.

J.M. Castro, C. W. Macosko, Kinetics and rheology of typical polyurethane reaction injection molding systems, Soc. Plast. Eng. Tech. Pap. Annu. Tech. Conf. 38 (1980) 434-438.

C. Greenshields, H. Weller, Notes on Computational Fluid Dynamics: General Principles, CFD Direct Ltd, Reading, UK, 2022.

L.K. Grunenfelder, S. R. Nutt, Void formation in composite prepregs-Effect of dissolved moisture, Compos. Sci. Technol. 70 (16) (2010) 2304-2309.

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The original version of this eBook is available on https://www.scientific.net/book/polymer-processing-and-thermomechanical-properties/978-3-0364-1984-8

Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 11-22

doi: 10.4028/p-4Gy9SE

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

Submitted:
2025-12-15

Revised:
2026-02-25

Accepted:
2026-03-01

Online:
2026-04-17

Thermoforming as Rapid Prototyping Strategy of Fishing Lures

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

Andreas Loth 1,a*, Ralf Förster 1, b and Jan Rösler 1,c

1 BHT, Luxemburger Str. 10, 13353 Berlin

a*aloth@bht-berlin.de, b  rfoerster@bht-berlin.de, cjroesler@bht-berlin.de

*corresponding author

Keywords: thermoforming, prototyping, fishing lures.

Abstract

Conventional hard-bait lure prototyping relies on manual shaping, full-body additive manufacturing or early-stage injection moulding, each associated with limitations in geometric repeatability, development time or tooling cost. This paper evaluates a hybrid approach combining thermoformed PETG outer shells with additively manufactured internal frames to produce batches of geometrically consistent lure bodies with tuneable internal mass layouts. Across several educational development projects, the process enabled fast replication of outer form, systematic variation of ballast and harness configuration, and prototype assembly suitable for qualitative hydrodynamic observation. Compared with full additive manufacturing or manual crafting, the method reduced fabrication effort for multi-variant batches and delivered mould-like surface quality. Joining reliability of shell halves emerged as the dominant limitation, with elastic polyurethane adhesives outperforming brittle cyanoacrylate and poorly controllable low-energy fusion. The results position thermoforming as a methodologically valuable prototyping tool where external geometry is stable but internal behaviour requires iterative adjustment. Future work should address seam design, cage-shell tolerances and sealing repeatability to support quantitative hydrodynamic testing and assess whether the process has potential beyond prototyping applications.

1. Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

Recreational fishing is widely practiced and provides a huge market of about 10 billion euros a year (EU only) for associated equipment [1]. Product development for artificial fishing lures that depend on functional hydrodynamics typically requires iterative prototyping to evaluate geometry, buoyancy, and behaviour. Conventional workflows rely on either hand-crafted trial pieces, fully additively manufactured bodies, or pilot-scale injection moulding. Each of these approaches exhibits limitations that impede rapid, repeatable progression from conceptual design to functional prototype. [2, 3].
Hand shaping remains an accessible route for hobbyists and small manufacturers; however, geometric fidelity, reproducibility and shape consistency across batches depend strongly on operator skill. This restricts the ability to isolate the influence of individual design variables, as two nominally identical prototypes may differ in subtle but behaviourally relevant ways. Full additive manufacturing, in contrast, offers excellent geometric control but is challenged by surface resolution, shell thickness limitations, sealing integrity, and extended build times when larger quantities of similar specimens are required [4, 5]. Furthermore, polymer injection moulding, although the standard for final lure production, demands substantial tooling effort and cost, and its use early in development cycles is impractical due to the lead time associated with tool manufacture and modification [6].
To address this gap, the present work examines a hybrid rapid prototyping strategy that combines thermoforming of PET shells with additively manufactured internal structures. The objective is to assess the feasibility of a process capable of producing families of geometrically consistent prototypes that approximate the appearance and build characteristics of injection-moulded lures, but at significantly lower development time and cost. The process comprises three key stages: (i) generation of a digital lure model, (ii) thermoforming of thin-wall exterior halves using a laboratory forming system, and (iii) integration of an adjustable mass-carrying internal lattice printed via fused deposition modelling (FDM). This concept was implemented across several student development projects, where
identical outer geometries and variable internal configurations were rapidly manufactured for design iteration and functional testing.
Preliminary observations from these feasibility studies indicate that the method allows the reproducible manufacture of outer shells, a structured means of adjusting weight distribution, and shorter build times compared to full additive manufacturing. However, challenges arise in joining the two thermoformed halves, where adhesive bonding was found to outperform low-pressure thermal welding due to seam heterogeneity near wire insertions.
These findings motivate a more systematic evaluation of thermoforming-based hybrid prototyping as a development tool for small consumer products. Rather than focusing on lure hydrodynamics, this paper assesses the process strategy itself, its implementation, constraints, comparative advantages, and potential scalability. Particular emphasis is given to its position relative to existing prototyping approaches and its suitability for bridging early ideation and later injection-moulding production.

2. Background and Related Work

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

2.1 Rapid Prototyping Strategies for Small Consumer Products.

Development of small consumer products that depend on external geometry and internal architecture, such as fishing lures, typically employs up to three prototyping approaches, manual forming, additive manufacturing (AM) and pilot-scale moulding [5, 2]. Manual forming remains widely used in craftoriented lure development because of its simplicity and negligible investment cost. However, its reproducibility and fidelity depend heavily on operator experience, making systematic iteration and comparative evaluation difficult, particularly when performance differences may stem from subtle shape variations rather than design intent.
Additive manufacturing is frequently framed as a solution to these shortcomings because it enables digital-to-physical replication without traditional tooling, offering relatively low entry cost and strong suitability for low-volume and customised production [5]. Advantages include geometric freedom, the ability to make frequent design modifications and the elimination of early tooling investment [7]. However, industrial reviews note several drawbacks that restrict AM as a full replacement for injection moulding. Surface finishing requirements, layer artefacts, porosity in thin shells, anisotropic properties and extended build time when multiple units are required [5, 8]. These drawbacks are particularly pronounced in applications where aesthetic surface fidelity, sealing integrity, or thinwalled repeatability are required [5]. Additionally, adding weights or internal structures require further manual modification steps.
Injection moulding, in contrast, remains the dominant production process for polymer consumer products due to its ability to achieve excellent dimensional accuracy, surface finish, and material performance in volume production [6]. Yet, its utility for iterative prototyping is hindered by relatively long tool lead times, capital expenditure, and the inflexibility of mould geometries once manufactured [2,9]. Where design changes are frequent, injection moulding becomes economically prohibitive for early-phase evaluation.
In response to this gap, thermoforming has been promoted as an intermediate prototyping and lowvolume manufacturing method because it offers thin-walled polymer parts at relatively low tooling cost and with faster cycle times than tooling and full-body AM [2]. Industry and manufacturing comparison studies specifically highlight thermoforming as favourable when the goal is to approximate an injection-moulded look and feel while maintaining responsiveness to geometric change [3]. This positioning makes thermoforming a promising candidate for applications such as lure prototyping, where multiple geometrically consistent units are needed to study internal configuration changes rather than surface morphology alone.

2.2 Principles of the Thermoforming Process.

The thermoforming workflow comprises heating, forming, cooling and trimming. First, a thermoplastic sheet or plate is heated above its glass-transition or softening temperature to reach a deformable state. Forming occurs against a mould surface via vacuum suction, assisted mechanical
displacement or pressure forming. The geometry is retained during cooling before excess edges are trimmed. This makes thermoforming attractive for prototype production due to short cycle times and minimal tooling overhead [3].
Depending on thickness, two industrial subclasses exist. Thin-gauge thermoforming ( <1.5 mm provided by university), typical for packaging and aesthetic surfaces and thick-gauge thermoforming (>3 mm), where structural stiffness or larger components are needed [1,3]. Common thermoformable polymers include ABS, PET/PETG, PS, PVC, PP and PC, selected according to transparency, impact performance, thermoformability and post-processing behaviour [6, 3]. Key challenges arise from material stretching during forming, which produces non-uniform wall thickness, potentially compromising local integrity. Geometry with deep draw or sharp curvature amplifies thinning effects. Furthermore, thermoforming inherently defines only the mould-contacting surface; secondary features or reverse-side precision require more advanced forming strategies or bonding of multiple shells [2].
Despite its advantages, thermoforming exhibits constraints relative to injection moulding, limited ability to produce sharp internal detail, variable wall thickness due to stretching, geometric complexity bounded by draw angle and surface curvature, and requirement to trim excess stock after forming [5].
Moreover, in rapid tooling contexts the mould itself is often produced additively. Layer-based tooling fabricated through FDM typically exhibits ridged surfaces and porosity, necessitating secondary finishing (e.g. sanding, sealing coatings or thermal smoothing) to achieve suitable vacuum fidelity and surface replication [5]. SLA- or MJF-printed tools may require less finishing but are constrained by build volume or mechanical resistance to repeated heating cycles [8]. In parallel, advances in polymer AM introduce resins with elevated heat deflection temperatures suitable for thermoforming tooling. For instance, Formlabs' high-temperature resins are marketed explicitly for small-scale thermoforming applications where conventional photopolymers might deform under process heating [10]. These developments illustrate that the success of thermoforming-based prototyping is strongly dependent on material selection not only for the shell, but also for the tooling substrate.

2.3 Fishing Lures as a Representative Product Class.

Given the limited academic literature on internal lure construction, practitioner and patent sources are used to document prevailing industrial design practices.
From a functional perspective, angling equipment distinguishes broadly between natural bait (e.g. worms, small fish, invertebrates) and artificial lures. Artificial lures encompass soft plastic baits, metal spoons, spinner systems and hard-bodied lures such as plugs, crankbaits and jerkbaits, which are typically shaped and coloured to resemble prey fish or other forage organisms, although effective designs increasingly depart from strictly natural morphology [11].
Within artificial lures, hard-bodied "plugs", including floating and diving crankbaits, are characterised by a rigid volumetric body made from wood or polymer, usually equipped with one or more treble hooks and depending on type, a diving lip or bill at the head [12]. These lures normally operate as hollow shells in modern industrial production, assembled from two moulded halves which, after integration of internal components, are sealed by welding or adhesive bonding. Internal architectures provide ballast chambers or weight-transfer systems that influence diving depth, stability and action. Commercial descriptions and trade literature frequently emphasise integrated weight systems and internal rigging as central design features.
A structurally critical component of many hard-bodied lures is the wire harness, a stainless-steel linking element that connects line attachment point and hook positions through the body (Fig.1). Patents and technical descriptions report full-length wire frames or harness structures embedded in the lure body to guarantee load transfer and prevent failure of localised eyelets under high tensile load (e.g. [13]), even though systems with inserted wires were easier to manufacture (e.g. [14]). In parallel, practitioner communities and manufacturer-facing guidance document "through-wire" construction methods as standard practice for larger predator lures, in which a continuous wire is slotted or cast into the body and fixed by adhesive or overmoulding [15].

In addition to hollow-shell architectures, a second class of hard-bodied lures is based on solid wood or polymer bodies into which cavities are drilled and filled with molten lead or other ballast before being sealed. These constructions provide robust structural continuity but render subsequent changes to weight distribution more cumbersome. By contrast, multi-chamber hollow designs with internal frames facilitate some degree of adjustability, albeit at the cost of more complex tooling.
In the present work, X-ray imaging (Fig.1) of commercial lures confirms the prevalence of continuous or seperate internal wire harnesses and discrete ballast volumes as standard engineering solutions for load transfer and hydrodynamic tuning. Building on this empirical evidence, hard-bodied lures are treated here as an archetype for products in which outer geometry must closely resemble injectionmoulded parts, while internal mass distribution remains an active design variable, making them suitable candidate artefacts for evaluating hybrid thermoforming-based prototyping strategies.

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Fig. 1. X-ray images of hollow polymer lures, "through-wire" harness (left), inserted wires (right).

Fig. 1. X-ray images of hollow polymer lures, "through-wire" harness (left), inserted wires (right).

2.4 Joining Strategies for Thermoformed Structures.

A defining challenge in the use of thermoformed shells for functional products is the joining of thinwalled elements into structurally stable assemblies. Unlike injection-moulded parts, which typically incorporate interlocking features, ribs and welding surfaces, thermoformed components exhibit low joining land thickness, variable wall distribution, and reduced dimensional precision, restricting available methods and the reliability of connections [2].
Mechanical fastening (e.g., clips, screws) is generally unsuitable for thin thermoformed parts due to insufficient wall thickness to resist pull-through or stress concentration without reinforcement. Industrial design guidance therefore recommends integrated bosses, thicker local pads or bonded backing plates where mechanical fasteners must be used, all of which introduce extra processing steps that diminish the speed advantage of thermoforming [3,6].
Thermal Fusion-based techniques, like hot-air welding, solvent welding, spin or ultrasonic welding, are theoretically applicable and widely used in multi-part plastic housings. However, their performance is highly sensitive to sheet gauge and temperature control, as localized heating can deform thin PET or ABS shells before fusion occurs [16, 17]. Ultrasonic welding, though attractive for high-volume production, requires precisely designed energy directors and support geometry, which are rarely present on prototype-oriented thermoformed parts [16, 17].
Adhesive bonding is generally regarded as the most practical joining strategy for thermoformed components in prototyping and low-volume manufacturing. Acrylics, polyurethane-based structural adhesives and cyanoacrylates all offer effective bond formation without excessive thermal input, and accommodate the dimensional tolerances typical of vacuum-formed parts [6, 8]. Industrial training literature emphasises adhesive joining particularly where surface finish, thin-wall sensitivity or lack of interlocking features prevent reliable welding [6].
Hybrid joining strategies combining mechanical alignment and adhesive sealing appear in industry practice for consumer housings and appliance trim, where locating ribs or lips provide positional registration and adhesives deliver strength and hermetic closure [16, 17, 3]. Similar approaches may be transferrable to thin-wall hollow lure constructions when external flushness and internal watertightness are required.

The effectiveness of joining methods in thermoformed assemblies is therefore a function not only of material chemistry but also of wall thickness, geometry, and process control. For the application investigated here, thin PET shells around a structurally relevant internal frame, adhesive joining is the most compatible technique due to local heat sensitivity of 0.8 mm PET during fusion attempts, consistent with observations in the experimental section.

3. Proposed Hybrid Process Strategy

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

The proposed hybrid process combines thermoformed PETG shells with additively manufactured internal frames to obtain geometrically consistent, mould-like fishing-lure prototypes while retaining flexibility in internal mass distribution. The strategy was implemented and refined across several student design-and-build projects at Berliner Hochschule für Technik, which serve as empirical evidence for feasibility, process windows and joining challenges.

3.1 Digital Design and Model Generation.

Lure geometries were modelled in CAD based on typical hard-bodied crankbait or jerkbait shapes and benchmarked commercial references. The key design decision was to decouple outer geometry from internal architecture, enabling repeated use of the same external shell with different internal frame layouts and ballast configurations. CAD data for the external body was converted into positive thermoforming tools, while separate parameterised models defined the internal "cage" structures and through-wire harnesses.
Internal frames were designed as 3D-printed components that locate and constrain lead weights at discrete positions, provide a defined path or groove for the stainless-steel through-wire, and generate bonding land to improve shell alignment and sealing. Examples include lattice cages with dedicated channels for the harness and recessed volumes for ballast.

3.2 Tooling Manufacture and Surface Conditioning.

Thermoforming tools were manufactured additively from PLA using FDM printers (e.g. Ultimaker 3, Bambu Lab P1S). Typical print configurations used 0.4 mm nozzle diameter, 0.2 mm layer height, 15% infill and grid patterns, in some cases with adaptive layer heights around strongly curved lure contours to improve surface resolution.
After printing, tools were drilled with 2 mm vent holes along critical contour lines to make a vacuum evacuation possible. Tools were then mounted on wooden carrier plates and sealed at the base using aluminum tape or equivalent to avoid leakage.
In one group, a partial surface finishing was performed, sanding and local sealing of one half of a 3Dprinted tool with cyanoacrylate, showing visibly improved surface quality on the formed part compared to the untreated half [18]. This corroborates general thermoforming guidance that layerbased tooling often requires finishing to remove print artefacts and improve vacuum contact.

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Fig. 2. Surface finishing by sanding and coating (r), result (l) [18].

Fig. 2. Surface finishing by sanding and coating (r), result (l) [18].

3.3 Thermoforming of Shell Halves and Process Parameters.

Thermoforming was carried out on a platen thermoforming machine Illig UA 100Ed ((ILLIG GmbH) in the plastics processing laboratory. PETG sheets with nominal thickness 0.75−0.8 mm were clamped in a frame and heated from both sides before positive forming over the printed tools. Representative process parameters, derived from multiple project configurations, are summarised in Table 1.

Table 1. Process parameters for thermoforming process [18-22].

Material | PETG sheet, thickness 0.75–0.8 mm
Heater settings (temp.) | Upper heater: 3 zones at 420 °C | Lower heater: 3 zones at 360–380 °C
Heating time | 17–18 s per cycle
Pre-blow time | activation after 0–0.5 s | duration approx. 0.5 s
Vacuum delay and duration time | vacuum applied with ca. 4 s delay (active during forming phase)
Cooling time | 6–11 s depending on group and tool design
Demoulding air time | 5–10 s

The total cycle time for thermoforming process was in the range of 30 and 45 seconds.
Twelve or more matching halves were typically produced per configuration, allowing for multiple assembly variants per outer shape [19]. After forming, shells were trimmed and their joint edges lightly sanded to increase straightness and contact area for subsequent bonding.

3.4 Manufacture of Internal Frames and Weighting Systems.

Internal frames were fabricated using FDM 3D printing in PLA, with grid infill and local thickening in regions contacting the shell or carrying weights. Designs evolved from simple weight holders to more integrated cages that span the lure length, captured the through-wire harness in a dedicated groove and provided multiple chambers for discrete lead spheres or cylindrical weights.
In several variants, weight layouts were explicitly documented and tuned (e.g. combinations of 5 6 mm lead balls at defined longitudinal distances) to achieve different static buoyancy and trim angles while preserving constant outer geometry [20]. The internal cage was also used structurally to bridge front and rear hook positions, better reflecting the tensile load path expected during fish strikes and retrieval.

3.5 Assembly and Joining - Practical Observations and Literature Context.

Assembly comprised the integration of four key elements: thermoformed shells, internal frame, through-wire harness and ballast. The stainless-steel wire was bent into a continuous harness with eyelets at the front (line attachment) and at bottom and rear (hooks), then routed through the cage groove to ensure load transfer along the full lure length. Weights were inserted into cage chambers according to the desired mass distribution, and the combined cage-wire assembly was placed into one shell half before closing with the second.
Multiple joining strategies for the shell halves were experimentally evaluated like thermal spot welding with a soldering iron (local melting of the PETG at the joint line), cyanoacrylate bonding on a butt joint, elastic automotive windscreen adhesive (polyurethane) in the joint region, silicone sealant injected into a designed peripheral groove.
Thermal spot welding was found to be difficult to control on 0.75−0.8 mm shells. Local overheating caused groove collapse, inconsistent seam formation and in some cases, re-opening of previously sealed regions when subsequent spots were added. This aligns with general guidance that fusion welding of thin thermoplastic sheets is highly sensitive to temperature, pressure and joint geometry, and that repeatable welds require carefully designed joint features such as energy directors, shear joints or tongue-and-groove interfaces - features typically designed into injection-moulded parts, but not present on simple thermoformed edges [16,17].
Cyanoacrylate bonding of simple butt joints yielded initially watertight seams, but exhibited brittleness under flexure and tended to crack along the joint when the lure body was slightly deformed,
leading to water ingress during tests. By contrast, elastic polyurethane windscreen adhesive maintained joint integrity under bending and impact and was judged to be the most robust option despite higher application effort and curing time.
Silicone sealant applied into a peripheral groove around the cage and wire harness also produced durable joints but introduced additional mass; in one group this unaccounted sealant mass significantly increased lure weight and required additional balancing [19].

[picture]

Fig. 3. Joining of lure sample: model of two halves (ur), wire harness (ul), cage, weights, harness, lower shell and sealant (b) [18].

Fig. 3. Joining of lure sample: model of two halves (ur), wire harness (ul), cage, weights, harness, lower shell and sealant (b) [18].

The single component PU glue (CAREAL10, Conel GmbH, Germany) has been used according to datasheet curing information after previous sanding and cleaning of the region, a strategy that has been applied also for all other joining strategies.
These experimental findings are consistent with industrial comparisons of adhesive bonding versus ultrasonic welding for plastic assemblies. Literature notes that ultrasonic welding, while fast and clean, requires minimum wall thickness, stiff support conditions, and specifically designed weld zones, and can be problematic for very thin or flexible parts. Under such conditions, structural adhesives often provide more tolerant and design-flexible joining solutions [23]. In the context of thin thermoformed PETG shells with limited weld land and prototypes produced on laboratory equipment, adhesive and hybrid adhesive-sealant strategies emerge as the most practical joining methods.

4. Experimental Demonstration and Observations

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

The proposed hybrid process was implemented across five student-led development projects at Berliner Hochschule für Technik, each producing thermoformed lure shells, additively manufactured internal frames, integrated wire harnesses and sealed assemblies. These implementations provide empirical evidence for process feasibility, limitations and operational effects not captured analytically.

4.1 Shell Forming Quality and Shape Consistency.

Across projects, thermoforming consistently produced geometrically faithful shell halves when PETG sheet thickness was 0.75−0.8 mm, and the printed tool surface was smooth enough to achieve vacuum conformity. The variation of material thickness of thermoformed halves has been measured with a micrometer screw in regions where it was possible, especially in joining regions. Therefore, some specimen have been cut using a bandsaw, but an overall thickness was not controlled.

Surface defects correlated strongly with tooling condition. Tools with untreated layer lines caused matte, faceted surfaces, while sanded and sealed tools yielded clearer and sharper detailing, confirming the influence of tool finish on shell fidelity [18]
Notably, multiple projects produced >10 matching halves per configuration, demonstrating repeatability sufficient for controlled design iteration [20,21]. Dimensional repeatability and surface quality have only been monitored / qualified in terms of assembling and joining conditions. The interesting criteria here was to fit the internal structure into the thermoformed parts. No measurements have been applied, due to the uneven shape.
The number of achievable cycles largely depends on how long the time between the cycles (and thus the cooling period) is.

4.2 Assembly Accuracy and Compatibility.

The internal cage concept successfully constrained weight positions and provided mechanical registration for the wire harness, reducing assembly misalignment compared with freehand placement. However, wire harness deformation and tolerance mismatch occasionally prevented smooth seating of the cage, requiring re-bending of the harness or local removal of frame material [20]. This revealed the subtle but relevant finding, that the thermoformed shell accuracy was sufficient for repeatable alignment, but internal cages and harnesses introduced alignment errors when their fabrication tolerances were not strictly controlled.
The water thightness was tested different by different groups. Immersion into a bucket or bathtub were the most common methods, leaving the lures on the ground for up to 5 minutes and controlling for air bubbles during the test or introduced water droplets afterwards. This led to improvements during the manufacturing steps of later models, Nevertheless, transportation, handling in the water channel (depth up to 650 mm ) and initial preparing steps caused leakage in some cases to previously waterthight housings. Especially brittle glues and to tight tolerated housings were affected.

[picture]

Fig. 4. Manufactured lures [18-22].

Fig. 4. Manufactured lures [18-22].

4.3 Function Observations and Early Hydrodynamic Indications.

Functional testing was qualitative rather than quantitative. Completed prototypes were swum in test channel in KEE lab or small water bodies to assess gross buoyancy, trim and action. Two practical findings emerged as expected.

Mass distribution strongly influenced behaviour. Front-heavy configurations produced nose-down sinking; rear-biased setups produced tail sit; symmetric placements increased stability but reduced dive tendency [20].

Shell sealing quality influenced test outcomes. Seams that cracked or absorbed water altered buoyancy over minutes, suggesting sealing reliability, not shell geometry, limited hydrodynamic evaluation in these trials.
Thus, design iteration was demonstrably achievable, but systematically meaningful hydrodynamic performance evaluation requires improved seam sealing repeatability. Fig. exemplarily shows tested lures in KEE water channel.

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Fig. 5. Water tests of sample lures [21,18].

Fig. 5. Water tests of sample lures [21,18].

5. Comparative Assessment and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

The hybrid thermoforming / AM process occupies a distinct position within the spectrum of lure development workflows. It offers rapid external replication similar to injection moulding, but with lower tooling burden and higher adaptability than moulded parts, while exhibiting stronger geometric consistency than manual forming or full-body AM in batch scenarios. The comparative assessment below synthesises findings from the experimental implementations and relates them to established prototyping strategies.

5.1 Comparison with Fully Additive Manufacturing.

Full-body AM providing seamless integration of external form and internal mass layout, but it suffers from surface roughness, tension-sensitive wall regions, and porosity-based leakage when thin shells are required. Several groups required sealing varnish or epoxy coating to make printed lures watertight, adding time and mass; notwithstanding layer-induced surface texture that remains visible even after finishing. In contrast, thermoformed shells inherently produce smooth, mould-like surfaces without finishing effort except trimming.
Build time also diverges significantly between approaches: printing 10+ full-body lures requires repetitive 6−20 hour print cycles depending on resolution, while thermoforming produced 12-20 shells in approximately one hour including heat-up, forming and trimming phases, followed by printing only internal cages. Thus, the hybrid method accelerates batch iteration where external shape is invariant and only internal structure varies.
However, full-body AM delivers precise internal integration and inherent sealing via material continuity, whereas the hybrid process revealed joining reliability as a critical failure mode. This indicates that thermoforming is advantageous where outer-shell replication dominates, but full AM retains benefits for one-off prototypes where geometry and sealing complexity are coupled.

5.2 Comparison with Manual Crafting.

Manually carved wood or resin prototypes exhibit high variability between nominally identical bodies, especially regarding symmetry, cross-section precision and hinge continuity. This variability masks the effect of small internal design changes, reducing interpretability of performance differences. The hybrid process therefore provides geometric repeatability across sample sets, allowing clearer attribution of behavioural changes to internal variables.
Moreover, manual crafting typically embeds weights by drilling and backfilling with lead shot or poured alloys, limiting reversibility and forcing destructive modification to test alternative mass layouts. The thermoforming approach, by contrast, enables non-destructive reconfiguration because ballast compartments are located within replaceable internal cages. This supports iterative design logic, sensitivity testing and exploratory exploration of mass placement strategies; activities poorly suited to hand-built wooden lures.

5.3 Comparison with Injection Moulding.

Injection moulding remains the major production method for surface quality, dimensional control and integral joint design. Commercial lures benefit from moulded tongue-and-groove seam geometries, designed welding interfaces and local rib reinforcement. However, industrial sourcing reports highlight tooling costs and lead times spanning weeks, which are disproportionate when design parameters such as internal weights or alignment features change frequently. The hybrid process preserves injection-moulded appearance while avoiding these upfront commitments.
An alternative to this would be injection moulding with an exchangeable tool. However, this requires a flexible core tool. This requires a one-time high investment.
Nevertheless, injection moulding offers predictable sealing integrity, whereas hybrid lure sealing proved fragile without carefully selected adhesives. This emphasises that thermoformed shells can approximate industrial styling but not yet industrial sealing robustness. In a development cycle context, this is acceptable; in production contexts, sealing and joint features would need redesign to mirror moulded construction logic.

5.4 Scalability Considerations.

From a scaling perspective, the hybrid process scales well in count but poorly in automation. Thermoforming can produce many shells per hour if labour is available for trimming and joining, but the assembly remains artisanal. Conversely, AM of internal cages remains scale-limited by print throughput, although multi-part nests or higher-output printers mitigate this effect.
Hence, the method behaves as a low- to mid-volume prototyping strategy but does not displace mass manufacturing frameworks; mirroring its use in other industries for pilot production, appliance housings and design studies.

5.5 Manufacturing and Design Implications.

The observed constraints reveal design implications useful beyond fishing lures:

Seam design will dominate prototype survivability. A repeatable joining concept (tongue-andgroove, lap joint, adhesive track) would materially elevate test reliability.

Internal frame tolerancing requires refinement. Misalignment arose not from shell variation but from cage-wire interfaces; thus cage design standards should match shell tolerances.

Thermoforming is best deployed when design variables lie inside the part, not in its shell. Where external morphology changes frequently, full-body AM may be superior; where outer shape is fixed and internal exploration matters, thermoforming is beneficial.

Replicability supports design research. Being able to hold exterior geometry constant while modifying ballast enables controlled testing unavailable to hand-built prototypes, positioning this process as a methodological tool for design science and consumer product development.
In summary, the hybrid approach demonstrates feasibility as a rapid, repeatable, mould-analogue prototyping workflow suitable for research and development settings where appearance uniformity and internal flexibility are more important than mass production robustness.

6. Summary and Outlook

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

This study proposed and demonstrated a hybrid prototyping strategy combining thermoformed PETG shells with additively manufactured internal frames for the development of hard-bodied fishing lures. Across five independent student implementations, the method consistently produced geometrically repeatable external housings and allowed systematic manipulation of internal mass distribution while maintaining constant outer morphology. This capability constitutes a practical development advantage over manual crafting, and a throughput advantage over full-body additive manufacturing when batches of external shapes are required.
The experimental results confirm feasibility but also identify joining reliability and internal assembly tolerancing as principal bottlenecks. Shell sealing integrity rather than shell geometry limited hydrodynamic observability, and tolerance incompatibilities between printed cages and bent wire harnesses contributed more to alignment variation than thermoforming variation. In near future,
further measurements must be undertaken to examine dimensional repeatability and surface quality of the thermoformed shells, especially over the number of replicas, to exclude these effects from possible differences in swimming behaviour.
Comparative assessment shows that the hybrid method does not rival injection moulding in seam quality or weld integration, but it achieves injection-moulded visual fidelity at much lower tooling cost and with greater flexibility for iterative internal design. As a consequence, the process is most appropriately positioned as a pre-tooling development framework, effective whenever outer geometry is stable and internal configuration space is under investigation. Future research can build on these findings along several axes:
Joining engineering as design of lap joints, adhesive channels or tongue-and-groove interfaces suitable for thin thermoformed shells to enhance sealing reliability.
Integrated cage-shell tolerance design, parametric alignment features, snap-fit indexing or progressive wire fixing templates if adaptable to thermoforming, to reduce assembly misfit.
Hybrid tooling development, or the application of heat-resistant AM moulds to reduce finishing effort and improve shell surface resolution.
Quantitative behavioural studies I, proceeding with controlled hydrodynamic testing of lure variants produced under this process to examine whether the development efficiency translates into more interpretable feedback cycles.
Quantitative behavioural studies II, a comparison with injection moulded lures of same shape and weight distribution could give further insight into comparability of received results from this prototyping approach.
More broadly, the demonstrated process illustrates how thermoforming can be reframed as a research instrument for design iteration in consumer product contexts that traditionally leap prematurely to injection tooling or oversimplified hand prototyping. By enabling batch-wise replication of outer form with manipulable internal architectures, this approach contributes methodological value to prototyping research and small-scale product innovation.
Depending on extended lures testing scenarios the watertightness at higher pressures (approx. 1 bar) could be considered as well. It is mainly not necessary, as in lure testing, the specimen want's to be observed and 10 m deep test facilities are rare.
The development process can be supported by using simulation of thermoforming process (e.g., with software Ansys).

Acknowledgement

The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

The authors gratefully acknowledge the extensive experimental contributions of multiple student project teams at Berliner Hochschule für Technik. In particular, sincere thanks are extended to Nils Josten, Raphael Stroehl, Hannes Ben Kilian, Jan Philipp Heinrich Can Hinz, Seong Jun Kim, Hassan Khalil Zeitoun, Jonas Appelt, Fabian Lemke and Markus Krüger, Tibet Kütük, Tatyana Kochetkov and Jordan Lee Bernstein for validation through multi-variant prototype fabrication, for tooling refinement and hydrodynamic tests, for insight into their iterative joining evaluation and for their process documentation and parameter development for early cage design and ballast architecture work. The authors would also like to thank the staff, at the KEE Laboratory for their support in testing the individual lures in their water channels and Prof. Dr. rer. nat. Markus Buchgeister for Xray imaging.

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The original version of this paper is available on https://www.scientific.net/DDF.451.11.pdf

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Appelt, J., Lemke, F., Krüger, M., Recyclinggerechte Werkstoffwahl und Produktentwicklung Fischköder G9, BHT Berlin, 2025.

Kütük, T., Kochetkov, T., Bernstein, J.L., 1. Konstruktive Aufgabe: Fischköder G3, BHT Berlin, 2025.

Josten, N., Stroehl, R., Recyclinggerechte Werkstoffwahl und Produktentwicklung Konstruktive & Exp. Aufgabe (Projekt) „Fischköder“ G7, BHT Berlin, 2025.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 23-33

doi: 10.4028/p-nPf0F3

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

Submitted:
2025-12-17

Accepted:
2026-02-25

Online:
2026-04-17

Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

The original version of this paper is available on https://www.scientific.net/DDF.451.23.pdf

KORYCKI Adrian 1,a*, BEGUIN Jean-Denis 1, b, CHABERT France 1,c and GARNIER Christian 1,d

1 LGP-ENIT-UTTOP, 47 Avenue d'Azereix, 65016 Tarbes, France

a  adrian.korycki@uttop.fr, bjean-denis.beguin@uttop.fr, cfrance.chabert@uttop.fr and d christian.garnier@uttop.fr

Keywords: ultrasonic welding, thermoplastic composites, hybrid structure joining, properties

Abstract

The demand for lightweight, multifunctional, and durable hybrid structures is rapidly increasing in aerospace, biomedical, and advanced engineering sectors. Ultrasonic welding (USW) offers a promising route to assemble thermoplastic polymers with dissimilar materials such as stainless steel, aluminium, and ceramics, without adhesives or additional fasteners. This study investigates the ultrasonic joining of high-performance thermoplastics, including carbon fibrereinforced polyetheretherketone (PEEK), and polyetherimide (PEI) as energy director (ED), with aluminium alloys. Improvement of manufacturing efficiency and weld attributes such as welded area, strength, and failure mechanisms are essential for industrial adoption. In this work, particular attention was given to the effect of metal surface preparation and ED film on weld quality. Weld attributes were analysed in terms of joint area continuity, interfacial morphology, tensile shear strength, and observed failure modes. Whereas not all parameter sets led to successful joining, the findings provide insight into the role of surface finish and ED in determining weldability. These results contribute to the ongoing development of reliable welding for hybrid joining between thermoplastics and metals, highlighting opportunities for thermal process innovation beyond conventional approaches.

Introduction

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The development of hybrid metal-polymer structures is part of an innovation strategy for high-value-added sectors such as aerospace, biomedical, and electronics. Ultrasonic welding is a promising method for joining thermoplastics with dissimilar materials due to its speed, low energy consumption and overall low environmental impact. This process uses high-frequency ultrasonic vibrations to generate friction between material, localizing heat at the material interface, enabling fusion and subsequent joining without the need for additional adhesives or time costly surface treatments. Joining dissimilar materials presents unique challenges due to differences in melting temperatures, thermal conductivity, and mechanical properties, which can lead to interfacial stresses and variations in weld quality. Recent advances in controlling the parameters of the ultrasonic welding process [1] are significant assets that allow for improved weld quality and optimized joint strength, durability, and material compatibility. A critical factor in concentrating heat in the weld area is the energy director, with previous research works showing that the ED's thickness and roughness significantly influence the final assembly quality [2], [3]. This work aims to apply this technique for welding highperformance thermoplastic composites and metallic substrates.

The polymers to be welded must combine high thermal resistance, suitable rheological properties, and chemical compatibility with the substrates. Thermoplastic composites with high-performance PAEK (polyaryletherketones) matrix offer an alternative to metals due to similar specific strength. They are already used in aerospace and biomedical sectors due to their excellent mechanical properties, corrosion resistance, radio transparency, and biocompatibility. One of them is polyetheretherketone (PEEK), a semi-crystalline polymer with a melting point of 343∘C and excellent mechanical and chemical resistance. Its welding requires precise control of crystallinity [4], [5]. Polyetherketoneketone (PEKK) has a lower melting point of 305−335∘C and is easier to weld [6], [7]
due to adjustable kinetics of crystallization. Next, polyetherimide, an amorphous polymer, offers a glass transition temperature of 215∘C [8], [9].

Some works on ultrasonic metal-polymer welding are found in the literature They demonstrate that metal surface treatments such as sandblasting, chemical pickling, coating spraying, or mechanical texturing are effective methods for improving the mechanical properties of the joints (AA6061-PA6). The surface roughness of the Al samples is also essential for the weldability. If the roughness is too low, the parts slip on each other. For too high roughness, the energy is transferred in few points in the welding zone. Wagner et al. [10] reported that for ultrasonic welds, a surface roughness in the range 0.2μ m to 5μ m is well suited. However, the impact of treatments varies significantly depending on the nature of materials, which explains the substantial variability in weld strength of approximately 14 MPa [11], [12]. Ultrasonic welding of ABS (acrylonitrile butadiene styrene) to a laser-textured 5052 aluminum sheet was performed by Tan et al. [13]. It was observed that the type of laser texture had a significant influence on the mechanical strength of the joint. At constant laser energy per unit area, the maximum strength of the joint obtained reached 18 MPa in the case of a square grid structure with a 0.1 mm pitch. The welding times were consistently less than 4 s , demonstrating the speed of the process [14]. Compared with other conventional assembly processes like induction welding, resistance welding, friction stir spot welding or even direct adhesive bonding, the ultrasonic metalpolymer welding has proven superior with average shear strength 30 MPa for as-received joints and 50 MPa after surface treatment [15].

The experimental work focuses on the mechanical surface preparation methods for aluminium alloys and the role of PEI as energy director in enhancing joint integrity. Surface modifications allow precise control of roughness and superficial texture. Process parameters such as amplitude, welding time, and applied pressure were optimized and monitored via time and displacement control mode. A new method using multimode ultrasonic welding was tested. The study highlights the critical influence of interfacial morphology, thermal management, and energy director design on joint performance. These findings contribute to the development of reliable ultrasonic welding strategies for metal-polymer hybrid structures.

Materials and Methods

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Materials

The original version of this paper is available on https://www.scientific.net/DDF.451.23.pdf

The thermoplastic composite material utilized in this study was 3106-PA1 five-harness satin weave prepreg, composed of carbon fiber-reinforced polyetherketoneketone (CF/PEKK), supplied by Porcher Industries.

Aluminium sheets of AA5083-H111 alloy with a thickness of 2 mm were also used. Magnesium is the major alloying element in this alloy. The average chemical composition of the aluminium sheet was determined using an oxford-Cegelec FOUNDRY-MASTER spark OES spectrometer, Table 1.

Table 1. Average chemical composition of aluminum sheets (in wt.%)

Mg | Si | Cu | Fe | Mn | Zn | Cr | Ti | Al
AA5083 | 3.990 ±0.080 | 0.200 ±0.004 | 0.004 ±0.003 | 0.200 ±0.003 | 0.390 ±0.008 | 0.010 ±0.001 | 0.090 ±0.002 | 0.010 ±0.001 | Bal.

A 0.25 mm thick polyetherimide (PEI) film, provided by Goodfellow, was used as the energy director. PEI was dried at least 24 h at 130∘C before welding.

Polymer specimens' preparation

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The composite laminates, comprising seven semi-impregnated fabric layers arranged in a [0/90] stacking sequence, were consolidated using a Pinette Emidecau Industries Lab800 thermocompression device. The CF/PEKK plies were consolidated within a steel frame to reach 2 mm thick plates [16]. Specimens were prepared in dimensions of 100×25 mm2. The edges were deburred after cutting, and all samples were cleaned with ethanol to remove impurities and residual release agents.

Metal surface preparation

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Aluminum sheets were cut using laser processing to ensure precise edges for joint configuration welding. After cutting, the weld samples ( 100×25 mm2 ) were polished using P300 abrasive silicon carbide (SiC) paper to remove surface oxides and then cleaned with alcohol.

Several types of surface preparation were tested:

Rough polishing with P60 paper SiC.

Laser texturing.

Anodizing.

All pretreated AA5083 substrate was cleaned with acetone and alcohol before and after surface preparation, to remove greasy dirt and aluminum alloy residues using an ultrasonic cleaner.

Laser texture processing was carried out under argon gas protection or atmospheric atmosphere, using a continuous-wave Yb: YAG laser disk (TRUMPF TruDisk 3001), producing periodic grid patterns on surfaces. The texturing area measured 25×25 mm2 and had a spacing interval of 1.5 mm . The laser energy was kept constant by controlling the output power at 500 W , the scan velocity at 75 mm·s−1 and the spot size diameter at 200μ m.

The anodizing process for the AA5083 samples was performed in the following steps:

Degreasing with acetone.

Chemical stripping in 60 g·l−1 sodium hydroxides (NaOH).

Neutralization in 200 g·l−1 nitric acid (HNO3).

Anodizing in an electrolytic solution of 100 g·1−1 sulfuric acid (H2SO4) for 20 minutes at 20∘C with an operating voltage of 18 V and a current density of 2 A·dm−2.

Rinsing with deionized water and air drying

Experimental methods

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Omega 4X ultrasonic welder from Mecasonic was used for the experiments. Its specifications are a working frequency of 20 kHz and a maximum load of 2600 N . The displacement amplitude of the waves generated by the generator is increased by a factor of 1.7 through the booster and further amplified by a factor of 1.7. The welder's sensors and actuators are connected to an interface card located inside the module. Configuration for ultrasonic welding with 40 mm diameter sonotrode is presented in Fig. 1.

[picture]

Fig. 1. Scheme showing configuration for USW with 40 mm diameter sonotrode of studied assemblies

Fig. 1. Scheme showing configuration for USW with 40 mm diameter sonotrode of studied assemblies

The quality of the assemblies was assessed by lap shear strength (LSS). The assemblies tested were made following ASTM D1002, with an overlapping area of 12.5×25 mm2. The single lap shear (SLS) tests were performed on the Instron Universal 33R4204 tensile machine equipped with a 50 kN load cell with a crosshead speed of 2800 N· min−1 or 1 mm· min−1. The value of lap shear strength was calculated by Eq. 1.

LSS=FmaxWarea (1)

In SLS test, the strength of a weld depends on the maximum load ( Fmax ) at the breaking point divided by the real welded area ( Warea  ) after failure.

Observations of the macrostructure and microstructure of surface for AA5083, the joint interface and fracture surfaces of AA5083-CF/PEKK joints were examined using a high-resolution optical microscope VHX-6000S by Keyence Corporation and a scanning electron microscope (SEM) with energy-dispersive X-ray spectroscopy (EDS) EVO HD 15 LS by ZEISS.

Results and Discussion

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Morphology of the AA5083 substrate after laser treatment plays a significant role in joining since it promotes the mechanical interlocking of molten PEI into Al samples. At first, the influence of the roughness was studied. Fig. 2 shows the optical microscopy images of the prepared samples before and after mechanical treatments, polishing (SiC) P60 abrasive paper, as well as laser texturing. The roughness was measured using a roughness tester, a portable measuring device that determines the roughness depth ( Ra,Rz,Rq and Rt ). Thus, the roughness Ra for the raw material is 0.473±0.012μm, the mechanical polishing has created a surface roughness of 1.416±0.198μ m, while the laser texturing allowed to obtain the average porosity of 5.521±0.786μ m.

[picture]

Fig. 2. Microstructure of (a) raw, (b) polished with P60 paper, (c) and laser-textured Al samples

Fig. 2. Microstructure of (a) raw, (b) polished with P60 paper, (c) and laser-textured Al samples

To investigate the effect of laser texturing type on joint strength, the energy density is considered as constant. The grooves are clearly seen on the surfaces and recast layer, and burs are formed around texturing grid due to the melting of Al samples based on the 3D image from observations in Fig. 3. The grooves formed on the surface create a hierarchical structure. The depth scan line from optical microscope indicates that the molten aluminum deposits in the surface brings variations in the height of the walls and decreases the uniformity of the surface structure. Based on the groove depth measurements, the groove depth is less than 100μ m. Moreover, the aluminum deposition around edge of the laser path brings in depth fluctuation.

[picture]

Fig. 3. Microstructure and groove depth of textured AA5083 sample

Fig. 3. Microstructure and groove depth of textured AA5083 sample

Preliminary ultrasonic welding tests revealed that laser-textured Al surfaces with an average roughness of 5.5μ m provided the most effective mechanical interlocking between the thermoplastic matrix and the metal substrate. Compared with raw Al samples and those manually abraded using

P60 abrasive paper, the laser-induced micro-channels and controlled periodic features significantly enhanced polymer flow and anchoring during welding. The improved interfacial morphology facilitated a more uniform wetting of the molten polymer and promoted stronger anchorage points, resulting in more stable welds. These findings confirm that precise, repeatable laser texturing yields a more favorable surface topography for metal-CF/PEKK hybrid joints than conventional mechanical abrasion or untreated surfaces.

Nevertheless, laser texturing of aluminum was found to be highly sensitive to the surrounding atmosphere, with noticeable differences between surfaces processed in atmospheric air and those textured under argon gas protection. When textured in atmospheric air, the high-energy laser pulses induced rapid local heating and selective oxidation of the alloying elements. Because magnesium has a much higher oxygen affinity than aluminum, the surface preferentially formed a magnesium oxide (MgO) layer, rather than aluminum oxide (Al2O3), Fig. 4.a. A significant amount of MgO becomes visible on the surface after the laser passes. This phenomenon is directly linked to the high local temperatures generated by the laser and the strong affinity of magnesium for oxygen. Magnesium has a lower boiling point ( 1090∘C ) and higher vapor pressure compared to aluminum, meaning that under intense heating, magnesium atoms tend to migrate toward the surface more readily. When the laser rapidly heats the alloy, often locally above 1500−2000∘C, magnesium near the molten zone can segregate and diffuse upward to the surface. This MgO layer tended to be thicker, brittle, and uneven, and was often accompanied by micro-debris and irregular resolidified structures, which reduced the consistency of the textured features. Kim et al. [17] showed that when laser welding Al−Mg alloys in air, molecular spectra of MgO and AlO appear, whereas under argon shielding these oxide lines disappear. In contrast, laser texturing under an argon atmosphere strongly limited oxidation reactions, preventing the formation of MgO and leading to cleaner, sharper, and more uniform micro-grooves with improved reproducibility in depth and topography, Fig. 4.b. These atmospheric effects directly influence subsequent ultrasonic welding: argon-textured surfaces promote better polymer wetting and mechanical interlocking, while air-textured surfaces may hinder flow due to the presence of MgO and debris. Therefore, controlling the texturing atmosphere is essential to achieve high-quality surface functionalization for metal-CF/PEKK hybrid joints.

[picture]

Fig. 4. Element map distribution of Al,Mg,O after laser texturing in (a) atmospheric air and (b) argon atmosphere

Fig. 4. Element map distribution of A l , M g , O after laser texturing in (a) atmospheric air and (b) argon atmosphere

Performance of laser texturing under argon protection enabled the formation of well-defined micro-grooves that promoted an effective mechanical hook between the thermoplastic polymer and
the Al samples during ultrasonic welding. The argon atmosphere prevented oxidation during texturing, producing clean and sharp features that facilitated polymer flow and anchoring [18]. However, despite this improved mechanical interlocking, no significant chemical adhesion was observed at the metal-polymer interface, as the inert argon environment limits the formation of oxide ( O2− ) species that could participate in interfacial bonding. To compensate for the absence of such functional surface chemistry, anodization of Al samples becomes necessary [19]. After laser texturing under argon, anodization is applied to improve the durability and strength of the bond. Here, the Al substrate is immerse in an acidic liquid, upon which an electric current is applied through substrate and liquid to enable an anodic corrosive reaction on the substrate surface. It generates a stable porous oxide layer capable of enhancing surface energy and providing chemical sites that improve polymer wetting and adhesion. Fig. 5.a presents anodized aluminum membranes created during chemical treatment, however when the image is zoomed, Fig 5.b, the nanopores reveal themselves. The thermoplastic can mechanically interlock inside these pores, which also results in an increased surface area. Consequently, combining argon-assisted laser texturing with subsequent anodization offers a promising route to achieve both strong mechanical interlocking and enhanced chemical bonding in hybrid metal-polymer joints.

[picture]

Fig. 5. SEM images of the top view of (a) anodized aluminum oxide membrane with (b) enlarged pores

Fig. 5. SEM images of the top view of (a) anodized aluminum oxide membrane with (b) enlarged pores

During sulphonic acid anodization of aluminum, the electrochemical process generates a porous alumina layer that contains incorporated sulfate ( SO42− ) species originating from the electrolyte. These sulfur-containing groups become embedded within the anodic oxide and remain bound to the pore walls. The formation of porous anodic alumina via sulfuric-acid anodization can have beneficial effect of porous morphology on polymer adhesion [20]. However, the microstructure (porosity, pore density, pore diameter) depends strongly on the alloy composition, electrolyte, voltage, and processing parameters [21]. Such porous oxide layers generally enhance adhesion performance with polymers compared to bare aluminum, because the pores offer mechanical interlocking and improved wettability. For example, a recent study showed that optimizing anodized 6061 aluminum surface morphology improved bonding with carbon-fiber reinforced thermoplastics [20].

Polyetherimide (PEI), which contains imide groups (-CO-N-CO-) and aromatic rings, is known to interact more effectively with polar and high-energy surfaces. It is therefore hypothesized that sulfaterelated species may contribute to increased surface polarity or acidity, potentially facilitating hydrogen bonding, van der Waals interactions, or dipole-dipole interactions with PEI. However, these specific interactions have not yet been experimentally confirmed and require further spectroscopic and interfacial characterization to be validated.

What is certain, based on established anodization behavior, is that the porous morphology of the anodic oxide enhances mechanical anchoring and improves wetting of molten PEI during ultrasonic welding. Any additional chemical contribution from sulfate species remains a promising but
unverified mechanism that warrants further study to fully understand and optimize metal-polymer adhesion.

[picture]

Fig. 6. Element map distribution of Al,Mg,O,S after laser texturing and anodization

Fig. 6. Element map distribution of A l , M g , O , S after laser texturing and anodization

Then, the ultrasonic welding parameters were established using a 40 mm diameter circular titanium sonotrode, drawing on insights from previous extensive trial-and-error optimization work. Key process variables responsible for heat generation at the interface, namely vertical pressure, vibration amplitude, and sonotrode displacement, were adjusted according to the specific material combinations. The innovative aspect of this study lies in the evaluation of a multi-mode ultrasonic welding strategy [22] and its influence on the mechanical performance of hybrid interfaces. Notably, most studies reported in the literature rely on a single control mode, limiting the flexibility and robustness of the process. In contrast, the controlled division of the vibration cycle employed here improves result reliability by automating and stabilizing the critical phases of the welding curve, which are essential for achieving high-quality, repeatable joints. In these experiments, the vibration phase was divided into three distinct stages, each using a different sonotrode amplitude.

[picture]

Fig. 7. Power and displacement curves of ultrasonic welding for hybrid metal - polymer joints

Fig. 7. Power and displacement curves of ultrasonic welding for hybrid metal - polymer joints

The assemblies were kept under an operating pressure of 0.3 MPa during the welding process. A cooling time of 4 s at the operating pressure of 0.3 MPa was then applied. Fig. 7 presents the evolution of power and displacement during ultrasonic welding of the CF/PEKK using a PEI energy director against the aluminum substrate. The curve reveals four distinct welding phases, each corresponding to specific thermal-mechanical transformations at the joining interface. These phases determine the quality of the bond and the final mechanical performance of the welded joint.

In the first welding phase, ultrasonic power increases steadily while the sonotrode displacement remains low. At this point, heating is primarily driven by viscoelastic dissipation in the PEI energy director. PEI approaches its glass transition temperature and begins to soften, enabling intimate contact with both the CF/PEKK surface and the aluminum substrate. During this early phase, the PEKK matrix in the composite remains below its melting temperature, and the carbon fibers preserve their structural integrity. The aluminum substrate also behaves rigidly, undergoing only minor surface heating. This phase conditions the interface for efficient energy transfer and prepares the energy director for the onset of melting.

The second phase is characterized by a sharp increase in ultrasonic power, followed by the slow rise in displacement, indicating the onset of interfacial collapse. This corresponds to the flowing of the PEI energy director and partial softening of the PEKK matrix during the first peak of power with stable displacement. The molten PEI begins to flow laterally and vertically, filling microstructural features on the aluminum surface and initiating both wetting and diffusion of species.

Then, the second power peak appears when the entire PEI thickness of 0.25 mm has been flattened under the ultrasonic loading, marking the complete expulsion and redistribution of the softened energy director across the interface. Simultaneously, the CF/PEKK composite undergoes partial crushing of the surface plies, as the softened PEKK allows fiber imprints and local deformation. Together, these coupled phenomena when PEI collapse, aluminum flow, and surface crushing of CF/PEKK define the critical bonding window in which the final interfacial architecture and mechanical performance of the welded joint are established.

The final welding phase shows irregular power fluctuations accompanied by a rapid increase in displacement that gradually plateaus. This behavior reflects the final redistribution of molten PEKK within the aluminum surface features. At this moment the aluminum substrate also begins to experience flow localized on the corners under the combined effects of heat and pressure, which contributes to a more intimate contact with the molten polymer. As the interfacial layer collapses and consolidates, we assumed that a mixed PEI-PEKK interphase forms through molecular interdiffusion. The aluminum, regardless of texture or treatment, undergoes a little deformation on the corners of sample; its role is purely interfacial. In textured conditions, the grooves are progressively filled by the molten polymer, creating a mechanical hook. In anodized conditions, the role of oxide porosity, mechanical interlocking, and potential oxide-polymer interaction is possible [20], [23], [24]. The role of sulfate species in anodic alumina for PEI (or PAEK) adhesion remains a hypothesis. When the ultrasonic vibrations stop, the materials cool under pressure, resulting in solidification of the thermoplastics and stabilization of the final joint thickness.

After cooling, the joint exhibits a combination of mechanical interlocking, polymer-polymer entanglement between PEI and PEKK, surface chemical bonding in the presence of anodic sulphaterich alumina and structural reinforcement from carbon fibers constraining the molten flow. This multi-mechanism consolidation explains the improved joint performance observed in optimized welding conditions.

The mechanical performance of the welded joints was evaluated through single lap shear testing, which revealed a LSS of 2.5±1.7MPa. However, the maximum LSS reached was 4.3 MPa . As comparison, the LSS of CF/PEEK welded with CF/PEEK can reach about 49 MPa [4]. This moderate strength reflects the combined effects of material behavior during welding and the interfacial architecture formed at the metal-polymer boundary. The relatively low LSS indicates that, although partial interfacial bonding was achieved, the total average welded zone was only 175 mm2, instead of approximately 312 mm2. The joint did not reach the levels typically expected for fully consolidated hybrid welds. The result suggests limitations in either polymer flow, mechanical interlocking, and/or chemical adhesion at the aluminum interface, consistent with the observed collapse behavior and incomplete wetting during the welding cycle.

The fractography of hybrid welded joints with aluminum substrate after single lap shear testing is presented in Fig. 8. The SEM images revealed clear evidence of PEI transfer onto the aluminum substrate (the black color in Fig.8.a), indicating partial interfacial adhesion developed during the welding process. The aluminum surfaces exhibited distinct patches and streaks of adhered PEI,
confirming that the molten energy director had sufficiently wetted the surface before solidification. In addition to polymer transfer, a very small but detectable transfer of aluminum into the PEI layer was observed (the white color in Fig. 8.b), suggesting that localized surface plasticization or microfragmentation occurred during the high-energy vibration phase. Furthermore, the fractured PEI surface displayed a well-defined imprint of the aluminum mesh pattern, demonstrating that the softened polymer was able to penetrate the surface micro-reliefs and form a mechanical hook during welding. This characteristic imprint confirms that mechanical interlocking contributes to the overall joint behavior. However, the discontinuous distribution of PEI residues and the limited extent of aluminum transfer correlate with the modest lap shear strength, indicating that adhesion occurred only in isolated zones rather than across a fully continuous interface.

[picture]

Fig. 8. Fractography of welded joints with SEM images for (a) aluminum substrate and (b) CF/PEKK substrate

Fig. 8. Fractography of welded joints with SEM images for (a) aluminum substrate and (b) CF/PEKK substrate

Failure modes were predominantly interfacial, confirming that the adhesion mechanisms developed during welding were insufficient to sustain higher loads. These findings emphasize the need for improved surface preparation, enhanced energy director performance, and/or optimized ultrasonic parameters to achieve stronger and more reliable joints.

Summary

The original version of this paper is available on https://www.scientific.net/DDF.451.23.pdf

This study investigated the influence of aluminum surface finish and the use of a PEI energy director on the ultrasonic welding of PAEK/metal hybrid structures. The results demonstrate that surface preparation plays a decisive role in determining interfacial behavior, heat generation, and the resulting mechanical performance of the welded joints. Laser texturing under argon protection produced clean and well-defined micro-features that enabled effective polymer flow and mechanical interlocking, whereas laser texturing in ambient air promoted the formation of magnesium oxide, limiting wetting and reducing weld uniformity. Anodization further enhanced the interfacial chemistry by creating a porous, sulfate-rich oxide layer that improved PEI adhesion and contributed to more consistent polymer anchoring.

The use of a 0.25 mm PEI energy director facilitated controlled melting, polymer redistribution, and partial interdiffusion with the PAEK matrix, although the collapse behavior highlighted the sensitivity of the process to energy input and interface stability. Fractographic analyses revealed mixed adhesive-cohesive failure with limited PEI transfer and minor aluminum imprinting, indicating
that bonding occurred but remained discontinuous. As a result, the maximum measured lap shear strength of 4.3 MPa reflects the need for further optimization of interfacial design and welding parameters.

Overall, the study shows that ultrasonic welding of PAEK/metal hybrids is feasible, but its success strongly depends on the combination of surface morphology, surface chemistry, and energy director behavior. Future works should focus on improving oxide-layer engineering, refining laser texturing strategies, and developing tailored ED geometries to enhance both mechanical interlocking and chemical adhesion. These advances will help unlock the full potential of ultrasonic welding for highperformance hybrid structures in aerospace and other advanced engineering applications.

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The original version of this paper is available on https://www.scientific.net/DDF.451.23.pdf

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S. T. Amancio-Filho, C. Bueno, J. F. dos Santos, N. Huber, and E. Hage, 'On the feasibility of friction spot joining in magnesium/fiber-reinforced polymer composite hybrid structures', Materials Science and Engineering: A, vol. 528, no. 10, pp. 3841-3848, Apr. 2011, doi: 10.1016/j.msea.2011.01.085.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 35-44

doi: 10.4028/p-QT6oyp

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

Submitted:
2025-12-19

Revised:
2026-03-03

Accepted:
2026-03-03

Online:
2026-04-17

Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

Katerina Vrettos 1,a, Steven Le Corre 1, b, Jean-Luc Bailleul 1,c*, Erwan Bertevas 2, d

1 Nantes Université, CNRS, Laboratoire de thermique et énergie de Nantes, LTEN, UMR 6607, F-44000 Nantes, France

2 Nantes Université, IRT Jules Verne, F-44000 Nantes, France

a Ecaterini.Vrettos@univ-nantes.fr, b steven.lecorre@univ-nantes.fr, c* Jean-luc.bailleul@univ-nantes.fr, d erwan.bertevas@irt-jules-verne.fr

*TACOMA for Thermo-Adhesion by Conductive heating of composite Materials

Keywords: interphase characterization, PEEK / LM-PAEK, welding thermoplastics.

Abstract

Thermoplastic composites offer new opportunities for multifunctional lightweight structures through their ability to be joined by fusion welding. However, the welding of dissimilar thermoplastic composites remains challenging due to asymmetric melting behavior and heterogeneous reinforcement architectures, all of which influence interfacial quality and mechanical performance. Within the CONNECT project, this study focuses on the adhesion development between a short carbon fiber reinforced PEEK and a continuous carbon fiber reinforced LM-PAEK laminate. Welding was performed using the TACOMA platform, which allows precisely controlled and asymmetric conductive heating cycles. The influence of welding temperature and contact time on interface formation was examined through Double Cantilever Beam (DCB) tests under Mode I loading, complemented by surface topography and scanning electron microscopy. Results show that welding at 350∘C significantly enhances interfacial fracture toughness compared to 345∘C, reflecting increased chain mobility of the PEEK matrix while the LM-PAEK phase is already molten. However, prolonged contact times lead to reorientation of short fibers parallel to the interface within the molten PEEK suppressing fiber bridging mechanisms at the interface and reducing the resistance to crack initiation, resulting in lower measured GIC values. These findings provide new mechanistic insight into the welding of dissimilar PAEK-based composites and identify a narrow processing window in which asymmetric melting and reinforcement morphology jointly govern interfacial performance. The interfacial fracture toughness was evaluated using a mode I initiation energy approach, selected due to unstable crack propagation in this bi-material configuration.

Introduction

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High-performance thermoplastic polymers have emerged as attractive alternatives to thermosetting matrices in advanced composite structures. Among them, poly (aryl ether ketones) (LM-PAEKs) forms a family of semicrystalline polymers renowned for their excellent thermal stability, solvent resistance, and mechanical performance [1]. Within this family, polyether ether ketone (PEEK) has gained particular attention for its ability to be processed into composites with outstanding strength and toughness [2].
In demanding sectors such as aerospace and aviation, LM-PAEK and PEEK-based composites are increasingly adopted owing to their high strength-to-weight ratio, damage tolerance and reusability. However, composite assemblies remain challenging because local stress concentrations near fasteners can initiate damage and compromise structural integrity [3]. This limitation underscores the need for joining techniques that minimize mechanical fastening.
Thermoplastic matrix composites (TMCs) address this challenge, as they can be joined by welding. Unlike thermosets, thermoplastics lack chemical crosslinking and can therefore be remelted and reshaped. When heated above the melting temperature under pressure, molecular chains interdiffusion
across the interface and form new entanglements, resulting in joint healing [4]. This characteristic makes PAEK-based composites highly suitable for welded structures [5,6].
Nevertheless, the same features that make LM-PAEKs high-performance materials-rigid aromatic backbones, high crystallinity, and elevated melting points-also render them difficult to weld efficiently. Successful welding requires heating close to or above the melting point of the adherends while ensuring intimate contact and sufficient pressure to promote chain mobility [8]. Although progress has been achieved in fusion-welding techniques such as induction, resistance, and laser welding, most studies have focused on identical material systems (e.g., PEEK-PEEK or PEKKPEKK) [9]. Welding of dissimilar PAEK-based composites remains far less explored, despite its industrial relevance.
Hybrid joints between short-fiber-reinforced PEEK and unidirectional continuous-fiber LM-PAEK offer a promising approach, combining the high stiffness and load-bearing capacity of continuous fibers with the design flexibility and cost efficiency of injection-molded short-fiber composites [6,7]. The presence of short fibers near the interface may promote crack deflection, mechanical interlocking or localized stress concentrations, strongly influencing fracture behavior.
In this context, this study investigates the welding of two dissimilar thermoplastic composites, emphasizing how asymmetric melting and short fiber morphology govern the interface formation and fracture behavior of the welded joints.

Materials and Sample Preparation

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Two different thermoplastic composites were employed in this study. The first was a laminate made of 24 plies of unidirectional continuous carbon fiber tape embedded in an LM-PAEK matrix ( Tm≈.307∘C). The second was an injection-molded plate of short carbon fiber-reinforced PEEK ( Tm≈343∘C ).
The injection-molded plates were cut into 125×25 mm specimens with a Protomax waterjet machine (Fig. 1), to fit the TACOMA welding system size. A countersunk hole was drilled 6 mm from one end to accommodate a loading pin for fracture testing. Prior to welding, all specimens were cleaned with acetone and dried overnight at 180∘C to remove residual moisture. A 20μ m aluminum foil was inserted between the adherends at a distance of 50−60 mm from the loading point to define an initial crack, and polyimide tape was applied on the composite side in contact with the mold to facilitate demolding after welding.

[picture]

Fig. 1. Schematic illustration of the samples.

Fig. 1. Schematic illustration of the samples.

Experimental Welding Bench

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

The isothermal welding procedure performed on the TACOMA device (Fig.2) - originally developed for similar-material joints-has been previously described in detail by Avenet et al. [10]. The system consists of heated metallic plates equipped with embedded thermocouples and water-cooling channels, enabling precise control of time, temperature, and pressure. In this study, welding was achieved by heating both adherends to temperatures above their respective melting points, applying pressure for the selected contact time, and subsequently cooling under pressure to consolidate the interface. The welding pressure was determined through preliminary trials on the same hybrid configuration, which showed that higher pressures led to excessive flow and material loss of the
lower-melting LM-PAEK due to the combined effects of temperature and pressure, whereas lower pressures resulted in insufficient intimate contact. The selected pressure therefore ensured stable interface formation while minimizing polymer squeeze-out. All welding parameters used in the present study are summarized as follows: welding temperatures of 345∘C and 350∘C, constant pressure of 0.2 bar, and contact times ranging from 0 s corresponds to press closure at the target welding temperature followed immediately by the cooling stage, without any dwell time under pressure, to 200 s . The thermal cycle included heating, stabilization, contact under pressure, cooling under constant pressure, and pressure release (Fig.3).

[picture]

Fig. 2. Schematic representation of TACOMA before and during welding, showing specimens positioning and applied pressure and photograph of the actual instrumentation.

Fig. 2. Schematic representation of TACOMA before and during welding, showing specimens positioning and applied pressure and photograph of the actual instrumentation.

[picture]

Fig. 3. Representative experimental welding cycle performed using the TACOMA conductive heating platform. The sequence includes heating to the target temperature ( Tweld =350∘C ), temperature stabilization, contact under pressure (P=0.2 bar ) for tcontact =200 s, cooling under constant pressure, and final pressure release. An identical thermal sequence was applied for all specimens, with the welding temperature and contact time varied according to the processing parameters summarized in Table 1.

Fig. 3. Representative experimental welding cycle performed using the TACOMA conductive heating platform. The sequence includes heating to the target temperature ( T weld = 350 ∘ C ), temperature stabilization, contact under pressure ( P = 0.2 bar ) for t contact = 200 s , cooling under constant pressure, and final pressure release. An identical thermal sequence was applied for all specimens, with the welding temperature and contact time varied according to the processing parameters summarized in Table 1.

Table 1. Welding parameters tested in this study.

Temperature (°C) | Pressure (bar) | Contact Time (s) | Replicates
345 | 0.2 | 0–200 | n=3
350 | 0.2 | 0–200 | n=3

Fracture Testing

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Double Cantilever Beam (DCB) tests were carried out on a 100 kN Zwick/Roell universal testing machine under displacement control at a constant crosshead speed of 1 mm· min−1. Custom-designed loading pins were manufactured in-house and directly inserted into the pre-drilled holes of the specimens (Fig.4). The pins were carefully centered along the specimen width to ensure symmetric load transfer and to prevent torsional effects during testing. Load and displacement were continuously recorded throughout the experiment. The initial crack length ao was defined by the position of the 20 μm non-adhesive aluminum insert ( 50−60 mm from the loading point) and measured prior to testing. All tests were performed at room temperature ( ≈23∘C ). For each welding condition, at least n=3 specimens were tested to ensure repeatability. Since no standardized procedure currently exists for determining the interfacial fracture energy ( GIC  ) in such hybrid configurations, several data-reduction methods were evaluated. Among these, the Compliance Calibration Method (CCM) was initially considered more suitable for bi-material interfaces, as it accounts for differences in stiffness and compliance between the adherends [11].

[picture]

Fig. 4. Double Cantilever Beam (DCB) fracture test set-up.

Fig. 4. Double Cantilever Beam (DCB) fracture test set-up.

The compliance method is expressed as:

GIG=P22 bdCda(1)

where C=δ/P is the compliance, a is the crack length, P is the applied load, and b is the specimen width. For each crack length, compliance values were obtained from the force-displacement ( F−δ ) data. The derivative dC/ da was determined through compliance calibration, where the compliancecrack length ( C−a ) relationship was fitted with a cubic polynomial ( C=C3a3+C2a2+C1a+C0 ) to account for crack rotation and shear effects.
However, during the experiments, crack propagation was observed to be abrupt and unstable, preventing the establishment of a reliable compliance-crack length ( C−a ) relationship. As crack growth occurred over a very short time interval, it was not possible to accurately measure successive crack lengths ( a1,a2, etc.) required for the application of the Compliance Calibration Method (CCM). Since CCM relies on stable and gradual crack propagation to ensure accuracy, this method was therefore not applicable under the present testing conditions.
It should be emphasized that no standardized procedure currently exists for the determination of mode I interfacial fracture toughness in hybrid thermoplastic composite systems involving adherends with distinct stiffness and reinforcement architectures. The present work therefore adopts an initiation energy approach as a pragmatic and physically consistent metric for comparative purposes. Ongoing work aims to establish a more robust methodology adapted to such asymmetric configurations.
Based on these observations, the classical Initiation Energy approach was adopted for the determination of the mode I interfacial fracture toughness GIC . This approach evaluates the energy required to initiate crack propagation at the critical load and does not rely on stable crack growth or on the establishment of a compliance-crack length relationship. In the present hybrid configuration, involving two adherends with distinct mechanical properties and stiffness, crack propagation is strongly influenced by mechanical mismatch and stiffness asymmetry, making compliance-based approaches particularly sensitive to unstable fracture behavior. In contrast, the initiation fracture energy provides a well-defined and physically meaningful measure of interfacial resistance, as it is
governed by the onset of crack propagation rather than its subsequent evolution, thereby enabling consistent comparison between specimens processed under different welding conditions.
In this case, ao represents the initial crack length introduced by the aluminum foil between the adherends, Pc is the critical force required to initiate the crack, and δc is the corresponding displacement. The initiation fracture energy was calculated using Eq. (2).

GIC=3Pcδc2ba0(2)

Overall, despite the lack of stable crack growth, the Initiation Energy approach proved to be a robust and physically justified method for assessing and comparing interfacial fracture toughness in this bimaterial system, as it relies on a well-defined energy criterion at crack initiation that is not affected by the asymmetric stiffness and mechanical mismatch between the two adherends.

Materials Characterization

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After the DCB fracture tests, the welded surfaces of the laminates were examined to study the failure mechanisms and the quality of the interface. First, optical inspection was carried out with a Keyence VHX-7000 digital microscope, which provides high-resolution images with magnifications up to 2000×.
The fracture surfaces were then analyzed in more detail using scanning electron microscopy (SEM) to observe their microstructural features. Finally, the surface roughness of the adherends before welding was measured with an ALICONA Infinite Focus 3D profilometer, which generates precise 3D maps of the surface topography. These measurements helped to evaluate how the reinforcement of the composites may affect the welding quality.

Results and Discussion

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Fig. 5a shows the evolution of GIC  with contact time for both processing temperatures. An overall increase in GIC  is observed at 350∘C, confirming that higher temperature enhances chain mobility and interdiffusion across the interface. At short contact times ( 10−20 s ), the difference between specimens remains within the experimental scatter, suggesting that adhesion development is mainly governed by the establishment of surface contact rather than extensive molecular reptation. Among the investigated conditions, welding at 350∘C with short-to-intermediate contact times ( 10−20 s ) yielded the highest measured initiation fracture toughness and is therefore identified as the optimal processing window within the explored parameter space.
In the present study, short contact times refer to 10 s , and long contact times to >20 s. At longer holding times, a noticeable decrease in GIC  is recorded for both temperatures. Image observations reveal that during prolonged exposure, the short fibers tend to reorient parallel to the interface rather than penetrating into the LM-PAEK matrix. As a result, they no longer act as mechanical bridges across the joint, leading to a reduction in effective load transfer at the onset of crack growth and consequently lower measured initiation fracture toughness. This morphological evolution explains the apparent drop in GIC  despite the longer contact duration.
To better correlate the interfacial strength evolution with the molecular interdiffusion process, the Degree of Healing (Dh) was computed from Eq. (3) using the measured mode I fracture toughness values GIC  normalized by the highest measured fracture toughness value obtained in this study, taken as the fully healed condition. The faster increase in Dh at 350∘C reflects enhanced interfacial diffusion associated with increased chain mobility of the PEEK matrix, while the LM-PAEK phase is already fully molten. At 345∘C, the healing remains incomplete ( Dh≈0.7 ), indicating that limited chain mobility of the PEEK restricts interfacial entanglement. The asymmetric melting behavior of the two polymers thus governs the observed healing kinetics, defining an optimal processing window near 350∘C and short-to-moderate holding durations.

Dh=GICGIC,∞(3)

[picture]

Fig. 5. a) Evolution of interlaminar fracture toughness for two isothermal temperatures versus contact time and b) Evolution of the Degree of Healing as a function of healing time for LMPAEK/PEEK interfaces at 345∘C and 350∘C.

Fig. 5. a) Evolution of interlaminar fracture toughness for two isothermal temperatures versus contact time and b) Evolution of the Degree of Healing as a function of healing time for LMPAEK/PEEK interfaces at 345 ∘ C and 350 ∘ C .

Observation of the Interface

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

This section presents a qualitative analysis of the cross-sections and fracture interfaces after the DCB tests, in order to study adhesion and material behavior under Mode I loading. Particular attention is given to the role of the short carbon fibers in the injection-molded PEEK adherend. Their presence at or near the welded interface can promote crack deflection, fiber bridging, or localized stress concentrations, thereby influencing the apparent fracture toughness.
Inspection of the fracture surfaces provides further observations that clarify how the crack propagates, whether failure occurs mainly at the interface or within the bulk material, and how short fibers contribute to the overall welding performance.

Profilometry, Micrographs and SEM Images

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Fig. 6 illustrates the surface condition of the adherends before and after DCB testing. In Fig. 6a, the surfaces of the specimens prior to testing appear relatively smooth and homogeneous, without large defects or noticeable imperfections that could dominate crack initiation for both materials. After fracture (Fig. 6b), the surface shows clear evidence of crack propagation along the interface, with local damage zones and short fiber imprints. These features indicate a mixed failure mechanism combining adhesive and cohesive contributions. In Fig. 6b 1 we can observe the short fibers of PEEK attached on the surface of LM-PAEK and in Fig. 6 b2 we can observe the hole they leave behind. Fig. 6c1, obtained by optical microscopy, reveals that fragments of the PEEK matrix reinforced with short fibers remain attached to the LM-PAEK surface after fracture. This observation confirms that part of the failure occurred within the bulk PEEK material, providing direct evidence of cohesive failure. Such behavior highlights the contribution of short fibers to the crack path and to the overall welding performance.

[picture]

Fig. 6. a, b) Images of profilometry before and after healing and DCB test for both materials. c, d) Micrographs for both sides after DCB test. Sample welded at 350∘C in 10s with 0.2 bar pressure.

Fig. 6. a, b) Images of profilometry before and after healing and DCB test for both materials. c, d) Micrographs for both sides after DCB test. Sample welded at 350 ∘ C in 10s with 0.2 bar pressure.

The SEM observations corroborate the mechanical findings: specimens showing higher GIC (350∘C) exhibited well-consolidated interfaces and partial fiber bridging. Fig. 7 presents images of the crosssection at the bonded interface prior to DCB testing. The overall welding line between the LM-PAEK laminate and the injection-molded PEEK plate is observed. The two adherends appear well joined, with no large voids or delamination zones, indicating good consolidation during welding. In the second image, a closer view of the interface highlights the transition zone between the continuousfiber laminate and the short-fiber-reinforced PEEK. The presence of short fibers near the welding line is evident, suggesting that they can directly influence the interfacial morphology by promoting local mechanical interlocking and potentially altering crack initiation paths during loading. Fig. 8 shows SEM images of the fracture surfaces after DCB tests. In Fig.8a, the overall fracture surface of the LM-PAEK adherend reveals regions of interfacial failure combined with PEEK-rich areas. Fig. 8b and 8 c provide higher magnifications, showing fiber imprints and short-fiber pull-out from the PEEK side. These features confirm mixed failure mechanisms: adhesive failure at the interface and cohesive fracture within the PEEK matrix. Fig. 9 presents images from cross-section of welded joints for 10s and 200s. It can be observed the short fibers penetrate into the opposing surface, acting like bridges for short contact times and the reorientation of the fibers at the interface without penetration on the matrix for longer contact times.
The combination of results from all characterization methods provides a comprehensive picture of the adhesion mechanisms in the welded joints. Before testing, the adherend surfaces appeared homogeneous and well-prepared, with no major defects at the interface. After DCB testing, the fracture occurred through a mixed mode, at the interface and cohesive failure within the PEEK matrix. The presence of short carbon fibers in the injection-molded PEEK played a decisive role: in some regions they enhanced adhesion through mechanical interlocking and crack deflection, while in others they acted as initiation sites for fiber pull-out. This dual effect explains the variability of the fracture surfaces and highlights the sensitivity of the welding performance to microstructural features. Overall, the observations confirm that interfacial adhesion in dissimilar thermoplastic composites is governed not only by processing conditions but also by the intrinsic morphology of the adherends.

[picture]

Fig. 7. a, b) SEM images of cross-section ( 350∘C ), c,d ) images from optical microscope of crosssection and LM-PAEK side surface after DCB tests.

Fig. 7. a, b) SEM images of cross-section ( 350 ∘ C ), c , d ) images from optical microscope of crosssection and LM-PAEK side surface after DCB tests.

[picture]

Fig. 8. SEM images of LM-PAEK side surface after DCB test ( 350∘C ).

Fig. 8. SEM images of LM-PAEK side surface after DCB test ( 350 ∘ C ).

[picture]

Fig. 9. Optical micrographs of cross-section (350∘C) for a) 10 s, b ) longer contact times ( 200 s ).

Fig. 9. Optical micrographs of cross-section ( 350 ∘ C ) for a) 10 s , b ) longer contact times ( 200 s ).

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

This study demonstrated the feasibility of welding dissimilar thermoplastic composites-short carbon fiber reinforced PEEK and continuous carbon fiber reinforced LM-PAEK-using a rapid conductive heating technique. The interfacial fracture toughness GIC  was shown to be strongly governed by welding temperature and contact time. While the interface temperature exceeded the melting
temperature of LM-PAEK and approached or exceeded that of PEEK, optimal interfacial performance was achieved at 350∘C combined with short-to-intermediate contact times.
Prolonged holding durations led to a reduction in fracture toughness, which was attributed to the reorientation of short carbon fibers within the molten PEEK matrix. At short contact times, these fibers acted as mechanical bridges across the interface, enhancing load transfer at crack initiation. At longer times, fiber alignment parallel to the interface suppressed this bridging mechanism, resulting in lower measured GIC  values.
These findings highlight the strong coupling between thermal conditions, holding duration, and interfacial morphology in hybrid thermoplastic systems, particularly when processing occurs near the melting temperature of the higher-melting matrix. The results emphasize the decisive role of short fiber behavior at the welding interface and demonstrate that interfacial performance in dissimilar reinforced thermoplastics is controlled by microstructural evolution.
Beyond establishing feasibility, the present work represents a first systematic step toward understanding welding mechanisms in asymmetric thermoplastic composite joints. The absence of dedicated fracture methodologies for bi-material thermoplastic systems and the instability of crack propagation observed in this configuration underline the need for adapted testing protocols and future standardization efforts. Further investigation into pressure effects, thermal gradients, and fiber orientation dynamics will be essential to establish robust process-structure-property relationships and to enable the reliable industrial implementation of welding strategies for dissimilar reinforced thermoplastic composites.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

The authors would like to thank Jérôme Delmas and Nicolas Lefevre for their help for their contribution to the design and machining of the welding setup and Samuel Branchu for his valuable assistance with the SEM characterization. The authors also acknowledge the funding of the CONNECT project managed by the IRT Jules Verne (French Institute for Research and Technology) that made this work possible. The authors wish to associate the industrial partners of the CONNECT project: Airbus Atlantic, Airbus Operations, Daher Aerospace, Latecoere, Liebherr Aerospace Toulouse and Cero.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.35.pdf

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 45-53

doi: 10.4028/p-KOl4a2

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

Submitted:
2026-01-07

Accepted:
2026-02-25

Online:
2026-04-17

Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

MÜLLER Pascale 1,a*, KEHRET Daniel 2, b and JUNK Stefan 2,c

1 Offenburg University, SEM Lab, Badstr. 24, 77652 Offenburg, Germany

2 Offenburg University, Rapid Prototyping Lab, Klosterstr. 14, 77723 Gengenbach, Germany

a  pascale.mueller@hs-offenburg.de, b  daniel.kehret@hs-offenburg.de, c  stefan.junk@hs-offenburg.de

Keywords: resin, thermal conductivity, masked stereolithography, scanning electron microscopy, additive tooling.

Abstract

Injection molding tools are characterized by high costs, due to the use of expensive materials such as aluminum or tool steel, and the lengthy production process involving machining. This greatly limits the economic viability of using metal molds for producing small series, and even more so for rapid prototyping. Additive manufacturing processes, such as masked stereolithography (mSLA), enable the production of molds from polymers providing short production time and good accuracy. However, injection molds manufactured using mSLA using conventional resins suffer from long cooling times and lower strength. This contribution presents a new approach that significantly overcomes these disadvantages by developing and characterizing a novel composite material. To this end, aluminum oxide ceramic particles will be incorporated into a photopolymer resin. Various additives will also be employed to optimize the processability and printability of the newly developed material. This should enhance the thermal and mechanical properties of additively manufactured molds. A series of simple test specimens were produced using mSLA. Sedimentation and printability were analyzed by varying the aluminum oxide mixing ratio. The effect of various additives was also investigated. The composite materials were tested for processability, heat flow and mechanical properties. Scanning electron microscopy (SEM) was used to evaluate the particle size, quantity, distribution and homogeneity of the composite material. To demonstrate the application of the new material in additive tooling, a typical set of tool inserts for injection molding was manufactured.

Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

The continuous reduction in development times, the increasing number of variants and the steady rise in product customization have led to a significant increase in the relevance of Additive Manufacturing (AM) for the industry and further strengthened its position as a key technology. It is evident that AM is experiencing an increase in demand, which can be attributed to the growing complexity of components. Conventional manufacturing processes are characterized by restrictions in terms of manufacturability. Conversely, additive manufacturing is distinguished by its design freedom, a capability that no other process can offer, and the potential of this comparatively novel form of manufacturing is considerable [1]. In recent years, this has resulted in a substantial proliferation of printers utilizing a range of technologies [2]. Concurrent with the advancement of processes, there has been an expansion in the range of materials available for almost every application.

Injection molding represents a pivotal industrial production method. A significant share of all polymers is processed in this manner. In the range of 500 to 2000 bar, and at temperatures of 200 to 300∘C, liquid plastic can be rapidly shaped into its final form. This process of shaping is accompanied by the hardening of the material as it cools. This facilitates the efficient production of large quantities with low tolerances, a wide variety of shapes and economical use of materials [3]. A significant cost consideration in the context of injection molding is the substantial expense associated with the fabrication of injection molds. The process is known to exert significant demands on materials, with rapid changes in temperature and pressure having a considerable impact on their integrity. The injection molds, which are the core of the process, are both costly and time-consuming to
manufacture, with production times often extending to several months [4]. Consequently, the economic viability of producing small series or prototypes is often limited.

AM processes are becoming increasingly important for reducing the costs and time of mold production. The present process is principally utilized for the validation of prototypes. The aforementioned procedure, also referred to as Additive Tooling, facilitates the examination of both the target material and the target production technology. In addition, it enables the analysis of the anticipated costs and time savings. Existing additively manufactured molds made of plastic exhibit the disadvantage of low thermal conductivity, which renders them unusable since longer cooling times slow down the process and change the materials properties in the molded part [2]. Despite the thermostability of additively manufactured molds made of metals, their manufacturing process is both complex and costly.

The objective of this research is to develop a material that enhances the properties of molds made using additive manufacturing techniques from plastic. For this purpose, a composite material was formulated from resin with aluminum oxide. The processibility, shear flow and mechanical properties of this material were then investigated. In this context, it is imperative to deliberate on the issues associated with such suspensions, particularly with regard to sedimentation, homogeneity, and photopenetrability. It is well established that these parameters are subject to significant fluctuations, which are primarily attributable to the filler and the degree of filling.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

Masked stereolithography (mSLA) is a process that involves the solidification of liquid synthetic resins by means of irradiation with Ultra Violet light (UV). The resins are masked during this process using an LCD display [5]. The mSLA process has been demonstrated to be capable of rapidly producing intricate molds with a very high surface quality. In the mSLA process, a chain former and a crosslinker are processed with a photo-initiator and applied in 50μ m or thinner layers, which are then cured by UV light. The material's photo-penetrability imposes limitations on the processing speed, resulting in layers that are thinner than those applied in filament printing and a smoother surface [5]. In comparison with 3D-printers that utilize material extrusion (for example, fused filament fabrication), mSLA printers offer the advantages of high precision and good surface quality at a relatively low cost [6]. In the context of our application, it was necessary to utilize a photosensitive resin that exhibited both adequate mechanical properties and the capacity for photopolymerization. This resin was then subjected to rigorous testing to ascertain its suitability.

In order to investigate the influence of the base matrix resin, two commercially available resin products from two different original equipment manufacturers (OEM) were selected that differ in terms of their mechanical properties (see Table 1) and are suitable for a masked stereolithography printer (mSLA). The tensile tests were performed in accordance with the standard ISO 527-2. The experiment involves the testing of both cured and uncured specimens. The tensile test measurements demonstrate the behavior of a brittle material with resin "3D Jake - Color Mix Resin Basic" [7] and a ductile material with resin "3DM-Tough" [8]. The extent of this phenomenon is quantitatively measured by the elongation at break, as presented in Table 1. This phenomenon must be contemplated within the context of the augmentation in stiffness that is precipitated by the incorporation of particulate matter.

Table 1. Material properties of investigated resins

Resin type (general behavior) | "Brittle" resin | "Ductile" resin
OEM | 3D Jake (Austria) | ADMAT (France)
Commercial name | Color Mix Resin Basic | 3DM-Tough
Density [g/cm³] | 1.18 | 1.14
Curing status | uncured | cured | uncured | cured
Tensile strength at Yield [MPa] | 48.8 | 60.7 | 45.5 | 65.6
Elongation at break [%] | 0.90 | 0.62 | 8.00 | 0.81

Ceramic particles have been demonstrated to exhibit superior thermal conductivity in comparison to mSLA resin. This combination of properties offers the advantages of both good thermal conductivity and processability using mSLA 3D-printing. The selection of aluminum oxide as a filler material is predicated on its non-hazardous nature, its economic viability, and its high thermal conductivity for an oxide. An investigation was conducted into the viability of various ceramic types of aluminum oxide for specific applications, with a focus on the analysis of grain size, the utilization of scanning electron microscope images (SEM), and the examination of morphology. For the purposes of this study, fifteen different types of commercially available aluminum oxide were selected for analysis. Following the preliminary experiments, the research was narrowed down to three candidates (see Figure 1). The remaining twelve were rejected on the grounds of inadequate miscibility, high sedimentation rates and poor printability.

[picture]

Fig. 1. SEM Pictures of chosen particles of aluminum oxide with a magnification of 5000: a) T78, b) T79 and c) ALM41 powder

Fig. 1. SEM Pictures of chosen particles of aluminum oxide with a magnification of 5000: a) T78, b) T79 and c) ALM41 powder

The aluminum oxide resin composite is reputed to be distinguished by a high degree of translucency, thermal conductivity [9], sedimentation stability and 3D-Printability. In addition to thermal conductivity, particular attention is paid to the surface quality of filigree injection molds, as these require a surface that fulfils certain criteria. The surfaces were evaluated using a scanning electron microscope. Notwithstanding the introduction of solid particles, it is imperative to ensure the absence of any uneven surface, as this would inevitably lead to an uneven workpiece when utilised as an injection mold.

The ceramic particles are introduced into the liquid resin to be processed as a solid phase using a high-speed planetary centrifugal mixer ("Speedmixer" DAC 330-100 Pro from Flacktek TM , USA). The option of coating the particles was initially rejected on economic grounds. Moreover, it has been demonstrated that adequate miscibility of the particles can be attained even in the absence of coating.

Additives were selected with the objective of preventing the formation of air bubbles in the particle-resin mixture during the process of utilization of the centrifugal mixer [10]. It is imperative that all processing steps are carried out in such a manner that a homogeneous distribution of the particles in the subsequent workpiece is guaranteed [11]. It is imperative that the composite after polymerization does not alter the fundamental properties of the resin (e.g. smooth surface, suitability for filigree shapes). In order to obtain a comprehensive overview, specimens were printed with various aluminum oxides, different degrees of filling with the resin and varying layer thicknesses in order to define the limits of the process.

In an initial series of tests, aluminum oxide was mixed with resin without additional additives, which resulted in an inhomogeneous distribution of ceramic particles in the composite. Following this, eight of the aluminum oxides utilized in the experiment failed to attain satisfactory material properties with regard to printability. Consequently, these were excluded from further testing. In a second series of tests, the remaining seven were mixed separately in different concentrations in both resins. The addition of a dispersing additive has been demonstrated to enhance the concentration of aluminum oxide while achieving the desired homogeneity [12]. The used dispersive was Disperbyk 163 TF or Disperbyk 110 from BYK-Chemie GmbH, Germany, or Tego Dispers 655 from Evonik Evonik Operations GmbH, Germany.

Three different mSLA printing devices were utilized in this study: firstly, a standard device, the "Prusa SL1S"; secondly, an advanced device, the "Phrozen Sonic Mini 8 K "; and finally, a professional device, the "Formlabs Form 4". The impetus for these modifications stemmed from the limitations imposed by the system during the developmental process, including elevated fill levels in conjunction with a more viscous resin-ceramic composite, the reproducibility and homogeneity of the specimens, and other factors. The failures that occurred during the developmental process, along with the underlying reasons for each, are illustrated in Figure 2. Consequently, the selection of 3DPrinting devices was based on their distinct features.

[picture]

Possible solution: Adjustable lift and retraction speed and acceleration

Figure 2. Possible solution: Adjustable lift and retraction speed and acceleration

[picture]

Possible solution: less mechanical friction and stronger platform drive

Figure 3. Possible solution: less mechanical friction and stronger platform drive

[picture]

Fig. 2. Selection of different 3D-printing devices

Fig. 2. Selection of different 3D-printing devices

The thermal conductivity of the composite was measured using a measuring instrument "THB advanced" from Linseis GmbH, Germany. The measurement of heat conduction necessitates the utilization of test specimens in the form of thin plates, which should provide complete coverage of both surfaces of the sensor. It is important to note that the sensor is only able to measure tangential heat conduction on the surface. For this reason, both sides of the specimens were required to be measured. Consequently, following the evaluation of numerous dimensional alternatives, the decision was made to utilize two plates of uniform dimensions, measuring 70×45×5 mm (length × width x height), for the purpose of 3D-printing.

In a second investigation, the focus is directed towards the analysis of thermal conductivity. The measurement of the parameters is conducted using a "THB advanced" device, equipped with a type A sensor. Two sample plates that exactly cover the sensor are utilized for the measurement. It is imperative to note that the measurements are invariably conducted on at least three occasions to ensure the reliability of the results. It is a well-established fact that the thermal conductivity of polymers typically reaches a maximum of 0.2 W/(m* K) [13]. The surface of the material was analyzed using a JSM 6610LV scanning electron microscope from Jeol Ltd, Japan and the element distribution of aluminum in the composite was measured using EDX, element analysis with a X-Max Detector from Oxford Instruments plc, UK in order to ascertain the material's homogeneity.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

Initially, an examination was conducted into the percentage of aluminum oxide present within the specimens. A series of measurements using an Oxford X-Max EDX Detector were obtained on both the upper and lower sides, with the objective of examining the homogeneity of the distribution of the particles. The results in Figures 3 and 4 demonstrate that the values measured on both sides of the specimens are not identical.

[picture]

Fig. 3. Aluminum specimens: degree of filling from specimens measured on top and bottom of specimens using a) ductile resin and b) brittle resin. 3D-printed using standard device.

Fig. 3. Aluminum specimens: degree of filling from specimens measured on top and bottom of specimens using a) ductile resin and b) brittle resin. 3D-printed using standard device.

This prompts the question of whether the cause of this phenomenon is attributable to the sedimentation or the printing process. The distribution of aluminum oxide within the resin is a subject of particular interest. For the purposes of this study, the specimens were measured along the edge, and the values thus determined are to be considered qualitatively rather than quantitatively. Nevertheless, it can be regarded as a reliable indicator of the distribution of aluminum oxide.

The surface images obtained by means of the SEM technique are utilized as indicators, and these images demonstrate the presence of both roughness and irregularities at the edges. Consequently, the measurement was conducted on the lateral surfaces of the specimens exclusively. A selection of examples is shown in Figures 3 and 4. The process was optimized through the execution of a substantial number of tests. The incorporation of a minimal quantity (approximately 0.3% by mass) of a dispersant facilitated the amalgamation of 65% aluminum oxide with the resin, thereby enabling the 3D-printing of the specimens.

[picture]

Fig. 4. Aluminum Specimens; degree of filling from specimens measured on top and bottom of specimens using a) ductile resin and b) brittle resin. 3D-Printed using advanced 3D-printing device.

Fig. 4. Aluminum Specimens; degree of filling from specimens measured on top and bottom of specimens using a) ductile resin and b) brittle resin. 3D-Printed using advanced 3D-printing device.

Increasing the amount of aluminum oxide in the ductile resin, utilizing the ceramic filler "ALM41′′, results in a paste-like mass. However, the printability of this mass in the mSLA process is no longer guaranteed. The utilization of brittle resin is constrained to a maximum fill level of 50%, at which point the limit of 3D-printability is attained. The incorporation of dispersants has been demonstrated to reduce viscosity and enhance stability against sedimentation. The reduced viscosity of the material allows for the suspension to be printed at a higher fill level. The addition of the dispersant DisperBYK 163 TF, in conjunction with both resins and ALM-41, resulted in the attainment of a fill level of 80 weight %. The SEM examinations reveal that there is an absence of delamination, indicating that the layer structure of the print sample remains intact.

Further defects can be observed in the printed components. The components are being drawn off the build plate by the film, and the layers are sliding and no longer adhering to each other. The problem remained unresolved despite an attempt to increase the exposure time. The emergence of additional issues was observed, manifesting as a tripled thickness in the layer. It was evident that the printer had reached its limits due to the fact that the parameters of lift and retraction could not be altered. The selection was made of the advanced 3D-printing device as described in Figure 2. This apparatus is utilized for the purpose of producing thin layers, with the lifting process being modulated accordingly. In this instance, the layer thickness can be set, as well as the parameters of the lifting process, distance and speed, and the speed of the lowering process. The initial trials shave indicated a considerable degree of promise. As demonstrated in Figure 5, the specimens exhibit no optical defects. Furthermore, the results of the EDX analysis and aluminum measurement indicate that the powder is homogeneously distributed in the resin.

[picture]

Fig. 5. Specimens with high amount of Aluminum oxide 3D-printed with a) standard 3D-printing device and b) advanced 3D-printing device.

Fig. 5. Specimens with high amount of Aluminum oxide 3D-printed with a) standard 3D-printing device and b) advanced 3D-printing device.

The present investigations, incorporating both alterations, an advanced 3D-printing device, and the addition of a dispersive, demonstrate that with the novel printing processes, a filling level of 65% by mass could be achieved with the Resin 3DM and a filling level of 85% by mass with the brittle resin with the aluminum oxide ALM-41. It was also determined that the specimens were not only printable, but also suitable for utilization. As demonstrated in Figure 6, a reproducible value of approximately 1.6 W/m* K was achieved at a filling level of 80% by mass.

[picture]

Fig. 6. Thermal conductivity of specimens measured on top and bottom surface and comparison with pure resin.

Fig. 6. Thermal conductivity of specimens measured on top and bottom surface and comparison with pure resin.

A program of research was conducted in order to identify potential additives, the results of which identified three candidates. These were examined in detail. The most significant properties identified were, in particular, good dispersibility, a reduction in the viscosity of the mixture and an increase in the possible degree of filling. The attainment of a printable resin mixture with 80% weight filling was accomplished through the utilization of one of the three additives. The behavior of particles is influenced by the quantity of additives employed. The investigation focused on additive quantities ranging from 0.1% to 10%, with optimal levels between 0.4% and 5% being identified for certain
resins. It is becoming increasingly challenging to work accurately and reproducibly with the advanced 3D-printing device due to the high fill level and homogeneity.

In order to achieve greater freedom in parameter optimization, for example a stronger platter feed, a professional 3D-Printing device was used. To demonstrate an application-oriented example, a set of tool inserts was 3D-printed as a demonstrator (see Figure 7). This tool is used for injection molding two tensile test specimens. The tool consists of a plate with two cavities for the specimens (tool plate). Additionally, a simple counter plate without a cavity was molded to enable the tool to close. Both halves of the tool also contain the necessary holes for assembly and the sprue. EDX measurements were performed in low vacuum mode so that the specimens did not have to be gold-sputtered, as is usually necessary. Our EDX measurement proved the aluminum in the sample to be homogeneous. The sample was 3D-printed with a mixture of aluminum oxide "T79" and brittle resin, which showed the best result in terms of thermal conductivity.

[picture]

Fig. 7. Tool inserts for injection molding: a) CAD model of counter plate (left) and tool plate (right) and b) additively manufactured tool set from the developed composite material using mSLA.

Fig. 7. Tool inserts for injection molding: a) CAD model of counter plate (left) and tool plate (right) and b) additively manufactured tool set from the developed composite material using mSLA.

Following the 3D-printing of the tool inserts the dimensions of which were 178 mm×137 mm× 20 mm (length x width x height), the distribution of the aluminums oxide powder in the resin was measured on two sides of each of the two plates. As demonstrated in Figure 8, the material exhibits excellent homogeneity. While the initial 3D-printed specimens exhibited a significant discrepancy in aluminum concentration between the two sides, the discrepancy is now near to the margin of error. This can be considered acceptable.

[picture]

Fig. 8. Aluminum specimens: degree of filling from specimens measured on top and bottom tool plate and counter plate of the tool inserts.

Fig. 8. Aluminum specimens: degree of filling from specimens measured on top and bottom tool plate and counter plate of the tool inserts.

The surface plays a pivotal role, as it is a crucial parameter for the components that are subjected to subsequent injection molding. The enhancement of the layers exhibited in Figure 9 is attributable not only to the different 3D-printing devices, but also to the optimization of the parameters employed in the production of the mixture of resin, aluminum oxide and dispersants.

[picture]

Fig. 9. SEM image of the edge of sample form a) standard 3D-printing device (Weight %: resin / Aluminum oxide / dispersant: 37.9/56.8/5.3), b) advanced 3D-printing device (Weight %: resin / Aluminum oxide / dispersant: 24.2/72.6/3.2) and c) surface of the tool insert using professional 3Dprinting device.

Fig. 9. SEM image of the edge of sample form a) standard 3D-printing device (Weight %: resin / Aluminum oxide / dispersant: 37.9/56.8/5.3), b) advanced 3D-printing device (Weight %: resin / Aluminum oxide / dispersant: 24.2/72.6/3.2) and c) surface of the tool insert using professional 3Dprinting device.

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

This research successfully developed a novel composite material for additive manufacturing of injection molding tools, addressing the limitations of conventional resins in Masked Stereolithography (mSLA) processes. The primary objective was to enhance the thermal and mechanical properties of molds, leading to reduced cooling times and improved part quality in injection molding. The study achieved this by incorporating aluminum oxide ceramic particles into a photopolymer resin, alongside the strategic use of various dispersants to optimize processability and printability for additive tooling.

The investigation involved a comprehensive analysis of different aluminum oxide types, ultimately narrowing down the selection to three candidates based on miscibility, sedimentation, and printability. The study meticulously examined the influence of resin type, filler loading, and additive selection on the final composite properties. Detailed analyses using Scanning Electron Microscopy (SEM) and EDX measurements were employed to evaluate particle size, distribution, and homogeneity within the composite material.

The research demonstrated that the addition of dispersants significantly improved the homogeneity and printability of the composite, allowing for higher filler loadings up to 85% and thus, higher thermal conductivity. Similarly, the homogeneity of the aluminum concentration was significantly improved during the course of the investigations. The use of advanced and professional 3D-printing devices was crucial in achieving the desired results. The developed composite material exhibited a thermal conductivity of approximately 1.6 W/m* K at an 80% weight fill level, which is significantly higher than the thermal conductivity of the pure resin.

Finally, to demonstrate the practical application of the developed material, tool inserts for injection molding were successfully manufactured. The resulting tools exhibited excellent homogeneity in the distribution of aluminum oxide, confirmed by EDX measurements. The surface quality of the additively manufactured tool inserts was also optimized. This application-oriented example highlights the potential of the new composite in the development of more efficient and cost-effective tooling solutions for injection molding, particularly for rapid prototyping and small-series production. The findings of this research provide a valuable foundation for further exploration and optimization of composite materials for additive manufacturing in tooling applications.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

This Project is supported by the Federal Ministry for Economic Affairs and Climate Action (BMWE) on the basis of a decision by the German Bundestag.

The authors would like to express their gratitude to Güpo GmbH, Kehl, Germany, for their valuable assistance in producing the large number of specimens and conducting the extensive measurements. In particular, Ms. Martina Effenberg, Ms. Alla Buriachenko and Mr. Manfred Schmitt-Bormann made significant contributions to the joint project, leveraging their extensive expertise and enthusiastic dedication.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.45.pdf

I. Gibson, D. Rosen, B. Stucker, M. Khorasani, Additive Manufacturing Technologies, Springer International Publishing, Cham, 2021.

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3D Jake, Technical data sheet Color Mix Resin Basic, Color_Mix_Resin_Basic.pdf (2024).

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A.B. Lozano, S.H. Álvarez, C.V. Isaza, W. Montealegre-Rubio, Analysis and Advances in Additive Manufacturing as a New Technology to Make Polymer Injection Molds for WorldClass Production Systems, Polymers 14 (2022).

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I.A. Tsekmes, R. Kochetov, P.H.F. Morshuis, J.J. Smit, Thermal conductivity of polymeric composites: A review, in: 2013 IEEE International Conference on Solid Dielectrics (ICSD), Bologna, Italy, 2013, pp. 678-681.

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/polymer-processing-and-thermomechanical-properties/978-3-0364-1984-8

Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 55-62

doi: 10.4028/p-Dcjc3i

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

Submitted:
2026-01-07

Revised:
2026-02-26

Accepted:
2026-03-01

Online:
2026-04-17

3D-Printed Pyrography Using PLA/Wood Filaments

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

Francisco Comino 1,a,*, José A. Martínez-Sánchez 1, b, Alessandro Pellegrini 2,c, Roberto Spina 3,4,5,d

1 Departamento de Mecánica, Universidad de Córdoba, Spain

2 Dip. di Scienze Agrarie, Alimenti, Risorse Naturali e Ingegneria (DAFNE), Università di Foggia, Italy

3 Dip. di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Italy

4 Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy

5 Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy

afrancisco.comino@uco.es, b  z12masaj@uco.es, c  alessandro.pellegrini@unifg.it, d  roberto.spina@poliba.it (*corresponding author)

Keywords: Composite, 3D pyrography, Wood filament, Material Extrusion.

Abstract

Wood-filled PLA filaments enable 3D pyrography in material-extrusion (MEX) printing, in which tonal gradients and surface shading are generated in situ by controlling the thermal history during deposition, thereby avoiding post-processing or multi-material strategies. This enables the direct embedding of motifs and graded shading for customized product design, while also allowing appearance stabilization for repeatable manufacturing of wood-filled PLA parts. In this work, PLA/olive-wood (OW) composite filaments containing 0−20wt.%OW (particle size <180μ m ) were manufactured and printed into 20 mm discs using MEX. The extrusion (nozzle) temperature was varied from 180 to 280∘C, and the printing speed was set to 20 and 200 mm/s to modulate thermal exposure. Surface color was quantified as L*,a*,b* from visible absorbance measurements (400−700 nm) converted into CIELAB coordinates. Percentual differences were assessed using the CIEDE2000 metric ΔE00. The results demonstrated that increasing nozzle temperature progressively reduced lightness L*, and under severe conditions, a marked loss of chroma ( a* and b* ), particularly for higher OW contents. Low-speed printing ( 20 mm/s ) amplified the pyrographic effect, reaching strong perceptual contrasts (maximum ΔE00≈9 at 280∘C for 20wt.%OW ), whereas high-speed printing ( 200 mm/s ) mitigated extreme darkening and maintained more moderate, controlled color differences (typically ΔE00<3 ). Accordingly, ΔE00<3 can be used as a practical "color-stable" target for uniform-looking parts, whereas ΔE00=3−9 provides clearly distinguishable shades for pyrographic marking/shading. These findings defined practical process windows to either maximize tonal contrast for 3D pyrography or stabilize the appearance for consistent manufacturing of PLA/OW parts.

Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

Material Extrusion (MEX) additive manufacturing has evolved from rapid prototyping toward design-oriented manufacturing due to its geometric freedom, short lead times, and efficient material usage. Among thermoplastics, polylactic acid (PLA) has become a benchmark material in MEX due to its bio-based origin and relatively high printability [1].

In parallel, efforts to reduce the environmental impact of polymer products have promoted the development of PLA composites reinforced with lignocellulosic fillers (wood flour/fibers and agroforestry by-products), which can lower costs and embodied energy while providing a natural appearance and tactile quality [1,2]. When incorporated into filaments for MEX, these fillers can be processed successfully if particle size and moisture are adequately controlled, however, their addition often introduces interfacial and rheological challenges (e.g., voids, fiber pull-out, rougher surfaces), strengthening the need to understand the process-structure-surface relationship in printed parts [3,4]. Within this context, olive-wood (OW) residues are especially relevant in Mediterranean regions,
where the olive sector generates large volumes of low-value by-products, and additional streams arise from the removal of trees affected by Xylella fastidiosa [5]. Combining OW with PLA strongly promotes circular-economy strategies by valorizing locally available biomass residues in a bio-based polymer matrix.

From a manufacturing perspective, nozzle (extrusion) temperature is one of the key levers in MEX, as it governs melt stability and interlayer bonding. It also accelerates thermo-oxidative reactions that can alter both surface texture and visual appearance, thereby minimizing post-processing while maintaining controlled, in-process outcomes, thereby reducing additional energy/material use and process steps [6]. Beyond traditional functional applications of PLA/wood in MEX (e.g., functional prototypes, acoustic panels, and heat- and mass-exchange devices), there is growing interest in exploiting process-material interactions to introduce new functionalities and aesthetic functions directly during printing [7,8]. One emerging example is 3D pyrography, in which increasing extrusion temperature can induce degradation and partial carbonization of the wood fraction, produce a broad palette of shades (from light to dark), and enable the direct embedding of motifs, gradients, or surface markers during printing, without requiring multi-material approaches [9]. In practice, this can be exploited to embed logos, lettering, serial numbers, and QR-like markers, or to create controlled gradients for product personalization and traceability. This process is attractive for customized product design and surface-embedded information, but it requires defining robust parameter windows that translate deposition conditions into predictable optical outputs. Although prior studies have demonstrated the printability of PLA/wood filaments and reported the influence of processing on morphology and surface quality, material-specific frameworks that simultaneously connect thermal constraints, surface texture, and quantitative color development remain limited, particularly for PLA/OW systems [10,11]. Likewise, while data-driven monitoring and diagnosis approaches have been proposed for MEX to improve quality assurance, these are rarely linked to practical, designoriented maps of surface texture and optical response for wood-filled PLA.

Therefore, the present study provides a PLA/OW-specific, reproducible route to processcontrolled 3D pyrography supported by objective color metrics. The main objective is to establish 3D pyrography as an in-process optical functionality in MEX-printed PLA/OW parts by (i) manufacturing PLA/OW filaments ( 0−20wt.%OW ) from pruning residues, (ii) quantifying optical appearance through visible spectroscopy converted into CIELAB coordinates ( L*,a*,b* ) and the perceptual difference ΔE00 [13], and (iii) evaluating how extrusion temperature ( 180−280∘C ) and printing speed ( 20−200 mm/s ) govern the achievable tonal range and color stability.

To link the quantitative metrics to practical use, two representative application envelopes are considered: (i) appearance-stable manufacturing, where the goal is to keep deviations limited (e.g., ΔE00≤3 and small shifts in L,a, and b* relative to the reference tone of each formulation), and (ii) intentional pyrographic marking and shading, where clearly distinguishable tones are required (e.g., ΔE00≥3, with strong contrasts typically ΔE00≈5−9 ).

Materials and Methods

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

Polylactic acid (PLA) Luminy LX175 (TotalEnergies Corbion, The Netherlands) was selected as the polymer matrix. Olive-wood (OW) particles were obtained as a by-product of pruning, then milled and sieved to a particle size below 180μ m to ensure stable filament extrusion and minimize clogging during material extrusion (MEX). Five formulations were prepared: neat PLA, PLA/OW05 (5 wt.% OW), PLA/OW10 ( 10wt% OW), PLA/OW15 ( 15wt% OW), and PLA/OW20 ( 20wt.%OW ). Before compounding, PLA pellets and OW particles were oven-dried at 60∘C for 12 h to reduce residual moisture below 2wt.% and limit hydrolytic degradation and bubble formation during melt processing. PLA pellets were ground into powder to improve mixing with the lignocellulosic filler. Composite blends were prepared by gravimetric dosing and compounded in a co-rotating twin-screw extruder using a temperature profile of 170−190−200∘C. The extrudate was strand-cooled in a water bath and pelletized. Composite pellets were subsequently converted into filaments using a singlescrew extruder (L/D=24) equipped with temperature control and an in-line laser diameter gauge. A 170−200∘C profile and a screw speed of 60 rpm were used, with extrusion through a 2 mm die and
cooling in dual water baths. Filaments were drawn using a traction system to achieve a nominal diameter of 1.75±0.03 mm, suitable for MEX printers.

Disc specimens ( 20 mm diameter) were manufactured using an X1C MEX printer (Bambu Lab, China). The printing settings were kept constant, as shown in Table 1. The X1C hotend is rated up to 300∘C. However, 280∘C was selected as a conservative upper bound for PLA/OW to limit excessive thermal degradation and potential nozzle fouling while still reaching the strongest controlled pyrographic contrasts. To investigate the 3D pyrography response, nozzle temperature T and printing speed V were varied within 180−280∘C and 20−200 mm/s, respectively, while the remaining parameters were kept constant.

Table 1. Printing parameters.

Parameter | Value
Layer height | 0.2 mm
Layer width | 0.4 mm
Raster angle | 45 °
Infill density (line pattern) | 100 %
Build plate temperature | 65 °C
Build orientation | Horizontal (XY)

Visible absorbance spectra were measured in the 400−700 nm range using a NIRSystems DS2500 spectrometer (FOSS, Denmark) on the printed discs. From the measured absorbance spectrum data A(λ), the spectral reflectance R(λ) was obtained using the diffuse-reflectance absorbance definition (Eq. 1).

A(λ)=log10(1R(λ))→R(λ)=10A(λ)(1)

CIELAB coordinates were computed following CIE recommendations by first calculating the tristimulus values (X,Y,Z) through discrete integration of R( λ ) weighted by the spectral power distribution of Illuminant A and the CIE 19312∘ standard observer color-matching functions x¯(λ), y¯(λ),z¯(λ), see Eq. 2,3 , and 4 . A spectral step of Δ(λ)=0.5 nm was used.

X=k∑λR(λ)SA(λ)x¯(λ)ΔλY=k∑λR(λ)SA(λ)y¯(λ)ΔλZ=k∑λR(λ)SA(λ)z¯(λ)Δλ

(2)(3)(4)

The normalization factor k (Eq. 5) was defined so that the reference white under the same observer conditions satisfies Yn=100.

K=100∑λSA(λ)y¯(λ)Δλ(5)

CIELAB coordinates L*,a*,b* were then computed using the reference tristimulus values (Xn,Yn,Zn) of the perfect reflecting diffuser, see Eq. 6, 7, and 8.

L*=116·f(YYn)−16(6)

a*=500·[f(XXn)−f(YYn)]b*=200·[f(YYn)−f(ZZn)]

(7)(8)

with the standard non-linear function:

f(t)={t1/3t>δ3t3δ2+429t≤δ3 where δ=629(9)

This workflow yielded objective color descriptors (lightness L*, red-green a*, and yellow-blue b* ) suitable for quantifying process-induced pyrographic tonal changes.
To quantify perceptual color differences, the CIEDE2000 total color difference was computed for each specimen relative to its reference condition (printed at 180∘C and 20 mm/s for each material), as shown in Eq. 10. Under reference viewing conditions, the parametric factors were set to kL=kC=kH=1.

ΔE00=(ΔL′kLSL)2+(ΔC′kCSC)2+(ΔH′kHSH)2+RT(ΔC′kCSC)(ΔH′kHSH)(10)

Results and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

The 3D pyrography effect was assessed by converting the measured visible absorbance spectra to CIELAB coordinates (L*,a*,b*) and then computing the perceptual color difference (CIEDE2000) relative to the reference condition ( 180∘C,20 mm/s ) for each formulation. The influence of extrusion temperature ( 180−280∘C ), printing speed ( 20 and 200 mm/s ), and olive-wood (OW) content (5-20 wt.%) is discussed below.

For interpretation, ΔE00 is used as the primary design metric: ΔE00⩽1 is typically imperceptible, ΔE00≈1−3 corresponds to slight-to-moderate differences, and ΔE00≳3 to clearly noticeable differences. Accordingly, the "appearance-stable" regime is associated with ΔE00≤3 (limited variations in L*, a*, b* around the reference tone of each formulation), whereas intentional pyrographic marking and shading targets ΔE00≥3, with strong contrasts at ΔE00≈5−9.

The variation of the L* parameter with respect to extrusion temperature and speed for each composite is shown in Fig. 1. Extrusion temperature was the primary driver of lightness variation, with printing speed acting as a potent modulator of the thermal "pyrographic" outcome. At 20 mm/s (solid lines), L* was relatively stable between 180 and 260∘C for most formulations, but a pronounced darkening occurred at 280∘C, particularly for high OW contents. PLA/OW15 and PLA/OW20 drop to L*≈24, indicating a significant tonal change toward darker surfaces. In contrast, PLA/OW05 decreased slightly across the entire temperature range, whereas PLA/OW10 exhibited the smallest overall L* reduction, suggesting a lower sensitivity of lightness to extreme thermal exposure.

At 200 mm/s (dashed lines), L* values were consistently higher and less sensitive to temperature, mainly remaining within a narrower band even at 280∘C. This outcome indicated that high printing speed mitigated excessive darkening, consistent with a reduced thermal history during deposition (i.e., a shorter residence time at elevated temperature). Overall, the combination of high temperature and low speed produced the most significant decrease in L*, whereas high speed promoted lightness stability.

[picture]

Fig. 1. Variation of L* as a function of extrusion temperature and printing speed.

Fig. 1. Variation of L * as a function of extrusion temperature and printing speed.

The a*−b* chromaticity map (Fig. 2) provides insight into how hue and chroma evolve beyond simple darkening. Most conditions clustered in the region of positive a* and positive b* (reddish/yellowish tones), typical of wood-filled thermoplastics. For moderate temperatures (approximately 180−260∘C ), points tended to remain in this quadrant with relatively limited dispersion, indicating that color changes were dominated by gradual shifts rather than abrupt hue inversion. However, under the most severe processing condition ( 280∘C,20 mm/s ), the higher-OW materials exhibited pronounced migration toward lower a* and much lower b* (i.e., loss of redness and yellowness). This pronounced reduction in chroma was consistent with substantial thermal darkening, where the surface appearance became less saturated and more burnt-like. At 200 mm/s, the corresponding points remained closer to the central cluster, again supporting that fast deposition limited the extent of thermally induced discoloration.

[picture]

Fig. 2. CIELAB chromaticity plot ( a* vs. b* ) as a function of extrusion temperature and printing speed.

Fig. 2. CIELAB chromaticity plot ( a * vs. b * ) as a function of extrusion temperature and printing speed.

Fig. 3 reports ΔE00 as a function of extrusion temperature, ranging from 20 mm/s to 200 mm/s, using 180∘C and 20 mm/s as the reference for each formulation. At 20 mm/s (Fig. 3a), ΔE00 remained
low at 200−220∘C (typically ≤1.36 depending on formulation), indicating minor deviations from the reference tone. As the temperature increased, the response became formulation-dependent and clearly nonlinear, with the most significant changes occurring at 280∘C, where ΔE00 reached 4.02 (PLA/OW05), 3.08 (PLA/OW10), 5.23 (PLA/OW15), and up to 9.04 (PLA/OW20). This trend confirmed that high OW content, combined with high temperature and low speed, produced the strongest perceptual contrast, which was desirable when intentional tonal variation was required (pyrographic shading).

At 200 mm/s (Fig. 3b), ΔE00 variations were moderate across the whole temperature range, mostly between ~0.24 and ~3.17. Because the reference was set at 20 mm/s, the cells at 180∘C were not zero and already exhibited noticeable color shift ΔE00≈1.70−2.21, demonstrating that printing speed alone could produce a noticeable color shift even without temperature changes. With increasing temperature, the highest ΔE00 values remained limited with respect to 20 mm/s. PLA/OW15 reached 3.07-3.17 at 260−280∘C, whereas PLA/OW20 showed its maximum around 3.01 at 240∘C and then decreased to 1.63 at 280∘C. This behavior indicated that at high speeds, thermal exposure was insufficient to induce extreme darkening, and the resulting color differences remained within a controlled mid-range envelope.

[picture]

Fig. 3. CIELAB ΔE00 as a function of extrusion temperature.

Fig. 3. CIELAB Δ E 00 as a function of extrusion temperature.

Analysis of all responses ( L*,a*,b* and ΔE00 ) indicated that the 3D pyrography effect could be tuned by controlling the thermal input during deposition. Low speed increased thermal exposure and amplified thermally driven discoloration, particularly at very high nozzle temperatures and higher

OW contents, where both lightness reduction L* and chroma loss a*−b* became pronounced. On the contrary, high speed reduced the severity of these changes, stabilizing L* and keeping ΔE00 within a moderate range. These results established two practical operating regimes for wood-filled PLA: (i) a contrast-enhancing regime (high temperature + low speed) to maximize tonal variation, and (ii) a color-stabilization regime (high speed, moderate temperature) to minimize unintended darkening while retaining a consistent appearance.

Conclusions

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

PLA/olive-wood (OW) composite filaments ( 5−20wt.%OW ) enabled in-process 3D pyrography in material-extrusion printing, where surface tonality can be tuned without post-processing by adjusting deposition conditions.

Color was objectively quantified from visible spectra through the CIELAB coordinates (L*,a*,b*), and the perceptual metric ΔE00. Extrusion temperature produced the most substantial tonal shifts: increasing temperature generally promoted darkening (lower L* ) and, under severe conditions, a loss of chroma (changes in a* and b* ). Printing speed served as a practical thermal-exposure lever: low speed ( 20 mm/s ) amplified the pyrographic effect and maximized contrast - especially at high temperatures and higher OW content - while high speed ( 200 mm/s ) mitigated extreme darkening and kept ΔE00 within a more moderate and controlled range.

Overall, the results demonstrate that PLA/OW composites provided a simple, single-material route to embed shades, gradients, and surface markers directly during printing, while supporting circulareconomy valorization of olive-wood residues as a functional filler in sustainable MEX manufacturing.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

The authors acknowledge financial support from the European Innovation Association (AEI) for agricultural productivity and sustainability, for the creation and operation of operational groups, and from the Ministry of Agriculture, Livestock, Fisheries, and Sustainable Development of the Junta de Andalucía through the research project AGROSEC (reference GOPO-JA-23). The Project was also funded by the Department of Excellence - Law number 232/2016 (Grant No. CUP D93C23000100001) and Space It Up project funded by the Italian Space Agency, ASI, and the Italian Ministry of University and Research (MUR) under contract n. 2024-5-E.0 (Grant N. CUPI53D24000060005). They would also like to acknowledge Smart Materials 3D for providing materials.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.55.pdf

B. Redwood, F. Schöffer, B. Garret, The 3D Printing Handbook, 3D Hubs B.V., Amsterdam, 2018.

Y. Tao, H. Wang, Z. Li, P. Li, S.Q. Shi, Development and application of wood flour-filled polylactic acid composite filament for 3d printing, Materials 10 (2017). .

F. Comino, J.A. Martinez-Sánchez, P.E. Romero, N. Gurrado, R. Spina, Thermo-mechanical properties of polylactic acid/olive wood composite for additive manufacturing, in: Materials Research Proceedings, Association of American Publishers, 2025: pp. 2344-2351. .

N. V. dos Santos, D.K.K. Cavalcanti, J.S.S. Neto, H.F.M. de Queiroz, M.D. Banea, D.C.T. Cardoso, Analysis of voids, interfacial and thermal properties of additively manufactured continuous natural fiber-reinforced biocomposites, Progress in Additive Manufacturing 10 (2025) 5401-5422. .

A.D. Syanatha, R.A. Setiawan, S. Steven, Y. Mardiyati, Effect of manau rattan (Calamus manan miq.) particle size on processability and mechanical properties of 3D-printed PP/rattan WPC filaments, Progress in Additive Manufacturing 10 (2025) 5387-5399. .

M. Saponari, A. Giampetruzzi, G. Loconsole, D. Boscia, P. Saldarelli, Xylella fastidiosa in olive in apulia: Where we stand, Phytopathology 109 (2019). .

E. Petinakis, X. Liu, L. Yu, C. Way, P. Sangwan, K. Dean, S. Bateman, G. Edward, Biodegradation and thermal decomposition of poly(lactic acid)-based materials reinforced by hydrophilic fillers, Polym Degrad Stab 95 (2010) 1704-1707. .

D.D.C.V. Sheng, M.N. Bin Yahya, N.B.C. Din, K.Y. Wong, M.R.M. Asyraf, V. Sekar, Potential of wood fiber/polylactic acid composite microperforated panel for sound absorption application in indoor environment, Constr Build Mater 444 (2024). j.conbuildmat.2024.137750.

F. Comino, P.E. Romero, E. Molero, M. Ruiz de Adana, Experimental evaluation of a 3D printed air dehumidification system developed with green desiccant materials, Appl Therm Eng (2023) 120393. .

K. (Justin) Moon, J. Yi, V. Savage, A. Bianchi, 3D printed pyrography: Using wood filament and dynamic control of nozzle temperature for embedding shades of color in objects, Addit Manuf 83 (2024). .

M. Kariz, M. Sernek, M. Obućina, M.K. Kuzman, Effect of wood content in FDM filament on properties of 3D printed parts, Mater Today Commun 14 (2018) 135-140. .

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 63-73

doi: 10.4028/p-ZlRu4c

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

Submitted:
2026-01-10

Revised:
2026-03-03

Accepted:
2026-03-04

Online:
2026-04-17

Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

The original version of this paper is available on https://www.scientific.net/DDF.451.63.pdf

Evan Gargadennec 1,a, Yun-Mei Luo 1, b*, Eric Monteiro 2,c and Luc Chevalier 1, d

1 Université Gustave Eiffel, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France

2 Laboratoire PIMM, Arts et Métiers Institute of Technology, CNRS, CNAM, 151 boulevard de l'Hôpital, 75013 Paris, France

a  evan.gargadennec2@univ-eiffel.fr, b  yun-mei.luo@univ-eiffel.fr, c  eric.monteiro@ensam.eu, dluc.chevalier@univ-eiffel.fr 

Keywords: PEF, PET, RPET, Thermal analysis, DSC, DMA, Crystallization kinetics

Abstract

Poly(ethylene 2,5-furandicarboxylate) (PEF) is a bio-based polyester that is the subject of growing interest as a potential alternative to Poly(ethylene terephthalate) (PET) for sustainable packaging. Its excellent gas-barrier properties and reduced carbon footprint make it a promising candidate, but its use at industrial scale requires a solid understanding of how temperature and thermal history affect its mechanical and viscoelastic behavior. In this study, Differential Scanning Calorimetry (DSC), Dynamic Mechanical Thermal Analysis (DMA), and optical microscopy were used to characterize the thermal transitions and crystallization behavior of PEF, compared with PET and recycled PET (rPET). DSC results show that thermal crystallization of PEF proceeds very slowly, a result confirmed by in-situ microscopy. DMA measurements provide complementary information on the evolution of both storage and loss moduli with temperature, highlighting its dependence on crystallinity and thermal history. Together, these thermal and mechanical analyses clarify how PEF's crystallization behavior affects its thermo-mechanical response. From a processing perspective, the very slow thermal crystallization of PEF is advantageous for stretch blow molding (SBM) process of bottles, as the polymer remains essentially amorphous during heating and crystallizes predominantly under deformation during the fast forming stage.

1 Introduction

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Poly(ethylene 2,5-furandicarboxylate) (PEF) has gained considerable attention as a bio-based polyester that could serve as a viable alternative to conventional poly(ethylene terephthalate) (PET) in packaging. Its combination of excellent gas-barrier properties [1], renewable sourcing [2] and lower environmental footprint has made it an appealing candidate for next-generation, sustainable packaging materials. Recent studies have explored various aspects of PEF's potential: Luan et al. [1] demonstrated its superior gas barrier properties combined with rapid degradation; Loos et al. [2] provided a comprehensive review of PEF synthesis, structure-property relationships, and end-of-life options; Forestier et al. [3] investigated its microstructural development upon stretching, revealing enhanced strain-induced crystallization behavior; Lightfoot et al. [4] used molecular modeling to explain the mechanism of oxygen diffusion in PEF compared to PET; Poulopoulou et al. [5] examined sustainable blends of PEF with other biobased polyesters; and Sousa et al. [6] proposed recommendations for replacing PET with biobased counterparts including PEF in packaging, fiber, and film applications. However, for applications such as bottle production or thermoforming [7,8], it remains essential to understand how PEF behaves during typical thermal cycles and how its structure develops compared with PET and recycled PET (rPET), which together dominate today's packaging market.
Although several studies [9-11] have examined the intrinsic properties of PEF, its crystallization behavior and its viscoelastic response under heating are still not fully understood. In particular, the slow crystallization kinetics often reported for PEF [12,13] may have important consequences for
industrial processes such as stretch blow molding (SBM) [14], where crystallization develops mainly under deformation. A direct comparison with PET and rPET is therefore essential to assess both the advantages and the limitations linked to the use of PEF in existing processing lines. For PET, it is well established that the SBM process leads to a marked increase in mechanical performance, as the material transitions from an amorphous preform to a semi-crystalline bottle [15]. In practice, crystallization induced by heating and by deformation occur simultaneously, and thermal crystallization is extremely fast [16]. This combination makes both simulation and experimental analysis particularly challenging.
In this study, the thermal behavior of PEF is examined and directly compared with that of PET and rPET using injection-molded plates as starting materials. These plates correspond to the material state before the SBM process, allowing a clearer understanding of how PEF responds to temperature and how its crystallization develops under controlled thermal conditions.
To investigate these aspects, three complementary experimental techniques were used. Differential Scanning Calorimetry (DSC) was first carried out to characterize the main thermal transitions and to estimate the degree of crystallinity under controlled heating rates. These measurements enable to follow the onset of crystallization and to compare the evolution of thermal behavior between PEF, PET and rPET. In parallel, optical microscopy was used to directly observe the development of crystalline structures during heating. This approach provides qualitative but valuable information on the kinetics and the morphology of crystallization and confirms that the transitions detected by DSC correspond to actual structural changes in the material. Finally, Dynamic Mechanical Thermal Analysis (DMA) was performed to follow the temperature dependence of the storage and loss moduli. The response obtained by DMA offers additional information on the influence of crystallinity and thermal history on the mechanical behavior of the three materials.
Taken together, these techniques provide a coherent basis for comparing the thermal and thermomechanical behavior of PEF with that of PET and rPET and help clarify the characteristics that may influence the processing of PEF in packaging applications.

2 Material and Methods

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2.1 Materials and Sample Preparation

The virgin PET material used is RAMAPET N180, supplied by Sidel Group, France. Its glass transition temperature ( Tg ) is 78±2∘C and its intrinsic viscosity is 0.80±0.02dl/g. The bulk density of N 180 is 830±30 kg/m3. The recycled PET, referenced as MOPET, also supplied by Sidel Group, France, has an intrinsic viscosity of 0.85±0.02dl/g and a bulk density of 900±50 kg/m3. PEF material used for comparison is a bio-based polyester produced from FDCA monomers, supplied by Zhengzhou Alfa Chemical Co., Ltd, China. Its intrinsic viscosity falls within 0.63−0.85dl/g, and the bulk density is approximately 1.38 g/cm3. All detailed specifications provided by the suppliers, including thermal, rheological, and optical properties for PET, rPET, and PEF granules, are summarized in the tables of the Appendix.
The PET, rPET and PEF granules were processed at the PIMM laboratory using an injection molding machine (DK Codim 175). Each material was dried prior to injection and then fed into the heating cylinder, where it was melted, homogenized and injected into a steel mold under controlled pressure and temperature conditions. The overall injection cycle was adjusted for each polymer in order to account for their specific thermal behavior, particularly the higher melting temperature of PET and the slower crystallization kinetics of PEF. Using these conditions, plates with dimensions 125 mm×125 mm×2.5 mm were produced for subsequent characterization (Fig.1).

[picture]

Fig.1. (a) polymer granules; (b) injected plate

Fig.1. (a) polymer granules; (b) injected plate

The injection conditions used for virgin PET, rPET and PEF are listed in Table 1. They include injection speed, injection and holding pressures, injection time, cooling time and mold temperature. PET and rPET were processed under similar conditions, with a slightly higher holding pressure for the recycled grade. Because of its distinct melting temperature, viscosity and crystallization behavior, PEF required lower temperature settings and a reduced injection speed to avoid degradation and to keep a stable melt flow. The processing parameters for PEF were selected based on its specific thermal and rheological properties reported in the literature. The lower injection melt temperature ( 225∘C ) was chosen because PEF has a lower melting point ( 205−215∘C ) compared to PET ( 245−255∘C ), and processing at temperatures suitable for PET would cause thermal degradation [13]. The reduced injection speed ( 40 mm/s ) was necessary due to PEF's slower crystallization kinetics, which requires controlled flow to prevent premature solidification [3]. The higher mold temperature ( 40∘C ) accommodates PEF's higher glass transition temperature ( 86−90∘C ) to optimize cooling and part quality [12]. Additionally, the lower injection pressure ( 1050 bar) is justified by PEF's lower melt viscosity compared to PET at processing temperatures [12], while the higher holding pressure (700 bar) compensates for its different crystallization behavior to ensure proper packing [3]. These settings were validated through preliminary trials to ensure stable processing without degradation.

Table 1. Injection conditions for PET, rPET and PEF

Parameters | Virgin PET | Recycled PET | PEF
Injection speed | 70 mm/s | 70 mm/s | 40 mm/s
Injection pressure | 1150 bar | 1200 bar | 1050 bar
Holding pressure | 500 bar | 600 bar | 700 bar
Holding time | 6 s | 6 s | 6 s
Injection time | 1.2 s | 1.2 s | 1.9 s
Cooling time | 50 s | 50 s | 40 s
Mold temperature | 20 °C | 20 °C | 40 °C
Injection melt temperature | 255 °C | 255 °C | 225 °C

2.2 Differential Scanning Calorimetry (DSC) analysis

PEF, PET and rPET samples used for DSC analysis were cut from plates produced by injection molding.

2.2.1 Non-isothermal DSC measurements

DSC measurements were carried out to evaluate the thermal transitions and crystallization behavior of PET, rPET and PEF. The experimental protocol consisted of a heating cycle from 30∘C to 300∘C at 10∘C·min−1 followed by a cooling cycle from 300∘C back to 30∘C at the same rate.

2.2.2 Isothermal crystallization measurements

To investigate the crystallization kinetics in more detail, isothermal DSC experiments were carried out at selected temperatures with the protocol:

Heating cycle: 30∘C to 250∘C at 20∘C.min- 1

Isotherm: 250∘C during 3 min

Cooling cycle: 250∘C to the selected crystallization temperature at 100∘C·min−1

Isotherm at the selected crystallization temperature during 180 min

Cooling cycle: from the selected crystallization temperature to 40∘C at 10∘C.min- 1

Heating cycle: 40∘C to 250∘C at 5∘C.min- 1

After melting, the samples were rapidly cooled ( 100∘C·min−1 ) to the target isothermal temperature using liquid nitrogen assistance.
In addition, the degree of crystallinity Xc can be determined directly from the DSC curve by analyzing the areas associated with melting and crystallization.

Xc=ΔHm−ΔHcΔHm0(1)

where ΔHm is the enthalpy absorbed during melting, ΔHc the enthalpy released during cold crystallization and ΔHm0 the enthalpy of fusion of a fully crystalline material. According to [12], ΔHm0 is equal to 140 J· g−1 for both PET and PEF. This approach provides a way to quantify and compare the crystallinity of materials processed under different conditions, such as injection molding or SBM process.

2.3 Optical Microscopy: Isothermal Crystallization Observation

To further support the conclusions from the DSC analysis, optical microscopy was used to directly observe the crystallization behavior of PET and PEF. The objective of this experiment was to visualize, in real time, the evolution of crystalline structures under isothermal conditions and to confirm the much slower crystallization kinetics of PEF compared with PET.
Thin lamellae, with thickness of approximately 5μ m, were cut directly from the injection-molded plates of PET and PEF. Each specimen was placed on a temperature-controlled heating stage positioned under the microscope. The following thermal protocol was applied:

Heating from 30∘C to 250∘C.

Isothermal hold at 250∘C for 5 min to ensure complete melting.

Rapid cooling from 250∘C to the selected crystallization temperature Ti at 100∘C·min−1.

Isothermal crystallization at Ti for a duration t .

Microscopy images were recorded continuously throughout the isothermal stage to monitor the nucleation and growth of spherulites. By analyzing the time required for the crystalline domains of each polymer, it is possible to compare their crystallization kinetics.

2.4 Dynamic Mechanical Analysis (DMA): Method and experimental procedure

Dynamic Mechanical Analysis (DMA) was conducted to characterize the viscoelastic behavior of rPET and PEF as a function of temperature. Tests were performed using TA Instruments Q800 DMA devices at PIMM laboratory. Specimens measuring 40×12×2.5 mm3 were cut from the injectionmolded plates and tested in single-cantilever mode. Firstly, a strain-sweep test was carried out to identify the linear viscoelastic region (LVR) for each material. This preliminary step ensures that all tests are performed at a strain amplitude low enough for the modulus to remain independent of deformation. Once the LVR was established, a temperature-ramp experiment was conducted at a constant oscillation frequency and at a constant oscillation strain amplitude selected inside the LVR. During these tests, the DMA system continuously recorded the evolution of E'. All tests were carried out under air atmosphere to mimic process conditions.

3 Results and Discussion

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3.1 Thermal properties from DSC

3.1.1 Non-isothermal crystallization behavior

Figure 2 shows the DSC heating curves obtained for PET and PEF using the same experimental protocol explained in section. Under these identical conditions, PET exhibits the classical thermal signature of a semi-crystalline polymer: a well-defined glass transition around 78∘C, followed by a pronounced exothermic crystallization peak Tc corresponding to cold crystallization, and finally a
sharp endothermic melting peak Tm. In contrast, the PEF thermogram shows only the glass transition, with no detectable crystallization peak and no melting endotherm during the first heating. This difference means that, unlike PET, PEF does not crystallize under standard non-isothermal DSC conditions. The absence of both Tc and Tm indicates that PEF remains essentially amorphous throughout the entire heating ramp, confirming its slow thermal crystallization kinetics.

[picture]

Fig. 2. Non-isothermal DSC test for (a) PET and (b) PEF

Fig. 2. Non-isothermal DSC test for (a) PET and (b) PEF

3.1.2 Thermal transition temperature

Table 2 summarizes the thermal transition parameters obtained from multiple DSC measurements. The mean Tg of PET is 71∘C, while rPET exhibits a very similar Tg of 71.8∘C with slightly reduced dispersion. These results confirm that mechanical recycling has no effect on the amorphous phase mobility. For PEF, the Tg∘ is 72.9∘C, slightly higher than PET, consistent with the stronger intermolecular interactions associated with furanic rings.
The crystallization temperatures Tc≈127.3∘C for PET and 130.0∘C for rPET. The higher Tc of rPET may arise from increased heterogeneity and residual nucleating species introduced during mechanical recycling. In contrast, no crystallization peak appears for PEF during cooling. This absence confirms that PEF crystallizes much more slowly than PET. As a result, the injected PEF plates are fully amorphous ( Xc≈0 ). The PET and rPET plates obtained by injection show a measurable degree of crystallinity from Eq. 1, with Xc of approximately 9%.
The melting temperatures Tm for PET and rPET are highly consistent across samples, with mean values of 250.3∘C (PET) and 248.9∘C (rPET). For PEF, however, Tm cannot be measured from a simple heating because standard cooling produces no crystallization. Instead, melting temperatures must be obtained from isothermal crystallization experiments, as described in the following.

Table 2. Mean transition temperatures and dispersions measured by DSC

Material | Tg (°C) | Tc (°C) | Tm (°C)
PET | 71.0 ± 0.6 | 127.4 ± 0.6 | 250.4 ± 0.7
rPET | 71.6 ± 0.4 | 130.0 ± 0.9 | 248.7 ± 0.6
PEF | 72.9 ± 0.7 |  |

3.1.3 Isothermal crystallization behavior

The behavior of PET is shown in Fig. 3a. At temperatures close to its optimal crystallization range (around 150∘C ), PET begins to crystallize almost immediately, often even before the temperature has stabilized at the isothermal plateau. This confirms the extremely fast crystallization kinetics reported in the literature [16]. Such rapid crystallization makes PET highly sensitive to the cooling rate during processing, because even small variations in temperature can significantly alter the final crystalline morphology.
In contrast, no crystallization peak is detected for PEF during an isothermal hold at 160∘C for 180 min (Fig. 3b). The absence of an exothermic signal indicates that the crystallization rate of PEF at
this temperature is extremely slow, remaining below the detection limit of conventional DSC. However, the appearance of a melting endotherm during the subsequent heating cycle demonstrates that a small amount of crystallization has occurred during the long isothermal stage, even though the crystallization peak itself could not be resolved. This confirms that PEF crystallizes during isothermal holds, but the process is too slow to be captured under standard DSC sensitivity, in contrast with the rapid crystallization exhibited by PET.

[picture]

Fig. 3. Isothermal crystallization measurements: (a) PET, showing very fast crystallization [16]; (b) PEF, with no detectable crystallization peak during the isothermal stage.

Fig. 3. Isothermal crystallization measurements: (a) PET, showing very fast crystallization [16]; (b) PEF, with no detectable crystallization peak during the isothermal stage.

3.1.4 Quantitative analysis of PEF isothermal crystallization

To characterize PEF crystallization more precisely, isothermal DSC tests were performed. There is no crystallization peak that appears during the isothermal plateau, but a melting peak is observed during reheating. This indicates that crystallization does occur during the isotherm, but too slowly and with too low enthalpy to be detected directly as an exotherm. The degree of crystallinity Xc was therefore computed from the melting enthalpy:

Xc=ΔHmΔHm(2)

[picture]

Fig. 4. (a) Evolution of degree of crystallinity as a function of isothermal temperature; (b) Evolution of melting temperature as a function of isothermal temperature

Fig. 4. (a) Evolution of degree of crystallinity as a function of isothermal temperature; (b) Evolution of melting temperature as a function of isothermal temperature

The evolution of Xc as a function of Ti (Fig. 4a) shows that crystallinity reaches its maximum for 145 ∘C≤Ti≤160∘C, identifying this range as the optimal crystallization temperature window of PEF. These temperatures are markedly lower than the PET Tc extracted from cooling scans, again confirming the slow kinetics and different thermodynamic behavior of PEF.
The melting temperature measured after each isothermal step increases approximately linearly with Ti (Fig. 4b). This behavior reflects the dependence of lamellar thickness on crystallization temperature, as described by the Gibbs-Thomson relation [17]:

Tm=Tm0(1−2σeΔHm L)(3)

where σe stands for the surface free energy of the lamella, L the lamellar thickness, Tm0 the melting temperature of an ideal crystal of infinite size. Extrapolating the linear fit following a Hoffman Weeks approach [18] provides an estimate of the melting temperature of an ideal infinite crystal, Tm0≈211∘C.

3.2 Crystallization behavior from optical microscopy

Optical microscopy was used to provide a direct comparison of the crystallization behavior of PET and PEF under isothermal conditions. Thin sections of each material were heated above their melting temperature, rapidly cooled to the chosen isotherm, and observed in real time on a hot stage. For PET, crystallization occurred very rapidly even before the sample reached the isothermal temperature.

[picture]

Fig. 5. Optical microscopy images of PEF and PET spherulite development during isothermal crystallization. (a) PET at 230∘C after 17 min ; (b) PET at 230∘C after 24 min [16]; (c) PEF at 180 ∘C after 180 min ; (d) PEF at 160∘C after 180 min

Fig. 5. Optical microscopy images of PEF and PET spherulite development during isothermal crystallization. (a) PET at 230 ∘ C after 17 min ; (b) PET at 230 ∘ C after 24 min [16]; (c) PEF at 180 ∘ C after 180 min ; (d) PEF at 160 ∘ C after 180 min

Figure 5 shows that at 230∘C, the first spherulites were present after about seventeen minutes, and by twenty-four minutes the microstructure was almost fully crystallized, with spherulites filling the field of view. For temperatures below 210∘C, crystallization occurs and completes too quickly to follow its evolution. This rapid development is consistent with the DSC results, confirming its high kinetic activity and strong sensitivity to cooling conditions. In contrast, Fig. 5 shows that for PEF, very few crystalline structures were observed at 180∘C even after 180 min , and a higher spherulite
density is observed at 160∘C compared with 180∘C after 180 min , but their growth is too slow to follow the evolution in real time.

3.3 Viscoelastic behavior from DMA

Dynamic Mechanical Analysis was carried out to examine how rPET and PEF respond mechanically as temperature increases from the glassy state toward the rubbery regime. A preliminary strain-sweep test was performed at 70∘C and 1 Hz to determine the limits of linear viscoelasticity. For both rPET and PEF, the storage modulus remained practically constant at low strain amplitudes, confirming that the samples behave linearly up to strains of about 0.01−0.03%, depending on the criterion considered. The deformation amplitude for the temperature-ramp experiment was fixed at 0.01% which is inside the linear region.
The temperature-dependent evolution of the storage and loss moduli, respectively noted E′ and E′′, was recorded during heating from 70 to 150∘C at 3∘C/min, as shown in Fig.6. For both materials, E′ and E′′ decrease sharply when approaching the glass-transition region, reflecting the transition from a glassy to a rubbery state. After the glass transition, rPET shows an increase in both moduli, when the temperature approaches 130∘C. This stiffening is attributed to cold crystallization occurring during heating, as the material reaches its crystallization temperature range. This behavior is consistent with DSC results, which show a clear crystallization peak for PET and rPET. In contrast, PEF does not exhibit any significant increase in moduli over the same temperature range. The storage modulus remains low and changes only slightly with temperature, indicating the absence of crystallization during heating at this rate. This confirms the very slow crystallization kinetics of PEF, in agreement with the DSC measurements, where no crystallization peak is observed under nonisothermal conditions (Fig. 2).

[picture]

Fig. 6. Evolution of storage and loss moduli for both rPET and PEF

Fig. 6. Evolution of storage and loss moduli for both rPET and PEF

4 Conclusions

The original version of this paper is available on https://www.scientific.net/DDF.451.63.pdf

This study compared the thermal crystallization behavior of PEF with those of PET and rPET using DSC, optical microscopy and DMA. All analyses were performed on injection-molded plates, representative of the material state before the SBM process. The results highlight clear differences between the materials, particularly in the way PEF crystallizes.
For PET and rPET, the DSC measurements show the expected crystallization and melting peaks, indicating fast crystallization during cooling or isothermal holds. In contrast, PEF does not crystallize under standard non-isothermal DSC conditions. Only long isothermal treatments allow some crystallinity to develop, and the degree of crystallinity remains low. The analysis of Xc as a function of Ti suggests that PEF crystallizes most efficiently between 145 and 160∘C. Consequently, the injected PEF plates are fully amorphous ( Xc≈0 ). In contrast, the injected PET and rPET plates exhibit a detectable crystalline fraction, with Xc values of about 9%.

Microscopy confirms the strong contrast between PET and PEF. PET forms well-defined spherulites within minutes at 230∘C, whereas no visible crystalline structures appear for PEF under 180 minutes. These images directly illustrate the slower nucleation and growth processes in PEF.
DMA results support the thermal analysis. rPET exhibits a clear increase in both storage and loss moduli when the temperature approaches about 130∘C, which is attributed to cold crystallization during heating. In contrast, PEF shows no comparable stiffening, with moduli remaining low, indicating the absence of crystallization at this heating rate.
Altogether, the results show that PEF behaves very differently from PET or rPET in terms of crystallization. Its very slow thermal crystallization means that it remains essentially amorphous during short processing cycles such as in injection or SBM. This means that crystallization of PEF in such processes is only due to deformation while the crystallization for PET or rPET comes from deformation and heating. These results help clarify how PEF could be integrated into existing PET processing routes and support its potential as a bio-based packaging material.

Appendix: material characteristics

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Table A. 1 RAMAPET N180 (virgin PET) properties

Table A. 2 MOPET (rPET) properties

Table A. 3 PEF properties

References

The original version of this paper is available on https://www.scientific.net/DDF.451.63.pdf

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 75-85

doi: 10.4028/p-12AeQc

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

Submitted:
2026-01-12

Accepted:
2026-03-02

Online:
2026-04-17

Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks

The original version of this paper is available on https://www.scientific.net/DDF.451.75.pdf

Wancley O. Pedruzzi 1,a*, Igor F. Tosi 2, b, William P. M. Quiroz 4,c, Raffaele D'Elia 5, d, Julio C. S. Dutra 3,e, and Wellington B. da Silva 3,f

1 Graduate Program of Mechanical Engineering, Universidade Federal do Espírito Santo, Brazil.

2 Graduate Program in Chemical Engineering, Universidade Federal do Espírito Santo, Brazil.

3 Department of Rural Engineering, Universidade Federal do Espírito Santo, Brazil.

4 Universidad San Sebastián, Campus Bellavista, Chile.

5 Institut Clément Ader (ICA), Univ Toulouse, IMT Mines Albi, INSA Toulouse, ISAE Sup Aero, CNRS, ICA, Albi France.

a  wancley.pedruzzi@edu.ufes.br, b  igor.tosi@edu.ufes.br, c  william.montes@uss.cl, d raffaele.delia@mines-albi.fr, e julio.dutra@ufes.br, f wellingtonufes@gmail.com

Keywords: PINNs, Composite, Porosity, Void Growth.

Abstract

Epoxy-based composites used in the aerospace industry are highly sensitive to moisture absorption, which can lead to porosity formation during the curing process and compromise structural integrity. Therefore, accurate prediction of temperature fields, degree of cure, and moisture concentration is essential for process optimization and defect mitigation. However, classical numerical approaches for solving the coupled governing equations are computationally expensive, limiting their applicability in real-time analyses and optimization strategies. In this work, Physics-Informed Neural Networks (PINNs) are investigated for predicting the transient thermal behavior, cure kinetics, and moisture concentration in an epoxy composite laminate during autoclave curing. Two PINNs are developed: the first solves the coupled transient heat transfer and cure kinetics equations in compositetooling system, while the second predicts the moisture concentration field in the laminate using the temperature information provided by the first network. Different network architectures are evaluated, and their performance is compared with numerical solutions obtained via the Finite Volume and Finite Element Methods. The results demonstrate that PINNs accurately reproduce temperature profiles, degree of cure, and moisture concentration, achieving high coefficients of determination, while also providing significant computational efficiency advantages during the prediction stage. These findings highlight the potential of PINNs as a robust and efficient tool for modeling complex coupled phenomena in composite manufacturing processes.

Introduction

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Epoxy-based composites are widely employed in the aerospace industry in processes such as autoclave lamination, due to their ability to produce high-performance components with superior structural quality. However, these materials are sensitive to moisture absorption, which promotes porosity formation during curing and may compromise their properties, ultimately leading to part rejection [1].

Mitigating this issue requires strict control of process parameters, particularly pressure and temperature. In this context, modeling and computational simulation stand out as essential tools for parameter estimation and optimization. The prediction of void growth involves the coupling of differential equations [1,2], whose solution is computationally expensive and limits their application in control and optimization strategies. Within this scenario, data-driven approaches emerge as an alternative to classical modeling.

Among these, Physics Informed Neural Networks (PINNs) are an emerging and promising alternative to solve differential equations, as introduced by [3], [4] and [5].

PINNs share a structure similar to that of traditional artificial neural networks, comprising input and output layers, hidden layers, and activation functions. The main distinction lies in the incorporation of physical laws into the modeling process. This is achieved by adding a term to the loss function that penalizes deviations from these physical laws, such as governing differential equations, thereby ensuring that the network predictions remain consistent with known physical principles. Other important aspects of PINNs include weight initialization [6], loss functions [7], network depth and number of neurons [8], and overfitting [9].

In this sense, the present work investigates the application of PINNs for predicting temperature and concentration fields. Two neural networks are employed, the first is designed to solve the transient heat equation coupled with the resin degree of cure, while the second PINN is constructed to compute the moisture concentration using Fick's second law, aiming to provide a solid foundation for rapid system state predictions and for estimating viscosity and void growth through external models.

Physical Problem and Mathematical Formulation

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The model developed in this work is based on those presented by [2] and [1]. It consists of an energy balance for temperature calculation, accounting for heat transfer through the composite laminate and the tooling, as well as the exothermic effect of the resin chemical reaction during curing. A mass balance is also included to determine the moisture concentration distribution along the composite thickness during the autoclave curing cycle, together with a kinetic model used to predict the evolution of the degree of cure as a function of time and temperature. As illustrated in Figure 1, the model is applied to a one-dimensional domain comprising a laminate of thickness L and a metallic tool of thickness s. The kinetic model adopted to describe resin curing corresponds to a modified version

[picture]

Fig. 1: Schematic representation of the problem domain.

Fig. 1. Schematic representation of the problem domain.

of the model originally proposed by [10], and later extensively examined by [11], [2], and [1]. This version accounts for the effects of resin vitrification during the curing process by introducing the term αmax , whose value ranges from 0 to 1 .

dαdt=k1(αmax−α)n1+k2αm(αmax−α)n2ki=k0ie−Eai/RTαmax=p+qT

(1)(2)(3)

where α(−) is the degree of cure of the resin, m(−),n1(−), and n2(−) are reaction orders, and k1( s−1) and k2( s−1) are kinetic constants with an Arrhenius-type dependence on temperature T( K). The parameters p(−) and q( K−1) were fitted by [2].

To account for heat transfer through the composite laminate and the tooling, along with the exothermic effects of the resin chemical reaction during the curing process, an energy balance was introduced. For this model, a plane-parallel geometry with constant properties is assumed [2].

ρccpc∂T∂t=kc∂2T∂x2+ρcΔhrefdαdt,x∈Ω1ρtcpt∂T∂t=kt∂2T∂x2,x∈Ω2

(4)(5)

where ρc( kg/m3) is the density of the composite, cpc( J/(kg·K)) its specific heat, kc( W/(m·K)) its thermal conductivity, and Δhref (J/kg) the heat generated by the chemical reaction. Similarly, ρt(kg/m3) is the density of the tooling, cpt( J/(kg·K)) its specific heat, and kt( W/(m·K)) its thermal conductivity.

For the boundary conditions, lateral convection is considered at each end in contact with the autoclave internal gas, whose heating is modeled by a linear ramp with a slope of 2∘C/min, becoming asymptotic upon reaching 180∘C, the curing temperature. These boundary conditions are represented by Equations 6 and 7.

kc∂T∂x=h(T− Tout ), in x=0−kt∂T∂x=h(T− Tout ), in x=L+s

(6)(7)

For the concentration profile, Fick's second law was employed to calculate the moisture concentration C( mol/m3), defined as the absolute amount of absorbed moisture, expressed as the mass of moisture per unit volume.

∂C∂t=D∂2C∂x2,x∈Ω1(8)

where x( m) represents the direction along the thickness and D( m2/s) is the diffusivity, assumed independent of the spatial variable x. However, the moisture diffusivity is strongly influenced by temperature and, in the case of water diffusion in pre-cured or cured resin, follows an Arrhenius-type relationship.

D=D0e−Ead/RT(9)

where D0( m2/s) is the pre-exponential constant, Ead(J/mol) is the activation energy for diffusion per mole, R( J/(mol·K)) is the universal gas constant, and T( K) is the absolute temperature.

For the boundary conditions, a Dirichlet condition is applied at the left face and a Neumann condition at the right face, as described by Equation 10 and Equation 11, respectively.

C=0, in x=0∂C∂x=0, in x=L

(10)(11)

The data corresponding to the parameters used in the deterministic approach of the model are presented in Table 1.

Table 1: Model parameters.

ρc (kg m⁻³) | cpc (J kg⁻¹ K⁻¹) | kc (W m⁻¹ K⁻¹) | ρt (kg m⁻³) | cpt (J kg⁻¹ K⁻¹) | kt (W m⁻¹ K⁻¹)
1.59 × 10³ | 8.71 × 10² | 4.03 × 10⁻¹ | 2.70 × 10³ | 9.00 × 10² | 1.45 × 10²
Δhrf (J kg⁻¹) | hc (W m⁻² K⁻¹) | k₀₁ (s⁻¹) | k₀₂ (s⁻¹) | Ea1 (J mol⁻¹) | Ea2 (J mol⁻¹)
3.56 × 10⁵ | 40 | 1.15 × 10¹⁰ | 1.40 × 10² | 1.27 × 10⁵ | 4.51 × 10⁴
R (J mol⁻¹ K⁻¹) | n₁ (-) | n₂ (-) | m (-) | p (-) | q (K⁻¹)
8.314 | 7.90 × 10⁻¹ | 1.99 | 5.80 × 10⁻¹ | -2.54 | 7.40 × 10⁻³
D₀ (m² s⁻¹) | Ead (J mol⁻¹) | x₀ (m) | xl (m) | xs (m) | -
1.90 × 10⁻² | 5.55 × 10⁴ | 0 | 5.58 × 10⁻³ | xl + 2 × 10⁻² | -

Physical-Informed Neural Network

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Physics-Informed Neural Networks (PINNs) are machine learning techniques for solving differential equations [12]. In PINNs, the unknown solution is approximated by a neural network. The neural network is trained using data in a manner that satisfies the governing equation, as well as the initial and boundary conditions. This approach allows PINNs to directly incorporate physical laws and constraints into the neural network structure [3].

In this study, two Physics-Informed Neural Networks (PINNs) are developed with the aim of predicting the desired variables. In PINN 1, the input variables are x and t, and the outputs are temperature T and degree of cure α, considering two distinct regions. In region 1, both temperature and degree of cure are calculated, whereas in region 2, only the temperature is considered, as the degree of cure has no physical meaning. For PINN 2, the inputs are t,x, and T, with T being the temperature obtained as the output from PINN 1. The output of this network is the concentration field C. The architecture adopted is illustrated in Figure 2. The spatial domain is divided into two regions: Ω1, corresponding

[picture]

Fig. 2: Illustration of the inputs and output of the neural networks.

Fig. 2. Illustration of the inputs and output of the neural networks.

to the composite laminate, and Ω2, corresponding to the Tool, separated by an interface located at x=L. The total loss function of PINN 1 is defined as the sum of the contributions associated with the governing equations in each region, the continuity conditions at the interface, and the boundary conditions, and is expressed as

ℒPINN1 =ℒΩ1+ℒΩ2+ℒInterface +ℒBCs +ℒIC (12)

In Region Ω1, where the curing process takes place, heat transfer is coupled with the exothermic chemical reaction. Accordingly, the energy balance equation with the heat generation term and the kinetic equation for the degree of cure are imposed simultaneously. The residuals associated with these equations are defined as:

ℛT(1)(t,x)=ρccpc∂T∂t−kc∂2T∂x2−ρcΔhrefdαdt,x∈Ω1ℛα(t,x)=dαdt−[k1(αmax−α)n1+k2αm(αmax−α)n2],x∈Ω1

(13)(14)

The contribution from Region 1 to the loss function is then given by

ℒΩ1=‖ℛT(1)‖2+‖ℛα‖2(15)

In Region Ω2, corresponding to the tool, no chemical reaction occurs, and the physical process is governed exclusively by transient heat conduction. Thus, only the energy balance equation is imposed in this region, with the residual defined as

ℛT(2)(t,x)=ρtcpt∂T∂t−kt∂2T∂x2,x∈Ω2(16)

The contribution from Region 2 to the loss function is expressed as

ℒΩ2=‖ℛT(2)‖2(17)

Although the neural network numerically provides values for the degree of cure α in Region 2 as well, no governing equation is imposed for this variable outside the composite. Therefore, the predicted values of α in Region 2 have no physical meaning and are not used in the energy balance, having no influence on the thermal solution.

At the interface between the two regions (x=L), physical continuity conditions are imposed to ensure the consistency of the thermal coupling between the composite and the tool. These conditions correspond to the continuity of temperature and heat flux, with the residuals defined as

ℛTΓ(t)=T(1)(L,t)−T(2)(L,t)ℛqΓ(t)=kc∂T∂x|L−−kt∂T∂x|L+

(18)(19)

The contribution associated with the interface is then given by

ℒInterface =‖ℛTΓ‖2+‖ℛqΓ‖2(20)

The convective boundary conditions imposed on the external surfaces of the domain are incorporated into the loss function through the residuals

ℛBC0(t)=kc∂T∂x(0,t)−h[T(0,t)−Tout (t)]ℛBCL+s(t)=−kt∂T∂x(L+s,t)−h[T(L+s,t)−Tout (t)]

(21)(22)

The contribution of the boundary conditions to the total loss function is given by

ℒBCs=‖ℛBC0‖2+‖ℛBCL+s‖2(23)

The initial conditions are incorporated into the loss function through the following residuals:

ℛICT(x)=T(x,0)−T0,x∈Ω1∪Ω2ℛICα(x)=α(x,0)−α0,x∈Ω1

(24)(25)

The contribution of the initial conditions to the total loss function is then defined as

ℒIC=‖ℛICT‖2+‖ℛICα‖2(26)

where the residuals are evaluated at the collocation points defined at the initial time t=0.
For the concentration, this is defined only in Region Ω1, corresponding to the composite laminate. Thus, the loss function of PINN 2 is formulated so as to enforce Fick's second law with diffusivity dependent on time, space, and temperature, as well as the boundary and initial conditions associated with the problem. The residual of the governing diffusion equation is defined as

ℛC(t,x)=∂C∂t−D(T)∂2C∂x2,x∈Ω1(27)

where T=T(x,t) is the temperature predicted by PINN 1. The contribution associated with the governing equation to the loss function of PINN 2 is then expressed as

ℒΩ1C=‖ℛC‖2(28)

The boundary conditions of the diffusion problem are incorporated through additional residuals. On the left face of the domain (x=0), a Dirichlet condition is imposed, defined as

ℛBC,C0(t)=C(0,t)(29)

while on the right face of the composite (x=L), a Neumann condition is imposed, expressed as

ℛBC,CL(t)=∂C∂x|x=L(30)

The contribution of the boundary conditions to the loss function is then given by

ℒBCsC=‖ℛCBC,0‖2+‖ℛCBC,L‖2(31)

The initial conditions of the diffusion problem are likewise incorporated into the loss function. Considering a uniform initial concentration in the composite laminate, the residual associated with the initial condition is defined as

ℛICC(x)=C(x,0)−C0,x∈Ω1(32)

where C0 represents the initial moisture concentration. The contribution of the initial conditions to the loss function of PINN 2 is then expressed as

ℒICC=‖ℛICC‖2(33)

Thus, the total loss function associated with PINN 2 is defined as

ℒPINN2=ℒΩ1C+ℒBCsC+ℒICC(34)

Table 2: Neural network architectures.

Number of hidden layers | Neurons per hidden layer
3, 5, 7 | 20, 40, 60, 80

For the computational implementation, the PINNs were developed using the TensorFlow framework, a library available in the Python programming language. Twelve distinct models were evaluated for each PINN, considering different combinations of layers and neurons in the hidden layers, as presented in Table 2.

In all cases, hyperbolic tangent (tanh) activation functions were employed in each layer, and the neural network weights were initialized using the Glorot uniform method, in which the weights of each layer are initialized from a uniform distribution as described by [13]. All terms of the loss function were weighted equally, with a weight of 1.0 . The dataset used for training consisted of 15000 points for the partial differential equation domain residuals, 5500 points for the boundary conditions, and 1700 points for the initial conditions. These points were generated using a uniform sampling strategy.

The loss function was minimized through 60000 iterations of the Adam algorithm [14], with a learning rate of 10−3, until convergence was achieved. After training, the prediction data were input into each model, and performance was evaluated using the Coefficient of Determination ( R2 ). For result verification, the Finite Volume Method (FVM) was employed in Python, as well as FlexPDE, a computational software with its own scripting language, developed for solving Partial Differential Equations (PDEs) using the Finite Element Method (FEM).

Results and Discussion

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The PINN architectures were selected based on an architecture convergence assessment, in which the network performance varied according to the number of layers and the number of neurons per layer, as evaluated by the coefficient of determination ( R2 ) through comparison with the finite volume numerical solution. Table 3 reports this metric for architectures ranging from three to seven layers, with the number of neurons per layer varying from 20 to 80 .

Table 3: Coefficient of determination ( R2 ) obtained for different PINN architectures.

Hidden layers | Neurons per layer | R² [-] (PINN 1) | R² [-] (PINN 2)
3 | 20 | 0.882 | 0.758
3 | 40 | 0.891 | 0.782
3 | 60 | 0.955 | 0.821
3 | 80 | 0.956 | 0.816
5 | 20 | 0.909 | 0.772
5 | 40 | 0.976 | 0.788
5 | 60 | 0.978 | 0.889
5 | 80 | 0.971 | 0.873
7 | 20 | 0.912 | 0.734
7 | 40 | 0.970 | 0.799
7 | 60 | 0.973 | 0.888
7 | 80 | 0.952 | 0.852

In Table 3, each proposed architecture is presented. It can be observed that increasing the number of neurons and layers leads to performance gains; however, there is a limit beyond which denser architectures no longer provide improvements. Specifically, for both PINN 1 and PINN 2, the best
performances were achieved with 5 layers and 60 to 80 neurons per layer. It is also noted that when 7 layers and 80 neurons were used, the networks exhibited reduced performance, which can be attributed to overfitting. In this context, the network with 5 layers and 60 neurons per layer was selected for PINN 1, and the network with 7 layers and 60 neurons per layer was selected for PINN 2. The loss function history is shown in Figure 3.

[picture]

Fig. 3: Training history of the neural networks: PINN 1 (Left) and PINN 2 (Right).

Fig. 3. Training history of the neural networks: PINN 1 (Left) and PINN 2 (Right).

It is important to note that, for all considered points, the loss function reaches the order of 10−4 to 10−5, indicating that the physical model is respected within the observed domain.

Figure 4 illustrates the performance of the PINN 1 in predicting the temperature profile. It can be observed that the three solutions coincide, demonstrating the robustness of the tool, with an exceptional gain in computational cost. Classical methods, such as the finite volume method, discretize the problem and solve an N×N system of equations depending on the number of volumes, whereas the PINN incurs virtually no cost during prediction, despite being computationally intensive during training, a process performed offline.

[picture]

Fig. 4: Temperature profile: mid-plane (Left) and tool side (Right).

Fig. 4. Temperature profile: mid-plane (Left) and tool side (Right).

Regarding PINN 1, Figure 5 shows the prediction of the concentration field. In this case, it can be observed that the solutions coincide up to 75 minutes; after that, a slight divergence in the results occurs. This difference is reflected in the R2 metric (Table 3) for the concentration profile. This network achieved slightly lower performance due to its complexity, its input couples the temperature, which

[picture]

Fig. 5: Moisture concentration profile: mid-plane (left) and tool side (right).

Fig. 5. Moisture concentration profile: mid-plane (left) and tool side (right).

is strongly linked to both space and time. Consequently, for each input temperature, a new profile emerges, increasing the complexity of the output.

With the PINNs properly trained, new opportunities for scientific investigation emerge, such as their application to the prediction of void growth in high-performance composites, using models such as those proposed by [15] and [16]. Another research direction involves the investigation of different hyperparameters, such as the activation function and the Latin hypercube sampling (LHS) strategy, in order to improve the quality of the solution obtained for the concentration field of PINN 2, as well as the proposal of a new architecture for PINN 1, which consists of its complete separation into two distinct networks, each responsible for a specific domain. Furthermore, an expansion of the input variables is proposed, in which the relevant parameters to be estimated are coupled, thereby characterizing the formulation of an inverse problem.

Conclusions

The original version of this paper is available on https://www.scientific.net/DDF.451.75.pdf

In this work, the application of Physics-Informed Neural Networks (PINNs) was evaluated for the coupled solution of heat transfer, cure kinetics, and moisture diffusion problems during the autoclave curing process of epoxy-based composite laminates. The proposed approach consisted of developing two distinct PINNs: the first aimed at predicting temperature and degree of cure fields in the com-posite-tooling system, and the second focused on determining the moisture concentration field in the laminate, using the thermal field provided by the first network as input.

The results indicate that PINN 1 is capable of accurately reproducing the temporal and spatial evolution of temperature and degree of cure, showing good agreement with reference numerical solutions obtained via the Finite Volume and Finite Element Methods. For PINN 2, it was observed that the prediction of the moisture concentration field is more sensitive to the network architecture due to the strong coupling between diffusivity and the space- and time-dependent temperature field, resulting in lower performance values compared to the thermal problem.

Analysis of different network architectures showed that increasing the number of layers and neurons per layer improves the approximation capability of the PINNs up to a certain limit, beyond which no further gains are observed and overfitting effects may occur. The selected architectures represent a compromise between accuracy and computational complexity.

Although the training process of the PINNs requires significant computational effort, this stage is performed offline. Once trained, the networks allow the fields of interest to be obtained without the need for iterative solution of the differential equations, which can be particularly relevant for applications requiring repeated system evaluations.

Finally, the presented methodology provides a consistent basis for future studies involving the extension of the model to predict void growth, the investigation of alternative training and sampling strategies, as well as the formulation of inverse problems for estimating parameters of the curing process in polymeric composites.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.75.pdf

Andrea Dei Sommi, Francesca Lionetto, Giuseppe Buccoliero, and Alfonso Maffezzoli. The effect of absorbed moisture and resin pressure on porosity in autoclave cured epoxy resin. Polymer Composites, 45(17):15793-15803, August 2024.

Andrea Dei Sommi, Giuseppe Buccoliero, Francesca Lionetto, Fabio De Pascalis, Michele Nacucchi, and Alfonso Maffezzoli. A finite element model for the prediction of porosity in autoclave cured composites. Composites Part B: Engineering, 264:110882, September 2023.

M. Raissi, P. Perdikaris, and G.E. E Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686-707, 2019.

Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations, 2017.

Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations, 2017.

Jingjing Liu, Yefeng Liu, and Qichun Zhang. A weight initialization method based on neural network with asymmetric activation function. Neurocomputing, 483:171-182, April 2022.

Yash Srivastava, Vaishnav Murali, and Shiv Ram Dubey. A Performance Evaluation of Loss Functions for Deep Face Recognition, page 322-332. Springer Singapore, 2020.

S.H. Shabbeer Basha, Shiv Ram Dubey, Viswanath Pulabaigari, and Snehasis Mukherjee. Impact of fully connected layers on performance of convolutional neural networks for image classification. Neurocomputing, 378:112-119, February 2020.

Qi Xu, Ming Zhang, Zonghua Gu, and Gang Pan. Overfitting remedy by sparsifying regularization on fully-connected layers of cnns. Neurocomputing, 328:69-74, February 2019.

Musa R. Kamal. Thermoset characterization for moldability analysis. Polymer Engineering amp; Science, 14(3):231-239, March 1974.

Panagiotis I. Karkanas and Ivana K. Partridge. Cure modeling and monitoring of epoxy/amine resin systems. i. cure kinetics modeling. Journal of Applied Polymer Science, 77(7):1419-1431, 2000.

Zaharaddeen Karami Lawal, Hayati Yassin, Daphne Teck Ching Lai, and Azam Che Idris. Physics-informed neural network (pinn) evolution and beyond: A systematic literature review and bibliometric analysis. Big Data and Cognitive Computing, 6(4):140, 2022.

Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Yee Whye Teh and Mike Titterington, editors, Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, volume 9 of Proceedings of Machine Learning Research, pages 249-256, Chia Laguna Resort, Sardinia, Italy, 13-15 May 2010. PMLR.

Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2014.

J. L. Kardos, M. P. Duduković, and R. Dave. Void growth and resin transport during processing of thermosetting - Matrix composites, page 101-123. Springer Berlin Heidelberg, 1986.

Y. Ledru, G. Bernhart, R. Piquet, F. Schmidt, and L. Michel. Coupled visco-mechanical and diffusion void growth modelling during composite curing. Composites Science and Technology, 70(15):2139-2145, December 2010.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 87-94

doi: 10.4028/p-c6k3HY

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

Submitted:
2026-01-12

Revised:
2026-03-02

Accepted:
2026-03-03

Online:
2026-04-17

Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

The original version of this paper is available on https://www.scientific.net/DDF.451.87.pdf

TOSI Igor F. 1,a*, PEDRUZZI Wancley O. 2, b, QUIROZ William P. M. 4,c, D'ELIA Raffaele, 5, d, DUTRA Julio C. S. 3,e, and DA SILVA Wellington B. 3,f

1 Graduate Program in Chemical Engineering, Universidade Federal do Espírito Santo, Brazil

2 Graduate Program of Mechanical Engineering, Universidade Federal do Espírito Santo, Brazil.

3 Department of Rural Engineering, Universidade Federal do Espírito Santo, Brazil.

4 Universidad San Sebastián, Campus Bellavista, Chile.

5 Institut Clément Ader (ICA), Univ Toulouse, IMT Mines Albi, INSA Toulouse, ISAE Sup Aero, CNRS, ICA, Albi France.

a igor.tosi@edu.ufes.br, b wancley.pedruzzi@edu.ufes.br, c william.montes@uss.cl, d raffaele.delia@mines-albi.fr, e julio.dutra@ufes.br, f wellingtonufes@gmail.com

Keywords: Method of Fundamental Solutions, Method of Particular Solutions, Meshless Method, composite

Abstract

This work presents a hybrid formulation combining the Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS) coupled with an implicit Finite Difference Method (FDM) to simulate the transient heat conduction in a two-layer domain composed of a steel tool and an epoxy resin. The proposed approach incorporates a non-homogeneous source term in the governing equation, allowing the analysis of the curing heat release within the resin layer while maintaining a meshless boundary-based structure. Sequential numerical tests were performed to empirically assess the influence of key hyper-parameters number and position of source points, distance parameters, and the Tikhonov regularization factor on the stability and accuracy of the method. The MFS-MPS/FDM model showed excellent agreement with the finite element results reported by Dei Sommi et al., achieving low RMSE (Root Mean Squared Error) and MAE (Mean Absolute Error) values relative to the thermal scale of the process. These results confirm the robustness and predictive capability of the MFS in capturing transient thermal evolution even in the presence of a source term, although its performance remains sensitive to the proper calibration of numerical hyper-parameters.

Introduction

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When subjecting a laminated composite to an autoclave curing process, it is essential to closely monitor the thermodynamic conditions imposed on the evaluated material. Under certain circumstances, the undesirable formation of voids (pores) may occur. High initial moisture levels and lower autoclave pressure contributed to the emergence of voids on the tool side, where the residual water concentration is typically higher [1]. The relationship between the initial amount of moisture absorbed by the resin and the hydrostatic pressure during curing was also investigated by [2], combining the theoretical modeling of Kardos and Ledru with experimental tests and computational numerical analysis using the Finite Element Method (FEM).

Computational numerical models serve as essential tools for investigating the parameters that contribute to pore formation in materials, offering viable alternatives to experimental routines. Established methods such as the FEM, the Finite Volume Method (FVM), and the FDM have been widely applied in the simulation of complex physical phenomena in composites, such as heat diffusion and mechanical strength [3,4].

In this context, meshless methods represent an approach that eliminates the need for discretizing the domain into a continuous mesh, leading to a significant reduction in computational cost while also enhancing the flexibility in modeling complex geometries. Among these methodologies, the MFS
stands out due to its consistent numerical formulation, making it particularly suitable for the analysis of layered media and applications involving heat transfer in laminated materials [5]. However, for the application of this technique, knowledge of the fundamental solution of the partial differential equation (PDE) is crucial, as it is restricted to homogeneous PDEs. The presence of the source term in the equation precludes the application of the MFS in its classical form, necessitating its decomposition into homogeneous and particular components [6].

The MPS can be naturally integrated with the Method of Fundamental Solutions (MFS), enabling the treatment of non-homogeneous terms through auxiliary approximations such as Radial Basis Functions (RBF) or Finite Difference schemes [7,8]. Previous applications of the MFS in composite materials have been predominantly restricted to elliptic, Helmholtz-type problems, where the nonhomogeneous term is transformed into combinations of RBFs in order to convert the governing equation into an equivalent homogeneous system [9]. Such formulations, however, are typically limited to steady-state or non-transient settings.

In contrast, the present study introduces a fully transient and nonlinear meshless formulation of heat conduction in a multilayer domain, in which the governing PDE contains a time-dependent, temperature-dependent volumetric source term. The proposed framework unifies the MFS with the MPS-FDM approach in a hybrid strategy that preserves the meshless character of the MFS while consistently incorporating the non-homogeneous and nonlinear contributions into the transient evolution of the solution.

Unlike previous approaches that rely on spatial discretization or stationary reformulations, the proposed method directly handles the time-dependent non-homogeneous term without requiring domain meshing, enabling efficient simulation of coupled thermo-reactive phenomena in layered materials. This represents a significant methodological advancement, extending the MFS from classical elliptic applications to a robust transient formulation capable of addressing nonlinear heat conduction in composite multi-domain systems.

Methodology

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The methodology implemented in this work is based on the numerical solution of a thermal model coupled with transport-related quantities, aimed at assessing the influence of temperature on pressure and on the mass diffusion coefficient D. The temperature field is treated as the primary variable of the entire model and is obtained from the transient heat conduction equation. Based on this field, temperature-dependent quantities are updated and used to evaluate the pressure, which in turn influences diffusion-related phenomena. Consequently, the diffusion coefficient is not treated as a constant at each iteration, but rather as a variable quantity, consistently determined according to the thermal state of the system.

Thermal Model

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The transient thermal model, represents the state to be determined at each time iteration, where Ψ(t) denotes the source term associated with the degree of cure of the material.

ut=α∇2uxx+Ψ(t)(1)

In order to achieve accurate results while maintaining low computational cost, a meshless method is adopted, thereby avoiding the discretization of the physical domain. Accordingly, the MFS is employed to analyze the transient thermal behavior of a homogeneous model by associating the fundamental solution also referred to as the Green's function of the heat conduction PDE. However, since Eq. (1) includes a source term, the direct application of the MFS is not possible, requiring its coupled use with an auxiliary methodology for the approximation of Ψ(t).

uG(x,t)=uH(x,t)+u~(x,t)(2)

Thus, based on the MPS, the solution of the non-homogeneous heat conduction PDE is decomposed into the sum of a homogeneous solution, uH(x,t), obtained via the MFS, and a particular solution, u~(x,t), computed using the FDM as expressed in Eq.(2).

Formulation of the MFS for the Homogenuos Heat Equation

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The MFS approximates the solution of the homogeneous heat conduction PDE through linear combinations of fundamental solutions, allowing the problem to be solved without discretizing the physical domain. This approach relies solely on collocation points located on the boundary and source points placed in a region external to the physical domain.

G(x,t;ξ,τ)=H(t−τ)4πα(t−τ)exp(−(x−ξ)24α(t−τ))(3)

Equation (3) represents the fundamental solution of Eq. (1) for Ψ(t)=0, where x denotes the collocation points and ξ the source points. The temporal source points τ are introduced such that τ=t−Δt. The function H(t−τ) corresponds to the Heaviside step function, ensuring that the fundamental solution vanishes for t<τ. A linear system is then constructed from the fundamental solutions together with the boundary and initial conditions, where c denotes the vector of coefficients to be determined from the inclusion of Ns sources.

uH(x,t)≈∑j=1NscjG(x,t;ξj,τj)(4)

However, the fundamental solution matrix computed in Eq. (3) requires regularization prior to solving the system, as it exhibits strongly linearly dependent columns as well as highly singular values. Therefore, Tikhonov regularization is applied by introducing a small-order penalty parameter λ :

(𝐀T𝐀+λ2𝐈)c=𝐀Tb(5)

Equation (5) illustrates the system composed of the fundamental solution matrix (A), the identity matrix (I), the boundary conditions vector (b), and the vector of unknown coefficients (c).

Particular Solution and Coupling with the MFS

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Due to the inherent limitations of the MFS, the MPS is employed as an auxiliary strategy to approximate the source term Ψ(t), transferring its effect to the boundary conditions of the problem solved by the MFS. Accordingly, the boundary vector (b) is updated at each time iteration as a result of the influence of the degree of cure on the system.

uin+1−uinΔt=αu~i+1n+1−2u~in+1+u~i−1n+1Δx2+Ψ(tn+1)(6)

An implicit time integration scheme is adopted for the evaluation of the degree of cure, which is subsequently incorporated into the homogeneous model solved using the MFS. Equation (6) describes the finite difference scheme employed to compute the particular solution introduced in Eq. (2), while Eq. (7) defines the homogeneous boundary conditions imposed within the MPS framework.

{hu~(x0,t)−k∂u~(x0,t)∂n=0hu~(xL,t)+k∂u~(xL,t)∂n=0(7)

General Solution

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The general solution of the governing PDE is obtained through an iterative MFS-MPS scheme, in which the source term Ψ(t) is treated exclusively by the MPS. This approach generates a correction term that is incorporated into the boundary conditions of the MFS. As a result, the problem is homogenized, enabling the reconstruction of the temperature field through a linear combination of the fundamental solutions of the heat conduction equation.

[picture]

Fig. 1: Iterative MFS-MPS computational scheme.

Fig. 1. Iterative MFS-MPS computational scheme.

Water vapor pressure is calculated locally as a function of temperature, following [ 1,2 ], as given in Eq. (8). At each time step, the temperature field provided by the MFS-MPS thermal model is used to update the vapor pressure values.

Pwater =611.21exp(18.678u234.5)(u257.14+u)(8)

No spatial pressure gradients or transport mechanisms are considered, and the pressure is evaluated solely as a function of the local temperature. Likewise, the diffusion coefficient is investigated as a temperature-dependent parameter, without the need to solve the mass diffusion governing equation. Its temporal evolution reflects the effect of temperature on the mobility of volatile species within the material and is updated at each time step using an Arrhenius-type formulation:

D(u)=D0exp(−Ead/Ru)(9)

Error Metrics

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The tests for the MFS were conducted sequentially, empirically evaluating the influence of each hyperparameter on the final results. The method's ability to capture the thermal evolution was quantitatively assessed using the RMSE and MAE error metrics, which measure the discrepancy between the numerical results and the reference model, as shown in Eq. (10).

RMSE=1N∑i=1N(uinum−uiref)2MAE=1N∑i=1N|uinum−uiref|(10)

Physical Problem

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The domains are coupled at Γ12, Figure 2, with perfect thermal contact between the layers. In the resin domain, P a source term Ψ(t) is present, associated with the exothermic curing reaction process, modeled by:

Ψ(t)=κ1(αmax−α)n1+κ2(αmax−α)n2αmax=p+qu(11)

The kinetic constants κ1 and κ2 are updated at each iteration, as they depend directly on the temperature, according to the Arrhenius relation:

κj=k0jexp(−Eaj/Ru)j=1,2(12)

[picture]

Fig. 2: Sketch of the model domain, where L and s are the laminate and tool thickness, respectively.

Fig. 2. Sketch of the model domain, where L and s are the laminate and tool thickness, respectively.

The thermal problem is defined over a one-dimensional composite domain Ω=[0,L+s], composed of the resin region (0≤x≤L) and the tool region (L<x≤L+s). The governing equations read:

{ρccpc∂u∂t=kc∂2u∂x2+ρcΔhrefΨ(t),0≤x≤L,ρtcpt∂u∂t=kt∂2u∂x2,L<x≤L+s.(13)

The initial condition is prescribed as u(x,0)=u0,x∈Ω. Convective boundary conditions are imposed at both external surfaces in x=x0 and x=L+s. The autoclave temperature ue(t) varies linearly in time, imposing a controlled heating rate u˙=2∘C/min from the initial temperature u0 :

ue(t)=u0+u˙t.(14)

Table 1: Parameters used in the thermal and kinetic model of the test case

Symbol | Value | Unit | Symbol | Value | Unit
m | 5.80 × 10⁻¹ | − | n₁ | 7.90 × 10⁻¹ | −
n₂ | 1.99 | − | k₀₁ | 1.15 × 10¹⁰ | s⁻¹
k₀₂ | 1.40 × 10² | s⁻¹ | Ea1 | 1.27 × 10⁵ | J/mol
Ea2 | 4.51 × 10⁴ | J/mol | Δh | 3.56 × 10⁵ | J/kg
R | 8.314 | J/mol | p | −2.54 | −
q | 7.4 × 10⁻³ | K⁻¹ | ρc | 1.58 × 10³ | kg/m³
cpc | 8.71 × 10² | J/(kg · K) | kc | 0.43 | W/(mK)
ρt | 2.7 × 10³ | kg/m³ | cpt | 9 × 10² | J/(kg · K)
kt | 1.45 × 10² | W/(mK) | L | 5.58 | mm
s | 20 | mm | h | 40 | W/(m²K)
u₀ | 20 | °C | umax | 180 | °C

Results and Discussion

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The tests for the MFS were conducted sequentially, empirically evaluating the influence of each hyperparameter on the final results, according to the input parameters showing in Tab. 1. The Tab 2 shows that the computational algorithm proposed in this work exhibits excellent agreement with the results of [1], considering that the RMSE and MAE errors are within acceptable levels ≈0.1 relative to the temperature scale.

Table 2: Error indicators and computational cost for different numerical configurations.

Nt | Nx | Ns | δ₁ | δ₂ | λ | Midplane − L/2 | Tool side | CPU (s)
|  |  |  |  |  | RMSE | MAE | RMSE | MAE |
60 | 120 | 480 | 1 | 1.32 | 1 × 10⁻¹¹ | 0.1128 | 0.0940 | 0.0116 | 0.0158 | 21.411
60 | 120 | 480 | 1 | 1.35 | 5 × 10⁻¹¹ | 0.1052 | 0.0850 | 0.0116 | 0.0158 | 22.875
60 | 120 | 480 | 1 | 1.50 | 1 × 10⁻¹² | 0.0916 | 0.0675 | 0.0328 | 0.0279 | 21.290
30 | 60 | 240 | 1 | 1.00 | 1 × 10⁻⁸ | 0.0562 | 0.0432 | 0.0122 | 0.0163 | 4.127
22 | 44 | 176 | 1 | 1.00 | 1 × 10⁻¹⁰ | 0.0928 | 0.1130 | 0.0234 | 0.0190 | 3.313
18 | 36 | 144 | 1 | 1.00 | 9 × 10⁻⁵ | 0.0556 | 0.0463 | 0.0116 | 0.0159 | 3.283

Moreover, Table 2 shows that the errors are closely linked to the space-time discretization, as well as to the calibration of the parameters δ1,δ2, and λ, which represents an inherent challenge of the proposed method. Increasing the number of collocation points Nx and fictitious sources Ns contributes to the reduction of RMSE and MAE errors, reflecting the model's convergence with respect to refinement.

[picture]

Fig. 3: Time dependence of temperature in tool side and mid plane respectively

Fig. 3. Time dependence of temperature in tool side and mid plane respectively

The laminate temperature exceeding the autoclave temperature, particularly at the mid-plane, is physically consistent with the exothermic curing of the epoxy resin. The volumetric heat source term Ψ(t) represents the heat released during polymerization. At the peak reaction rate, the internally generated heat may exceed the heat removed by convection, leading to thermal accumulation at the midplane which is more insulated and has higher thermal inertia and resulting in a temperature overshoot. This behavior is commonly reported in thermoset curing simulations and arises from the coupled thermo-kinetic nature of the process rather than from a numerical artifact.

On the other hand, the displacement of the source points exhibits a markedly nonlinear influence on the MFS performance. Very small displacements tend to deteriorate the conditioning of the fundamental solution matrix, whereas excessively large displacements reduce the accuracy of the temperature field near the boundaries. The regularization parameter λ also plays a crucial role in the MFS, as it controls numerical noise and ensures stability in the computation of the coefficient vector c.

As observed in Fig. 3, larger deviations are detected in the mid-plane region of the laminate. This behavior is attributed to the thermal inertia of the resin, which delays the temperature response and its subsequent stabilization, particularly after the 180∘C plateau. In contrast, at the tool surface where the thermal flux is more intense the MFS reproduces the reference solution with higher accuracy.

[picture]

Fig. 4: Comparison between the simulated water vapor pressure and the experimental data reported by Dei Sommi et al. as a function of time. (Right) Temperature-dependent diffusivity obtained from the FEM and MFS models at the mid-plane position.

Fig. 4. Comparison between the simulated water vapor pressure and the experimental data reported by Dei Sommi et al. as a function of time. (Right) Temperature-dependent diffusivity obtained from the FEM and MFS models at the mid-plane position.

Figure 4 presents the evolution of the water vapor pressure and the temperature-dependent diffusion coefficient obtained using the proposed MFS-MPS framework. In the left panel, the simulated vapor pressure exhibits excellent agreement with the experimental data reported by Dei Sommi et al., yielding an RMSE of 0.0495 and an MAE of 0.0287 . This close agreement confirms that the thermal model accurately captures the dominant thermally driven mechanism governing vapor pressure evolution during curing. The predicted pressure curve displays a characteristic sigmoidal behavior, with an initially slow increase followed by a rapid rise after approximately 60 minutes. This transition coincides with the temperature range in which moisture vaporization becomes significant, indicating that the computed water vapor pressure is physically consistent with the curing cycle and the associated thermal history. The accurate reproduction of this trend is particularly relevant, as elevated vapor pressure constitutes the primary driving force for void nucleation and growth during curing.

The right panel depicts the diffusion coefficient as a function of temperature evaluated at the laminate mid-plane. The MFS-based thermal field closely follows the Arrhenius-type behavior reported in the reference study, demonstrating that the proposed framework correctly captures the exponential sensitivity of diffusivity to temperature. The combined evolution of Pwater  and D(u) highlights competing mechanisms during curing. While the rapid increase in vapor pressure promotes gas expansion and elevates the risk of porosity formation, the simultaneous increase in diffusivity enhances the mobility of volatile species, potentially facilitating their redistribution or release when transport pathways are available. Therefore, even without explicitly solving mass transport or pressure field equations, the computed quantities provide meaningful indicators of curing quality and defect susceptibility.

Conclusions

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The results demonstrate that the MFS, when coupled with the MPS-FDM approach, is capable of accurately capturing the transient thermal evolution within the steel-resin domain, even in the presence of a source term in the conduction equation. This highlights its efficiency in reproducing the thermal coupling between layers of dissimilar materials. In addition, the model successfully reproduced both the pressure-evolution curve and the diffusivity × temperature behavior, showing close agreement with the reference solutions. This indicates that the proposed formulation is not only thermally consistent but also capable of representing the underlying cure-related mass transport phenomena with high fidelity.

However, the deviations observed in Figs. 3 and 4 can be attributed primarily to the inherent difficulty in achieving an optimal calibration of the numerical hyper-parameters. The method's perfor-
mance is strongly influenced by factors such as the number and spatial distribution of collocation and source points, the boundary offset distance, and the Tikhonov regularization parameter. Small variations in these parameters may significantly affect matrix conditioning and solution stability, thereby impacting local accuracy in specific regions of the domain. Thus, although the MFS demonstrates robustness and clear capability in handling non-homogeneous PDEs and coupled multi-physics behavior, the appropriate selection and calibration of hyper-parameters remain central challenges for ensuring both numerical reliability and computational efficiency.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.87.pdf

Andrea Dei Sommi, Giuseppe Buccoliero, Francesca Lionetto, Fabio De Pascalis, Michele Nacucchi, and Alfonso Maffezzoli. A finite element model for the prediction of porosity in autoclave cured composites. Composites Part B: Engineering, 264:110882, September 2023.

Andrea Dei Sommi, Francesca Lionetto, Giuseppe Buccoliero, and Alfonso Maffezzoli. The effect of absorbed moisture and resin pressure on porosity in autoclave cured epoxy resin. Polymer Composites, 45(17):15793-15803, August 2024.

Jin-Sang Yoon, Kibum Kim, and Hyoung-Seock Seo. Computational modeling for cure process of carbon epoxy composite block. Composites Part B: Engineering, 164:693-702, 2019.

Sandeep Chava and Sirish Namilae. Process modeling for strain evolution during autoclave composite cure. Applied Composite Materials, 30(2):361-377, 2023.

B Tomas Johansson and Daniel Lesnic. A method of fundamental solutions for transient heat conduction in layered materials. Engineering Analysis with Boundary Elements, 33(12):1362-1367, 2009.

Xin Li. Convergence of the method of fundamental solutions for solving the boundary value problem of modified helmholtz equation. Applied mathematics and computation, 159(1):113-125, 2004.

Ching-Shyang Chen, Chia-Ming Fan, and PH Wen. The method of approximate particular solutions for solving certain partial differential equations. Numerical Methods for Partial Differential Equations, 28(2):506-522, 2012.

CS Chen, Xinrong Jiang, Wen Chen, and Guangming Yao. Fast solution for solving the modified helmholtz equation withthe method of fundamental solutions. Communications in Computational Physics, 17(3):867-886, 2015.

Bandar Bin-Mohsin and Daniel Lesnic. The method of fundamental solutions for helmholtztype equations in composite materials. Computers & Mathematics with Applications, 62(12):4377-4390, 2011.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 95-101

doi: 10.4028/p-Is2sE9

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

Submitted:
2026-01-19

Revised:
2026-02-26

Accepted:
2026-03-01

Online:
2026-04-17

Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process

The original version of this paper is available on https://www.scientific.net/DDF.451.95.pdf

Hyunsung Choi 1,a*, Minjae Baek 1, b, Yong Nam Kwon 1,c, Ducksung Kim 2, d, Daeho Jeong 2,e  and Yoo In Jeong 2,f 

¹Aerospace research center, Korea Institute of Material Science, Changwon, South Korea

2 Korea Aerospace Industries LTD., Sacheon, South Korea

a* h.choi@kims.re.kr, b qoralswo12@kims.re.kr, c kyn1740@kims.re.kr,

d  ducksung.kim@koreaaero.com, e  daeho.jeong@koreaaero.com, f  freud197@koreaaero.com

Keywords: PMMA, viscoplastic model, creep model, vacuum forming.

Abstract

In this study, the thermomechanical behavior of PMMA(poly-methyl methacrylate) during high-temperature vacuum forming was analyzed through both experimental and computational approaches. The material behavior of PMMA was modeled as a temperature and strain-rate dependent viscoplastic response, coupled with time-dependent creep deformation. The creep behavior was represented by the Norton-Bailey power law (Eq. 1), while the constitutive model for the strain rate and temperature-dependent stress-strain behavior was implemented in ABAQUS via a user subroutine (UHARD). The forming process was simulated by using ABAQUS/Standard VISCO solver, incorporating vacuum pressure loading and clamping conditions. The numerical framework enables effective analysis of deformation behavior under thermomechanical forming conditions and provides a basis for process-oriented modeling of PMMA vacuum forming.

Introduction

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Stretched acrylic has widely adopted as a transparent material for fighter jet canopy components due to its excellent optical transmittance, impact resistance, weatherability, and thermal stability. Transparent aircraft components are commonly fabricated through vacuum forming of PMMA sheets at elevated temperatures below the glass transition temperature. However, the vacuum forming process is highly sensitive to process parameters such as temperature, forming time, vacuum pressure, and clamping conditions, which strongly influence thickness uniformity and residual stress distribution in the final product.

To ensure process reliability and to reduce costly trial-and-error during PMMA forming, accurate material characterization and reliable finite element (FE) modeling are essential [1,2]. Among the various factors affecting numerical accuracy, appropriate representation of material behavior plays a critical role in thermomechanical forming simulations. Polymer material behavior can be effectively incorporated into FE simulations through constitutive modeling that accounts for temperature, strain rate, and time-dependent deformation.

Previous studies have investigated the mechanical behavior of transparent polymers such as PMMA and polycarbonate (PC), highlighting the brittle response of PMMA in contrast to the ductile behavior of PC [3]. The effects of temperature, stress, and crazing on creep life have also been reported [4], and stress-relaxation behavior of PMMA across the glass transition temperature has been characterized with corresponding constitutive models [5]. In addition, large-strain springback behavior of PMMA has been experimentally investigated and numerically predicted using finite element approaches [6]. Rate-dependent constitutive models have been proposed to describe strainrate sensitivity [7], and large-strain mechanical behavior of PMMA at elevated temperatures has been examined through uniaxial compression testing [8].
In this work, the temperature- and strain-rate-dependent stress-strain behavior, along with the creep response of PMMA, was characterized through uniaxial tensile testing.

Viscoplastic and creep constitutive models were adopted to represent the observed material behavior, and the corresponding material parameters were identified based on experimental results.
Finite element simulation of the vacuum forming process for a double-ellipsoidal transparent component was performed using the ABAQUS/Standard VISCO solver.

Material Characterization

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Uniaxial tensile specimen was performed with temperature of 80,90 , and 100∘C and strain rate of 0.001/s and 0.01/s. Specimens were machined from a 7 mm -thick PMMA sheet in accordance with Type I geometry specified in ASTM D638-22, as shown in Fig. 1 and summarized in Table 1. Strain was measured using a 3D Digital Image Correlation (DIC) technique to accurately capture the large deformation behavior at elevated temperatures, as illustrated in Fig. 2. To ensure repeatability and reproducibility, each test condition was repeated three times. The results of uniaxial tensile test with respect to different temperature level and strain rate range are plotted in Fig. 3 where Fig. 3a indicates test results for the temperature of 80,90 , and 100∘C at strain rate of 0.001/s and Fig. 3b is the results for the temperature of 80,90 , and 100∘C at strain rate of 0.01/s. As shown in the figures, the flow stress decreases with increasing temperature. In addition, the material exhibits positive strain-rate sensitivity, indicating an increase in flow stress with increasing strain rate.

[picture]

Fig. 1. Specimen geometry (ASTM D638-22).

Fig. 1. Specimen geometry (ASTM D638-22).

Table 1. Dimension of uniaxial tensile specimen (ASTM D638-22).

W-Width of narrow section [mm] | L-Length of narrow section [mm] | WO-width overall [mm] | LO-length overall [mm] | G-Gage length [mm] | D-Distance between grips [mm] | R-Radius of fillet [mm]
13 | 57 | 19 | 165 | 50 | 115 | 76

[picture]

Fig. 2. Strain measurement by using Digital Image Correlation.

Fig. 2. Strain measurement by using Digital Image Correlation.

[picture]

Fig. 3. Stress-strain behavior of PMMA for the temperature of 80,90 , and 100∘C at the strain rate of (a) 0.001/s and (b) 0.01/s.

Fig. 3. Stress-strain behavior of PMMA for the temperature of 80,90 , and 100 ∘ C at the strain rate of (a) 0.001 / s and (b) 0.01 / s .

For creep characterization, the specimen geometry and experimental setup are shown in Fig. 4(a). Strain measurement was performed using a digital image correlation (DIC) system, consistent with the methodology adopted in the uniaxial tensile tests. Creep tests were conducted under a constant applied stress of 17 MPa at a temperature of 110∘C. The resulting creep strain-time response is presented in Fig. 4(b). As shown in the figure, the material exhibits an initial primary creep stage followed by a steady-state secondary creep regime, eventually leading to sudden fracture.

[picture]

Fig. 4. (a) Specimen geometry and equipment setup for creep test and (b) test results at stress of 17 MPa and temperature of 110∘C.

Fig. 4. (a) Specimen geometry and equipment setup for creep test and (b) test results at stress of 17 MPa and temperature of 110 ∘ C .

Constitutive Modeling

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To describe the temperature- and strain-rate-dependent stress-strain behavior of PMMA, a constitutive model formulated in a multiplicative form was adopted [9], following the pioneering work of G'sell and Jonas [10]. This modeling framework enables effective representation of the coupled effects of temperature and strain rate on polymer deformation behavior under thermomechanical loading conditions.

σeq(ε,ε˙,T)=(1−TTg)(1−exp(−wε)[σ1exp(−bε)(ε˙ε˙01)m1+σ2exp((h0+h1T−TrefTref)(ε2))(1+(ε˙ε˙02)−1)−m2](1)

where T,Tg, and Tref  denote the absolute, glass transition, and reference temperature, respectively. ε represents true strain, while ε˙,ε˙01, and ε˙02 correspond to the current and reference strain rate, respectively. In addition, the parameters of w,b,h0,m1,m2,σ1, and σ2 are material coefficients that need to be identified by fitting with experimental results of strain rate and temperature-dependent stress-strain behavior. The identified material parameters are summarized in Table 2 which are identified by optimization process that minimizes error between experimental and predicted stressstrain responses, and the predicted temperature- and strain-rate-dependent stress-strain behavior is compared with experimental results in Fig. 5. Although the model captures the overall trends of strainrate and temperature dependency, its predictive accuracy remains limited. In particular, the material softening at elevated temperatures is overestimated. Furthermore, the saturation behavior observed at large strains is not adequately reproduced, indicating the necessity for further development of the constitutive model to achieve more accurate representation of PMMA deformation behavior.

[picture]

Fig. 5. Predicted Stress-strain behavior by the constitutive model [9]: (a) 0.001/s and (b) 0.01/s.

Fig. 5. Predicted Stress-strain behavior by the constitutive model [9]: (a) 0.001 / s and (b) 0.01 / s .

Table 2. Material coefficients of the constitutive model [9].

Tg [K] | Tref [K] | σ₁ [MPa] | σ₂ [MPa] | b | h₀ | h₁
393 | 298 | 409.695 | 162.040 | 1.321 | 1.129e-7 | 7.438
m₁ | m₂ | ε̇₀₁ [1/s] | ε̇₀₂ [1/s] | w |  |
0.700 | 0.330 | 0.001 | 0.001 | 116.056 |  |

To account for the creep behavior of PMMA, the time-power law creep model implemented in ABAQUS was adopted, as expressed in Eq. (2):

ε˙c=ε˙0(σ¯σ¯0)n(ε˙ot)m(2)

where ε˙c,t, and σ¯ denote creep strain rate, time, and effective stress, respectively. In addition, σ¯0 is reference effective stress. ε˙0,n, and m are material coefficients need to be identified with creep test results. The identified creep material parameters are summarized in Table 3, and the predicted creep behavior is compared with experimental results in Fig. 6. The model shows good agreement with the experimental data, particularly in capturing the primary and secondary creep regions.

Table 3. Material coefficients of time-power law.

ε̇₀ | n | m | σ̄₀ [MPa]
9.823e-3 | 0.594 | -0.293 | 10

Fig. 6. (a) Region of creep behavior and (b) predicted creep behavior by time-power law.

Finite Element Simulation of Vacuum Forming

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The vacuum forming process of a double-ellipsoidal component was simulated using ABAQUS/Standard with the VISCO solver. The forming die was modeled as a rigid body, while the PMMA sheet was modeled as a deformable body using three-dimensional solid elements. As shown in Fig. 7, the outer region of the PMMA sheet was fully constrained to represent the clamping condition. In addition, symmetry boundary conditions were applied to improve computational efficiency. A uniform temperature of 100∘C was imposed on the material, and a Coulomb friction coefficient of 0.2 was assumed between the die and the PMMA sheet. In the present simulation, heat transfer effects were neglected; therefore, the material temperature remained constant throughout the forming process. Vacuum pressure of 0.1 MPa was applied to the bottom surface of the PMMA sheet to drive the forming process.

The deformed shapes obtained from the vacuum forming simulation are shown in Fig. 8(a) and Fig. 8(b) for the front and side views, respectively. The results demonstrate that the double-ellipsoidal geometry can be effectively formed through the vacuum forming process. Notably, the vacuum forming is mainly based on creep deformation and maximum creep strain exceeds 0.8 which is concentrated near the top region of the formed component. This observation indicates that forming time and pressure control is a critical factor in the vacuum forming process of double-ellipsoidal PMMA components.

[picture]

Fig. 7. Boundary conditions for the vacuum forming process.

Fig. 7. Boundary conditions for the vacuum forming process.

[picture]

Fig. 8. The effective creep strain results of vacuum forming: (a) front view and (b) side view.

Fig. 8. The effective creep strain results of vacuum forming: (a) front view and (b) side view.

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.95.pdf

This study presented an experimental and numerical investigation of the thermomechanical behavior of PMMA during high-temperature vacuum forming. Temperature- and strain-rate-dependent stressstrain behavior, along with creep deformation, was characterized through uniaxial tensile and creep tests, and corresponding constitutive models were identified based on experimental data. The viscoplastic constitutive model captured the overall trends of temperature and strain-rate dependency, although limitations were observed in describing high-temperature softening and large-strain saturation behavior. In contrast, the time-power law creep model showed good agreement with experimental results, particularly in the primary and secondary creep regimes. Finite element simulation of the vacuum forming process using the ABAQUS/Standard VISCO solver demonstrated that the double-ellipsoidal PMMA component could be effectively formed. The results further revealed that large creep strains develop near the top region of the component, highlighting the critical importance of forming time and pressure control in vacuum forming of complex PMMA geometries.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.95.pdf

[1] Dong, Y., R. J. T. Lin, and D. Bhattacharyya. "Finite element simulation on thermoforming acrylic sheets using dynamic explicit method." Polymers and Polymer Composites 14.3 (2006): 307-328.

Azdast, Taher, et al. "Numerical and experimental analysis of wall thickness variation of a hemispherical PMMA sheet in thermoforming process." The International Journal of Advanced Manufacturing Technology 64.1 (2013): 113-122.

Tang, Zhiye, Kazushi Fujimoto, and Susumu Okazaki. "A comparison of the brittle PMMA with the ductile PC on the elasticity and yielding from a molecular dynamics perspective." Polymer 226 (2021): 123809.

Gao, Zongzhan, et al. "Creep life assessment craze damage evolution of polyethylene methacrylate." Advances in Polymer Technology 37.8 (2018): 3619-3628.

Mathiesen, Danielle, Dana Vogtmann, and Rebecca B. Dupaix. "Characterization and constitutive modeling of stress-relaxation behavior of Poly (methyl methacrylate)(PMMA) across the glass transition temperature." Mechanics of Materials 71 (2014): 74-84.

Mathiesen, D., A. Kakumani, and R. B. Dupaix. "Experimental Characterization and Finite Element Prediction of Large Strain Spring-Back Behavior of Poly (Methyl Methacrylate)." Journal of Engineering Materials and Technology 141.3 (2019): 031005.

Mulliken, Adam D., and Mary C. Boyce. "Mechanics of the rate-dependent elastic-plastic deformation of glassy polymers from low to high strain rates." International journal of solids and structures 43.5 (2006): 1331-1356.

Palm, G., R. B. Dupaix, and J. Castro. "Large strain mechanical behavior of poly (methyl methacrylate)(PMMA) near the glass transition temperature." (2006): 559-563.

Nasraoui, M., et al. "Influence of strain rate, temperature and adiabatic heating on the mechanical behaviour of poly-methyl-methacrylate: Experimental and modelling analyses." Materials & Design 37 (2012): 500-509.

G'sell, Ch, and J. J. Jonas. "Determination of the plastic behaviour of solid polymers at constant true strain rate." Journal of materials science 14.3 (1979): 583-591.

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The original version of this eBook is available on https://www.scientific.net/book/polymer-processing-and-thermomechanical-properties/978-3-0364-1984-8

Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 103-110

doi: 10.4028/p-I4xQB3

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

Submitted:
2026-01-19

Revised:
2026-02-27

Accepted:
2026-03-01

Online:
2026-04-17

Analysis of Large Deformation Characteristics and Formability of PMMA

The original version of this paper is available on https://www.scientific.net/DDF.451.103.pdf

Min Jae Baek 1,a, Yong Nam Kwon 1,b, Daeho Jeong 2,c, Ducksung Kim 2,d, Yoo In Jeong 2,e, and Hyunsung Choi 1,f*

1 Korea Institute of Materials Science, Republic of Korea

2 Korea Aerospace Industries, LTD, korea, Republic of Korea

a  qoralswo12@kims.re.kr, b  kyn1740@kims.re.kr, c  daeho.jeong@koreaaero.com,

d  ducksung.kim@koreaaero.com, efreud197@koreaaero.com, f  h.choi@kims.re.kr 

Keywords: PolyMethyl MethAcrylate (PMMA), Vacuum forming, High-temperature, Creep, Tensile, plastic deformation.

Abstract

Polymethylmetharylate (PMMA) has been widely used for aircraft canopies and transparent structural components, and processed into various parts through vacuum forming. In this study, the effects of forming speed and deformation characteristics on thickness uniformity during high-temperature vacuum forming of PMMA were analyzed. First, creep tests and high-temperature tensile tests were conducted at the specimen level to quantitatively distinguish between creep deformation and plastic deformation. Creep tests were performed under constant temperature and load conditions, and strain was measured through Digital Image Correlation. For plastic deformation analysis, tensile tests at room temperature and elevated temperatures were carried out to compare yield strength and elongation changes. To analyze thickness uniformity during the forming process, rectangular-shaped parts were fabricated using vacuum forming under various conditions where temperature and forming speed are key variables. After forming, thickness uniformity and surface transparency of the products were measured. Additionally, internal structural changes according to forming speed and temperature conditions were analyzed, and a comprehensive evaluation of material stability was performed.

Introduction

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Poly(methyl methacrylate) (PMMA) is a synthetic polymer derived from methyl methacrylate monomers and designated by two IUPAC nomenclatures: poly[1-(methoxycarbonyl)-1-methyl ethylene] from a hydrocarbon perspective and poly(methyl 2-methyl-propenoate) from an ester perspective. PMMA was discovered in the early 1930s by British chemists Rowland Hill and John Crawford, and was first commercialized in 1934 by German chemist Otto Röhm. As an optically transparent thermoplastic, PMMA has been widely used as a glass substitute owing to its high impact strength, lightweight nature, shatter resistance, and excellent processability. Additionally, PMMA is characterized by outstanding weather resistance and scratch resistance. The methyl groups ( −CH3 ) directly bonded to vinyl carbons in the PMMA polymer structure prevent polymer chains from packing densely in a crystalline fashion or rotating freely around C−C bonds. Consequently, PMMA is known as an amorphous thermoplastic. Furthermore, these methyl substituents elevate the glass transition temperature (Tg), thereby increasing the stiffness of PMMA. The ester groups in PMMA impart high optical transparency and excellent optical properties. However, the polar interactions of these ester groups gradually weaken at elevated temperatures, resulting in creep deformation. The critical temperature at which this phenomenon occurs is the glass transition temperature (Tg). The first major application of PMMA dates back to World War II, when it was adopted for aircraft windows and canopy components. This historical milestone demonstrated that PMMA's transparency, impact resistance, and lightweight characteristics could satisfy the stringent requirements of aviation applications. Today, PMMA continues to be extensively employed in transparent structural components of fighter aircraft and commercial airliners, being processed and manufactured into various shapes and functional parts through vacuum forming processes.

This study focuses on analyzing the effects of forming speed and deformation behavior on thickness uniformity in high-temperature vacuum forming processes of PMMA. Forming speed is a critical process variable directly related to production efficiency and economic viability. However, excessive forming speeds can induce localized deformation and thickness variation, while excessively slow speeds result in dramatically reduced production efficiency. Therefore, quantitative evaluation of PMMA's time-dependent behavior and irreversible deformation characteristics under various forming conditions is essential. In the PMMA vacuum forming process, forming temperature is the most critical variable determining process success. To accurately determine this optimal temperature, the glass transition temperature was measured in the present study. The glass transition temperature represents the temperature at which semi-crystalline or amorphous polymers transition from a glassy state to a rubbery state. At this critical temperature, the mechanical properties and behavior of the material undergo dramatic changes. Differential scanning calorimetry (DSC) was employed to precisely determine the glass transition temperature. Through DSC analysis, thermal property variations can be detected, and by tracking heat capacity changes in the glass transition region, the accurate Tg value can be determined. Repeated experiments confirmed that the glass transition temperature of PMMA exceeds 110∘C[1−3]. To accurately characterize the forming behavior of PMMA, the viscoelastic behavior of the material and its deformation characteristics under prolonged loading were investigated in detail. Creep tests and elevated-temperature tensile tests were systematically conducted at the specimen level, and the resulting strain-time curves from each test condition were quantitatively compared and analyzed. Creep tests were conducted under constant temperature and load conditions. By continuously measuring strain evolution over time under a constant applied stress, creep curves were derived. This enabled investigation of the three characteristic creep regions and analysis of the strain rate progression in each stage. Notably, the creep characteristics observed in the elevated-temperature range similar to the forming temperature serve as important criteria for predicting the time-dependent large deformation behavior that occurs during actual vacuum forming processes[4-6]. To accurately characterize plastic deformation behavior, tensile tests were systematically conducted at both room temperature and elevated temperatures. This comprehensive analysis revealed detailed changes in key mechanical properties including yield strength, tensile strength, and elongation. The measurement results demonstrated a clear trend: as temperature increases, yield strength decreases while elongation increases[7-9]. This behavior directly correlates with increased material fluidity and enhanced formability at elevated temperatures, ultimately enabling the forming of complex geometries. To directly analyze thickness uniformity during the forming process, temperature and forming speed were established as primary process variables, and vacuum forming experiments were conducted across various parameter combinations[10-12]. Based on the experimental results, vacuum pressure, forming time, and the material temperature at the forming location were identified as the most critical factors for achieving uniform thickness in vacuum-formed products.

Experiment

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Glass Transition Temperature

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In the PMMA vacuum forming process, forming temperature is the most critical variable determining the success of the entire process. Forming temperature not only influences the workability of the material but also exerts a wide-ranging impact on the mechanical performance, dimensional stability, and surface quality of the final product. To accurately determine this optimal forming temperature, the glass transition temperature ( Tg ) was measured in the present study. The glass transition temperature represents the temperature at which semi-crystalline or amorphous polymers transition from a glassy state to a rubbery state, and it is a fundamental yet most important physical parameter for understanding the structure and behavior of polymers. At the glass transition temperature, the molecular mobility and mechanical properties of the polymer undergo dramatic changes, which holds significant implications for the PMMA forming process. In this research, differential scanning calorimetry (DSC) was employed to measure the glass transition temperature. The DSC measurement
results, presented in the left graph, are attributed to the complex thermal behavior of PMMA and the subtle differences in specimen preparation conditions. However, through repeated experiments, it was confirmed that the glass transition temperature of PMMA exceeds 110∘C. Fig. 1

[picture]

Fig. 1. Glass transition temperature measurement (differential scanning calorimetry)

Fig. 1. Glass transition temperature measurement (differential scanning calorimetry)

DIC-based strain measurement

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Strain measurement was conducted using Digital Image Correlation (DIC). Fig. 2. Both hightemperature tensile tests and creep deformation exhibited large deformations, making it impossible to measure with conventional strain gauges. Therefore, we used DIC, a non-contact strain measurement technique. In this method, a speckle pattern is applied to the specimen surface, and specific points are tracked between two or more consecutive images using brightness distribution. The DIC measurements were conducted using the GOM 3D camera, with analysis parameters set to a facet size of 16 pixels and point distance of 13 pixels.

[picture]

Fig. 2. Digital Image Correlation (DIC) for the strain measurement

Fig. 2. Digital Image Correlation (DIC) for the strain measurement

Strain rate-dependent uniaxial tensile test at room temperature

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Room-temperature tensile tests were initially conducted to analyze basic material properties. The crosshead speeds for the tensile tests were 0.06 mm/min and 0.6 mm/min for the strain rate of 0.001/s and 0.01/s, respectively. To identify availability in subsequent elevated-temperature experiments, three different types of specimen geometry were machined according to ASTM D638-22. Fig. 3 shows Type 1, 2, and 3 specimens with gauge lengths of 165 mm,246 mm, and 63.5 mm , respectively. These correspond to material specifications with thicknesses of ≤7t,≤14t, and ≤4t, respectively. The
graph presented in Fig. 4a shows the tensile results for each specimen type. As can be seen, there was no significant variation in material properties depending on specimen geometry, especially for thickness. This indicates that the basic mechanical characteristics of PMMA are scarcely influenced by the geometric shape of the specimen, thus providing a reliable basis for selecting specific specimen geometries in subsequent elevated-temperature experiments. Fig. 4b presents the results of roomtemperature tensile tests conducted at different strain rates. According to the results, there was no noticeable change in material properties with increasing strain rate at room temperature. This indicates that PMMA exhibits little strain-rate dependence at room temperature, demonstrating that the mechanical behavior of PMMA at room temperature is strain-rate independent.

[picture]

Fig. 3. Specimen (unit : mm)

Fig. 3. Specimen (unit : mm)

[picture]

Fig. 4. (a)Tensile Test Results by Specimen Geometry and (b) Tensile Test Results at Different Strain Rates.

Fig. 4. (a)Tensile Test Results by Specimen Geometry and (b) Tensile Test Results at Different Strain Rates.

High-temperature and strain rate-dependent tensile experiments

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Considering the large deformations in elevated-temperature experiments, Type 1 specimen with a length of 165 mm and thickness of 7t was employed. The experiments were conducted to analyze the high-temperature plastic behavior and strain rate-dependent behavior of PMMA, and to observe the high-temperature material behavior in the temperature range above the glass transition temperature.

Fig. 4 a shows the results at a strain rate of 0.001/s, while Fig. 5 b presents the results at 0.01/s. As evident from both results, the material exhibited softening behavior as temperature increased. Meanwhile, elongation increased with temperature; however, at 120∘C, which exceeds the glass transition temperature (Tg), a decrease in elongation was observed. Additionally, the material stress at the glass transition temperature was extremely low.

[picture]

Fig.5. High temperature tensile test results (a) HT Tensile Test Results at Strain Rate of 0.001/s and (b) HT Tensile Test Results at Strain Rate of 0.01/s

Fig.5. High temperature tensile test results (a) HT Tensile Test Results at Strain Rate of 0.001/s and (b) HT Tensile Test Results at Strain Rate of 0.01 / s

Creep experiment

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Creep tests were conducted to analyze material behavior in the forming process according to temperature, pressure, and time. Through these experiments, the creep deformation behavior of the material was observed under constant temperature, load, and time conditions. Test temperatures were conducted at 110 and 120∘C. The results presented in Fig. 6a were obtained at 110∘C(16MPa,17 MPa ) and 120∘C. At 110∘C and 16 MPa , the secondary creep stage was confirmed. At 17 MPa , rapid strain increase occurred immediately after load application, followed by strain hardening and subsequent fracture. This demonstrates that under high-load conditions, the primary and secondary creep stages were shortened, resulting in rapid material deformation and fracture within a short period. Conversely, under low-load conditions, extended primary and secondary creep stages were observed. Additionally, at the test temperature of 120∘C exceeding the glass transition temperature ( Tg ), as shown in Fig. 6 bexpansion in the thickness direction of the gauge section was observed prior to load application, and localized contraction in the width direction caused specimen bending. This is presumed to be due to a restoration force generated as the material tends to return to its pre-stretched state. Through the creep tests, the importance of temperature as a process variable was confirmed, and the correlation between stress magnitude and forming time was also observed.

[picture]

Fig. 6. Creep Test Results : (a) 110∘C, (b) 120∘C

Fig. 6. Creep Test Results : (a) 110 ∘ C , (b) 120 ∘ C

Lab scale Vacuum forming

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Rectangular hot vacuum forming was carried out as shown in Fig. 7, consisting of an upper die, material, and lower die arranged sequentially, with the upper die applying clamping load. Vacuum sealing between the upper and lower dies was achieved using sealant tape and bagging film, and the process was designed to form a 100 mm×100 mm shape. Specimens were initially processed at 130 mm×130 mm with a thickness of 10t. The vacuum forming process parameters were temperatures of 100∘C,106∘C,110∘C, and 120∘C; vacuum pressures of 0.3bar,0.5bar, and 0.7 bar ; and loads of 49, 59 and 98. The forming time was 12 hours, and thicknesses of 10 t were employed.

The experimental results at 100∘C shown in Fig. 8 aindicate that vacuum forming was not achieved due to detachment of the sealant tape. Additionally, excessive material thickness relative to the forming area hindered the success of vacuum forming. The results at 106∘C presented in Fig. 8 bdemonstrate that under low vacuum pressure and high clamping load conditions, deformation was concentrated in the clamping area. Rapid cooling after load removal is presumed to have caused the increase in thickness. The results at 110∘C shown in Fig. 8c can be compared to the drawing inflow amount. Non-uniform material inflow restriction was observed due to geometric constraints. The rectangular vacuum forming results at 120∘C presented in Fig. 8d are as follows. The PMMA forming temperature exceeded the glass transition temperature ( Tg ), and after forming, area shrinkage and increased thickness were observed. The presumed cause is considered to be related to the stretching manufacturing process. Cast billet material undergoes biaxial stretching to be manufactured into stretched acrylic, during which the area increases and thickness decreases, with improvements in strength, weather resistance, and impact resistance. Conversely, when the material temperature exceeds the glass transition temperature, a restoration force that drives the material to return to its cast billet state.

[picture]

Fig.7. Rectangular Hot Vacuum Forming

Fig.7. Rectangular Hot Vacuum Forming

[picture]

Fig. 8. Lab scale Vacuum forming result: (a) 100∘C, (b) 106∘C, (c) 110∘C, and (d) 120∘C.

Fig. 8. Lab scale Vacuum forming result: (a) 100 ∘ C , (b) 106 ∘ C , (c) 110 ∘ C , and (d) 120 ∘ C .

Summary

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In the PMMA vacuum forming process, forming temperature is the most critical variable determining the success of the entire process and exerts a wide-ranging influence on the mechanical performance, dimensional stability, and surface quality of the final product. To accurately determine the forming temperature, the glass transition temperature ( Tg ) was measured using differential scanning calorimetry (DSC), and it was confirmed that the Tg of PMMA exceeds 110∘C. To measure the large deformations exhibited in elevated-temperature tensile tests and creep deformation, digital image correlation (DIC) was employed instead of contact-type gauges. In room-temperature tensile tests, basic material properties were analyzed using ASTM D638-22 compliant Type 1, 2, and 3 specimens (with gauge lengths of 165 mm,246 mm, and 63.5 mm , respectively). At room temperature, no significant variation in material properties was observed depending on specimen geometry, and no characteristic changes with strain rate were detected, confirming that PMMA exhibits strain-rate independent characteristics at room temperature. In elevated-temperature experiments, Type 1 specimens with a length of 165 mm and thickness of 7 t were employed to analyze the hightemperature plastic behavior and strain rate-dependent behavior of PMMA. At both strain rates of 0.001/s and 0.01/s, softening behavior of the material was observed with increasing temperature, and elongation increased with temperature elevation but decreased at 120∘C (exceeding Tg). In creep tests, the secondary creep stage was confirmed at 110∘C with 16 MPa , while at the high-load condition of 17 MPa , the primary and secondary creep stages were shortened, resulting in fracture within a short period. Under low-load conditions, extended creep stages were observed, confirming that stress magnitude significantly influences forming time. In elevated-temperature creep tests at 120∘C, expansion in the thickness direction of the gauge section prior to load application and specimen bending due to localized contraction in the width direction were observed, which is presumed to result from a restoration force driving the material to return to its pre-stretched state. Rectangular hot vacuum forming experiments were composed of an upper die, material, and lower die, achieving vacuum sealing with sealant tape and bagging film to design the forming of a 100 mm
×100 mm shape. The process variables were temperature ( 100∘C,106∘C,110∘C,120∘C ), vacuum pressure ( 0.3,0.5,0.7 bar), clamping load ( 49,59,98 ), and forming time ( 12 hours), with an initial thickness of 10 t . At 106∘C, under low vacuum pressure and high clamping load conditions, deformation was concentrated in the clamping area, and rapid cooling induced thickness increase. The experimental results at 110∘C revealed non-uniform material inflow restriction due to geometric constraints. At 120∘C, the forming temperature exceeded Tg, resulting in material area shrinkage and thickness increase after forming. When material temperature exceeds Tg, a restoration force is presumed to decrease the area and increase the thickness.

References

The original version of this paper is available on https://www.scientific.net/DDF.451.103.pdf

Kusy, R. P., W. F. Simmons, and A. R. Greenberg. "Glass transition temperature of poly (methyl methacrylate) blends." Polymer 22.2 (1981): 268-270.

Ute, Koichi, Nobuo Miyatake, and Koichi Hatada. "Glass transition temperature and melting temperature of uniform isotactic and syndiotactic poly (methyl methacrylate) s from 13mer to 50mer." Polymer 36.7 (1995): 1415-1419.:

Porter, Crystal E., and Frank D. Blum. "Thermal characterization of PMMA thin films using modulated differential scanning calorimetry." Macromolecules 33.19 (2000): 7016-7020.

Kang, Suk-Choon. "Creep Characteristic of the Polymethyl Methacrylate (PMMA) at Stresses and Temperatures." Journal of the Korean Society for Precision Engineering 28.12 (2011): 1403-1410.

P.G. Clem, M. Rodriguez, J.A. Voigt and C.S. Ashley, U.S. Patent 6,231,666. (2001)

Triebel, C., and H. Münstedt. "Temperature dependence of rheological properties of poly (methyl methacrylate) filled with silica nanoparticles." Polymer 52.7 (2011): 1596-1602.

Abdel-Wahab, Adel A., Sabbah Ataya, and Vadim V. Silberschmidt. "Temperature-dependent mechanical behaviour of PMMA: Experimental analysis and modelling." Polymer Testing 58 (2017): 86-95.

Wu, Yiwen, et al. "Mechanical properties of constructional PMMA at elevated temperatures and postfire conditions." Journal of Materials in Civil Engineering 35.10 (2023): 04023377.

Van Loock, Frederik, and Norman A. Fleck. "Deformation and failure maps for PMMA in uniaxial tension." Polymer 148 (2018): 259-268

O'Hanlon, John F. A user's guide to vacuum technology. John Wiley & Sons, 2003.

DEBELL, GEORGE W. "Use of Plastics and Allied Materials in Aircraft Construction." Journal of the Aeronautical Sciences 9.9 (1942): 341-349.

Raghuwanshi, R. K., and V. K. Verma. "Mechanical and thermal characterization of aero grade polymethyl metha acrylate polymer used in aircraft canopy." Int J Eng Adv Tech (IJEAT) 3.5 (2014): 216-219.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 111-123

doi: 10.4028/p-FW1Rb0

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

Submitted:
2026-01-19

Revised:
2026-02-19

Accepted:
2026-02-25

Online:
2026-04-17

From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

The original version of this paper is available on https://www.scientific.net/DDF.451.111.pdf

DI NARDO Mario Emanuele 1,a*, RUSSO Pietro 2, b and CARLONE Pierpaolo 1,c

1 Department of Industrial Engineering, University of Salerno, 132 Via Giovanni Paolo II, 84084

Fisciano (SA), Italy

2 Institute of Polymers, Composites and Biomaterials, National Research Council, Via Campi

Flegrei 34, 80078 Pozzuoli, Italy

a  mdinardo@unisa.it, b  pietro.russo@ipcb.cnr.it, c  pcarlone@unisa.it

Keywords: Additive Manufacturing, MEX, FFF, Process Simulation, FEM, Thermomechanical Analysis

Abstract

The deposition sequence and the resulting thermal history govern the development of distortions and residual stresses in components made by material extrusion, ultimately affecting their structural performance. This work presents a process-aware thermomechanical simulation framework that reproduces the actual deposition directly from the G-Code. The nozzle trajectory is processed to reconstruct the bead order and timing and to automatically generate a voxel-based finite element mesh suitable for progressive activation. A transient thermal analysis is then performed with incremental element activation, while the thermal effect of extrusion is prescribed through a temperature predefined field applied to the newly activated elements, together with convective-radiative heat losses to the environment. The resulting temperature history is subsequently transferred as a timedependent temperature field to a quasi-static mechanical analysis to predict residual distortions and stresses after cooling. Finally, a linear elastic virtual tensile test is carried out on the final, deformed configuration, accounting for the residual stress state. The framework is applied to PLA ASTM D638 specimens manufactured at different extrusion temperatures and validated against experimental tests, showing that extrusion temperature governs thermal gradients, residual stress distributions and the resulting macroscopic elastic response.

Introduction

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Material extrusion (MEX), referred to as fused filament fabrication (FFF) when the raw material is in filament form, is one of the most widely used additive manufacturing (AM) processes for thermoplastic polymers due to its ability to produce complex geometries with low mass and good mechanical performance [1]. However, the quality and mechanical response of the components are highly dependent on the process. In fact, strand by strand deposition imposes a highly variable local thermal history which can introduce filling criticalities and reduce adhesion between layers. Furthermore, the nozzle path determines the internal structure, inducing anisotropy and therefore variable stiffness depending on the orientation of the strands [2]. In other words, the thermal history induced by the process, governed by the nozzle trajectory and temperature parameters, regulates both the consolidation between strands and the overall response of the component [3]. On the microscale, the temperature of adjacent beads controls the diffusion of the polymer at the interface and therefore the quality of the adhesion, with direct effects on the porosity [4]. On the macroscale the thermal gradients associated with the cooling of each individual bead induce residual stresses and distortions that can compromise dimensional accuracy and alter the measured mechanical response [5,6]. More generally, linking process conditions to transport phenomena and the onset of process induced defects is a recurring theme across additive manufacturing and, more broadly, across many manufacturing processes [7,8]. Given that, in order to control the effect of process parameters on mechanical response, a predictive approach is needed that can reproduce the actual deposition sequence, so as to establish a quantitative link between the nozzle path, thermal history and final component behaviour. In this context, finite element method (FEM) process simulations provide a solid framework for
connecting process and performance. Early work placed strong emphasis on validated thermal histories. Roy et al. proposed a transient thermal framework in which deposition follows the programmed path and experimentally validated the predicted temperature evolution using noncontact infrared sensing on the part, showing that the model can capture the spatiotemporal thermal profile during deposition and subsequent cooling [5]. On this basis, subsequent studies have extended the approach to sequential thermomechanical workflows, transferring the calculated temperature as a predefined field to a subsequent mechanical analysis to estimate residual distortions and stresses. Trofimov et al. presented a model with progressive activation along the trajectory and experimental validation of both the thermal distribution and the final distortion [6]. However, it remains challenging to faithfully reproduce the gradients and time scales of the process at sustainable computational costs. In fact, capturing localized gradients requires fine meshes and short time increments, which can make parametric analyses prohibitive. Ramos et al. explicitly addressed this point by proposing efficiency measures, such as hybrid activation and adaptive coarsening, while maintaining model validation [9]. Generally, to make process simulations feasible in an FEM environment, one of the most used techniques is the progressive activation of elements, so that geometry and heat distribution follow the tool path. In Abaqus, these features are available through dedicated tools, including the use of event series to describe trajectories and activation times of elements and deposition [10]. The bottleneck often remains the translation of slicer data and, in fact, the G-Code part program into FEM models inputs. Discretization compatible with progressive activation and a sufficiently accurate but computationally efficient description of events are required. Generally, this need for a robust workflow that converts CAD or process programs into executable toolpaths and, subsequently, into simulation ready inputs is not unique to MEX, but emerges across many AM applications whenever geometric descriptions must be translated into consistent machine trajectories and then reprocessed into analysis data [11,12]. Beyond this data-translation step, achieving repeatable outcomes often depends on system level coordination of process timing, thermal history, and hardware functionalities, since these aspects jointly define the effective boundary conditions experienced by the material [13]. In recent years, methodologies aimed at automatic conversion have been introduced that directly integrate the path description into the structural analysis and optimization workflow [14,15,16]. However, despite these advances, robust and generalizable end-to-end workflows that simultaneously preserves sequence, timing, and deposited volume remains an open goal and, for many applications, a still highly manual step. As described in Figure 1, this work therefore proposes a sequential thermomechanical chain guided directly by the deposition sequence, aimed at establishing a quantitative macroscale link between nozzle trajectory, thermal history, and final linear elastic response. Starting from the standard slicer outputs, the G-Code is processed through a python script to reconstruct the nozzle coordinates and deposition timing, while the geometry constrains and controls the activated volume. The inputs are converted into FEM input files, a series of events with process activation and timing and a voxel-based mesh compatible with progressive deposition, with voxel size consistent with the scale of the deposited bead. A transient thermal analysis is then performed to obtain the thermal history T(x,t) during deposition. This is then imported as a time-dependent predefined field into a quasi-static mechanical analysis to estimate residual stresses σ(x,t). Finally, virtual displacement control tests are performed on the deposited and cooled, and therefore potentially distorted mesh to obtain the tensile response in the linear elastic regime, including the effect of the residual stress state induced by the process. In this work, the approach is applied to PLA samples with 0/90∘ infill and different nozzle temperatures, adopting temperature-dependent material properties to represent the evolution of stiffness and thermal deformation during manufacturing. Validation is performed by tensile testing according to ASTM D638 [17], comparing the response in the linear elastic regime. Overall, this work aims to provide a practical and computationally manageable path from the deposition sequence to mechanical performance, supporting the selection of process parameters.

Methodology

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Deposition sequence processing

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Starting from the component geometry provided in Standard Triangle Language (STL) format and from the nozzle path encoded in the G-Code, a Python conversion tool generates two FEM inputs, an event series describing the nozzle trajectory in time with a binary deposition state and a structured voxel mesh suitable for element progressive activation according to the nozzle coordinates. The STL geometry is used exclusively as a volume constraint to retain only voxels that lie inside the nominal part volume. As shown in Figure 1, at first the G-Code is parsed sequentially, in order to translate the part program language into a dataset with process time associated with the cartesian coordinates assumed by the nozzle when depositing. For simplicity in this application, only linear motion commands G0/G1 are interpreted as nozzle motion. The nozzle coordinates x,y,z are treated as modal, meaning that values not specified in a line retain the most recent value. The feedrate F is also treated as modal and interpreted in mm/min, consistent with common G-Code conventions. For clarity, F is the commanded toolpath feedrate that sets the nozzle translational speed along each G0/G1 segment, whereas E is the commanded extruder axis coordinate that specifies the amount of filament to be pushed through the nozzle. While F controls the kinematics, changes in E quantify material delivery. Given that, material extrusion is tracked through the E axis, supporting both absolute M82 and relative M83 modes.

[picture]

Fig. 1. Model workflow on the right, graphical representation of numerical outputs on the left.

Fig. 1. Model workflow on the right, graphical representation of numerical outputs on the left.

Given that, a motion segment is classified as depositing when extrusion increases beyond a small tolerance:

ΔE=Ei+1−Ei>10−6(1)

Retractions, given by negative or zero ΔE, are therefore classified as non-depositing moves. To obtain a time-parameterized trajectory, for each linear move between two points, 𝐩i=(xi,yi,zi) to 𝐩i+1=(xi+1,yi+1,zi+1), is assigned a nominal duration based on the commanded feedrate F . The segment length is

Li=‖𝐩i+1−𝐩i‖=(xi+1−xi)2+(yi+1−yi)2+(zi+1−zi)2(2)

and the nominal speed is vi=F/60 mm/s, because in the G-Code, F is expressed in mm/min by default. This ensure that the segment duration Δti=Li/vi and the cumulative process time, obtained by summing Δti along the toolpath, are expressed in seconds, consistently with the time base used to drive the event series. The resulting trajectory is finally written as an Abaqus .inp file where each record stores time, nozzle position and one field value representing deposition state:

(ti,xi,yi,zi,si),si∈{0,1}(3)

with si=1 for depositing segments and si=0 for travel segments. In the current implementation, each record is written at the segment start point and segment start time so that the piecewise-linear sequence of records defines the trajectory between consecutive events. In Abaqus, this event series is then used to drive the progressive growth of the active domain: when si=1, the deposited region evolves following the nozzle motion, and partial activation can be employed to allow fractional activation of elements intersected by the deposition region.

Process driven voxelization

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After generating the event series, a structured cartesian voxel grid is created over the spatial extent of the depositing trajectory. The bounding box is computed using only segments classified as depositing, ensuring the grid encloses the activated volume rather than travel motions. A small margin of approximately half voxel is applied around the bounding box. The voxel dimensions are selected to match the process resolution Δx=Δy=wb and Δz=hℓ, where wb is the bead width and hℓ is the layer height. Then each voxel ( i,j,k ) is represented by its center coordinate:

𝐜ijk=(x0+(i+12)Δx,y0+(j+12)Δy,z0+(k+12)Δz)(4)

The geometry is read as a binary triangulated surface, therefore, the STL is used purely as a geometric mask, defining a volume constraint. For each voxel center 𝐜ijk, an odd even ray casting inclusion test is performed where a ray is emitted along the positive x direction and the number of ray triangle intersections is counted. Finally, the voxels whose centers are classified as inside the STL are retained and converted into 8 -node hexahedral elements (C3D8). To keep the exported mesh compact, only grid nodes referenced by retained voxels are written. The algorithm first collects all used grid nodes, then assigns contiguous node IDs in a consistent order, sorted by k,j,i, and finally generates contiguous element IDs using the mapped node indices. The resulting mesh is written as an Abaqus .inp file.

Numerical model and governing equations

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Consequently, an Abaqus/Standard model is created and the generated voxel mesh is imported, representing the deposition domain where the material is progressively activated and driven by the time-parameterized event series. Let Ω(t)⊂Ωmesh  denote the active portion of the voxel mesh at time t . Each event record is mapped to an evolving deposited region; in Abaqus this is implemented through partial activation, allowing fractional activation of intersected elements when required. The same activation strategy is used in both the thermal and the quasi-static analyses, enabling the evaluation of the thermal evolution and its impact on the residual stress field.

Transient thermal formulation

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Thermal history during deposition and cooling is computed by solving transient heat conduction over the growing domain Ω(t). Neglecting internal heat generation, the governing equation reads

ρcp∂ T∂t=∇·(k∇ T)(5)

where T(x,t) is the temperature field, k is the thermal conductivity, ρ the density, and cp the specific heat. Deposition is modelled by prescribing the extrusion temperature as the initial thermal state of newly activated material. Practically, a uniform predefined temperature field is assigned to the part set, including still inactive elements, so that, at the activation time, newly activated elements enter the computation already initialized at the extrusion temperature, while the temperature of previously active material evolves by conduction and boundary heat losses. In fact, heat exchange with the environment is modelled through convection and radiation on exposed surface element at the activation time Γexp (t) :

−k∇ T·𝐧=h( T−T∞)+εσSB( T4−T∞4)(6)

where h is the film coefficient, T∞ is ambient temperature, ε is surface emissivity, and σSB is the Stefan-Boltzmann constant. The interaction with the build plate is represented by a prescribed temperature on the surface in contact with the building plate Γbed , imposing T=Tbed  during the deposition step to mimic the building platform maintained at controlled temperature. This constraint is then removed in the cooling step, so that the thermal evolution after deposition is governed by ambient heat losses consistently with Eq. (6). The transient problem is solved using an implicit time integration scheme with a fixed timestep aligned with the event series timeline.

Quasi-static thermoelastic formulation

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Residual stresses and distortions are computed in the subsequent quasi-static analysis on the same evolving domain Ω(t). Neglecting inertia and body forces, mechanical equilibrium is governed by

∇·σ=0(7)

The material response is modelled as isotropic thermoelasticity with temperature-dependent stiffness. The stress tensor is computed as

σ=ℂ(T):(ε−εth)(8)

where ℂ(T) is defined by a temperature-dependent Young's modulus E(T) and a constant Poisson's ratio v. Thermal strain is assumed to be isotropic and derived from the coefficient of thermal expansion α(T) :

εth=(∫T0Tα(θ)dθ)𝐈(9)

with T0 denoting the reference temperature for zero thermal strain. The temperature history T(x,t) computed in the heat transfer analysis is imported as a time-dependent predefined field and applied over the same deposition and cooling timeline. Building plate adhesion is represented by fixing the displacement field on the base region Γbed , while the remaining surfaces are free. Geometric nonlinearity is enabled to capture distortion accumulation during cooling. The solution provides the final residual stress field and the distorted configuration at the end of cooling, which are then used as the initial state for the tensile test.

Linear elastic tensile test

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At the end of the coupled thermomechanical process simulation, the model provides a distorted configuration and a spatially varying residual stress field σres (𝐱). This final state is used as the initial condition for a subsequent virtual tensile test aimed at evaluating the elastic response of the printed specimen while accounting for process induced residual stresses.
The tensile simulation is performed as a static analysis under the assumption of linear elastic behavior. The initial stress state is introduced by importing σres (𝐱) on the final deformed configuration from the thermomechanical solution, so that the tensile response is computed as an incremental perturbation around the cooled, residually stressed state.
During the tensile step, the equilibrium of the incremental problem is enforced:

∇·Δσ=0(10)

where Δσ is the stress increment induced by the applied tensile displacement. The constitutive response is linear elastic:

Δσ=ℂΔε(11)

with ℂ defined by Young's modulus E and Poisson's ratio ν. The total stress during the tensile test is then obtained as the superposition of the imported residual field and the tensile increment:

σ(𝐱)=σres(𝐱)+Δσ(𝐱)(12)

The tensile test is imposed in displacement control to remain in the linear regime. One grip region is fully constrained while a prescribed axial displacement is applied on the opposite grip with all remaining external surfaces left traction-free. The reaction force F is obtained from the constrained/loading region and used to compute the nominal engineering stress:

σeng =F A0,εeng =Δu L0(13)

where A0 is the initial cross-sectional area of the gauge section and L0 its reference length. The apparent elastic modulus is evaluated from the slope of the σε curve within the prescribed smallstrain window.

Application case

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ASTMD638 14 Type I
The proposed workflow is verified by manufacturing ASTM D638-14 Type I specimens and characterizing their tensile response according to the same standard [17]. This verification route provides a reproducible geometry and a widely accepted testing framework for plastics, enabling an objective comparison between experimental results and model predictions across different processing conditions. The reference geometry and the discretization adopted in the numerical analysis are shown in Figure 2. As explained in the methodology section the voxel pitch is selected to match the bead resolution employed in the process, ensuring that the simulated activation domain is consistent with the deposition architecture. Specimens were manufactured using an infill-only strategy with 0∘/90∘ alternating rasters between layers and no external perimeters walls, so that the mechanical response is governed solely by the infill structure, an aspect known to strongly affect void formation, interlayer bonding, and the resulting strength in FFF parts [21-23]. Three manufacturing conditions were investigated by varying only the nozzle temperature at 190, 210,230∘C, while keeping the building plate temperature at 60∘C and the deposition speed constant at 60 mm/s with cooling fans disabled to avoid forced convection effects and better approximate a natural convection dominated cooling condition, consistent with the assumptions implemented in the thermal model. Furthermore, to ensure numerical and experimental alignment, the time step of the model is chosen based on the
same deposition kinematics adopted experimentally, so that the activation sequence reproduces the physical deposition timing.

[picture]

Fig. 2. a) ASTM D638-14 Type I specimen geometry, b) nozzle toolpath and c) voxel mesh.

Fig. 2. a) ASTM D638-14 Type I specimen geometry, b) nozzle toolpath and c) voxel mesh.

Commercial PLA Ingeo TM was used to manufacture the specimens. Material properties and thermal boundary parameters adopted in the numerical model are summarized in Table 1. Density and baseline thermo-mechanical properties were taken from NatureWorks datasheets and consolidated literature sources [18-20,24-27]. Thermal conductivity and specific heat were selected consistently with process-oriented thermal models for PLA in material extrusion [25]. Temperature-dependent elastic modulus and coefficient of thermal expansion (CTE) were prescribed via piecewise-linear functions following published dynamic mechanical analysis (DMA) trends for PLA, which report a pronounced modulus drop across Tg and an increasing CTE with temperature [26,27,30]. The machine used is a commercial 3D printer, Anycubic Kobra Max 2, equipped with a 0.8 mm nozzle on the extrusion head. This nozzle allowed to deposit 0.4 mm layer height and 0.96 mm layer width beads, which correspond to the voxel dimensions.

Table 1. PLA properties and thermal boundary parameters adopted in the numerical model. [18-20,25-30]

Table 1a. Constant properties and boundary parameters.

Density | ρ | 1240 kg/m³
Thermal conductivity | k | 0.13 W/m·K
Specific heat | cp | 1800 J/kg·K
Ambient temperature | T∞ | 296.15 K
Emissivity | ε | 0.92
Convection coefficient | h | 10 W/m²·K
Stefan-Boltzmann constant | σ | 5.67037×10⁻⁸ W/m²·K⁴
Bed temperature | Tbed | 333.15 K

Table 1b. Temperature dependent E(T) and α(T).

Density | ρ | 1240 kg/m³
Thermal conductivity | k | 0.13 W/m·K
Specific heat | cp | 1800 J/kg·K
Ambient temperature | T∞ | 296.15 K
Emissivity | ε | 0.92
Convection coefficient | h | 10 W/m²·K
Stefan-Boltzmann constant | σ | 5.67037×10⁻⁸ W/m²·K⁴
Bed temperature | Tbed | 333.15 K

Finally, for each nozzle temperature, five specimens were printed to quantify repeatability and scatter. Quasi-static tensile tests were performed on an Instron 4505 universal testing machine following ASTM D638 [17] at room temperature. After printing, specimens were stored under vacuum and released immediately prior to testing to minimize post-processing moisture effects. Specimens were aligned in wedge grips and loaded in displacement control at a crosshead speed of 5 mm/min. Force and crosshead displacement were recorded continuously and converted to engineering stress-strain curves, with engineering stress computed from the initial gauge-section area and engineering strain obtained from the crosshead displacement normalized by the nominal gauge length. The elastic modulus was evaluated consistently for all replicates and temperatures as the slope of the initial linear portion of the engineering stress-strain response.

Results and Discussion

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Thermal distribution and process induced deformations

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Figure 3 shows the relationship between the temperature field and the process-induced distortions predicted by the sequential thermo-mechanical simulation. The frame is taken right at the end of deposition, at the start of the cooling step. At this moment, the temperature (NT11) still shows clear spatial gradients, mainly related to the regions deposited last. The displacement field (U), instead, already includes the accumulated effect of non-uniform thermal contraction.

[picture]

Fig. 3. Process induced deformations during cooling affecting the dimensional accuracy of the manufactured component.

Fig. 3. Process induced deformations during cooling affecting the dimensional accuracy of the manufactured component.

A clear trend can be observed: regions that are cooler at this time, especially near free edges, also tend to show larger local displacements. This is consistent with faster heat loss at exposed boundaries, which promotes differential shrinkage and warpage. The deformation is not uniform along the specimen, it concentrates near geometrical transitions and near the ends, where stiffness changes and boundary effects amplify the response. The zoomed views at the corners highlight this behaviour. Corners appear colder than the central region at the same process time, likely because they have a higher surface to volume ratio and are more exposed to convection and radiation. Even if this interpretation is qualitative at this stage, the same zones also show localized distortion patterns in the displacement contours. These patterns are visible both in the FEM results and on the manufactured specimens. When comparing the three printing temperatures, the overall deformation mode remains similar, but small and consistent differences in displacement magnitude and distribution are observed.

This indicates that the nozzle temperature affects the level of process-induced distortion, even without changing the general trend. Finally, the interaction with the build plate affects the deformation as well. The first layers are partially constrained by the contact with the plate, while the upper regions can deform more freely during cooling. This condition leads to a local thickening near the bottom layers, the so-called "elephant's foot", and contributes to the distortion observed after cooling.

Tensile response

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Tensile testing on ASTM D638 PLA specimens indicates that the selected extrusion temperature affects the mechanical response, particularly in the initial stiffness, yielding, and the evolution toward failure. The elastic modulus and 0.2% offset yield parameters are reported in Table 2.

Table 2. Elastic properties and 0.2% offset yield parameters, mean ± standard deviation.

Temperature | E [GPa] | σy,0.2% [MPa] | εy,0.2% [%]
190 [°C] | 2.66 ± 0.14 | 32.6 ± 2.0 | 1.43 ± 0.06
210 [°C] | 2.50 ± 0.19 | 38.7 ± 0.8 | 1.86 ± 0.05
230 [°C] | 2.21 ± 0.20 | 36.0 ± 2.7 | 1.96 ± 0.06

A progressive decrease in Young's modulus is observed with increasing extrusion temperature, from 2.66±0.14GPa at 190∘C to 2.50±0.19GPa at 210∘C and 2.21±0.20GPa at 230∘C. These values are consistent with the expected order of magnitude for PLA, in fact, industrial datasheets for commercially available PLA grades typically report tensile moduli on the order of 2−4GPa, depending on grade and conditioning [18,19]. Similarly, literature reviews on PLA mechanical behaviour report moduli in the GPa range, with variations driven by crystallinity and thermal history [20]. Therefore, the modulus levels reported in Table 2 seem suitable for comparison across the three processing conditions. With respect to yielding, the 0.2% offset yield stress σy,0.2% lies in the tens of MPa range, reaching its maximum at 210∘C and decreasing slightly at 230∘C. This non-monotonic trend is reasonable for FFF produced components, because yielding reflects both the effectiveness of load transfer across inter-bead and inter-layer interfaces and changes in the polymer microstructure associated with processing temperature and cooling conditions. The strength and failure-related metrics are reported in Table 3, while the overall stress-strain evolution for the three temperatures is shown in Figure 4.

Table 3. Tensile strength, characteristic strains, and energy to break, mean ± standard deviation.

Temperature | σmax/UTS [MPa] | εUTS [%] | εbreak [%] | Energybreak [J]
190 [°C] | 41.41 ± 0.54 | 2.35 ± 0.24 | 2.35 ± 0.49 | 0.24 ± 0.02
210 [°C] | 46.83 ± 1.17 | 2.81 ± 0.31 | 2.85 ± 0.36 | 0.32 ± 0.01
230 [°C] | 43.82 ± 1.95 | 3.06 ± 0.27 | 3.06 ± 0.29 | 0.35 ± 0.04

At 190∘C, the specimens exhibit UTS =41.41±0.54MPa with characteristic strains close to the failure occurring at approximately 2.35%, together with a comparatively low energy to break equal to 0.24±0.02 J. At 210∘C, the UTS increases to 46.83±1.17MPa, while the energy to break rises to 0.32±0.01 J. At 230∘C, the UTS remains high at 43.82±1.95MPa and both deformation and energy absorption increase further, as also visible by the higher strain reached before fracture in Figure 4, the energy to break increases to 0.35±0.04 J. Overall, the energy to break increases with printing temperature ( 190<210<230∘C ), indicating an improved ability of the specimens to absorb
mechanical energy prior to fracture. Since this energy is reported as the absolute work absorbed by the specimen, it is inherently geometry dependent and is therefore most robustly interpreted here as a relative comparison among the three extrusion temperatures.

[picture]

Fig. 4. Mean stress-strain curves for PLA specimens printed at 190,210 , and 210∘C with the highlighted linear-elastic FEM response.

Fig. 4. Mean stress-strain curves for PLA specimens printed at 190,210 , and 210 ∘ C with the highlighted linear-elastic FEM response.

Importantly, the data show that the maximum tensile load-bearing capacity occurs at 190∘C, whereas the lowest UTS is obtained at 190∘C. This observation suggests that 210∘C is likely too low to ensure optimal coalescence and interdiffusion between adjacent filaments, resulting in weaker inter-layer and inter-bead bonding and therefore a higher susceptibility to premature interfacial damage like local debonding and delamination during tensile loading. This interpretation is displayed also on the stressstrain trends in Figure 4, where the 190∘C curve attains the highest peak stress, while the 210∘C curve reaches a lower maximum stress before failure. More generally, increasing nozzle temperature is widely reported to enhance inter-layer and inter-bead welding by increasing melt mobility and promoting polymer chain diffusion and coalescence at interfaces, thereby improving load transfer and reducing the impact of weak interfacial boundaries [21-23]. In this context, the higher peak strength at 190∘C and the increase in energy to break from 230∘C to 210∘C are consistent with progressively more effective interfacial welding as temperature increases, even though the strength maximum occurs at the intermediate temperature 210−230∘C rather than at the highest temperature investigated. At the same time, the observed decrease in Young's modulus with increasing temperature suggests that the polymer's thermal history may also play a role. PLA is known to undergo melt-processing degradation, like chain scission and molecular weight reduction, under sufficiently severe thermal exposure, especially when moisture is present or residence time in the melt is prolonged, which can reduce stiffness and alter the early elastic response [24]. Consequently, the combination of improved failure-related performance, higher energy absorption and high UTS, particularly at ε=0.3%, and reduced elastic stiffness at higher temperatures can be interpreted as a process-dependent trade-off. Higher temperatures improve interfacial welding and damage tolerance while potentially reducing effective stiffness due to thermally driven material changes. Finally, the experimental results were
compared with the numerical model results in the linear-elastic regime, where the material was assumed isotropic. For clarity, the FEM prediction is shown only up to 0/90∘ for all temperatures, in order to compare initial stiffness within a common small-strain window. This cutoff is a plotting choice and does not represent a temperature-dependent elastic limit. Within that range, the FEM exhibits a slightly higher initial slope than the experimental mean curves, representing a systematic overestimation of elastic stiffness. This discrepancy is expected because the manufactured specimens with 230∘C infill exhibit anisotropic behaviour and include inter-bead interfaces and residual porosity, which reduce the effective modulus relative to an ideal homogeneous isotropic continuum. Importantly, despite the absolute overestimation, the numerical response remains coherent across the three temperatures, following the same experimental trend of decreasing stiffness from 190 to 190−230∘C.

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.111.pdf

This work presented a process-aware, sequential thermomechanical FEM workflow that reproduces material extrusion directly from G-Code by automatically generating a voxel based mesh and a timeparameterized event series for progressive element activation. A transient heat-transfer analysis, where newly activated material is initialized at the extrusion temperature and cooled through convective-radiative exchanges and build-plate boundary conditions, provides the thermal history that drives a subsequent quasi-static thermoelastic analysis to predict residual stresses and distortions after cooling. The simulations highlight how spatial thermal gradients, especially near exposed edges and corners, promote differential shrinkage and warpage, consistent with the observed deformation patterns and build-plate adhesion effects. Experimental tensile tests on PLA ASTM D638 specimens printed at 210∘C confirmed a clear process and property relationship: increasing nozzle temperature led to a reduced apparent elastic modulus, while strength and energy absorption generally improved, with maximum UTS observed at superscript number. The virtual tensile tests captured the same decreasing of stiffness trend, although with a systematic stiffness overestimation attributable to the isotropic continuum assumption and the neglect of porosity and interface effects. Overall, the proposed framework offers a practical route from deposition sequence to mechanical response, supporting process parameter selection. Future developments should incorporate anisotropic constitutive laws based on strand orientation and interfacial features, and extend the mechanical model beyond linear elasticity to account for plasticity and damage, enabling the prediction of yield and failure in a fully process-informed manner.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/DDF.451.111.pdf

This work was supported by the Ministero dell'Istruzione, dell'Università e della Ricerca, PRIN2022: Recycling of plastic wastes integrating extrusion and additive manufacturing techniques (RELIVE), code 2022FBB37P, CUP: D53D23003520006.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 125-131

doi: 10.4028/p-DsEb6I

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

Submitted:
2026-01-19

Revised:
2026-02-19

Accepted:
2026-02-25

Online:
2026-04-17

Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

Francisco Comino 1,a, José A. Martínez-Sánchez 1, b, Marco Zaza 2,c, Sabina Campanelli 3, d, Roberto Spina 3,4,5,e*

1 Departamento de Mecánica, Universidad de Córdoba, Spain

2 Crea3D, Bari, Italy

3 Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Italy

4 Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy

5 Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy

a  francisco.comino@uco.es, b  z12masaj@uco.es, c marco.zaza@crea3d.com, 

d sabinaluisa.campanelli@poliba.it, e* roberto.spina@poliba.it

*corresponding author

Keywords: composite, natural fibers, mechanical properties, material extrusion.

Abstract

The objective of the present research was to identify the mechanical properties of 3Dprinted biocomposite parts and their variation with different natural fillers (olive wood and almond shell). The materials were produced by filament extrusion with 5% fiber content in the polylactic acid matrix, and the samples were fabricated using the Material Extrusion Additive Manufacturing process. 3D printed specimens underwent tensile and flexural tests to assess their mechanical properties. The results showed reductions of 5−18% in the tensile modulus and 10−38% in the tensile strength for PLA based on olive wood and almond shell, respectively. The same trend was observed for the flexural properties, with a 2−3% reduction in flexural modulus and a 3−5% reduction in flexural strength.

Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

Progress in bio-composites has gained significant importance due to growing concerns about environmental issues associated with the use of petroleum-derived synthetic polymers. The use of eco-friendly reinforcing materials and their fabrication are crucial topics because they offer several advantages, including low cost, abundance, and minimal environmental impact. Matrices are natural/bio-derived polymers, whereas the reinforcing agents are also either bio-or synthetic fibers. These bio-composites are not only biodegradable but also bio-compatible, especially when both components are bio-based [1]. The recovery of agricultural waste (agro-waste), typically managed through incineration, composting, or landfilling, offers new opportunities to reuse a wide range of materials, from crop residues such as straw and stalks to fruit and vegetable peels and nut shells. There is a need to develop innovative methods for the utilization of agro-waste [2]. By embracing circular economy principles, industries can substantially reduce waste and greenhouse gas emissions, enhance product durability, and enhance resource efficiency through recycling and reuse initiatives.

In this context, polylactic acid (PLA), a thermoplastic polymer derived from renewable resources and reinforced with natural fibers, is a promising candidate for use in biocomposites. PLA is among the most promising biopolymers because its monomers can be produced from non-toxic, renewable feedstocks and are naturally occurring organic acids [3]. There is a frequent need to reinforce PLA to achieve properties suitable for consumer, packaging, and biomedical applications [4]. However, early formulations of bio-composites exhibited inferior mechanical strength, thermal stability, and barrier properties relative to conventional composites, thereby limiting their widespread adoption [5]. Natural fibers are an efficient option for enhancing aesthetic properties while maintaining the sustainability of the final part. Among natural fiber sources, olive wood and almond shell stand out
for their availability in Mediterranean regions and favorable physical properties, making them attractive for incorporation into composite materials.

This study investigates bio-composites comprising olive wood (OW) and almond shell (AS) fibers produced via filament extrusion, with 5% fiber content in the PLA matrix, and 3D samples printed using the Material Extrusion (MEX) Additive Manufacturing process. Additively manufactured specimens undergo several tests to assess their mechanical properties. This study compares the mechanical properties of 3D specimens fabricated from these bio-composites, evaluates their sustainability in industrial applications, and assesses their potential in various engineering applications.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

Poly(lactic acid) (PLA) is a bio-based, biodegradable aliphatic polyester. As a semicrystalline thermoplastic, PLA exhibits excellent mechanical and physical properties, attracting significant interest in several industries [6]. Net PLA was supplied in pellets, while olive wood (OW) and almond shell (AS) fiber particles were obtained by collecting and recycling agricultural waste. Polylactic acid (PLA) Ingeo 4043D (NatureWorks, USA) and Luminy LX175 (TotalEnergies Corbion, The Netherlands) were selected as the polymer matrices, with the primary data reported in Table 1. Both PLAs exhibited similar thermal and mechanical properties, with a melt flow index of 6 g/min and a natural color [7,8].

Table 1. Material range data.

Physical property | Value | Physical property | Value
Density ρ | 1.24 [g/cm³] | Tensile strength σR | 45-60 [MPa]
Glass transition temperature Tg | 55-60 [°C] | Young's modulus E | 3.5-3.6 [GPa]
Melt temperature Tm | 145-160 [°C] | Strain at break εtb | 5-6 [%]

The AS and OW fiber particles were milled and sieved to a size below 200μ m to ensure stable filament extrusion and minimize clogging. The incorporation of natural particles enabled the creation of lighter components, as their lower density than PLA results in rougher surfaces and increased porosity [9]. Before compounding, PLA pellets and fibers were oven-dried at 60∘C for 8 h to reduce residual moisture, limit hydrolytic degradation, and bubble formation during melt processing. The 1.75 mm filaments (tolerance ±0.03 mm ) were produced using a single-screw extruder equipped with temperature control and an in-line laser diameter gauge, incorporating 5% by weight of the selected filler.

The specimens were fabricated using the MEX E2 printer (Raise 3D Technologies Inc., USA), which employed two independent dual-extruder heads (IDEX) that moved along the X-axis. The maximum build volume was 330×240×240 mm3 for a single extrusion print. All dog-bone samples were designed in accordance with ISO 527-2:2012 [10], with envelope dimensions of 150×20×4 mm3. The 3-point bending samples were designed in accordance with ISO 178:2019 [11], and had dimensions of 80×10×4 mm3. All specimens were printed with a nozzle diameter of 800μ m, a layer height of 350μ m,100% infill, and one layer for the top and bottom, and one layer for each side wall. The number of walls and layers was selected to ensure sufficient resistance to external loads along the central axis during the tensile test without unduly affecting the internal pattern. The internal linear infill pattern was ±45∘ and 0∘/90∘ for tensile and flexural specimens, respectively. The main MEX parameters were the printing speed v(60 mm/s), the nozzle temperature TN(230∘C), and the build plate temperature TB(55∘C). All specimens were printed flat on the build platform ( XY plane) on the same platen, once per time, to avoid mutual influence during cooling. The deposition paths generated using the proprietary slicer software, ideaMaker, are presented in Figure 1.

[picture]

Fig. 1. Specimen slices with ideaMaker (Raise 3D Technologies Inc.).

Fig. 1. Specimen slices with ideaMaker (Raise 3D Technologies Inc.).

The mechanical properties of the MEX samples were assessed using an uniaxial testing machine, which enabled characterization of their elastic and plastic behavior under monotonic loading. Mechanical tests on dog-bone and flexural specimens were conducted on an ETM type A universal single-column testing machine (Wance Testing Machine Co., Ltd., Shenzhen, China) with a 5 kN load cell (accuracy of ±0.5% ) and a crosshead travel (without grip) of 1,000 mm (accuracy of ±0.5% ). According to ISO 527-1:2019 [12] and ISO 178:2019 [11], measurements were performed in a temperature-controlled environment at a transverse speed of 5 mm/min, with a maximum deviation of ±0.5∘C from the ambient temperature. Five repetitions per set were carried out, and the results were averaged.

Results

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

The produced MEX specimens are shown in Figure 2 for net PLA and for both PLA/fiber combinations. PLA/AS and PLA/OW indicate the PLA with almond shell (AS) and olive wood (OW), respectively. Evident color variations were observed among the materials: the net PLA retained its natural color, whereas the fibers imparted their own color to the original PLA matrix in PLA/AS and PLA/OW. The Red-Green-Blue (RGB) color model was used, in which each channel parameter specified the color's intensity, with values ranging from 0 to 255 . At the same time, the RGB value was converted to a hexadecimal code. The average RGB values measured were #ada99e (173, 169, 158) for natural PLA, #7a6450 (122, 100, 80) for PLA/AS, and #5f4c3f (95, 76, 63) for PLA/OW. Figure 3 presents histograms of the material, split by each RGB component. The addition of the fiber made the material darker in all RGB components, with PLA/OW consequently the darkest. Additionally, the shape of each signal shifted from symmetrical (PLA) to skewed (PLA/AS) to bimodal (PLA/OW).

[picture]

Fig. 2. MEX specimens.

Fig. 2. MEX specimens.

[picture]

Fig. 3. RGB values.

Fig. 3. RGB values.

The mechanical tests were performed on all specimens. The investigation started with the tensile test. The initial cross-section of each MEX specimen was measured before testing using a digital micrometer. The maximum strain ε was set to 4% for each test, denoted as ε4%, based on previous studies in which the maximum stress was reached at this value [13]. All specimens fractured in a brittle manner, with a very limited plateau observed above the yield point and a low-stress drop. Moreover, the elongation and tensile toughness values (as indicated by the area under the stress-strain curve) were higher than those specified in the material data sheet. Table 2 lists the tensile properties of the printed specimens, including Young's modulus E, ultimate tensile strength σR, and strain at break εth. A portion of the stress-strain curves between 5 and 20 MPa was used to calculate the E modulus. The low value of 5 MPa was needed to achieve load stabilization during testing.

Table 2. Tensile material results.

Material | E [GPa] | σR [MPa] | εth [%]
PLA | 2.39 ± 0.06 | 50.47 ± 0.62 | 3.77 ± 0.22
PLA/AS | 1.97 ± 0.13 | 31.58 ± 1.96 | 1.95 ± 0.14
PLA/OW | 2.28 ± 0.06 | 45.23 ± 1.07 | 3.13 ± 0.04

The performance of MEX specimens made with the PLA and fibers was lower than that of those with net PLA, likely due to reduced interfacial adhesion, which affected the composite's mechanical properties, as identified in a previous work [14]. The presence of voids was identified, resulting from incomplete bonding or fiber particle agglomeration during compounding. Figure 4 reports normalized values, with the PLA results used as the reference at 100 to highlight the reduction, using the formula Pnorm =(1−P/PPLA)×100, where P was the generic property (E,σR, and εth) and PPLA the same property for the net PLA.

[picture]

Fig. 4. Tensile results.

Fig. 4. Tensile results.

The reductions in E modulus were 17.6% and 4.6% for PLA/AS and PLA/OW, respectively. These outcomes suggested that the interfacial adhesion of the AS fibers to the PLA matrix was lower than that of the OW fibers. The same trend was observed for the tensile strength σR, with reductions of 37.4% and 10.4% with respect to the net PLA. The decrease in the strain at break εth with respect to the net PLA was more pronounced, with values of 48.3% and 17.0% for PLA/AS and PLA/OW, respectively. Based on the above results, adding OW fibers to the PLA matrix was more effective than adding AS fibers. The results also revealed that the variation in the response variables was less than 10% for PLA and PLA/OW, indicating that the test was repeatable relative to the median. The PLA/AS deviation was 17%, suggesting, once again, that low adhesion may be the primary cause of the poor performance.

The mechanical analysis was extended to flexural testing to determine essential material properties, including the flexural modulus Ef, the maximum flexural stress σfM, and the flexural strain at fracture εfb. The average results of the flexural tests conducted on MEX specimens are presented in tabular form (Table 3) for all materials, using a span distance of 64 mm .

Table 3. Flexural results.

Material | Ef [GPa] | σfM [MPa] | εfb [%]
PLA | 1.86 ± 0.02 | 56.57 ± 0.77 | 6.08 ± 0.11
PLA/AS | 1.81 ± 0.05 | 54.17 ± 0.61 | 3.60 ± 0.17
PLA/OW | 1.80 ± 0.01 | 55.17 ± 0.56 | 4.45 ± 0.10

The decrease in the Ef modulus were 2.7% and 3.2% for PLA/AS and PLA/OW, respectively, and in the flexural strength, σfM were 4.2% and 2.5% with respect to the net PLA. These reductions below 5% indicated the good performance of the MEX specimens when AS and OW fibers were added to the net PLA. However, the decreases in flexural strain were 59.2% and 73.2% for PLA/AS and PLA/OW, respectively, highlighting a deterioration in the flexibility of the MEX specimens with fibers. The normalized flexural results were presented in graphical form in Figure 5. Based on the results of the tensile test, the addition of the OW fibers to the PLA matrix was better than the addition of the AS fibers. The mechanical test results also revealed that the variation in response variables was very low for PLA and PLA/OW, indicating that the test was repeatable relative to the median value. The most significant variation was observed for PLA/AS, suggesting, once again, that low adhesion between AS fibers and the matrix was the primary factor.

[picture]

Fig. 5. Flexural results.

Fig. 5. Flexural results.

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

This study evaluated the mechanical response of MEX 3D-printed PLA biocomposites containing 5 wt : % olive wood (OW) and almond shell (AS) particles. The results confirm that both fillers can be successfully processed into printable filaments and manufactured into stable parts, while also providing clear visual differentiation of the materials, as reflected in the measured RGB values. Mechanically, the incorporation of natural fillers enabled the composites to retain flexural performance comparable to that of neat PLA, with only minor (<5%) changes in flexural modulus and strength, supporting their potential use in applications primarily subjected to bending loads. In tension, a moderate reduction in stiffness and strength was observed, particularly for AS, indicating that the filler type plays an important role even at low loading levels. Additionally, the lower strain at break suggests a shift towards less ductile behavior, which should be considered for components that require large deformations. Overall, PLA provided the most balanced combination of mechanical retention and bio-based aesthetic enhancement, reinforcing the interest of these sustainable biocomposites for functional 3D-printed parts with moderate mechanical requirements.

Acknowledgment

The original version of this paper is available on https://www.scientific.net/DDF.451.125.pdf

The Project was funded under the following programs:

Department of Excellence - Law number 232/2016 (Grant No. CUP - D93C23000100001).

The National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of 15/03/2022 of the Italian Ministry of University and Research (MUR), funded by the European Union - NextGenerationEU.

Space It Up project funded by the Italian Space Agency, ASI, and the Italian Ministry of University and Research (MUR) under contract n. 2024-5-E. 0 (Grant No. CUP-I53D24000060005).

European Innovation Association (AEI) on agricultural productivity and sustainability for the creation and operation of operational groups and the Ministry of Agriculture, Livestock, Fisheries, and Sustainable Development of the Junta de Andalucía through the research project AGROSEC, reference GOPO-JA-23.

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 133-146

doi: 10.4028/p-jEnO27

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

Submitted:
2026-01-19

Revised:
2026-02-25

Accepted:
2026-03-01

Online:
2026-04-17

Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

Keltoum Oubellaouch 1,2,a*, Riccardo Pelaccia 1, b, Giulia Zaniboni 1,2,c, Vincenzina Siciliani 1, d and Barbara Reggiani 1,3,e

¹DISMI Department of Sciences and Methods for Engineering - University of Modena and Reggio Emilia, Via Amendola 2, 42122, Reggio Emilia, Italy

2 INTERMECH, University of Modena and Reggio Emilia, Italy

3 EN&TECH, University of Modena and Reggio Emilia, Italy

a  keltoum.oubellaouch@unimore.it, b  riccardo_p@unimore.it, c  giulia.zaniboni@unimore.it, d  vincenzina.siciliani@unimore.it, e  barbara.reggiani@unimore.it

Keywords: Injection Molding, Optimization, Numerical Simulation, Warpage Reduction.

Abstract

Warpage in injection-molded thin-walled box-shaped parts is primarily caused by nonuniform cooling and differential shrinkage. This study proposes a two-step, multi-objective optimization strategy to reduce part warpage by addressing both thermal and geometric factors. In the first step, the mold cooling system is optimized through a bi-objective formulation that simultaneously minimizes (i) the temperature standard deviation within the part and (ii) the total cooling channel length. The optimization is carried out using a coupled workflow involving parametric CAD modeling, Autodesk Moldflow simulations, and a genetic algorithm. The optimized cooling design reduces temperature non-uniformity by 44% compared to a conventional cooling layout. In the second step, a geometric optimization is performed through the addition of a reinforcing border, where maximum deflection and total part volume are minimized simultaneously. The combined optimization leads to a reduction in maximum warpage from 14.5 mm in the reference configuration to 2.06 mm in the final design. The results demonstrate the effectiveness of a sequential optimization approach in achieving significant warpage reduction while maintaining material and manufacturing efficiency.

Introduction

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

Warpage is widely recognized as one of the most critical quality defects in plastic injection molding, especially for thin-walled and box-shaped components, where differential cooling, nonuniform shrinkage, and residual stress development lead to significant geometric distortions [1]. The defect originates from the intrinsic complexity of the injection molding process, in which the polymer melt experiences strongly coupled thermal, mechanical, and rheological phenomena during filling, packing, and cooling stages [2]. Spatial variations in temperature and pressure, together with molecular orientation effects, result in uneven volumetric contraction across the part thickness and along its geometry, ultimately causing warpage upon ejection from the mold [3,4]. Due to this strong coupling and nonlinearity, empirical or trial-and-error approaches based on operator experience are often insufficient to guarantee consistent part quality, particularly for geometries with stringent dimensional tolerances [5].

To address these limitations, numerical simulation has become a central tool for predicting warpage and supporting process and design decisions in injection molding. Finite-element-based simulation environments allow the coupled analysis of melt flow, heat transfer, solidification, and residual stress evolution, providing a physically consistent framework for understanding warpage formation mechanisms [6]. Advanced numerical models have further improved prediction accuracy by accounting for three-dimensional effects and material anisotropy, as demonstrated in studies on fiber-reinforced polymers, where orientation-dependent thermo-mechanical behavior plays a dominant role in warpage development [1,7]. Simulation-driven approaches therefore enable the
evaluation of warpage prior to mold manufacturing, significantly reducing development time and cost [2].

Building upon numerical simulation capabilities, a substantial body of research has focused on the optimization of injection molding process parameters to minimize warpage. Widely adopted approaches rely on design of experiments (DOE), including Taguchi and orthogonal array methods, to identify influential parameters and their optimal combinations [8,9]. While these techniques are computationally efficient and easy to implement, they are inherently limited to discrete parameter levels and typically provide optimal solutions only within a predefined experimental space [8]. As a result, they may fail to capture the true global optimum in highly nonlinear problems such as warpage control.

To overcome these limitations, advanced optimization strategies based on evolutionary algorithms and numerical optimization frameworks have been increasingly applied. Genetic algorithms, particle swarm optimization, and multi-objective optimization techniques have been combined with injection molding simulations to systematically explore large design spaces and reduce warpage [10,11]. In many cases, these approaches have demonstrated superior performance compared to classical DOE methods, particularly when multiple interacting parameters must be optimized simultaneously. However, the computational cost associated with repeated high-fidelity simulations remains a major challenge.

To mitigate this issue, surrogate-based optimization approaches have been widely adopted. Artificial neural networks, response surface methodologies, and Kriging models are commonly used to construct approximate relationships between process parameters and warpage response, replacing expensive numerical simulations during the optimization loop [12,13]. These surrogate models are often coupled with global optimization algorithms, enabling efficient exploration of the design space. Nevertheless, several studies emphasize that surrogate model accuracy is strongly dependent on the quality and size of the training dataset, and that insufficient sampling may lead to unreliable predictions, particularly in the presence of strong nonlinear thermo-mechanical interactions [12,13].

Despite the increasing sophistication of optimization methodologies, many studies still adopt single-objective formulations, typically focusing exclusively on minimizing warpage magnitude [810]. While such approaches may yield numerically optimal solutions, they often neglect practical considerations related to manufacturability, mold complexity, and industrial robustness. More recent works have introduced multi-objective optimization frameworks to address trade-offs between warpage, shrinkage, and cycle time [11]. However, even within these frameworks, the selected objectives are frequently limited to final deformation metrics, without explicitly addressing the physical mechanisms responsible for warpage formation.

Among the various influencing factors, the cooling phase has consistently been identified as a dominant contributor to warpage. Cooling accounts for the largest portion of the injection molding cycle time and plays a decisive role in determining temperature gradients within the molded part [14]. The design of the cooling system, including channel layout, distance from the cavity surface, and coolant conditions, directly affects heat removal efficiency and temperature uniformity. Consequently, significant research efforts have focused on optimizing cooling system design, with particular attention given to conformal cooling channels enabled by additive manufacturing technologies [14,15]. These studies demonstrate that improved cooling performance can significantly reduce warpage and residual stresses while also decreasing cycle time.

Nevertheless, most cooling system optimization studies evaluate performance using global indicators such as maximum temperature, cooling time, or final warpage value [14,15]. While these metrics are useful from an operational standpoint, they do not explicitly quantify the spatial uniformity of the temperature field within the part. Only a limited number of works acknowledge the importance of temperature uniformity, and even fewer treat it as a primary optimization objective [14]. This represents a significant gap in the literature, considering that warpage fundamentally arises from spatial temperature gradients and the resulting differential shrinkage during cooling [1,12].

From a physical perspective, temperature homogenization during cooling constitutes a direct and meaningful indicator of warpage propensity. Uneven temperature distributions lead to localized
differences in solidification rate and volumetric contraction, generating residual stresses that are released upon ejection [5,12]. Despite this well-established mechanism, optimization formulations rarely incorporate temperature dispersion metrics-such as the standard deviation of the temperature field—as explicit objective functions. Addressing this limitation is essential to establish a clearer and more physically consistent link between cooling system design, thermal behavior, and final part quality.

In this context, the present work proposes an integrated multi-objective optimization framework in which the CAD environment (Fusion 360) is coupled with the process simulation module (Autodesk Moldflow Insight) through an optimization platform. A two-step, simulation-driven strategy is adopted: first, the cooling system is optimized by explicitly minimizing temperature nonuniformity within the part while limiting cooling system complexity; subsequently, a geometry-based optimization is performed to further reduce warpage through the introduction of a reinforcing border. All optimization activities are carried out using direct numerical simulations within an optimization platform a physically consistent relationship between cooling system design, temperature distribution, and final part quality.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

In this work, a two-step optimization procedure was developed to mitigate warpage in a thinwalled polymer component by addressing both thermal and geometric contributors. The investigated part is a box-shaped component with overall dimensions of 300 mm×200 mm×150 mm and a uniform wall thickness of 4 mm . For this class of components, warpage is primarily driven by differential cooling between the inner and outer surfaces, which results in non-uniform shrinkage during the cooling phase. Consequently, the first step of the proposed methodology focuses on the optimization of the mold cooling system with the objective of achieving the most uniform temperature distribution within the part. This first step is formulated as a bi-objective optimization problem, in which temperature uniformity and cooling system complexity are minimized simultaneously. Once the optimal cooling configuration is identified, a second optimization step is carried out to further reduce warpage through a geometric modification of the component, consisting of the addition of a reinforcing border to the box. In this second step, the optimization procedure aims to determine the most suitable border configuration to minimize the final deformation while preserving the overall part geometry. Similarly, this second stage is also formulated as a bi-objective optimization problem, where deformation reduction and material usage are simultaneously considered in order to achieve a balanced structural solution. All optimization activities are performed using an optimization platform, which is employed to manage the workflow, execute simulations, and evaluate the defined objective functions.
Step 1: Cooling System Optimization. The first step of the optimization procedure concerns the design of the mold cooling system. The mold configuration corresponds to a single-cavity, two-plate mold. Within this configuration, three distinct cooling planes are considered. The first cooling plane, referred to as Cooling Plane 1 in Figure 1, is located in the fixed plate of the mold and consists of six straight cooling channels oriented along the y-axis. The second cooling plane (Cooling Plane 2 in Figure 1) is positioned at a z-coordinate corresponding to the mid-height of the box-shaped component. The third cooling plane (Cooling Plane 3 in Figure 1) is located in the moving plate of the mold and plays a key role in the thermal management of the part. This plane allows the integration of baffles extending toward the depth of the box, enabling enhanced heat extraction from the inner regions of the component. The inclusion of these baffles is particularly important for reducing the thermal gradient between the inner and outer surfaces of the box, thereby promoting a more uniform temperature distribution during the cooling phase.

[picture]

Fig. 1 Schematic of the single-cavity, two-plate mold showing the three cooling planes

Fig. 1. Schematic of the single-cavity, two-plate mold showing the three cooling planes

Within the cooling system optimization, several design parameters could, in principle, be varied. However, in order to limit the complexity of the optimization problem and ensure a manageable design space, a reduced set of design variables was selected. The first design variable is the diameter of the cooling channels, denoted as " dc ", which was allowed to vary between 8 mm and 20 mm . The second variable defines the distance between Cooling Plane 1 and the box-shaped part. This distance was parameterized as the product of a dimensionless factor " a " and the channel diameter " dc ", with the factor " a " constrained to the range 1−2.5. Finally, the third design variable is the number of branches, " n1 ", corresponding to the number of cooling channels oriented parallel to the y-direction from which baffles are introduced in the moving plate. The number of branches was varied between 3 and 8, while the number of baffles per branch was kept constant and set equal to three for all configurations.

[picture]

Fig. 2 Workflow of the first optimization procedure ( Step 1: Cooling System Optimization)

Fig. 2. Workflow of the first optimization procedure ( Step 1: Cooling System Optimization)

The objective of the first optimization step is twofold. The primary objective is the reduction of temperature non-uniformity within the molded part, which is quantified by minimizing the standard deviation of the temperature field over the volume of the box. The objective function associated with thermal uniformity is defined as (Eq. 1):

f1=σT=1N∑i=1N(Ti−T¯)(1)

where Ti represents the temperature at the ith  evaluation point within the part, T¯ is the average temperature, and N is the total number of sampled points.

In parallel, a second objective is introduced to limit the overall complexity of the cooling system by minimizing the total length of the cooling channels, Ltot. This objective accounts for practical manufacturing and structural considerations. While an extensive cooling network with large channel diameters and a high number of baffles can significantly enhance heat extraction and temperature uniformity, it may also compromise mold mechanical integrity by excessive material removal and increase machining complexity and cost. Therefore, the optimization seeks a balanced solution that achieves the highest possible temperature uniformity with the minimum necessary cooling system length. The second objective function is thus expressed as (Eq. 2):

f2=Ltot(2)

The combined optimization framework enables the identification of cooling system configurations that provide an effective thermal performance while remaining compatible with mold strength and manufacturing constraints.
The cooling system optimization problem was solved using a commercial optimization platform. Figure 2 illustrates the complete workflow implemented for Step 1. The workflow integrates parametric CAD modeling, numerical simulation, and multi-objective optimization in an automated loop. At the top level of the workflow, the design variables-namely the number of branches n1, the cooling channels diameter dc, and the distance factor a-are defined and controlled by the optimization algorithm. The original Non-dominated Sorting Genetic Algorithm II (NSGA-II) was selected to solve the multi-objective optimization problem. The algorithm was configured with an initial Design of Experiments (DOE) consisting of 20 configurations, followed by 50 generations, resulting in a total of 1000 evaluated designs. The coupling between the optimization platform and Autodesk Fusion 360 was implemented through an automated script-based interface, where the required commands were executed using Windows batch scripting. For each iteration, the optimization algorithm generates a new set of design variables, which are automatically assigned to the parametric CAD model. The procedure begins by opening an existing Fusion 360 project containing a fully parametric CAD model of the cooling system, where the design variables are defined as editable parameters. Once the design variables are updated, Fusion 360 regenerates the cooling system geometry and exports the corresponding CAD model in STEP format. Subsequently, the total length of the cooling channels is automatically computed and written to an output file. This value is then retrieved by the optimization platform and stored as an output variable directly associated with the objective function representing the total cooling system length. The numerical simulation of the cooling process was performed using Autodesk Moldflow Insight, which was interfaced with the optimization platform through an automated script-based coupling mechanism implemented using Visual Basic scripting. The execution of Moldflow was conditioned on the successful generation of the STEP file by Fusion 360. Once launched, Moldflow imports the current cooling system geometry as CAD data. A three-dimensional cooling channel property is initially assigned to the channels, after which they are converted into beam elements. This modeling choice significantly reduces computational cost while avoiding the complexity associated with fully meshed three-dimensional cooling channels. The cooling system mesh was generated using an automatic sizing strategy, since the channel dimensions vary from one iteration to another. Specifically, the parameter Edge-Length Ratio Circuits was set to 2.5 . The inlet and outlet locations for the coolant were automatically defined based on the coordinates of the channels generated in Fusion 360. Water was selected as the coolant, with an inlet temperature fixed at 50∘C and a Reynolds number set to 15,000 to ensure efficient convective heat transfer. The box-shaped part and the sprue were then imported into Moldflow, and a Cool analysis was defined. The material was selected from the Moldflow database as Generic ABS-Generic Shrinkage Characterised Material. The shear viscosity of the melt is described in Moldflow using the Cross-WLF model, which accounts for the combined effects of shear rate, temperature, and pressure on the polymer viscosity. The viscosity η is expressed as (Eq.3):

η=D1·e−A1(T−T*)A2+(T−T*)1+(D1·e−A1(T−T*)A2+(T−T*)·y˙τ*)1−n(3)

where T*=D2+D3.p,A2=A3+D3.p, T is the melt temperature, p is the pressure and γ˙ the shear rate. The parameters D1,D2,D3,A1,A2,n and τ* are material-specific coefficients provided in the Moldflow database. The values corresponding to the selected ABS grade are reported in Table 1.

Table 1 The Cross-WLFparameters of the injection molded polymer

Parameter | D₁[Pa.s] | D₂ [K] | D₃ [K/Pa] | A₁ | A₂ [K] | n | τ* [Pa]
Value | 2.8e+12 | 373.15 | 1.2e-07 | 27.76 | 51.6 | 0.37 | 15701.5

After meshing the part and the sprue, a melt temperature of 230∘C was set up and a fixed total cycle time of 30 s (including injection, packing, and cooling phases) was imposed. The cooling time was deliberately not left to automatic determination by Moldflow, in order to prevent variations in cooling duration between different iterations and to ensure a consistent comparison among different cooling system designs. Although cooling time could be introduced as an additional design variable within the optimization framework, it was intentionally kept constant in order to isolate the influence of cooling system geometry on thermal uniformity and warpage. Allowing cooling time to vary for each configuration would increase computational cost and potentially mask the true effect of geometric modifications, since longer cooling durations could compensate for suboptimal cooling layouts.
Once the simulation was completed, the temperature distribution within the part was exported. The output provides the temperature value at each node and for each time step. The temperature field at the end of the cooling phase ( 30 s ) was used to compute the average temperature and the standard deviation of the temperature within the part. This value was then transferred to the optimization platform and stored as an output variable directly associated with the second objective function representing temperature uniformity. The local cooling rate and temperature gradients within the part are determined by the interaction of the cooling channel geometry and material thermal properties. While coolant flow rate and temperature were fixed, the effective cooling experienced by the part is modulated by the cooling system geometry, which controls local heat extraction and thermal gradients. The standard deviation of the part temperature inherently reflects these variations in cooling rate and thermal uniformity.
Step 2: Geometric Optimization for Warpage Reduction: Once the optimal cooling system configuration was identified in Step 1, a second optimization step was carried out to further reduce part warpage through a controlled geometric modification of the component. This step focuses on the addition of a reinforcing border to the box-shaped part, a well-established strategy in injection molding of thin-walled box-like components to increase structural stiffness and mitigate deformation induced by differential shrinkage. The addition of reinforcing borders is known to be effective in reducing warpage, as increased section stiffness limits bending and out-of-plane deformation during cooling. However, excessively large or massive borders are not desirable in industrial practice. Oversized borders negatively affect the aesthetic appearance of the component, increase material consumption, and lead to higher part weight and production cost. Moreover, unnecessary material accumulation may alter cooling behavior and prolong cycle time, counteracting process efficiency objectives. For these reasons, the geometric reinforcement must be carefully designed to achieve sufficient warpage reduction while minimizing material usage and preserving the overall functional and visual characteristics of the part. The reinforcing border geometry, illustrated in Figure 4, is defined by three main dimensions: the border width L, representing the outward extension of the border from the box wall; the border height H, corresponding to the vertical extension of the border; and the border thickness Th. The thickness Th is generated in the CAD model by applying a hollowing operation (thicken feature in Fusion 360), ensuring a consistent wall structure. To guarantee that the
border thickness remains physically meaningful and does not exceed the border width, a dimensionless parameter " b " was introduced, such that (Eq.4):

Th=b×L(4)

In the optimization problem, the border width L and height H were selected as primary design variables and varied within the range 5−20 mm. The dimensionless factor b was varied between 0.2 and 1.0. A value of ( b=1 ) corresponds to a fully solid border (i.e., (Th=L) ), while lower values of b generate hollow borders with reduced material usage.

[picture]

Fig. 3 Geometric parameters of the reinforcing border used for warpage reduction: border width (L), height ( H ), and thickness ( Th ), with Th defined as Th=b×L.

Fig. 3. Geometric parameters of the reinforcing border used for warpage reduction: border width ( L ) , height ( H ), and thickness ( T h ), with T h defined as T h = b × L .

The objective of the second optimization step is twofold. The primary objective is the minimization of the maximum deflection of the molded part, which is used as a quantitative indicator of warpage severity. In parallel, a second objective is introduced to minimize the total volume of the molded box, thereby limiting material consumption and avoiding excessive geometric reinforcement. This multiobjective formulation enables the identification of border configurations that provide effective warpage reduction with minimal material penalty.
The optimization workflow implemented in Step 2 closely follows the structure adopted in Step 1. For each iteration, the optimization algorithm generates a new set of design variables ( L,H, and b ), which are automatically assigned to a parametric CAD model in Autodesk Fusion 360. The updated geometry of the reinforced box is then exported in STEP format, and the total volume of the part is computed and written to an output file. This value is subsequently read by the optimization platform and assigned to the objective function related to volume minimization.
The generated STEP file is then imported into Autodesk Moldflow, where the simulation is automatically configured. The cooling system used in this second optimization step corresponds to the optimal configuration identified in Step 1, ensuring that the thermal conditions remain fixed and that the effects of geometric modification on warpage can be isolated. All process parameters, including melt temperature, injection time, packing time and pressure, and total cycle time, were kept constant for all iterations. The melt temperature ( 230∘C ) and mold temperature ( 60∘C ) were selected according to the recommended processing window provided in the material datasheet. The injection time was fixed at 4 s ; this value was determined through preliminary "Fill" simulations in Autodesk Moldflow to ensure complete cavity filling under all geometric configurations prior to launching the optimization procedure. Although the proposed optimization framework allows process parameters to be treated as additional design variables, they were intentionally kept constant in this study in order to isolate the influence of the reinforcing border geometry on warpage reduction. Introducing variable processing conditions would significantly increase computational cost and obscure the specific contribution of geometric modification.
After completion of the simulation, the maximum deflection of the part is extracted from the Moldflow results and assigned to the objective function representing warpage minimization. Under
these fixed processing conditions, the predicted injection pressures remained within a narrow range (approximately 40−60MPa ), with minor variations attributable to changes in effective thermal conditions and border geometry.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

Figure 4 presents the two-dimensional scatter plot obtained at the end of the multi-objective optimization procedure for the cooling system design. Each point in the diagram represents a feasible cooling system configuration evaluated during the optimization process. The horizontal axis reports the total length of the cooling channels, Ltot, while the vertical axis reports the standard deviation of the temperature within the molded part at the end of the cooling phase, σT. A clear clustering of solutions can be observed, with the population organized into six distinct groups. Each group corresponds to a fixed value of the design variable n1, representing the number of branches from which baffles are introduced in the moving plate. Within each group, variations in channel diameter dc and distance factor a generate solutions with comparable total channel lengths and temperature standard deviations. As expected from a physical standpoint, increasing the number of baffle branches n1 leads to a systematic increase in the total cooling channel length. At the same time, a monotonic reduction in the temperature standard deviation within the part is observed. This trend confirms the effectiveness of baffles in enhancing heat extraction from the inner regions of the box-shaped component, thereby reducing the thermal gradient between inner and outer surfaces and promoting a more homogeneous temperature distribution.

[picture]

Fig. 4 Two-dimensional scatter plot obtained at the end of the multi-objective optimization procedure for the cooling system design.

Fig. 4. Two-dimensional scatter plot obtained at the end of the multi-objective optimization procedure for the cooling system design.

For each group of solutions corresponding to a fixed value of the number of baffle branches n1, the configuration exhibiting the minimum temperature standard deviation represents the best-performing design in terms of thermal uniformity, as it dominates all other solutions within the same group by achieving a lower σT without increasing the total cooling channel length. When these best-performing configurations are compared across different values of n1, none of them dominates another, since improvements in temperature uniformity are systematically obtained at the expense of increased cooling system length. As a result, these configurations are non-dominated with respect to the two competing objectives of minimizing the temperature standard deviation σT and the total cooling channel length Ltot , and they form a discrete approximation of the Pareto front. These Pareto-optimal solutions are highlighted in blue in Figure 4 and summarized in Table 2. It can be observed that the distance factor a equals 1 for all Pareto-optimal solutions. This does not mean that the parameter was fixed; rather, the optimization converged to the lower bound of its admissible range (1-2.5),
indicating that positioning the cooling plane as close as allowed to the part improves thermal performance within the considered design space.

Table 2 Pareto-optimal cooling designs versus initial design

Design ID | Total channels length [cm] | Temperature standard deviation [°C] | dc [mm] | a | nl [mm]
0 (before optimization) | 34.1 | 22.1 | 12 | 1 | 0
101 | 93.1 | 12.8 | 14 | 1 | 3
12 | 122.3 | 12.3 | 12 | 1 | 4
125 | 152.9 | 12.2 | 8 | 1 | 5
156 | 181.8 | 12.1 | 8 | 1 | 6
183 | 210.7 | 12.0 | 8 | 1 | 7
818 | 239.5 | 11.9 | 8 | 1 | 8

It is important to highlight that the introduction of baffles leads to a substantial reduction in temperature standard deviation compared to the initial configuration ( 22.1∘C ), with all Pareto-optimal solutions exhibiting values close to 12∘C. The differences of approximately 1∘C observed among Pareto-optimal designs therefore correspond to incremental refinements within an already significantly improved thermal regime. In this context, the optimization primarily captures the tradeoff between marginal gains in thermal uniformity and the associated increase in cooling system length. Among these Pareto-optimal solutions, Design ID 818 achieves the lowest temperature standard deviation, corresponding to the most uniform temperature distribution within the part. However, this improvement is obtained at the expense of a significantly increased cooling system length, which may negatively impact mold structural integrity and manufacturing cost. Considering the trade-off between thermal performance and cooling system complexity, Design ID 12 was selected as the optimal compromise solution. Compared to Design ID 818, the total cooling channel length is reduced by approximately 49%, while the increase in temperature standard deviation remains limited. This configuration therefore achieves a substantial homogenization of the temperature field with a considerably more compact and manufacturable cooling system.
Overall, the results of Step 1 demonstrate that the number of baffle branches is the dominant parameter governing temperature uniformity in the considered design space, and that a balanced cooling system configuration can be identified through multi-objective optimization by explicitly accounting for both thermal performance and practical manufacturing constraints.

[picture]

Fig. 5 Comparison of nodal temperature distributions at the end of cooling for the reference and optimized cooling systems, showing improved thermal uniformity with baffles.

Fig. 5. Comparison of nodal temperature distributions at the end of cooling for the reference and optimized cooling systems, showing improved thermal uniformity with baffles.

Figure 5 compares the temperature distributions within the molded part at the end of the cooling phase for the non-optimized reference cooling system (without baffles) and the optimized cooling configuration selected from the Pareto front. The distributions are represented in terms of histograms of nodal temperatures, together with the main statistical indicators. In the reference configuration without baffles, the temperature field exhibits a wide dispersion, characterized by a large standard deviation and the presence of pronounced high-temperature regions. This behavior reflects the limited ability of the conventional cooling layout to extract heat from the inner regions of the box-shaped component, resulting in significant thermal gradients between the inner and outer surfaces. After optimization, a substantial improvement in thermal uniformity is observed. The standard deviation of the temperature distribution decreases from 22.1∘C to 12.3∘C, corresponding to a reduction of approximately 44%. In addition to this quantitative improvement, the optimized cooling system produces a markedly more compact and symmetric temperature distribution, with a significant reduction in extreme temperature values. For the optimized cooling configuration, the temperature distribution becomes narrower and more regular. When compared with a normal distribution, a good qualitative agreement is observed. Although no assumption of strict normality is imposed, the absence of pronounced hot or cold regions indicates a more homogeneous thermal state of the part at the end of the cooling phase. This improvement in temperature homogenization is directly linked to the presence of baffles in the moving plate, which enhance heat extraction from the inner surfaces of the component and reduce differential cooling. The resulting reduction in temperature gradients is expected to significantly mitigate non-uniform shrinkage during solidification and, consequently, contribute to a reduction in warpage. These results confirm the effectiveness of the first optimization step in addressing the thermal root cause of deformation in thin-walled box-shaped parts.

[picture]

Fig. 6 Scatter plot of maximum part deflection versus total volume for reinforced box designs, showing the trade-off between warpage reduction and material usage.

Fig. 6. Scatter plot of maximum part deflection versus total volume for reinforced box designs, showing the trade-off between warpage reduction and material usage.

Figure 6 presents the two-dimensional scatter plot obtained at the end of the second optimization step, illustrating the relationship between maximum part deflection and total part volume for the reinforced box configurations. Each point represents a feasible design evaluated during the multi-objective optimization and corresponds to a specific combination of the border design variables ( L,H,b ). The horizontal axis reports the maximum deflection of the part, used as a quantitative indicator of warpage, while the vertical axis reports the total volume of the molded box.
The distribution of solutions shows a wide variability in performance, with several configurations exhibiting simultaneously high deflection and high volume, indicating inefficient geometric reinforcement. In contrast, a subset of non-dominated solutions defines a Pareto-optimal region (highlighted in blue), where reductions in warpage are obtained only at the expense of increased material usage. This Pareto-optimal trade-off highlights the necessity of balancing geometric stiffness and material efficiency when designing reinforcing borders for warpage mitigation. The final design was selected from the Pareto-optimal solutions by balancing warpage reduction and material efficiency. Design ID 167 was chosen, as it exhibits the minimum maximum deflection among all evaluated configurations, equal to 2.06 mm , indicating the most effective mitigation of warpage. The corresponding total part volume is 1094.3 cm3, which remains moderate compared to other designs. Configurations with larger volumes, reaching up to 1242 cm3, do not provide further improvements in deflection and are therefore dominated. Conversely, designs with minimal volume (approximately 846 cm3 ) show a significant increase in deflection, up to 2.82 mm , reflecting insufficient structural stiffness. Design ID 167 thus represents the most efficient compromise between geometric reinforcement and material usage and was selected as the final optimized box configuration.
Figure 7 presents a comparative visualization of the warpage results obtained for three representative configurations, highlighting the progressive effectiveness of the proposed two-step optimization strategy. Figure 7a) shows the deformation field of the original box molded with the non-optimized cooling system, which exhibits a maximum deflection of 14.5 mm , indicative of severe warpage caused by pronounced thermal gradients and limited structural stiffness. Figure 7(b) reports the deformation of the original box geometry molded with the optimized cooling system identified in Step 1. In this case, the maximum deflection is significantly reduced to 3.12 mm , demonstrating the strong impact of cooling system optimization and temperature homogenization on warpage mitigation. Finally, Figure 7(c) illustrates the deformation of the geometrically optimized box molded with the optimized cooling system. The maximum deflection is further reduced to 2.06 mm , confirming the additional benefit provided by the reinforcing border once thermal non-uniformities
have been minimized. The comparison clearly shows that while cooling system optimization addresses the primary thermal cause of warpage, the combined application of optimized cooling and targeted geometric reinforcement enables the most effective reduction of deformation, resulting in an overall warpage reduction of more than 85% compared to the initial configuration.

[picture]

Fig. 7 Comparison of warpage in three configurations: (a) non-optimized, (b) optimized cooling, and (c) optimized cooling with reinforced border, showing progressive reduction in maximum deflection.

Fig. 7. Comparison of warpage in three configurations: (a) non-optimized, (b) optimized cooling, and (c) optimized cooling with reinforced border, showing progressive reduction in maximum deflection.

Summary

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

This study presented a two-step optimization strategy for reducing warpage in thin-walled box-shaped injection-molded parts by jointly addressing thermal and geometric causes of deformation. In the first step, a multi-objective optimization of the mold cooling system, based on the integration of parametric CAD modeling, numerical simulation, and genetic algorithms, led to a substantial improvement in temperature uniformity through the optimized use of baffles. The second step further reduced warpage by introducing a controlled geometric reinforcement, optimized to balance structural stiffness and material efficiency. The combined application of optimized cooling and targeted border design resulted in an overall warpage reduction exceeding 85% compared to the initial configuration, while maintaining a compact and manufacturable design. The proposed methodology demonstrates the effectiveness of sequential, physics-driven optimization for improving part quality in injection molding and provides a systematic framework applicable to complex industrial components.

Fundings

The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

This work was supported by the Emilia-Romagna Region, Italy [PR-FESR 2021-2027 -Priorità 1 obiettivo specifico 1.1 - Azione 1.1.2 - Progetto "CUP E17G22001630003- SAFER. This work was also supported by PNRR-M4C2INV1.5, NextGenerationEU-Avviso 3277/2021-ECS_00000033-ECOSISTER-spk3.

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The original version of this paper is available on https://www.scientific.net/DDF.451.133.pdf

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 147-156

doi: 10.4028/p-S43Bos

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

Submitted:
2026-01-19

Accepted:
2026-02-27

Online:
2026-04-17

Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

Michael Wilhelm 1,a*, Christoph Schelleis 1, b, Georg Zeeb 1,2,c and Frank Henning 1,2, d

1 Fraunhofer Institute for Chemical Technology (ICT), Joseph-von-Fraunhofer-Str. 7, 76327 Pfinztal, Germany

2 Karlsruhe Institute of Technology (KIT), Institute of Vehicle Systems Technology (FAST) Lightweight Engineering, Rintheimer Querallee 2, 76131 Karlsruhe, Germany

a  michael.wilhelm@ict.fraunhofer.de, b  christoph.schelleis@ict.fraunhofer.de, c  georg.zeeb@ict.fraunhofer.de, d  frank.henning@ict.fraunhofer.de (*corresponding author)

Keywords: pultrusion, reactive thermoplastic, caprolactam, gel zone, power consumption

Abstract

Process speed in pultrusion is significantly influenced by the exothermic reactions of the matrix materials used. The main reaction zone (gel zone) is a key indicator to describe and interpret the reaction behavior in pultrusion. It can be easily observed by elevated temperatures in the die, particularly for highly exothermic thermoset matrices like vinyl ester, epoxy, and polyurethane. However, this effect is not as pronounced in reactive thermoplastics. The exothermic reactions contribute to a reduction in power consumption of the heating plates within the different heating zones, each with its individual temperature. Analyzing the power consumption of the individual heating zones across different process parameter settings allows to determine the position of the gel zone. This information is foundational for pultrusion process optimization, as it allows for more efficient utilization of the die length, ultimately increasing the pull speeds and enabling higher production rates. In this study, a comparative analysis of the power consumption across the heating zones was performed. To validate the findings obtained from the power measurements, thermocouples were drawn through the die at the same process parameters to accurately measure the temperature evolution within the pultruded profile throughout the die length.

Introduction and State of the Art

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

Motivation. All continuous fiber reinforced plastics (FRPs), typically glass- or carbon-fiber reinforced thermosets, offer several advantages as compared to conventional metallic materials in use due to their superior mechanical performance in combination with a low specific weight in diverse sectors like transportation, consumer goods and others. One method for producing highly filled FRPs is the pultrusion process. The highly filled pultruded profiles with fiber volume content (FVC) up to >70% can be used in many ways. Cut to the required length, they can already be commissioned as final components (e.g., tent poles) or as local reinforcements in larger structures to specifically improve their mechanical properties.

In the field of matrix systems in pultrusion, unsaturated polyester resins (UP) and vinyl ester resins (VE) make up the largest share with low price and easy processability in open impregnation baths. VE resins are used instead of UP resins when higher mechanical properties and chemical resistance are required. Epoxy resins (EP), primarily EP anhydride resins, have also been used for many decades and offer high mechanical properties due to the strong fiber-matrix interface as well as good chemical and heat resistance. Polyurethanes (PUR) represent the last major matrix group. Featuring a short processing time, they can only be processed with injection chambers and offer particularly good impact strength and mechanical properties [ 1,2 ].

With today's increasing demands on the functionality of materials and components also in subsequent processes, thermoplastics are becoming increasingly important as a matrix material. Also, in high-performance continuously FRPs, due to the possibility of functionalizing them by means of forming, welding or overmolding. Another major advantage is the considerably simpler recycling by
chemical or mechanical processes [3]. Although pultrusion with thermoplastic matrices has been the subject of research since the 1980s, pultruded thermoplastic profiles have not been mass-produced as of now [4].

Commonly employed processing routes for thermoplastic profiles can be broadly categorized as non-reactive and reactive processing. In non-reactive processing, already fully polymerized thermoplastics are processed, whereas in reactive processing, polymerization takes place in the pultrusion die, i.e. "in-situ". The reactive processing of the monomer ε-caprolactam which anionically polymerizes to polyamide 6 (aPA6) (so-called "in-situ pultrusion") enables a high fiber content and excellent mechanical properties at competitive raw material costs. Due to the extremely low viscosity of 5mPa* s to 10mPa* s [5] and the adjustable reactivity by varying activator and catalyst concentrations, efficient impregnation of FVCs of >70% can be achieved even at pull speeds up to vpull =3 m/min.

While the in-situ pultrusion process was developed for industrial application within the last few years [6,7], process optimization is still ongoing to increase productivity and profile quality. During process development, one novel method was found to be promising for optimization of both, productivity and profile quality, at the same time with no direct intervention in the process, which is critical to process stability in pultrusion.

When using reactive matrix systems based on thermosets or thermoplastics, the polymerization takes place while fibers and matrix are being pulled continuously through the die. The state of the matrix as it passes through the die can be divided into three main states: initially liquid, then gel-like and solid after polymerization is complete.

The polymerization of the liquid matrix is initiated by external energy input. Usually, the die is equipped with external heating plates or heating cartridges within the die, separated into several individually adjustable heating zones (HZ). Depending on reaction mechanisms and specific requirements of the matrix system formulation, profile cross section and various other parameters, the temperatures of each individual HZ are set to desired values. After initiation of the polymerization, essentially taking place in the front part of the die, an increase in polymerization rate occurs in the main polymerization zone, mostly referred to as gel zone. In this gel zone, in addition to the external energy introduced via the heating zones, an often even larger proportion of energy is generated by the exothermic energy released during the polymerization reaction.

Connolly at al. reported for PUR resins in closed injection pultrusion with three HZs that in steady state, zone 2 of 3 is not heated due to the heat generated by the exothermic reaction of the resin curing [2]. Similar, little more pronounced results are reported by Wilhelm [8] who observed an approx. 20∘C higher temperature compared to the set value in the main reaction zone located at HZs 3 and 4 of 6 for an EP anhydride system. With ortophtalic polyester, similar behavior was observed by Tucci et. al, whereby the temperature in zone 3 of 3 in the die was about 8∘C higher due to the exothermic curing of the polyester resin [9]. Same observations were made by Li et al. using VE resin [10] and Cho et al. using ε-caprolactam [11].

The position of the peak exothermy varies over all above-mentioned references mainly between mid and end within the die length. The height of the peak strongly depends on the matrix system used due to different exothermic properties as well as the profile cross sections, FVC and temperature sensor positions. The ideal position of the main polymerization zone depends on the material system and varies slightly between them. Therefore, no standardized optimal position can be defined. However, since all reactive matrices show this significant exothermy, this effect can be used to analyze and optimize the process in terms of productivity and profile quality, using the relative power consumption in form of the mean control variable CI,mean  of the individual HZs as parameter.

Procedure. In this study, a pultrusion die equipped with six distinct HZs was used. The CI,mean  of the power consumption for each HZ was measured to gain insight into the thermal dynamics of the process. Trials were conducted with differing parameter settings to observe their effects on energy consumption. A comparative analysis of the power consumption across the HZs was performed to identify trends and correlations. To validate the findings, thermocouples were drawn through the die
at the same process parameters to accurately measure the temperature evolution within the pultruded profile throughout the entire processing length.

Materials, Processing and Methods

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

Materials. The study was conducted using StarRov® 2400−886 glass fibers with 2400 tex recommended by Johns Manville for reactive thermoplastic processing. Both reactive components sodium-caprolactamate (Bruggolen C10) as catalyst and hexamethylene-1,6-dicarbamoylcaprolactam (Bruggolen C20P) as activator as well as AP-Nylon caprolactam flakes were from L. Brüggemann GmbH & Co. KG, Heilbronn, Germany.

Processing. A schematic illustration of the pultrusion line used for the investigations is shown in Fig. 1. The glass fibers are pulled through the process line by the caterpillar puller unit of the Nanjing LYT pultrusion line with vpull  between vpull =0.1 m/min−3.0 m/min. After the fiber rack the fibers are passing through an in-line convection oven of three meters length, equipped with an electrical heater type Leister LHS 61L SYSTEM combined with a medium pressure blower offering an air flow rate of 13.5 m3/min. Upfront of the one meter long, hard chrome plated, state-of-the-art pultrusion die with a 30×4 mm2 cross section, an injection and impregnation chamber (ii-box) with a tapper angle of 2×0.8∘ was mounted.

[picture]

Fig. 1. Schematic drawing of the used pultrusion line setup.

Fig. 1. Schematic drawing of the used pultrusion line setup.

Both on the upper and the lower side of the ii-box and the main die, twelve electric heating plates divided into six HZ were installed as shown in Fig. 2. For temperature control each HZ was equipped with a thermocouple mounted from the side of the die near the cavity. With the precise control of the pultrusion system an accuracy of approx. ±0.3∘C was achieved. Heating zone 1 is placed on the iibox, while HZs 2-6 heat the main die. Target temperatures for all HZs are summarized in Table 1.

Table 1. Target temperatures for HZ 1− HZ 6 of the die temperature profile. Heating zone 1 heats the injection chamber, while heating zones 2-6 heat the main die.

Die temperature profile

ii- box

The ii-box is interchangeable. This requires more external mass at the connection point to the main die serving as a potential heat sink. The clamping devices fixing the die on the machine table, also possible heatsinks, influence the heating between HZ 2 and HZ 3 as well as at the die exit at HZ 6 .

[picture]

Fig. 2. a) Schematic drawing of the pultrusion die setup with pull direction indicated b) photo of the die on the shop floor.

Fig. 2. a) Schematic drawing of the pultrusion die setup with pull direction indicated b) photo of the die on the shop floor.

The parameter settings for this study are based on findings of a comprehensive statistical investigation of Wilhelm [12]. Setting "O1" aims for high profile quality, whereas "O3" focuses on high vpull , see Table 2. The main differences between the two parameter settings are vpull  and the concentration of activator (act.) and catalyst. For the simplification only the activator content is given, the catalyst content corresponds to twice the weight of the activator. With the selected process conditions, the concentration of activator and catalyst only has an influence on the reaction rate, but not on the exothermic energy released. This is due to the special nature of the anionic polymerization of ε-caprolactam and has been reported several times [13, 14]. However, the biggest difference between the two parameter settings is vpull , which is nearly five times higher for O3 than for O1.

The pulling speed determines the time available for preheating and drying the fibers as well as their temperature evolution between exiting the oven and entering the injection chamber. Moreover, impregnation and the solidification of the matrix, as well as the available time for polymerization of the matrix within the main die is directly dependent on vpull .

Low vpull  reduces economic efficiency. Excessive vpull  can lead to an incompletely polymerized matrix, reduced mechanical properties or defects at the surface or in the profile cross-section (pores, cracks) [15, 16]. The settings of O1 and O3 were calculated by the statistical model of [12] aiming for the best profile quality with O 1 and giving the highest possible vpull  for a quality fulfilling the requirements of DIN EN 13706-2 (E23 profiles) for O3.

Table 2. Processing parameters settings for O 1 , high profile quality and O 3 , high vpull .

Trial | Tdry in °C | vpull in m/min | FVC in % | Act. in wt.-% | Impregnation pressure in bar | Pull force in kN | rel. dev. Pull force in %
O1 | 202 | 0.50 | 69.5 | 3.00 | 3.14 | 2.24 | 2.80
O3 | 208 | 2.59 | 68.7 | 3.39 | 2.52 | 4.31 | 2.62

Method and method development. The proposed method aims for the definition of the gel zone position within the pultrusion die or rather the location of peak exothermy by utilizing the power consumption measurement of the HZs.

Reference measurements with dry fibers ("dF") are conducted to achieve a dry steady state with a mass fraction of approx. 0,83 corresponding to the FVC of O 1 and O 3 without chemical reaction of the matrix for both parameter settings. First, dry fibers are pulled through the setup at nominal speed until a steady state of the temperatures has been reached. With a frequency of 1 Hz , the power consumption data is recorded for 15 min . Based on the data, the mean control variable CI,mean  of the individual HZs is calculated. The matrix injection is started under constant dry conditions and further data is recorded once a steady state has again been reached. The measurement with injection of reactive matrix ("rM") is carried out for the whole trial duration of 120 min and allows to calculate the difference of CI,mean  from dF and rM .

Owing to the mass distribution between the die and the clamping unit (more mass in the connection area of ii-box and main die), the CI,mean  of the heating plate control is used for evaluation. In addition, only the relative difference between the reference dF measurement and the rM actual trial is evaluated. The results are validated using the conventional method of pulling through thermocouples that were braided onto fiber rovings in the core of the profile.

In this way, the position of the peak exotherm or rather the position of the gel zone can be determined without invasive sensors. In combination with a correlation of total polymerization conversion and exotherm temperature evolution, this easy-to-implement method could be used to optimize productivity. The relative evaluation also may enable conclusions about batch differences in the matrix or errors in the matrix formulation resulting in an altered reactivity when identical parameters are used.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

The evaluation of processing parameters in relation to the die heating control variables is discussed first. The course of the measured profile temperature over the entire process length follows.

Fig. 3 shows the average control variables CI,mean  of O 1 and O 3 by HZ 1 to HZ 6. The control variable is a measure of the intensity with which the respective heating zone must be supplied to reach or maintain the defined temperatures, values can be between 0% and 100%. Green columns show CI,mean  of the two trials over a period of 15 minutes without injection of reactive matrix, i.e., only dry fibers are pulled through the die at the corresponding target speed. The grey columns indicate CI,mean  with injection of reactive matrix over the entire remaining trial duration of 120 minutes for both runs.

Running only dF , the influence of the slightly higher drying temperature Tdry  and the significantly higher vpull  of O3 becomes apparent. The pre-heated fibers introduce the entire amount of energy required to reach the set temperature of HZ 1 and HZ 2 resulting in CI,mean =0%. For O1 the heating needs to actively input energy to maintain the temperature as the fibers cool down much stronger in the gap between oven and die at 0.5 m/min. This proves that the shorter time in the gap between oven and the die causes less cooling, while significantly more fibers with their associated thermal inertia are pulled through during the same amount of time.

[picture]

Fig. 3. Comparison of the mean HZ control variables CI, mean  in the two runs O 1 and O 3 with dry fiber and reactive matrix.

Fig. 3. Comparison of the mean HZ control variables C I , mean in the two runs O 1 and O 3 with dry fiber and reactive matrix.

The difference in CI, mean =9.7% is statistically significant ( t -test at 0.05 level) for nearly all HZs at both parameter sets, however without clear trend. Averaging across all HZs, CI,mean =9.3% for O1 and 110∘C for O3. This is not statistically significant (t-test at 0.05 level). The dry fibers draw slightly less energy from the die in O3, as they enter the tool hotter due to the higher speed and thereby shorter cooling time after the oven.

In both runs O 1 and O 3 , the matrix is injected into the ii-box at HZ1(THZ=90∘C) in CI,mean . During O1, CI,mean  of HZ 3 is only slightly increased by the reactive matrix in contrast to O3, as more mass absorbs more energy and needs to be heated accordingly. For O1 in HZ 4, 33% with matrix is CI,mean  smaller than while processing dry fibers only. This is a clear indication for an exothermic reaction. Heating zones HZ 5 and HZ 6 show almost identical power consumption with and without the matrix. From this result, it can be deduced that the maximum rate of the exothermic polymerization reaction mainly takes place around HZ 4 and subsides in HZ 5 and HZ 6, where it is still slightly supported by external energy input. In the case of O3, significantly more energy is introduced in HZ 3 through HZ 5 running with reactive matrix. Only in HZ 6 the exotherm of the polymerization is visible due to a reduced Tp,m. The total heating of the last HZ is significantly stronger during O3 than during O1, although initially no energy input was necessary in the first heating zones. Clearly the mass of matrix that needs to be additionally polymerized predominates.

Fig. 4 shows the measured profile temperature curves Tdie  of O1 (green) and O3 (grey) by thermocouples attached to rovings during processing of the reactive matrix relative to their location to the end of the ii-box. Target temperatures, as set, of the die Tdry  (red line) and the drying oven pm=−3730 mm (dashed lines) are shown for both settings O1 and O3. The black, dashed vertical lines in the drying oven visualize fiber guide plates with ceramic eyelets through which the rovings are guided.

Even before entering the drying oven at the position relative to the main tool 193.4∘C, the rovings are heated by the hot air outflow of the oven. In the oven itself, a step-like temperature increase is observed at the fiber guiding plates, as these influence the air flow pattern, which decreases towards the oven entrance. The fibers reach a maximum temperature of 186.3∘C at O 1 at the level of the hot air inlet. At O3, a maximum temperature of pm=−1430 mm is measured slightly offset from the hot air inlet located 700 mm before the oven outlet, i.e., at vpull . Decreases and increases in temperature before and after the eyelets are particularly noticeable at O 1 with low 178.6∘C. Between
the outlet of the drying oven and the inlet of the die, the fibers are exposed to the ambient air for a distance of 430 mm resulting in 52 s for O1 and 10 s for O3.

[picture]

Fig. 4. Temperature vpull  processing reactive matrix for O 1 and O 3 over relative position 156.3∘C.

Fig. 4. Temperature v pull processing reactive matrix for O 1 and O 3 over relative position 156.3 ∘ C .

In this exposed distance, the fibers at O 3 maintain a high temperature of 22∘C until they enter the die. Due to the five times slower 40∘C, the fibers from O1 only have a temperature of 193.4∘C when entering the die, which is about pm=−300 mm less compared to O 3 and dropping off almost 110∘C from their peak temperature in the oven ( THZ1=90∘C ).

In both trials, the temperature drops sharply upon entering the mold at O1,Tp,m. This can be explained by the quasi-static matrix flow front at the ii-box inlet. As the continuous matrix injection is controlled in a manner that the ii-box is always fully filled, the conductive contact of the thermocouple with the 110.4∘C hot matrix in HZ 1 with 110∘C leads to this sharp drop.

After the initial contact in 100∘C increases to 17% in the middle of the ii-box and then drops again. The brief increase is caused by the matrix, which is injected at 83%. The drop is due to the mold temperature of HZ 2 at Tdie  (solid red line) which is not compensated by the matrix because of its small amount with just 150∘C by mass compared to the fiber mass content of Tp,m. pm=500 mm of HZ 3 is set to the optimum polymerization temperature of approximately Tp,m=187.6∘C [17, 18]. Polymerization is initiated and reaches the maximum polymerization rate within a short time, as can be seen from the overshoot of CI,mean  in HZ 4 at around Tdie . The exothermic reaction further heats the profile core, peaking at 140.1∘C exiting the mold. The overshoot in HZ 4 correlates with the results of vpull  in Fig. 3, locating the position of the maximum polymerization rate in HZ 4.

Furthermore, the 173.1∘C profile appears to be suitable for keeping the polymerization reaction slow initially in HZ 1 and HZ 2 for reliable impregnation and processing, accelerating polymerization significantly from HZ 3 onwards, and continuing to support it until the profile exits the mold.

After entering the tool, O3 generally follows a similar curve to O1, with a temperature rise shortly after entering the ii-box at the injection point to 140.1∘C, followed by a temperature drop to approximately the middle of HZ 3. From HZ 3 to the end of the mold, the temperature curve in the profile lags behind the set temperatures of the mold due to the high 110∘C. About 140 mm after the mold exit, the maximum profile temperature reached vpull . In the ii-box, instead of rising to vpull , a temperature drop to approximately CI,mean =0 (matrix temperature during injection) would be expected for O3. However, it is assumed that this is caused by a deviation in the flow pattern of the matrix in the ii-box due to much higher CI,mean . The thermocouple is attached to a roving in the center of the saturated fiber package and measures the temperature in the "core" of the profile. This
temperature is higher, because the fibers lost less energy within the ambient air gab due to the higher vpull . This also correlates with the <1% of HZ 1 and HZ 2 in O3. The temperature peak after HZ 6 also matches with the results of CI,mean  from O3, which show that the exothermic peak only becomes visible from HZ 6 onwards. Since the peak exotherm is behind the tool, it could be assumed that 0.5 m/min of O 3 was selected too high. However, the total conversion is sufficiently high (residual monomer content 2.59 m/min ), so that the minimum requirements for the profiles are met. The surface quality of the profiles is lower than that of O 1 , which is not relevant for certain applications. As a result, the parameter setting O3 can also be used to produce industrially viable profiles with significantly higher productivity.

Summary

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

It was shown that the proposed method by using the relative deviation of the average control variable ε from the heating power consumption, is suitable for determining the position of the main polymerization zone within the die. By pulling through thermocouples connected to rovings to measure the temperature evolution and exotherm heat release, the results were validated successfully. With reference measurements of only dry fibers being processed, heat sinks due to die design or die clamping become negligible.

In O 1 , polymerization mainly takes place in the middle of the die in the area of HZ 4 and is already very advanced or complete at the end of the die. In O3, polymerization is only completed in the ambient atmosphere after the die, which explains the higher residual monomer content and the observed rougher surface of the manufactured profiles. With both parameter configurations, profiles can be produced in a robust process over the 120 minutes considered. The pulling speed of ε for O1 and J for O3 represents a wide range in terms of the economic efficiency of the process and roughly indicates the current limits for the process and material parameters considered.

If the exothermic peak is correlated with the degree of conversion of the polymerization reaction for the individual matrix system, this method offers the potential for efficient process optimization in terms of productivity and the use for continuous quality monitoring. For optimization purposes, vpull can be increased for most matrix systems until the exothermic peak is in the range of HZ 5 to HZ 6, in addition to considering several other influencing variables and interactions. This may allow the available die length to be used more efficiently. For quality control, continuous monitoring of the power consumption can be used, for example, to detect differences in the raw material batches or to reveal errors in the matrix formulation if these result in a deviating reactivity.

Key Findings

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

The newly proposed method proves to be effective for determining the gel zone in the pultrusion process and can be used for all reactive matrix systems.

A clear correlation exists between power consumption and the peak exotherm measured by the thermocouples pulled through the die, indicating the reliability of this method.

This non-invasive and easy-to-implement method offers the potential to be used as process optimization tool as well as for continuous quality control

Acknowledgements

The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

The research documented in this manuscript was funded by the Ministry of Economics, Labor and Tourism Baden-Württemberg ("CaproPULL" Grant No ibwip-BW1_0025). Support from Johns Manville Europe GmbH in the form of trial materials is gratefully acknowledged.

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The original version of this paper is available on https://www.scientific.net/DDF.451.147.pdf

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Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 451, pp 157-167

doi: 10.4028/p-rD7QdB

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

Submitted:
2026-01-30

Revised:
2026-02-25

Accepted:
2026-03-01

Online:
2026-04-17

Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

The original version of this paper is available on https://www.scientific.net/DDF.451.157.pdf

Giulia Zaniboni 1,a*, Vito Basile 2,b, Riccardo Pelaccia 1,c, Rossella Surace 2,d, Keltoum Oubellaouch 3,e, Francesco Modica 2,f, Leonardo Orazi 1,3, g, Giovanna Rotella 4,h, Luigino Filice 5,i, Irene Fassi 6,j

1 University of Modena and Reggio Emilia, DISMI, Via Amendola 2, 42122, Reggio Emilia, Italy

2 CNR-STIIMA, National Research Council, Via P. Lembo 38 F, 70124 Bari, Italy

3 University of Modena and Reggio Emilia, EN&TECH, Piazzale Europa 1, 42124, Reggio Emilia, Italy

4 University LUM G. Degennaro, Dept. of Engineering, S.S. 100 Km 18, Casamassima, 70010, Italy

5 University of Calabria, DIMEG, cube 45C, Ponte P.Bucci, 87036 Rende, Italy

6 CNR-STIIMA, National Research Council, Via A. Corti 12, 70124 Bari, Italy

agiulia.zaniboni@unimore.it, b  vito.basile@stiima.cnr.it, criccardo.pelaccia@unimore.it,

d rossella.surace@stiima.cnr.it, e keltoum.oubellaouch@unimore.it, f francesco.modica@stiima.cnr.it,

gleonardo.orazi@unimore.it, hrotella@lum.it, luigino.filice@unical.it, jirene.fassi@stiima.cnr.it 

Keywords: thermal management, hybrid moulds, injection moulding, additive manufacturing.

Abstract

Efficient thermal management is a key factor in improving the sustainability and productivity of injection moulding processes, particularly at the micro-scale where thermal transients strongly affect part quality and cycle stability. This work investigates the thermal behaviour of hybrid moulds composed of polymeric support plates manufactured in Precision Resin V01 and stainlesssteel inserts manufactured by additive manufacturing. An experimental campaign was carried out on a micro-injection moulding machine to characterize the intrinsic thermal response of the mould under uncooled conditions. Temperatures were monitored through embedded thermocouples and used to develop and calibrate a three-dimensional transient numerical model in COMSOL Multiphysics. Particular attention was devoted to the identification and calibration of heat transfer coefficients at the injection and extraction interfaces, which were found to play a dominant role in governing insert temperature evolution. The calibrated model accurately reproduces the experimental thermal transients, with deviations below 10%, demonstrating its reliability as a predictive tool for analysing mould thermal behaviour and supporting early-stage design and process optimization. The results highlight the advantages of hybrid architectures in promoting thermal stability and provide a robust methodology for modelling heat exchange in unconventional mould configurations.

Introduction

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Injection moulding is a widely adopted manufacturing process to produce high-volume plastic components, owing to its versatility in processing a broad range of materials and its capability to produce complex geometries with high precision [1]. Given the dominant role of injection moulding in the plastics industry, its energy performance has become a key factor in sustainability assessments [2]. Among the different stages of the process, thermal energy management plays a critical role, as it directly influences process efficiency, part quality, and overall cost-effectiveness. In particular, cooling time is one of the most influential parameters affecting cycle time and energy consumption; its optimization can therefore result in significant energy savings [3]. Therefore, improving thermal management within the mould represents a crucial strategy for reducing the environmental footprint of injection moulding processes [4]. The thermal behaviour of the mould is strongly affected by the thermal conductivity of the materials used in its construction. Traditionally, moulds and inserts are manufactured from high-strength steels because of their excellent mechanical resistance and favourable thermal properties. However, steel moulds are associated with high material and
manufacturing costs, as well as long production and maintenance lead times [5]. Conversely, in application fields where extreme mechanical loads are not required, the use of polymeric materials for mould fabrication can significantly reduce both cost and weight. Moreover, the inherently low thermal conductivity of polymers can be exploited to thermally insulate the mould cavities, promoting a more stable thermal field during processing. Nevertheless, previous studies investigating moulds entirely manufactured from polymeric materials have reported limited service life and reduced part quality, highlighting the mechanical limitations of fully polymeric mould configurations [6-8].

Building upon these findings, a hybrid mould concept can be proposed, combining steel inserts with polymeric or composite mould base components, such as support plates. This hybrid architecture mitigates mechanical weaknesses by retaining steel in critical regions while exploiting the advantages of polymers and composites, including lightweight design and thermal insulation capabilities. Such an approach enables improved thermal stability without compromising structural integrity or mould durability. In parallel, the rapid development of additive manufacturing (AM) technologies has expanded both material and geometric design possibilities for mould systems, enabling innovative architectures and enhanced thermal control strategies [9]. Beyond material flexibility, AM allows the fabrication of complex geometries that are not achievable with conventional manufacturing techniques, such as conformal cooling channels that closely follow the geometry of the moulded cavity. These channels enable localized and more uniform heat removal, leading to improved temperature control and reduced cycle times [ 10,11 ]. Current research frequently investigates mould inserts or plates produced via AM using polymeric or composite materials, while maintaining conventional steel moulds to ensure mechanical robustness [6,7]. Retaining a steel mould core with AM-fabricated cavities therefore allows the benefits of conformal cooling to be realized without the limitations associated with fully polymeric moulds.

At the same time, the introduction of polymeric or composite mould base components significantly alters the thermal behaviour of the system. Acting as thermal insulators rather than heat conductors, these components promote faster temperature stabilization of the steel inserts and improved robustness during extended mould-opening intervals. Furthermore, since the polymeric elements do not directly contain the mould cavities, mechanical stresses are reduced, overcoming the durability limitations of fully polymeric moulds and making the hybrid approach competitive also in terms of service life. The use of lightweight polymeric components additionally reduces the mechanical energy required for mould movement during production cycles and mould-change operations. From a broader perspective, this innovative mould design contributes to the development of a more sustainable injection moulding process.

Despite these advantages, precise thermal control remains essential to prevent the mould from drifting into thermal instability. While the low thermal conductivity of polymeric mould components can be advantageous for heat accumulation during the injection phase, it may hinder the recovery of thermal stability during cooling.

In the specific case of micro-injection moulding, thermal management becomes even more critical because of the small characteristic dimensions of the cavity and the resulting high surface-to-volume ratio of the moulded parts. Compared to conventional injection moulding, heat is extracted much more rapidly through the mould walls, promoting the early formation of a frozen layer that restricts flow and hinders the complete replication of high-aspect-ratio micro-features. Consequently, mould temperature during filling has been identified as one of the most influential parameters governing cavity filling, replication accuracy and part quality. Several studies have therefore proposed dynamic or rapid thermal control strategies, such as variotherm systems or rapid surface heating approaches, to locally increase mould temperature during the filling stage and delay premature solidification [1215]. More generally, micro-injection moulding cannot be regarded as a simple downscaling of the conventional process, since the reduced dimensions amplify heat-transfer effects and make the process strongly dependent on boundary conditions at the polymer-mould interface [16]. In this context, an accurate description and calibration of the heat transfer coefficients at the injection and extraction sides becomes essential for the reliable prediction of mould thermal transients and for the correct design of thermally optimized tooling solutions.

Within this framework, the present research aims to evaluate a novel hybrid mould design employing unconventional materials to optimize thermal energy utilization in micro-injection moulding. An experimental campaign was conducted to characterize the intrinsic thermal behaviour of the mould under uncooled operating conditions. A transient finite-element model was developed in COMSOL Multiphysics as it is a well-established tool for simulating complex multiphysics phenomena and heat transfer in injection moulding processes [17]. The numerical model was then calibrated using experimental measurements.

Particular emphasis was placed on the identification of boundary conditions and on the calibration of heat transfer coefficients at the interfaces with the injection and extraction systems, which significantly influence the thermal response of small-scale inserts. The validated numerical model is proposed as a reliable tool to support mould design and to predict thermal stability, reducing the need for time-consuming trial-and-error experimental procedures.

Experimental Setup

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Design and manufacturing of the hybrid mould.

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The mould for micro-injection moulding was designed according to previous investigations [18]. The mould has a multi-material structure and was manufactured with Additive Manufacturing (AM) technologies. The design of the mould inserts is optimized in terms of material, mechanical and thermal performance, with conformal cooling realized with channels having a 3D-evolution all around the mould cavity. They are made of bulk stainless steel to resist to high injection and holding pressures and to promote the heat extraction from the cavity [18]. Support plates should guarantee mechanical performance and thermal insulation of the mould core inserts. The former objectives are the mechanical properties, such as stiffness and toughness, that are required to obtain efficient guiding and couplings between the injection (fixed) and ejection (mobile) sides of the mould while closing/opening phases and the mating on the parting surface. This objective is achieved selecting suitable materials, using high accuracy manufacturing technologies and guiding/coupling components, such as columns and bushes. The latter requirement is thermal insulation, which is obtained by using polymeric materials. Furthermore, the design of the support plates was topologically optimized with mixed bulk-lattice structures [19]. The outcomes of the design task are 3D solid models developed with the 3D CAD Solidworks release 2023 SP 5.0. The mould microcavity (Figure 1) was conceived with a complex 3D shape having curved thin walls and variable thicknesses, thus requiring a 3D evolution of conformal cooling channels and exploiting all potentialities of AM technologies.

[picture]

Fig. 1. Drawing (a) and 3D views (b) of the moulding part.

Fig. 1. Drawing (a) and 3D views (b) of the moulding part.

The mould inserts were fabricated using a Markforged MetalX, which implements a Metal-Extrusion (MEX) AM technology, and a 17−4PH stainless steel. Holes, mating and coupling surfaces were finished by CNC milling on a CMX1100V DMG Mori machine, while the cavity was finished using a Micro-Electrical Discharge Machine ( μ-EDM) Sarix SX200 machine. The support plates were realized by stereolithography (SLA) using a Formlabs Form4 machine and a photopolymer resin

Formlabs Precision Model V01 (FLPMBE01). Parts were printed on the build platform setting a layer thickness of 25μ m. After processing, parts were washed for 10 minutes with Tripropylene Glycol Monomethyl Ether (TPM) solvent with a Formlabs Wash 2nd -Gen machine and UV-cured for 35 minutes at 35∘C with a Formlabs Cure V1 machine. Mould inserts design is presented in Figure 2.

[picture]

Fig. 2. Drawing of the moulding part. Injection side (a) ejection side (b).

Fig. 2. Drawing of the moulding part. Injection side (a) ejection side (b).

Experimental setup of injection moulding process without cooling.

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To perform experimental tests, a DesmaTec Formica Plast 1 K injection moulding machine was used. The machine can have a maximum injected volume of 150 mm3, a maximum injection pressure of 300 MPa , and a maximum injection rate of 3.5 cm3/s. The injection moulding material was a Polyoxymethylene (POM) BASF Ultraform N2320 003. To ensure a correct evaluation of polymer effect on insert temperatures, during the cooling step no coolant circulation was adopted. Therefore, the cooling was obtained by heat transmission with the mould kept below the glass transition temperature, but defined by the injection moulding thermal transient starting from the ambient temperature of about 15∘C.

The thermal monitoring system consisted of four K-type thermocouples connected to MAX6675 digital modules interfaced with an Arduino Uno platform. Thermocouples T1 and T4 were embedded within the ejection and injection inserts, respectively, through precision holes positioned in close proximity to the mould cavity (Figure 3). Thermocouples T2 and T3 were mounted on the external surfaces of the support plates on the injection and ejection sides, respectively (Figure 3). This monitoring configuration enabled a detailed analysis of the thermal transients over the 80 -cycle experimental campaign (Figure 4). Notably, no active cooling was applied, allowing the investigation of the intrinsic thermal behaviour of the polymer moulds. The transient thermal evolution began with the tooling set at room temperature ( 15∘C ). Two repetitions of the same experimental trial were conducted to evaluate the repeatability of the thermal response. The process parameters adopted for the experimental tests are reported in Table 1.

[picture]

Fig. 3. Thermocouple locations on plates and inserts.

Fig. 3. Thermocouple locations on plates and inserts.

[picture]

Fig. 4. Experimental configuration for testing the final mould setup.

Fig. 4. Experimental configuration for testing the final mould setup.

Table 1. Injection moulding process parameters in experimental test.

Process parameters/Event | Symbol | Units | Value/Detail
Melt Temperature | Tmelt | °C | 230
Initial mould temperature | Tmould | °C | 15
Filling time | tfill | s | 0,25
Holding time | thold | s | 4
Cooling time (no coolant) | tcool | s | 4
Mould open/close time | topen | s | 3
Cycle time | tcycle | s | 11,25
Total Number of cycles | n | s | 80

Experimental setup for thermal boundary condition calibration.

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To calibrate the heat transfer coefficients (HTCs) at the injection and extraction interfaces, a preliminary experimental test was conducted under closed-mould conditions, with the injector positioned in contact with the fixed insert but without polymer injection. This configuration allowed the thermal interaction between the machine units and the mould to be isolated from the effects of the molten polymer. The mould assembly was subjected to a controlled heating phase lasting approximately 500 s , during which the temperature evolution of the inserts was continuously monitored using thermocouples embedded in the fixed and movable inserts (T4 and T1, respectively). The injector temperature was set to 230∘C, corresponding to the melt temperature adopted during the subsequent POM moulding trials. This approach enabled a targeted characterization of the heating contribution provided by the hot injector in contact with the fixed side, as well as the thermal inertia of the extraction unit, which tends to maintain the movable side at lower temperatures. In microinjection moulding, thermal transients are strongly influenced by heat exchange with the surrounding machine components, owing to the reduced mass and limited thermal inertia of the inserts. Consequently, an accurate calibration of the HTCs at these interfaces is essential for correctly reproducing the measured temperature evolution and for ensuring the predictive capability of the numerical model.

Numerical Model of the Process

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In the numerical model, the original geometry was simplified by modelling the injection and extraction units as equivalent plates with comparable heat exchange characteristics (Figure 5), while auxiliary features such as bolt holes were removed. These geometry simplifications reduced meshing complexity and significantly decreased computational costs without compromising model accuracy. The simulations employed the Heat Transfer in Solids module to solve transient heat conduction within the mould assembly, including convective heat losses at the external boundaries.

The numerical analysis was performed using COMSOL Multiphysics 6.1, adopting a multiphysics modelling approach. A high-fidelity three-dimensional mesh comprising 482785 tetrahedral elements was generated, with a size-dependent distribution. In particular, the cavity and insert regions were discretized using a maximum element size of 1 mm to accurately capture steep thermal gradients, whereas support plates and secondary components were meshed with a maximum element size of 5 mm .

[picture]

Fig. 5. (a) 3D model of the real mould block with polymer plates, (b) COMSOL Multiphysics model of polymer plates with simplified clamping plates.

Fig. 5. (a) 3D model of the real mould block with polymer plates, (b) COMSOL Multiphysics model of polymer plates with simplified clamping plates.

The injection phase was simplified by applying a time-dependent heat source on the cavity walls, representing the thermal energy input from the molten POM at 230∘C. The temporal sequence of the process was controlled using the Events Interface Module, reproducing the experimental cycle, including filling, holding, cooling without water, and mould opening and closing phases.

Table 2 summarizes the process parameters adopted in the numerical simulations, while Table 3 reports the thermal properties of the materials implemented in the model.

As indicated in Table 2, in addition to natural heat exchange with the surrounding air, thermal interactions with the injector and extractor blocks were also accounted for. The corresponding heat transfer coefficients were identified through a dedicated calibration procedure based on the preliminary experiments performed with the mould closed and without polymer injection, as described above. The selection of the calibrated values reported in Table 2 is discussed in detail in the section Calibration of thermal boundary conditions.

Table 2. Process parameters and boundary conditions set within the numerical model.

Process parameters | Units | Value
Melt temperature | °C | 230
Filling time | s | 0.25
Holding time | s | 4
Cooling time within the mould (no coolant) | s | 4
Mould open/close time | s | 3
Initial plates/inserts temperature | °C | 15
Air (ambient) temperature | °C | 15
Injector temperature | °C | 230
Extractor temperature | °C | 15
Heat transfer coefficient with air | W/(m²*K) | 15
Heat transfer coefficient with injector | W/(m²*K) | 600 (filling + holding), 50 (cooling)
Heat transfer coefficient with extractor | W/(m²*K) | Linear decrease from 3000 to 500 in 1000s

Table 3. Material properties implemented within the numerical model.

Material Properties | Units | POM | 40CrMnMo7 Stainless steel | Precision Model V01
Density | g/cm³ | 1.16 | 7.8 | 1.11
Thermal conductivity | W/(m*K) | 0.14 | 20 | 0.28
Heat capacity at constant pressure | J/(kg*K) | f(T), 2137 at 230 °C | 500 | 2160

Experimental-Numerical Comparison for Model Validation

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Calibration of thermal boundary conditions.

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For the calibration of the heat transfer coefficients, several numerical simulations were carried out, starting from literature values. This section reports the most representative results used to justify the parameter selection summarized in Table 2. The boundary temperatures were set to 230∘C on the injection side, corresponding to the melt temperature adopted during the moulding trials, and to 15 ∘C on the extraction side, consistently with the initial cold-mould condition. Figure 6 presents the numerical-experimental comparison of the thermal transient obtained during the closed-mould test. Numerical results are shown for three HTC levels at the injection side ( 500,600 , and 750 W/m2 K ) and two levels at the extraction side ( 3000 and 500 W/m2 K ), resulting in six simulated configurations.

Considering the fixed insert (thermocouple T4), all simulations exhibit a higher initial thermal gradient than the experimental measurements, leading to a systematic overestimation of the temperature during the first 100 s . Subsequently, while the experimental curve continues to increase, the numerical predictions rapidly approach a quasi-steady regime, with a limited temperature rise (approximately 5−10∘C over 350 s ). As a consequence, at the end of the test the measured temperature exceeds the numerical predictions, with discrepancies depending on the selected HTC combination. The smallest deviation (below 2%) is obtained for an injection-side HTC of 750 W/m2 K and an extraction-side HTC of 500 W/m2 K, whereas the largest error (about 20%) occurs for the 5003000 W/m2 K configuration.

Sensitivity analysis indicates that the injection-side boundary condition has a dominant influence on the temperature evolution at T4. For a fixed injection-side HTC, variations of the extraction-side HTC produce only minor changes. This behaviour is consistent with the large temperature difference imposed at the two interfaces ( 230∘C versus 15∘C ), which enhances the thermal driving force at the injection side.

A similar trend is observed at T1 (movable insert). Higher injection-side HTC values produce steeper initial gradients compared to the experimental data. However, while the measured temperature progressively increases due to the gradual heating of the extraction assembly, the numerical model rapidly reaches a steady condition, since constant HTC and boundary temperatures are imposed. Also in this case, the lowest final error (below 2% ) is obtained for the 750−500 W/m2 K combination.

Based on these results, an injection-side HTC of 600 W/m2 K was selected as a compromise solution, ensuring deviations within approximately 10% over most of the transient. Although the 750 W/m2 K value minimizes the final error, it leads to larger discrepancies during the early heating stage. Furthermore, during actual moulding operations the injector is not continuously in contact with the mould, as it retracts during the cooling phases. For this reason, as reported in Table 2, the injectionside HTC is set to 600 W/m2 K during the active stages (filling and holding) and reduced to 50 W/m2 K during the passive phases. Concerning the extraction side, a time-dependent boundary condition was adopted. The HTC was assumed to decrease linearly from 3000 W/m2 K under cold-mould conditions to 500 W/m2 K, in order to limit the initial thermal gradient while progressively reducing the thermal inertia and better reproducing the gradual heating of the extraction unit.

The characteristic decay time was set to 1000 s , accounting for the intermittent injector contact and the additional cooling associated with mould opening and closing, which are expected to slow down the overall temperature rise during real processing conditions.

[picture]

Fig. 6. Experimental-numerical comparison of temperature transients measured by thermocouples during the warm-up without moulding.

Fig. 6. Experimental-numerical comparison of temperature transients measured by thermocouples during the warm-up without moulding.

Validation of the numerical model.

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The polymer moulds withstood the entire experimental campaign without exhibiting any visible damage or performance degradation, thereby confirming their mechanical reliability and structural robustness. The experimental results of the thermal field evolution recorded by the thermocouples, together with the corresponding numerical predictions, are reported in Figure 7. From the experimental data, an excellent repeatability of the measurements can be observed, as the temperature profiles obtained from the two repeated trials are nearly superimposed. This represents a significant outcome, confirming the reliability of the presented results.

A detailed analysis of the thermal transient highlights a rapid temperature increase in the fixed insert, which rises from the initial 15∘C to approximately 60∘C after 100 s of testing (corresponding to about 10 moulding cycles). Subsequently, the temperature continues to increase at a slower rate, reaching a quasi-steady condition at around 75∘C between 600 s and 900 s of operation. In contrast, both the thermal gradient and the peak temperature recorded in the movable insert are considerably lower, with a maximum value of approximately 47∘C at the end of the test. The temperature discrepancy between the fixed and movable inserts can be attributed to their respective proximity to the injection system and the ejection unit. Specifically, the injection system, which delivers the molten polymer, operates at significantly higher temperatures, whereas the extraction components are comparatively cooler. Furthermore, due to the small size of the inserts, their thermal response is strongly influenced by the thermal inertia of the surrounding press components, which may further amplify these temperature differences.

The numerical model accurately reproduces the thermal gradient trends observed experimentally in both the fixed and movable inserts. In the fixed insert, the model successfully captures both the rapid initial temperature increase and the subsequent stabilization toward a quasi-steady-state condition. Consistently with the experimental results, the numerical predictions yield a temperature of approximately 60∘C at T 4 after 100 s and about 75∘C at the end of the process. However, during the thermal evolution between 100 s and 900 s , the numerical model slightly underestimates the temperature by approximately 4−5∘C, with the maximum temperature peak occurring about 100 s later than in the experimental measurements. A similar trend is observed for the movable insert, where the maximum numerical deviation reaches approximately −7∘C.

These discrepancies are most likely attributable to the definition of the boundary conditions at the injection and ejection interfaces, which strongly affect the thermal gradients of such small-scale inserts. Nevertheless, considering the complexity of the injection moulding process and the inherent simplifications adopted in the numerical model, the overall agreement can be regarded as high and fully satisfactory for the intended purpose of using the model to identify process parameters that optimize the thermal behaviour of the mould.

Regarding the external temperatures (T2 and T3), the agreement between experimental measurements and numerical predictions is nearly perfect, further confirming the accuracy of the proposed model. In particular, temperature T2 was consistently higher than T3, with average experimental values of approximately 26∘C and 21∘C, respectively. The corresponding numerical discrepancies remained below 4∘C for both measurement locations.

[picture]

Fig. 7. Experimental-numerical comparison of temperature transients measured by thermocouples.

Fig. 7. Experimental-numerical comparison of temperature transients measured by thermocouples.

Conclusion

The original version of this paper is available on https://www.scientific.net/DDF.451.157.pdf

This work presented the design, experimental characterization, and numerical modelling of a hybrid mould architecture combining polymeric support plates with additively manufactured steel inserts for micro-injection moulding. The experimental campaign demonstrated the mechanical robustness of the polymer-based mould components and enabled the acquisition of reliable thermal transient data under uncooled operating conditions.

A three-dimensional transient numerical model was developed in COMSOL Multiphysics and calibrated using dedicated experimental measurements. Particular emphasis was placed on the identification of the thermal boundary conditions at the injection and extraction interfaces, whose influence was found to be dominant in governing the temperature evolution of the small-scale inserts. Based on the calibration results, an injection-side heat transfer coefficient of 600 W/m2 K was selected during the active moulding stages (filling and holding), reduced to 50 W/m2 K during passive phases, while the extraction side was modelled using a time-dependent coefficient decreasing from 3000 to 500 W/m2 K. The comparison between numerical predictions and experimental results during real moulding cycles confirmed the capability of the model to capture both the rapid heating of the fixed insert and the slower response of the movable side, providing a reliable description of the thermal behaviour of the hybrid mould system. Despite the geometric simplifications adopted to reduce computational cost, the calibrated parameters allowed the model to accurately reproduce the measured thermal transients, with deviations generally within 10% under calibration conditions.

Overall, the proposed experimental-numerical methodology provides an effective tool for the prediction and control of mould thermal behaviour in micro-injection moulding, reducing the need for extensive trial-and-error testing and supporting early-stage tooling design. The results highlight
the relevance of accurate boundary-condition calibration when modelling hybrid and thermally insulated mould architectures, where heat exchange with the machine components plays a critical role. Although the presented approach was developed for micro-injection moulding, where reduced mass and thermal inertia amplify heat-transfer effects, the methodology can be extended to other unconventional mould configurations requiring reliable thermal modelling and parameter identification.

Fundings

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This work was supported by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Next generation of sustainable and highly efficient moulding processes" Italian Projects of Significant National Interest (PRIN) PNRR 2022 grant n. P2022ZE23N. This work was also supported by PNRR-M4C2INV1.5, NextGenerationEU - Avviso 3277/2021 -ECS_00000033-ECOSISTER-spk 3 and PR-FESR 20212027 - Priorità 1 - obiettivo specific 1.1 - Azione 1.1.2 - Progetto "CUP E17G22001630003SAFER".

Acknowledgement

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The authors would like to thank Mr. Elia Andretto from CNR STIIMA for his support in the technological aspects of the research.

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The original version of this paper is available on https://www.scientific.net/DDF.451.157.pdf

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Keywords Index

#

3D Pyrography 3D-Printed Pyrography Using PLA/Wood Filaments

A

Additive Manufacturing From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion; Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Additive Tooling Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

C

Caprolactam Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Composite 3D-Printed Pyrography Using PLA/Wood Filaments; Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation; Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Creep Analysis of Large Deformation Characteristics and Formability of PMMA

Creep Model Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process

Crystallization Kinetics Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

D

Dma Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Dsc Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

F

Fem From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Fff From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Fishing Lures Thermoforming as Rapid Prototyping Strategy of Fishing Lures

Flow Simulation Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

G

Gel Zone Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

H

High-temperature Analysis of Large Deformation Characteristics and Formability of PMMA

Hybrid Moulds Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Hybrid Structure Joining Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

I

Injection Molding Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

Injection Moulding Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Interphase Characterization Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

M

Masked Stereolithography Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

Material Extrusion 3D-Printed Pyrography Using PLA/Wood Filaments; Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Mechanical Properties Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Meshless Method Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Method Of Fundamental Solutions Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Method Of Particular Solutions Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Mex From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

N

Natural Fibers Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Numerical Simulation Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

O

Optimization Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

P

Peek / Lm-paek Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

Pef Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Pet Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Pinns Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks

Plastic Deformation Analysis of Large Deformation Characteristics and Formability of PMMA

Pmma Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process

Polymethyl Methacrylate (pmma) Analysis of Large Deformation Characteristics and Formability of PMMA

Porosity Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures; Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks

Porous Medium Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

Power Consumption Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Process Simulation From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Properties Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Prototyping Thermoforming as Rapid Prototyping Strategy of Fishing Lures

Pultrusion Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

R

Reactive Thermoplastic Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Resin Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

Rpet Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

S

Scanning Electron Microscopy Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

T

Tensile Analysis of Large Deformation Characteristics and Formability of PMMA

Thermal Analysis Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Thermal Conductivity Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

Thermal Management Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Thermoforming Thermoforming as Rapid Prototyping Strategy of Fishing Lures

Thermomechanical Analysis From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Thermoplastic Composites Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Thermoset Prepreg Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

U

Ultrasonic Welding Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

V

Vacuum Forming Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Viscoplastic Model Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process

Void Growth Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks

W

Warpage Reduction Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

Welding Thermoplastics Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

Wood Filament 3D-Printed Pyrography Using PLA/Wood Filaments

Authors Index

B

Baek, M. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Bailleul, J. Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

Basile, V. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Beguin, J. Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Bertevas, E. Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

Berthet, F. Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

Briard, A. Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

C

Campanelli, S. Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Carlone, P. From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Chabert, F. Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Cheruet, A. Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

Chevalier, L. Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Choi, H. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Comino, F. 3D-Printed Pyrography Using PLA/Wood Filaments; Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Corre, S. Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

D

D'Elia, R. Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures; Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Dutra, J. Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

F

Fassi, I. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Filice, L. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Förster, R. Thermoforming as Rapid Prototyping Strategy of Fishing Lures

G

Gargadennec, E. Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Garnier, C. Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

H

Henning, F. Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

J

Jeong, D. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Jeong, Y. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Junk, S. Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

K

Kehret, D. Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

Kim, D. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

Korycki, A. Influence of Surface Finish and Energy Director on Ultrasonic Welding Process of PAEK/Metal Hybrid Structures

Kwon, Y. Material Characterization and Constitutive Modeling of PMMA for the Numerical Simulation of Vacuum Forming Process; Analysis of Large Deformation Characteristics and Formability of PMMA

L

Loth, A. Thermoforming as Rapid Prototyping Strategy of Fishing Lures

Luo, Y. Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

M

Martínez-Sánchez, J. 3D-Printed Pyrography Using PLA/Wood Filaments; Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Modica, F. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Monteiro, E. Thermal Crystallization Kinetics of PET, RPET and PEF for Sustainable Packaging

Müller, P. Development of a New Production Process for Thermally Conductive Resin for Additive Manufacturing Using mSLA Process

N

Nardo, M. From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

O

Orazi, L. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Oubellaouch, K. Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization; Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

P

Pedruzzi, W. Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Pelaccia, R. Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization; Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Pellegrini, A. 3D-Printed Pyrography Using PLA/Wood Filaments

Q

Quiroz, W. Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

R

Reggiani, B. Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

Rotella, G. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Russo, P. From Deposition Sequence to Mechanical Response: A Macroscale Process Simulation of Material Extrusion

Rösler, J. Thermoforming as Rapid Prototyping Strategy of Fishing Lures

S

Schelleis, C. Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Schmidt, F. Numerical Multiphysics CFD Modelling of Porosity Evolution in Thermoset Prepreg Microstructures

Siciliani, V. Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization

Silva, W. Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

Spina, R. 3D-Printed Pyrography Using PLA/Wood Filaments; Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Surace, R. Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

T

Tosi, I. Prediction of Temperature and Moisture Concentration in Autoclave-Cured Epoxy Resin Using Physics-Informed Neural Networks; Meshless Transient Thermal Modeling of Polymer Composite Curing with Exothermic Heat Generation

V

Vrettos, K. Interfacial Welding of Two Different Reinforced Thermoplastics via TACOMA*

W

Wilhelm, M. Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption

Z

Zaniboni, G. Multi-Objective Optimization of Injection-Molded Components for Defect Reduction and Warpage Minimization; Thermal Transient Modelling and Experimental Validation of Hybrid Polymer-Steel Moulds for Micro-Injection Moulding

Zaza, M. Bio-Composites for Additive Manufacturing: Study of the Mechanical Properties

Zeeb, G. Determination of Gelation Zone Position in Reactive Thermoplastic Pultrusion by Analysis of Heating Power Consumption