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ISBN print: 978-3-0357-1815-7
ISBN eBook: 978-3-0357-3774-5
DOI book: 10.4028/b-LhqU3q
© 2026 Trans Tech Publications Ltd, All Rights Reserved

Modeling and Numerical Approach in Composites Forming Processes

Edited by
Luise Kärger
Pierpaolo Carlone

Modeling and Numerical Approach in Composites Forming Processes

Special topic volume with invited peer-reviewed papers only

Edited by
Luise Kärger and Pierpaolo Carlone

Scientific.Net

Copyright © 2026 Trans Tech Publications Ltd, Switzerland

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Volume 1182 of
Materials Science Forum
ISSN print 0255-5476
ISSN web 1662-9752

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp -1-0

© 2026 Trans Tech Publications Ltd, All Rights Reserved

Accepted:
2026-04-08

Online:
2026-04-10

Kärger, Luise

Carlone, Pierpaolo

Preface

The original version of this paper is available on https://www.scientific.net/MSF.1182.-1.pdf

High-level applications of composite materials at affordable development and manufacturing costs create significant demand for scientific knowledge and computational tools for composite manufacturing. The mechanical behaviour of composite parts in service is dominated by fiber orientation and density, which in turn are determined by the forming process. Hence, predicting inservice performance requires a full understanding of, and preferably a prediction of, the complex material behaviour during manufacturing.

Experimental and numerical standards are discussed and established in the context of the composite forming process. The presented research results are dedicated to material characterisation, constitutive laws, contact and friction, forming simulations, multiscale analyses, textile forming, thermoforming, resin injection, compression moulding, fiber suspensions, natural fibers, additive manufacturing of composites, etc.

Editors

The original version of this paper is available on https://www.scientific.net/MSF.1182.-1.pdf

Karlsruhe Institute of Technology
University of Salerno

Co-editors

The original version of this paper is available on https://www.scientific.net/MSF.1182.-1.pdf

Akkerman, Remko | University of Twente
Grouve, Wouter | University of Twente
Ivanov, Dmitry | University of Bristol
Lomov, Stepan | KU Leuven
Sherwood, James A. | University of Massachusetts
Vidal Salle, Emmanuelle | INSA Lyon

Table of Contents

Preface

Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

Johannes Mitsch, Tobias Würth, Jan Paul Wank, Luise Kärger

The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

Jan Paul Wank, Levin Villing, Bastian Schäfer, Johannes Mitsch, Luise Kärger

Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

Vitantonio Esperto, Felice Rubino, Fausto Tucci, Pierpaolo Carlone

Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Fausto Tucci, Antonio Viscusi, Barbara Palmieri, Alessia Serena Perna, Alfonso Martone, Antonello Astarita

Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Hao Yuan, Burak Ogun Yavuz, Yuncong Feng, Ian Hamerton, Byung Chul Kim, Stephen R. Hallett, Jonathan P.H. Belnoue

Fabric Patching: A Simple Approach to Mitigate Defects

Siyuan Chen, Jonathan P.H. Belnoue, Dmitry S. Ivanov

Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Olivia H. Margoto, Mohammad Amin Batouei, Victor Yang, Yasmine Abdin, Abbas S. Milani

Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

Kari D. White, James A. Sherwood

Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Elias Delsol, Philippe Olivier, Bruno Castanié, Wiyao Azoti, Leon Ratsifandrihana

Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Pierre Waroquier, Arthur Levy, Steven Le Corre, Jean Luc Bailleul, Joël Serra, Erwan Bertevas

Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

Mouadh Boubaker, Arthur Cantarel, Gérald Debenest

Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Manoj R. Gongati, Laurent Warnet, Francesco Rondina, Edwin T.J. Klompen, Remko Akkerman

Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

Nihad Siddig, Mohamed Mtibaa, Marie Coupé, Alexandre Guinoiseau

A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Miro Duhovic, Lukas Handl, Martin Müller, Dominic Schommer, Thomas Hoffmann, Jens Schlimbach, Thomas Neumeyer

Keywords Index

Authors Index

The original version of this eBook is available on https://www.scientific.net/book/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 1-11

doi: 10.4028/p-aI6KaL

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

Submitted:
2025-12-19

Revised:
2026-02-11

Accepted:
2026-02-14

Online:
2026-04-10

Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

Johannes Mitsch a*, Tobias Würth b, Jan Paul Wank c, and Luise Kärger d

Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST) Lightweight Engineering, 76131 Karlsruhe, Germany

a  Johannes.Mitsch@kit.edu, b  Tobias.Wuerth@kit.edu, c  Jan.Wank@kit.edu, d  Luise.Kaerger@kit.edu

Keywords: Forming, Process Simulation, Finite Element Analysis (FEA), Validation Techniques

Abstract

Accurate yet computationally efficient simulation models are essential for the virtual design and optimization of thermoforming processes for fiber-reinforced composites. Selecting an appropriate material model remains challenging, particularly when balancing model fidelity against computational cost. In this work, a framework is developed to validate material models used in thermoforming simulations for fiber-reinforced composites. The framework evaluates model performance based on time-series data using covariance-based input-output statistics, without prior calibration. Two numerical studies of increasing complexity demonstrate the versatility of the approach. First, the framework is applied to one-dimensional rheological models, verifying its applicability to mechanical problems relevant to thermoforming simulation. These insights are then applied to complex finite element thermoforming simulations to assess the ability of isothermal material models to predict wrinkling behavior in comparison to a fully coupled thermomechanical reference model. A curvature-based method is introduced to quantitatively evaluate wrinkling severity relative to natural curvatures induced by the tool geometry. The results show that isothermal models are sufficient for short total process times with minor temperature-driven effects, whereas longer total process times with pronounced thermal effects require thermomechanical models to ensure accurate predictions. The findings offer practical guidance for selecting appropriate material models based on specific process conditions, as well as objective criteria for assessing model validity in virtual process design.

1. Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

In numerical model development, the goal is to create mathematical representations that capture experimentally observed phenomena and accurately predict system behavior while maintaining computational efficiency. In virtual process design for fiber-reinforced composites, this balance is particularly important due to the need for rapid simulations that support design and process optimization. With the growing number of modeling approaches for composite forming [1], systematic strategies for model selection and validation are increasingly required to determine when simplified models are sufficient and when higher-fidelity approaches are necessary.

Traditional model validation is typically performed after calibration by comparing model predictions point-wise to independent experimental data. However, calibration errors can obscure fundamental modeling deficiencies and compromise the validity of the results [2]. To address this issue, Vogel and Sankarasubramanian [2] proposed a model validation framework for watershed models that separates calibration from validation. Rather than relying on point-by-point agreement, the framework evaluates whether the model reproduces the underlying system dynamics by comparing input and output time series and their statistical dependencies. These dependencies are assessed over an ensemble of simulations with varying model parameters to explore the system's dynamic behavior and compare it systematically to reference data. Unlike traditional validation approaches, the framework is not able to confirm model validity with certainty but can reject models that fail to reproduce the system dynamics adequately. While it has been successfully applied in hydrological modeling [3], its use in mechanical problems, particularly forming simulations of composite materials, remains largely unexplored.

The objective of this work is to adapt and apply the model validation framework originally proposed by Vogel and Sankarasubramanian [2] to thermoforming simulations of fiber-reinforced composites. The framework is first tested on simplified one-dimensional rheological models to demonstrate its applicability to mechanical problems relevant to thermoforming. The insights gained are then used to extend the framework to complex finite element simulations for thermoforming of composite materials. Finally, the validation approach is applied to systematically compare the performance of isothermal [4] and thermomechanical [5] material models, providing insights into the role and necessity of thermomechanical coupling in forming simulations.

2. Numerical Study on One-Dimensional Rheological Models

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

Material models. To demonstrate the applicability of the proposed validation framework to mechanical models used in thermoforming simulations, two simplified one-dimensional (1D) rheological models are considered: a standard (isothermal) Voigt-Kelvin model and a thermomechanical Voigt-Kelvin model. The standard Voigt-Kelvin model consists of a spring and a damper connected in parallel. The constitutive equation of the isothermal Voigt-Kelvin model is given by

σ(t)=Eε(t)+ηε˙(t),(1)

where σ(t) is the stress, ε(t) the strain, E the elastic modulus and η the viscosity. The thermomechanical Voigt-Kelvin model extends this formulation by including thermal expansion in the spring element. The constitutive equation of the thermomechanical Voigt-Kelvin model is given by

σ(t)=E(ε(t)−α(T(t)−T0))+ηε˙(t),(2)

where α is the thermal expansion coefficient, T(t) the current temperature, and T0 a reference temperature. The input-output behavior of both models is illustrated in Fig. 1 for a given stress input σ(t), temperature profile T(t), and reference parameter set (cf. Table 1). The stress input and strain output are normalized between 0 and 1 for comparability. As expected, the thermomechanical model's response varies with temperature, whereas the isothermal model remains unaffected. This substantial difference in model behavior will be used to demonstrate the validation framework.

[picture]

Fig. 1: In- and output time series of the variotherm and isotherm Voigt-Kelvin models.

Fig. 1. In- and output time series of the variotherm and isotherm Voigt-Kelvin models.

Experimental setup and material parameters. To apply the validation framework, both models are simulated under identical input conditions, specifically the time-dependent stress input σ(t) and the temperature profile T(t) shown in Fig. 1 (left). A total of 4000 simulations are performed for each model, with material parameters varied to comprehensively assess the performance of the validation framework. The parameters are sampled using Latin Hypercube Sampling (LHS) [6] to ensure a welldistributed exploration of the parameter space. Parameters spanning more than one order of magnitude are sampled on a logarithmic scale. A summary of the sampled parameter ranges is provided in Table 1.

Table 1: Parameter ranges for the LHS of the 1D rheological models

Description | Symbol | Reference | Range | Unit | Log-scaling
Elastic modulus | E | 10² | [10¹, 10⁴] | MPa | Yes
Viscosity | η | 10² | [10¹, 10⁴] | MPa · s | Yes
Thermal expansion coefficient | α | 5 · 10⁻⁶ | [10⁻⁹, 10⁻⁴] | 1/K | Yes
Reference temperature | T₀ | 250 | [100, 500] | K | No

Note that, in reality, material parameters such as the elastic modulus E and viscosity η can be temperature-dependent. This effect is neglected here for simplicity and to isolate the influence of temperature on the thermal expansion coefficient α.

Covariance-based validation metrics. To apply the validation framework of Vogel and Sankarasubramanian [2] to the 1D rheological models, the variance Var(f) and the Pearson correlation coefficient ρ(f,g) between two discrete time series f and g are used as covariance-based validation metrics. The variance Var(·) quantifies the spread of a time series around its empirical mean value (·¯)

Var(f)=∑i=1Nt|(f(ti)−f¯)2|Nt with the empirical mean value f¯=1Nt∑i=1Ntf(ti),(3)

where Nt denotes the number of discrete time steps ti. The Pearson correlation coefficient ρ(f,g) measures the linear relationship between two time series

ρ(f,g)=Cov(f,g)Var(f)Var(g)=∑i=1Nt(f(ti)−f¯)(g(ti)−g¯)Var(f)Var(g),(4)

where Cov(f,g) denotes the covariance between f and g.
Vogel and Sankarasubramanian [2] originally proposed using the lag-one autocorrelation instead of the variance Var(f), which is equivalent to the Pearson correlation of a time series with a onestep time lag ρ(f,flag ).This captures the correlation of a time series with its immediate past values. Since the output time series of the 1D rheological models do not exhibit rapid fluctuations between consecutive time steps, the variance Var(f) is adopted here as a more suitable metric to quantify the spread of the time series.

Results and discussion. The validation metrics defined in Eq. 3 and Eq. 4 are computed for all 4000 parameter sets of both the isothermal (Eq. 1) and thermomechanical (Eq. 2) Voigt-Kelvin models using the stress σ(t) and temperature T(t) time series as inputs and the resulting normalized strain ε^(t) time series as outputs. The results are shown in Fig. 2, where each point represents a simulation with a specific parameter set. Orange and blue points correspond to the isothermal and thermomechanical models, respectively, while green markers highlight the reference parameter set ( E,η,T0 ) from Table 1 where the thermal expansion coefficient α is varied.

In both plots of Fig. 2, the points of the isothermal model (orange) form a subset of those of the thermomechanical model (blue), as the former represents a special case of the latter with α=0. The thermomechanical simulations highlighted in green, where only α is varied, form a curve within the thermomechanical model's point cloud and approach the isothermal points as α approaches small values. This indicates that for small thermal expansion coefficients α, the system dynamics of the thermomechanical model converge to those of the isothermal model. According to the validation framework [2], the isothermal model should be rejected as an invalid simplification when the value of α is large, since this simplified model does not capture the significant influence of temperature on system dynamics. However, for small α values, the isothermal model might still be considered valid if the material parameters are chosen appropriately. It should be noted that individual locations in the

[picture]

Fig. 2: Evaluation of validation metrics across thermal expansion coefficients α, comparing isothermal and thermomechanical Voigt-Kelvin models. Left: stress-strain correlation vs. strain variance. Right: temperature-strain correlation vs. strain variance

Fig. 2. Evaluation of validation metrics across thermal expansion coefficients α , comparing isothermal and thermomechanical Voigt-Kelvin models. Left: stress-strain correlation vs. strain variance. Right: temperature-strain correlation vs. strain variance

covariance-based metric space cannot be uniquely interpreted in terms of specific material parameters, as the framework evaluates system-level dynamic behavior rather than parameter-wise effects.

These results confirm that the covariance-based metrics (variance and Pearson correlation) are suitable for evaluating mechanical material models. Finally, Fig. 2 also shows that using normalized input and output time series produces a well-distributed point cloud, confirming that normalized input and output time-series are preferable for the covariance-based validation framework. The one-dimensional study therefore serves as a methodological verification step, demonstrating that the covariance-based framework can be meaningfully transferred from hydrological [2] to mechanical modeling contexts.

3. Adaption and Application to Thermoforming Simulation

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

Approach. To apply the validation framework proposed by Vogel and Sankarasubramanian [2] to finite element simulations of thermoforming composite materials, two material models of different complexities are employed. A state-of-the-art, fully coupled, high-fidelity thermomechanical simulation model is used as a reference. It serves as a substitute for experimental data. A lower-fidelity, isothermal simulation model is evaluated based on its ability to reproduce the input-output behavior of the reference model's wrinkling response. Both models are implemented in the commercial finite element software Abaqus/Explicit and are based on the works of Dörr et al. [4, 5]. The validation framework is applied to investigate the necessity of considering thermomechanical coupling in forming simulations of thermoplastic composite materials based on the wrinkling behavior during forming. To quantify the severity of wrinkling during forming as a time series, a quantitative metric, based on the Wrinkled Element Ratio ( rw ) [7], is introduced as the output time series for the validation framework.

Material modeling. The lower-fidelity simulation is based on the work of Dörr et al. [4], who developed an isothermal thermoforming simulation approach for thermoplastic composite materials, neglecting temperature-driven phenomena during forming. Superimposed two-dimensional membrane (M3D3) and shell (S3) element formulations with VUMAT and VUGENS user subroutines are employed. This allows for a decoupled description of the membrane and bending behavior in each individual ply [4]. Both the membrane and bending behaviors are modeled using an isothermal Voigt-Kelvin material model

S2PK=Selast 2PK+Svisc 2PK(5)

employing a hyperelastic St. Venant-Kirchhoff model for the elastic part,

Selast 2 PK =ℂ[E],(6)

while the viscous behavior is described by an isotropic Newton model with a nonlinear Cross approach for the viscosity [4],

σvisc =η(γ˙)D with η(γ˙)=η01+(mγ˙)1−n.(7)

The inter-ply behavior is modeled according to the isotropic approach of Dörr et al. [8], accounting for non-penetration, adhesion, and sticking-sliding interactions between adjacent plies. A detailed description of the isothermal forming simulation model is provided in the original publications [4, 8].

The high-fidelity thermomechanical reference simulations are based on the work of Dörr et al. [5], who developed a fully coupled thermomechanical forming simulation approach for thermoplastic composite materials. Unlike the isothermal model, this model also accounts for temperature-dependent material behavior, tool-ply and ply-ply heat transfer, crystallization kinetics, and the phase transitions between the molten and solid states of the thermoplastic matrix during cooling. Similar to the lowerfidelity model, the simulation is implemented in Abaqus/Explicit using triangular membrane (M3D3) and shell (S3) element formulations with VUMAT and VUGENS subroutines for a decoupled description of the membrane and bending behavior in each ply. Heat transfer and crystallization kinetics are modeled using an additional layer of superimposed triangular elements in combination with VUEL and VUFIELD subroutines. The resulting temperature T and crystallization degree χ fields are then transferred into the VUMAT and VUGENS subroutines, enabling a temperature-dependent material description of the molten matrix material (cf. Eq. 6 and Eq. 7)

ℂm=ℂm(T) and η0m=η0m(T)(8)

The phase transition between the molten and solid states of the thermoplastic material is modeled using a linear mixture rule based on the degree of crystallinity χ and the mechanical properties of the molten (·)m and solid (·)s states

S2PK(T,χ)=(1−χ)Sm(T)+χSs(9)

A more comprehensive description of the high-fidelity thermoforming simulation model is provided by Dörr et al. [5].

Experimental simulation setup and material parameters. For both simulation approaches, the same complex shaped tool geometry with the same spatial mesh resolution is used. The spatial discretization of the 410×410 mm sized blank consists of 6724 triangular elements for both simulation models and has an initial thickness of d=0.16 mm per ply. The blank is initially situated between the forming tools. A biaxial laminate stack of [ 0∘,90∘ ] is selected to avoid wrinkling phenomena caused by complex stacking sequences, which could obscure wrinkling induced by temperature-driven effects. The forming process is executed by moving the forming tool downwards to shape the blank into the tool geometry. A smoothed tool displacement utool (t) profile is used for all simulations. Four different tool closing velocities with total process times tu ranging from 1.6 s to 6.4 s are simulated. Longer total process times tu increase the influence of temperature-driven phenomena on the forming result, as they lead to more cooling of the blank during forming and thereby raise the necessity to consider temperature-driven phenomena for accurate simulation [9].

For the high-fidelity thermomechanical forming simulations, a uniform initial blank temperature of T0=280∘C and a constant tool temperature of Ttool =80∘C are selected, representing typical industrial forming conditions for the thermoplastic composite material used in this study [10]. The material parameters required for the thermomechanical simulations are obtained from in-house mechanical and thermal characterization tests of unidirectional carbon fiber reinforced polyamide composite material
[5]. In the four high-fidelity reference simulations, all material parameters are kept constant, and only the process time tu∈{1.6 s,3.2 s,4.8 s,6.4 s} is varied. For the lower-fidelity model, eight material parameters defining the isothermal material models for both the membrane and bending behavior are varied within physically reasonable ranges. The parameter ranges are obtained by means of an in-house database of material parameter sets for various material systems, with different matrix and fiber materials. Parameters varying over more than one order of magnitude are sampled in logarithmic space to ensure a uniform distribution across their range. A summary of the varied parameters and their ranges is given in Table 2. In total 1000 isothermal forming simulations are performed for each process time tu using different parameter sets.

Table 2: Varied material parameters of the isothermal material models used in the lower-fidelity forming simulation. The resulting simulation data is provided by Mitsch and Kärger [11].

Material model | Description | Parameter | Range | Unit | Log-scaling
Membrane | Matrix elasticity | EM | [10⁻³, 10⁻¹] | MPa | Yes
Zero-strain viscosity | η₀M | [8 · 10⁻³, 8 · 10⁻¹] | MPa·s | Yes
Time constant | mM | [10⁻¹, 5 · 10¹] | s | Yes
Shear-thinning index | nM | [−1, 1] | - | No
Bending | Flexural modulus 0° | C₁₁B | [3 · 10¹, 6 · 10²] | MPa | Yes
Zero-strain viscosity | η₀B | [1 · 10⁰, 7 · 10³] | MPa·s | Yes
Time constant | mB | [1 · 10⁻¹, 5 · 10⁷] | s | Yes
Shear-thinning index | nB | [−1, 1] | - | No

Note that under the assumption of negligible Poisson's ratio effects in the membrane ( νM=0 ), the membrane shear modulus GM can be directly derived from the Young's modulus EM of the matrix material as GM=1/2EM. Furthermore, the flexural modulus in the 90∘ direction C22B and the flexural shear modulus G12B are derived from C11B using knock-down factors of k22=100=C11B/C22B and k12=200=C11B/G12B [4].

Generation of input and output time series for thermoforming simulation. In order to apply the proposed validation framework [2] to forming simulations, one time series defining the model's input and one time series defining the model's output must be extracted from the simulation data. For the input time series, the relative tool stroke Δu is chosen, defined as the displacement of the forming tool utool  normalized by the maximum tool displacement umax 

Δu=utool /umax.(10)

As the output time series, the wrinkled element ratio rw originally proposed by Chen et al. [7] is used to quantify the amount of wrinkling occurring during the forming process. The wrinkled element ratio rw is defined as the area-weighted ratio of the number of wrinkled elements Nw to the total number of elements Ntot  on the blank

rw=AwAtot=∑i=1NwAi∑j=1Ntot Aj=∑i=1NtotwiAi∑j=1NtotAj with wi={1, if element i is wrinkled ,0, else. (11)

A finite element is classified as wrinkled ( wi=1 ) if its absolute curvature |κi| exceeds a threshold curvature κcrit . The curvature κi is calculated based on the node coordinates using the methodology proposed by Dong and Wang [12]. Note, that both quantities Δu and rw are naturally normalized to the range [0,1] which was found to be beneficial for the application of the validation framework to the 1D rheological models above.

To objectively evaluate rw for different tool geometries and process parameters, the threshold curvature κcrit  must be defined. In this work, κcrit  is defined as the 95 th percentile of the curvature distribution of the blank mesh projected onto the tool geometry. This approach ensures, that the natural curvature induced by the tool geometry is used as a baseline for defining wrinkled elements while also accounting for the specific mesh resolution of the blank. The 95th percentile is selected to mitigate the influence of numerical noise and local mesh imperfections that may create small regions of artificially high curvature. This methodology enables an objective and consistent definition of wrinkled elements across different forming geometries. Note that the proposed method depends on the mesh resolution. Therefore, a consistent mesh resolution must be ensured when comparing rw values across different simulations and when defining κcrit .

A visualization of the rw is shown in Fig. 3a, where wrinkled elements are highlighted in red and non-wrinkled elements in light gray. The selected threshold curvature κcrit  effectively separates wrinkled from non-wrinkled regions, demonstrating that this approach can quantitatively describe the amount of wrinkling in formed parts. As a global metric, however, rw aggregates wrinkling information over the entire part and does not capture the spatial distribution of wrinkles. Some highly curved regions caused by the tool geometry are also partially classified as wrinkled due to the chosen thresholding approach, which is a trade-off between neglecting artificial numerical noise using the 95th percentile threshold and capturing genuine wrinkling phenomena. Since this effect is consistent across all simulations, it does not affect the comparative assessment of wrinkling behavior.

[picture]

Fig. 3: Quantitative assessment of the degree of wrinkling in forming simulations. (a) Visualization of wrinkled elements in red. (b) rw curves for different total process times tu in thermomechanical forming simulations.

Fig. 3. Quantitative assessment of the degree of wrinkling in forming simulations. (a) Visualization of wrinkled elements in red. (b) r w curves for different total process times t u in thermomechanical forming simulations.

The results of the rw evaluation for the high-fidelity thermomechanical forming simulations with different total process times tu are shown in Fig. 3b. In all cases, rw increases during forming, indicating progressive wrinkle formation as the blank conforms to the tool geometry. It also rises more rapidly with increasing total process time tu, suggesting that longer processes promote stronger wrinkling. This trend can partly be attributed to cooling effects at longer total process times tu, which increases the material's viscosity and stiffness during forming [9] and contribute to crystallization effects (cf. Eq. 8 and Eq. 9). However, longer total process times tu also reduce deformation rates, further increasing viscosity due to the shear-thinning behavior of the thermoplastic matrix material (Eq. 7). Thus, the observed wrinkling behavior results from the combined influence of thermomechanical coupling and deformation-rate effects.

Results and discussion of the validation framework. In order to apply the validation framework [2] to thermoforming simulation, four high-fidelity thermomechanical forming simulations at different total process times tu∈{1.6 s,3.2 s,4.8 s,6.4 s} serve as reference simulations. For each process time tu, 1000 lower-fidelity isothermal forming simulations with varying material parameters (cf. Table 2 ) are performed. The simulation data is provided as a dataset alongside this publication [11]. The inputoutput behavior of the simulations are then compared using the variance Var(rw) of the rw time series (cf. Eq. 3) and the correlation ρ(Δu,rw) between the input tool stroke Δu and the output rw (cf. Eq. 4). The results are summarized in Fig. 4. Green crosses represent the high-fidelity thermomechanical simulations, while black dots represent the lower-fidelity isothermal simulations with varied material parameters. Deep black regions indicate a high density of points, while lighter gray regions indicate lower point densities.

[picture]

Fig. 4: Validation metrics for thermomechanical and isothermal forming simulations at varying total process times tu. For isothermal cases, material parameters are varied as in Table 2.

Fig. 4. Validation metrics for thermomechanical and isothermal forming simulations at varying total process times t u . For isothermal cases, material parameters are varied as in Table 2.

At tu=1.6 s, the lower-fidelity simulations form a dense cluster at low variance values Var(rw), with a smaller number of points extending toward higher variance and correlation values ρ(Δu,rw). As the process time increases, the cluster becomes less compact and spreads toward higher variance and correlation values. This trend indicates that wrinkling behavior is highly sensitive to process time, which influences the deformation rate and thereby the viscosity of the thermoplastic matrix material due to its shear-thinning behavior (Eq. 7). For short total process times tu∈{1.6 s,3.2 s}, the highfidelity thermomechanical simulations fall within the dense clusters of the lower-fidelity isothermal simulations. This suggests that temperature-driven effects are of minor relevance under these conditions because short total process times tu result in limited cooling of the blank and thereby limiting the significance of reduced temperature-driven phenomena during forming. Analysis of the high-fidelity data shows that the blank temperature remains above T>200∘C for most of the forming process, with crystallization confined to small regions near the tool contact areas. Since crystallization effects occur only at the final stages of tool stroke utool  and remain spatially limited, their impact on overall wrinkling behavior is minimal. Consequently, the isothermal model can reproduce the wrinkling behavior of the thermomechanical reference model when its material parameters are properly calibrated. According to the proposed validation framework, the isothermal model does not need to be rejected for these short total process times tu which is in line with the physical considerations discussed above.

For longer total process times tu∈{4.8 s,6.4 s}, the thermomechanical simulations exhibit higher variance and correlation values, deviating from the clusters of the isothermal simulations (cf. Fig. 4). This indicates that the isothermal model fails to reproduce the wrinkling behavior predicted by the thermomechanical reference. Analysis of the high-fidelity simulation data reveals that for these longer total
process times tu, the blank temperature decreases earlier in the forming process, leading to pronounced thermomechanical coupling effects. In particular, for tu=6.4 s, regions in tool contact become fully crystallized at a relative tool stroke of Δu≈0.55 (cf. Fig. 3b), resulting in a substantial increase in stiffness and viscosity due to the phase transition of the thermoplastic matrix material from the molten to the solid state (cf. Eq. 9). As significant deformation still occurs after this transition, the wrinkling behavior is strongly influenced by these effects. By the end of the forming process ( Δu=1 ), large portions of the blank have crystallized for both tu=4.8 s and tu=6.4 s. It can be concluded that at longer total process times tu, thermomechanical coupling and phase transitions play a decisive role in the wrinkling behavior, which the isothermal model cannot capture. As the covariance-based metrics of variance and correlation for the isothermal simulations do not overlap with those of the thermomechanical reference (cf. Fig. 4), the isothermal model must be rejected for these conditions. This finding aligns with the physical considerations discussed above.

The number of simulations required for model interrogation is not fixed and was chosen here to demonstrate the framework. In practice, fewer simulations may be sufficient, and simplified characterization or benchmark cases that capture the dominant physical mechanisms can be used instead of complex part geometries. Similarly, the framework does not require a large number of experimental tests. A limited number of representative, time-resolved experimental input-output series can be compared to an ensemble of model predictions to assess whether the relevant system dynamics are captured.

4. Conclusion and Outlook

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

In this work, a model validation framework was adapted and applied to both one-dimensional rheological models and finite element simulations of thermoforming thermoplastic composite materials. Applying the validation framework to one-dimensional rheological models showed that isothermal models become insufficient when thermal effects are significant, confirming the framework's capability to assess model validity in mechanical contexts. These insights were then transferred to complex finite element simulations, where the validity of an isothermal material model was evaluated against a fully coupled thermomechanical reference. A curvature-based method was introduced to quantitatively evaluate wrinkling severity also considering the natural curvature imposed by the tool geometry. The results showed that the isothermal approach becomes invalid for long total process times with pronounced thermal effects. However, for short total process times, the isothermal model was found to capture the system dynamics adequately, suggesting that with properly chosen material parameters, the lower-fidelity model can be sufficient.

The study demonstrated the versatility of the validation framework for both simplified and complex simulation scenarios, providing objective criteria for assessing model validity based on dynamic behavior rather than point-wise accuracy, and without prior calibration. Future work will apply the framework to experimental data from characterization and application stages to evaluate model validity throughout the virtual design process and to accelerate material model selection. Although the proposed wrinkle evaluation metric rw effectively quantifies wrinkling severity, it simplifies complex three-dimensional phenomena and depends solely on simulated curvature data, which may limit experimental application. A more sophisticated metric for quantifying wrinkling than a threshold-based approach may capture more detailed characteristics of wrinkling. Further work should refine the metric to capture more detailed and localized wrinkling characteristics and integrate real manufacturing data to enhance the framework's robustness and practical relevance for material model selection in virtual process design. Additionally, exploring the definition of a distance measure in a covariancebased metric space relative to an experimentally obtained system response could facilitate automated model selection and parameter optimization.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

This work is part of the DFG AI Research Unit 5339 (project no.459291153) and the DFG-funded Heisenberg project "Digitalization of fiber-reinforced polymer processes for resource-efficient manufacturing of lightweight components" (project no. 455807141), which are both funded by the Deutsche Forschungsgemeinschaft, Germany (DFG, German Research Foundation).

Data availability

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

The simulation data for the isothermal forming simulations used in this work is provided alongside this publication [11] and can be accessed at https://doi.org/10.5281/zenodo. 17977470.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.1.pdf

Philippe Boisse, Remko Akkerman, Pierpaolo Carlone, Luise Kärger, Stepan V. Lomov, and James A. Sherwood. Advances in composite forming through 25 years of ESAFORM. International Journal of Material Forming, 15(3):99, January 2022. ISSN 1960-6214. doi: 10.1007/s12289−022−01682−8.

Richard M. Vogel and A. Sankarasubramanian. Validation of a watershed model without calibration. Water Resources Research, 39(10), January 2003. ISSN 00431397. doi: 10.1029/ 2002WR001940.

Annie Visser-Quinn, Lindsay Beevers, and Sandhya Patidar. Replication of ecologically relevant hydrological indicators following a modified covariance approach to hydrological model parameterization. Hydrology and Earth System Sciences, 23(8):3279-3303, August 2019. ISSN 1027-5606. doi: 10.5194/hess-23-3279-2019.

Dominik Dörr, Fabian J. Schirmaier, Frank Henning, and Luise Kärger. A viscoelastic approach for modeling bending behavior in finite element forming simulation of continuously fiber reinforced composites. Composites Part A: Applied Science and Manufacturing, 94:113-123, January 2017. ISSN 1359835X. doi: 10.1016/j.compositesa.2016.11.027.

Dominik Dörr, Tobias Joppich, Daniel Kugele, Frank Henning, and Luise Kärger. A coupled thermomechanical approach for finite element forming simulation of continuously fiberreinforced semi-crystalline thermoplastics. Composites Part A: Applied Science and Manufacturing, 125, January 2019. ISSN 1359835X. doi: 10.1016/j.compositesa.2019.105508.

M. D. McKay, R. J. Beckman, and W. J. Conover. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics, 21 (2):239-245, 1979. ISSN 0040-1706. doi: 10.2307/1268522.

Siyuan Chen, Adam J. Thompson, Tim J. Dodwell, Stephen R. Hallett, and Jonathan P. H. Belnoue. Fast optimisation of the formability of dry fabric preforms: A Bayesian approach. Materials & Design, 230:111986, June 2023. ISSN 0264-1275. doi: 10.1016/j.matdes.2023.111986.

Dominik Dörr, Markus Faisst, Tobias Joppich, Christian Poppe, Frank Henning, and Luise Kärger. Modelling Approach for Anisotropic Inter-Ply Slippage in Finite Element Forming Simulation of Thermoplastic UD-Tapes. In AIP Proceedings of the 21th International ESAFORM Conference on Material Forming, January 2018.

Dominik Dörr, Daniel Kugele, Tobias Joppich, Frank Henning, and Luise Kärger. On the relevance of thermomechanics and crystallization kinetics for FE thermoforming simulation of semicrystalline thermoplastic tapes. In Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019, page 020011, Vitoria-Gasteiz, Spain, 2019. doi: 10.1063/1.5112516.

Georg Zeeb, Johannes Mitsch, Michael Wilhelm, Luise Kärger, and Frank Henning. Influence of gripper positions on the formation of wrinkles during the thermoforming process of thermoplastic UD-tape laminates. In Materials Research Proceedings, volume 54, pages 544-553. Materials Research Forum LLC, 2025. doi: 10.21741/9781644903599-59.

Johannes Mitsch and Luise Kärger. Process simulation data for thermoforming of continuous fiber-reinforced composite materials, Zenodo, December 2025.

Chen-shi Dong and Guo-zhao Wang. Curvatures estimation on triangular mesh. Journal of Zhejiang University-SCIENCE A, 6(S1):128-136, January 2005. ISSN 1673-565X. doi: 10. 1631/jzus.2005.AS0128.

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/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 13-22

doi: 10.4028/p-PywJ3U

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

Submitted:
2025-12-19

Revised:
2026-02-09

Accepted:
2026-02-17

Online:
2026-04-10

The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

Jan Paul Wank 1,a*, Levin Villing 1,b, Bastian Schäfer 1,2,c, Johannes Mitsch 1,d and Luise Kärger 1,e

1 Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST) Lightweight Engineering, Rintheimer Querallee 2, 76131 Karlsruhe, Germany

2 Simutence GmbH, Rintheimer Querallee 2, 76131 Karlsruhe, Germany

a jan.wank@kit.edu, b levin.villing@student.kit.edu, c bastian.schaefer@kit.edu, d  Johannes.Mitsch@kit.edu, e  luise.kaerger@kit.edu

Keywords: Non-Crimp Fabric, Forming Simulation, Bending

Abstract

Accurate prediction of forming behavior in dry textile reinforcements requires constitutive models that capture both in-plane and out-of-plane deformation mechanisms. This work presents the development and validation of advanced bending models for unidirectional non-crimp fabrics (UD-NCFs) that exhibit two distinct characteristics: side-dependent behavior arising from asymmetric stitching and glass fiber backing, and nonlinear behavior characterized by decreasing bending stiffness with increasing curvature. Based on cantilever bending tests with optical moment-curvature measurement, five mathematical formulations (piecewise linear, polynomial, power law, logarithmic, and exponential) used to describe the moment-curvature relation were systematically evaluated using the coefficient of determination R2. The piecewise linear and logarithmic models achieved the highest accuracy, with R2 values approaching unity across all fiber orientations and bending directions. These models were implemented in Abaqus/Explicit via the VUGENS user subroutine and validated through virtual cantilever tests, demonstrating good agreement with experimental deflection curves within the standard deviation bands. Application to hemispherical forming simulations revealed significant differences in wrinkle prediction between linear and nonlinear models. While the classical linear model based on Peirce predicted a single pronounced wrinkle in fiber direction, the nonlinear models captured additional wrinkles in the transverse direction and wider wrinkle patterns in fiber direction. Sidedependent models exhibited slightly increased wrinkle amplitudes compared to non-side-dependent models, particularly in fiber direction. The developed framework allows for a more accurate virtual process design than the current state of the art for composite forming operations by accounting for the side-dependent and nonlinear bending characteristics of UD-NCF materials.

1. Introduction

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Finite element simulations have become a proven tool for analyzing process-induced deformations of textile reinforcements. They enable virtual process design and the prediction of forming defects such as wrinkles and fiber misalignment [1]. The predictive accuracy of these simulations strongly depends on constitutive models that describe both in-plane and out-of-plane deformation mechanisms. A detailed understanding of the forming behavior of engineering textiles is essential for minimizing forming defects during manufacturing and achieving optimal structural performance.

To simulate the forming behavior of textile reinforcements, experimental characterization must be performed. A standard test to characterize the bending behavior of textiles is the cantilever test according to [2]. This test provides a single bending stiffness value based on the overhang length of a fabric strip. When using optical measurement techniques, the bending moment-curvature relationship can be determined more accurately compared to the Peirce method [3]. The curve exhibits an initially linear region corresponding to elastic bending, followed by a degressive region at higher curvatures indicating nonlinear behavior. The Peirce bending stiffness, therefore, provides a reasonable approximation for small curvatures, while the nonlinear, degressive behavior at larger curvatures requires more advanced modeling approaches.

The ratio of bending stiffness to membrane stiffness is critical for the formation of wrinkles and other out-of-plane defects [4, 5]. This ratio governs the transition between in-plane deformation and out-of-plane buckling and is therefore a key parameter for forming simulation. The influence of bending stiffness on preforming has received increasing attention in recent years. [6, 7] and [8] showed that curvature-dependent, nonlinear bending laws are essential for predicting realistic wrinkle formation. [9] further observed a strong dependence of bending stiffness on curvature, temperature, and strain rate in unidirectional prepregs. These studies underline that nonlinear bending behavior must be included for a physically consistent representation of textile forming.

Despite these advances, most conventional bending models for dry reinforcements assume constant and side-symmetric stiffness. However, experimental findings on UD-NCFs reveal two key phenomena that are not captured in conventional models: a side-dependent bending response due to topside asymmetric stitching and bottom-side glass fiber backing, and a pronounced nonlinear stiffness reduction at increasing curvature. These effects substantially influence wrinkle initiation and evolution during forming and must therefore be considered.

The present work addresses these limitations by developing and validating advanced bending models for UD-NCFs that explicitly account for side-dependent and nonlinear curvature-dependent behavior. Several mathematical formulations, including piecewise linear, polynomial, power-law, logarithmic, and exponential functions, are evaluated based on experimental cantilever bending tests. The most accurate models are implemented in Abaqus/Explicit using the VUGENS user subroutine and validated against experimental results. Hemispherical forming simulations are performed to analyze the influence of the new models on wrinkle formation and stiffness distribution.

2. Model Development for the Bending Behavior

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Material characterization of the bending behavior. The investigated material is a unidirectional non-crimp fabric (UD-NCF) without binder, produced by Zoltek TM . The reinforcement consists of PX35-50K continuous carbon fiber heavy tows, consolidated by a 76 dtex polyester (PES) yarn arranged in a tricot stitching pattern as shown in Figure 1 a). The fabric exhibits an areal weight of approximately 300 g m−2. Additionally, a thin layer of glass fiber yarns is integrated on the backside of the aligned fibers to enhance the fabric's stability and handling characteristics during forming operations (cf. Figure 1 b)).

[picture]

Fig. 1: Unidirectional non-crimp fabric from the a) front and b) back.

Fig. 1. Unidirectional non-crimp fabric from the a) front and b) back.

Cantilever bending tests were conducted by [10] to characterize the bending behavior of the UDNCF material. The tests were performed on specimens with a width of w0=100 mm, following the procedure outlined in the [11]. Each specimen was moved with a constant speed. The specimen bent under its own weight due to gravitational force. The specimen was moved until the first contact with the inclined surface with an incline angle of θ=41.5∘ was established. The experiment was repeated six times for each configuration, using a new specimen for each repetition. The bending behavior was investigated in fiber direction ( 0∘ ) and transverse to fiber direction ( 90∘ ). Additionally, the tests were conducted with the front and back sides facing upwards. The back side is defined as the side with the
backing of glass fibers. The average experimental deflection curves for the different configurations are included in Figure 2.

To measure the nonlinear bending behavior, an optical measurement of the curvature and calculation of the bending moment was performed. This was done by [10] using an optical evaluation method proposed by [12]. The bending moment-curvature curves determined from the experimental deflection curves are included in Figure 3 for the configurations 0∘-orientation front up and 0∘-orientation back up. Detailed information regarding the experimental setup and evaluation procedure can be found in [10].
Modeling the side-dependent bending behavior. The 0∘-orientation test resulted in a significantly higher bending stiffness compared to the 90∘-orientation test. In the 90∘-orientation test the load is mainly transmitted via the glass fiber backing and the stitching. It can be seen in Figure 2 that the overhang length is consistently higher when the front side is facing upwards.

[picture]

Fig. 2: Cantilever deflection curves: experimental (solid) and simulated (dashed) with different linear and nonlinear bending models for 0∘(a,c) and 90∘(b,d) orientations. The solid black line indicates the inclined surface of the cantilever test setup.

Fig. 2. Cantilever deflection curves: experimental (solid) and simulated (dashed) with different linear and nonlinear bending models for 0 ∘ ( a , c ) and 90 ∘ ( b , d ) orientations. The solid black line indicates the inclined surface of the cantilever test setup.

This can be attributed to the zigzag pattern of the stitching, as shown in Figure 1 a), which is under tension in these configurations and actively contributes to the bending stiffness. This is in contrast to the negligible stiffness of the stitching under compression. Therefore the experimental results indicate a side-dependent bending behavior of the material. This behavior is characterized by different bending moments and curvatures for the front and back sides of the material as shown in Figure 3 a) and b) for the 0∘-orientation.

To capture the side-dependent bending behavior, a piecewise function is proposed. This model assumes different bending stiffness values for positive and negative curvatures, which correspond to the front and back sides of the material respectively. The mathematical description of the proposed model is summarized in Table 1.

[picture]

Fig. 3: Bending moment over curvature ( a,b ) and bending stiffness over curvature ( c,d ) for 0∘-UDNCF front up (a, c) and back up (b, d). Experimental data (solid) and model fits (dashed).

Fig. 3. Bending moment over curvature ( a , b ) and bending stiffness over curvature ( c , d ) for 0 ∘ -UDNCF front up (a, c) and back up (b, d). Experimental data (solid) and model fits (dashed).

Modeling the nonlinear bending behavior. In addition to the side-dependent bending behavior, a nonlinear bending behavior is observed for both orientations of the UD-NCF material. This nonlinear behavior is evident from the experimental bending moment-curvature curves shown in Figure 3 a) and b). The bending stiffness-curvature curves in Figure 3 c) and d) further illustrate the nonlinear behavior, as the bending stiffness decreases with increasing curvature for the shown 0∘-orientation. The experimental stiffness-curvature curves were obtained by numerical differentiation of the mo-ment-curvature data. To capture this nonlinear bending behavior accurately, several mathematical functions are evaluated. These functions include a piecewise linear function, a second-order polynomial function, a power law function, a logarithmic function, and an exponential function. The mathematical descriptions are summarized in Table 2. The parameters of the different models are determined by fitting the bending moment-curvature curves obtained from the cantilever tests.

Table 1: Side-dependent bending models.

Fiber direction | B₁bu κ₁,    κ₁ < 0 B₁fu κ₁,    κ₁ ≥ 0
Transverse direction | B₂bu κ₂,    κ₂ < 0 B₂fu κ₂,    κ₂ ≥ 0

Table 2: Nonlinear bending models.

Model validation and parameter identification of the developed bending model. A common measure of model accuracy is the coefficient of determination, R2. It quantifies the proportion of variance in the observed data that is explained by the model and is defined as

R2=1−SSRSST=SSESST,(1)

where SST denotes the total sum of squares, SSE the explained sum of squares, and SSR the sum of squared residuals. These quantities are given by

SSE=∑i=1n(y^i−y¯)2, and SST=∑i=1n(yi−y¯)2.(2)

Here, yi represents the observed value at data point i,y^i the corresponding model prediction, y¯ the mean of all observed values, and n the total number of data points. An R2 value of 1 indicates a perfect model fit, meaning the model fully explains the observed variation.

In Figure 4 the R2 values for the different developed bending models are presented for both fiber orientations and bending directions. The results indicate that the linear and the exponential functions are not suitable for capturing the nonlinear bending behavior of the UD-NCF material, as they yield low R2 values across all configurations. Only for the 90∘-orientation with back side up a reasonable performance is observed because the bending moment-curvature curve in this configuration is almost linear. The other evaluated functions achieve consistently high R2 values, indicating their capability to represent the nonlinear bending behavior accurately. Due to their consistently high performance for all configurations, the piecewise linear function and the logarithmic function are selected for description of the nonlinear bending behavior.

[picture]

Fig. 4: Validation of the developed bending model in terms of the coefficient of determination R2. A higher R2 value indicates a better agreement with the experimental data.

Fig. 4. Validation of the developed bending model in terms of the coefficient of determination R 2 . A higher R 2 value indicates a better agreement with the experimental data.

The bending moment-curvature curves fitted with the piecewise linear function and the logarithmic function are shown in Figure 3 a) and b) for the 0∘-orientation with front side up and back side up, respectively, confirming the good agreement with the experimental data. Additionally, the linear bending moment-curvature curve obtained from the bending stiffness calculation according to [2] is included. The corresponding bending stiffness-curvature curves are shown in Figure 3 c) and d). For moderate curvatures, the derivation of the logarithmic model shows a better agreement with the experimental bending stiffness than the piecewise linear model. For low and high curvatures, the logarithmic model shows deviations from the experimental bending stiffness. The piecewise linear model exhibits constant bending stiffness up to the switching curvature κs, followed by a discontinuous stiffness drop at higher curvatures.

3. Validation on Coupon Test

The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

Simulation setup. The cantilever bending tests are simulated using Abaqus/Explicit. The side-dependent and nonlinear bending models are implemented in the user-subroutine VUGENS previously developed by [12, 13]. The VUGENS subroutine enables direct specification of the moment-curvature relationship at each integration point. Given that the cantilever tests represent a pure bending load, membrane effects are not considered in the simulations. The Young's modulus Eanalytical cant  required for the VUGENS user subroutine is derived from the bending stiffness B(κ) according to classical beam theory as

Eanalytical cant=B(κ)I(3)

with I being the area moment of inertia of the cantilever cross-section. The model geometry corresponds to the average experimental overhang length for each configuration. The specimen is discretized with SR3 shell elements of approximate size 5 mm . Boundary conditions are defined with one edge fully fixed and the opposite edge free. Loading is applied as a gravitational force, represented by equivalent concentrated forces acting on all mesh nodes, reproducing the distributed specimen weight observed experimentally.
Comparison of experimental and simulation results. The deflection curves obtained from the cantilever tests for both 0∘ - and 90∘-UD-NCF specimens are presented in Figure 2. The experimental results (solid lines) are compared to the simulation results (dashed lines) using the developed sidedependent, nonlinear bending models. The side-dependent, piecewise linear, and logarithmic bending models predict nearly identical deflection curves for all configurations. In contrast, the linear model following [2] consistently overestimates the deflection. Notably, at higher curvatures (corresponding to smaller values of the x-coordinate), the side-dependent, nonlinear models provide noticeably improved accuracy compared to the linear bending model. Overall, the simulated deflection curves lie within the experimental standard deviation bands, confirming the accuracy of the implemented bending formulations.

4. Demonstration on a Complex Forming Geometry

The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

Simulation setup. The hemisphere forming tests are simulated using Abaqus/Explicit. The hemisphere forming test is a common benchmark for evaluating forming simulation approaches [13-15]. The simulation model is shown in Figure 5. The setup consists of a hemispherical punch with a radius of 75 mm (green) and a flat die featuring a circular opening of radius 80 mm (blue). No blankholders are used to intentionally promote the development of wrinkles during forming. Both the punch and die are modeled as discrete rigid surfaces. The punch motion is prescribed by a Dirichlet displacement boundary condition of u3=60 mm in direction of e3, while the die is fully constrained in all translational and rotational degrees of freedom. The ply specimen is represented as a quadratic sheet with an edge length of 280 mm . The fibers are oriented in e1-direction. Therefore, due to symmetry of the problem, the setup can be simplified to model only one quarter of the entire configuration using symmetry boundary conditions along the planes defined by the e1 - and e2-axes, as illustrated in Figure 5.

The edge length of the quarter-ply (beige) is 140 mm . The ply is discretized using a superimposed mesh of 3136 M3D3 and 3136 S3R elements with an element edge length of 5 mm . The superimposed element formulation with shared nodes is chosen to decouple the membrane and bending behavior of the fabric material [16]. The elements of the meshed ply are aligned along the fiber direction to prevent numerical intra-ply locking [17]. The ply represents a single layer of the UD-NCF material with a thickness of 0.4959 mm .

[picture]

Fig. 5: Hemisphere forming simulation setup without blankholders, adopted from [10].

Fig. 5. Hemisphere forming simulation setup without blankholders, adopted from [10].

The membrane material response is modeled using a pseudo-invariant-based hyperelastic formulation according to [15], implemented via the user-defined material subroutine (VUMAT) and applied to the M3D3 elements. The bending behavior is described using the standard linear bending model of [2] as well as the developed side-dependent, nonlinear bending models, both implemented through the VUGENS subroutine and applied to the S3R elements. The tool-ply interaction is defined using the built-in general contact algorithm of Abaqus/Explicit.
Comparison of simulation results. The simulations were performed on an AMD EPYC 7313P system with 16 cores and 256 GB of RAM.

Each simulation was executed in parallel using 4 cores, resulting in an average computation time of approximately 2 min per simulation.

Figure 6 shows a comparison of the resulting displacement fields u3, contrasting the models without side-dependency in a) with the models considering side-dependency in b). Due to symmetry, the result of the linear bending model in I is mirrored to fill the upper half. The nonlinear models II and III predict very similar wrinkle characteristics in terms of both location and amplitude. In the linear model I, a pronounced wrinkle appears in the e1-direction, caused by the fibers being aligned along e1, whereas in e2-direction only a slight indentation can be observed. In contrast, the wrinkles predicted by the nonlinear models in e1-direction are wider that those of the linear model, and the nonlinear models now predict a clearly developed wrinkle in e2-direction. The wrinkle amplitude is increased for the piecewise linear model II compared to the logarithmic model III, especially for the wrinkle in e1-direction. When comparing side-dependency effects, the non-side-dependent models in Figure 6 a) and the side-dependent models in Figure 6 b) show similar overall wrinkle patterns. However, the side-dependent models in Figure 6 b) exhibit a slightly increased wrinkle amplitude compared to the non-side-dependent models in Figure 6 a), with this effect being particularly noticeable for the wrinkle in e1-direction.

Figure 7 illustrates the stiffness distribution E1 in the fiber direction e1 without differentiating whether the stiffness is used for positive or negative curvatures. For the linear model I in Figure 7 a), the stiffness remains constant because side-dependent and nonlinear effects are not captured. In contrast, the nonlinear models II and III in Figure 7 a) and b) show a stiffness variation depending on the curvature. Due to the continuity of the logarithmic function, the stiffness distribution of model III is smoother than that of model II, which is based on a piecewise definition. For small curvatures, the higher stiffness of model III compared to model II, as shown in Figure 3 c) and d), can be attributed to the shape of the underlying functions of the bending models. Overall, the results confirm that regions with low curvature exhibit lower stiffness values, whereas areas with higher curvature display

[picture]

Fig. 6: Displacement field u3 for the hemisphere forming test, comparing a) non-side-dependent and b) side-dependent bending models (I: linear Peirce, II: piecewise linear, III: logarithmic).

Fig. 6. Displacement field u 3 for the hemisphere forming test, comparing a) non-side-dependent and b) side-dependent bending models (I: linear Peirce, II: piecewise linear, III: logarithmic).

[picture]

Fig. 7: Stiffness distribution E1 (front-up/back-up) for the hemisphere forming test, comparing bending models a) without side-dependency and b) with side-dependency
(I: linear Peirce, II: piecewise linear, III: logarithmic).

Fig. 7. Stiffness distribution E 1 (front-up/back-up) for the hemisphere forming test, comparing bending models a) without side-dependency and b) with side-dependency (I: linear Peirce, II: piecewise linear, III: logarithmic).

increased stiffness, as expected. When comparing side-dependency effects, the side-dependent models in Figure 7 b) show slightly lower stiffness values compared to the non-side-dependent models in Figure 7 a). The lower stiffness values for the side-dependent models correlate with the slightly increased wrinkle amplitudes observed for the side-dependent models in Figure 6. The logarithmic model is preferred over the piecewise linear model because it avoids stiffness jumps and is therefore more physically plausible.

5. Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

This study presents the development and validation of advanced bending models to accurately represent the mechanical response of unidirectional non-crimp fabrics (UD-NCFs) during forming. Two key characteristics were identified and modeled: side-dependent behavior arising from the glass fiber backing that contributes to bending stiffness, and nonlinear bending behavior characterized by decreasing stiffness with increasing curvature. Several constitutive formulations were evaluated, among which the piecewise linear and logarithmic models achieved the highest accuracy, with R2 values approaching unity across all fiber orientations and bending directions.

The models were implemented in Abaqus/Explicit via the VUGENS subroutine and validated against cantilever bending tests. The simulations showed good agreement with measured deflection curves. Both nonlinear formulations reproduced the experimental response within the experimental standard deviation, while the classical linear model by [2] consistently overestimated deflections, confirming the necessity of including nonlinear and side-dependent effects.

Application to hemispherical forming simulations demonstrated significant differences between the linear and nonlinear bending models in predicting wrinkle formation. While the linear Peirce model predicted a single pronounced wrinkle exclusively in fiber direction ( e1 ), the nonlinear models captured additional wrinkles in the transverse direction ( e2 ) and exhibited wider wrinkle patterns along e1. The piecewise linear and logarithmic models showed very similar wrinkle characteristics, with the piecewise model predicting slightly larger wrinkle amplitudes, especially along e1. The comparison of side-dependency effects revealed that side-dependent models exhibited slightly increased wrinkle amplitudes compared to non-side-dependent models, particularly in fiber direction. The predicted stiffness distribution reflected the expected curvature dependence, with the logarithmic model providing smoother transitions due to its continuous derivative.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

The authors thank the Bundesministerium für Wirtschaft und Klimaschutz (BMWK, German Federal Ministry for Economic Affairs and Climate Action) for funding the "LuFo" research project "Efficient aerospace structures manufactured from carbon fiber-reinforced polymers using fully automated, linked and ultra-high-speed processes" (ELECTRA, project no. 20W1912D), for which the work was performed. This work is also part of the Heisenberg project "Digitalization of fiber-reinforced polymer processes for resource-efficient manufacturing of lightweight components" (project no. 455807141), funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation).

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The original version of this paper is available on https://www.scientific.net/MSF.1182.13.pdf

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F. Yu, S. Chen, J. V. Viisainen, M. Sutcliffe, L. T. Harper, and N. A. Warrior, "A macroscale finite element approach for simulating the bending behaviour of biaxial fabrics," Composite Science and Technology, vol. 191, Jan. 2020.

F. Yu, S. Chen, L. Harper, and N. Warrior, "Simulating the effect of fabric bending stiffness on the wrinkling behaviour of biaxial fabrics during preforming," Composites Part A: Applied Science and Manufacturing, vol. 143, Jan. 2021.

P. H. Broberg, E. Lindgaard, A. J. Thompson, J. P. H. Belnoue, S. R. Hallett, and B. L. V. Bak, "An accurate forming model for capturing the nonlinear material behaviour of multilayered binder-stabilised fabrics and predicting fibre wrinkling," Composites Part B: Engineering, vol. 274, p. 111268, Apr. 2024.

Z. Zhao, K. Zhang, H. Cheng, Y. Zeng, and B. Liang, "Experimental characterization and numerical modelling of bending behavior of carbon fiber unidirectional thermoset prepregs," Journal of Reinforced Plastics and Composites, p. 073168442311613, Jan. 2023.

B. Schäfer, Macroscopic forming simulation of unidirectional non-crimp fabrics: Hyperelastic material modeling and 3D-solid-shell approach. Doctoral Thesis, KIT, Karlsruhe, 2024.

ASTM D1388-18 standard, "ASTM D1388-18: Standard Test Method for Determining the Flexural Stiffness of Medical Textiles," Apr. 2018.

C. Poppe, T. Rosenkranz, D. Dörr, and L. Kärger, "Comparative experimental and numerical analysis of bending behaviour of dry and low viscous infiltrated woven fabrics," Composites Part A: Applied Science and Manufacturing, vol. 124, p. 105466, Jan. 2019.

D. Dörr, F. J. Schirmaier, F. Henning, and L. Kärger, "A viscoelastic approach for modeling bending behavior in finite element forming simulation of continuously fiber reinforced composites," Composites Part A: Applied Science and Manufacturing, vol. 94, pp. 113-123, Jan. 2017.

F. J. Schirmaier, D. Dörr, F. Henning, and L. Kärger, "A macroscopic approach to simulate the forming behaviour of stitched unidirectional non-crimp fabrics (UD-NCF)," Composites Part A: Applied Science and Manufacturing, vol. 102, pp. 322-335, Jan. 2017.

B. Schäfer, D. Dörr, R. Zheng, N. Naouar, and L. Kärger, "A hyperelastic approach for modeling the membrane behavior in finite element forming simulation of unidirectional non-crimp fabrics (UD-NCF)," Composites Part A: Applied Science and Manufacturing, vol. 185, p. 108359, Oct. 2024.

P. Boisse, N. Hamila, E. Vidal-Sallé, and F. Dumont, "Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses," Composites Science and Technology, vol. 71, pp. 683-692, Jan. 2011.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 23-29

doi: 10.4028/p-ScfP7t

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

Submitted:
2026-01-18

Revised:
2026-02-14

Accepted:
2026-02-14

Online:
2026-04-10

Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

Vitantonio Esperto 1,a*, Felice Rubino 1, b, Fausto Tucci 1,c and Pierpaolo Carlone 1, d

¹Department of Industrial Engineering, University of Salerno, Fisciano (SA) 80084, Italy

a  vesperto@unisa.it, b  frubino@unisa.it, cftucci@unisa.it, d  pcarlone@unisa.it, (*corresponding author)

Keywords: Composites, Machine learning, In-process measurement, Digital twin.

Abstract

The impregnation represents a crucial phase in liquid composite molding (LCM) processes. Researchers over the years have used various approaches for monitoring, based on smart weave, pressure sensors, dielectric. Among the LCM processes, the vacuum bag allows the use of visual systems for detecting the resin flow front. The integration of monitoring systems with controllers for automated management of process parameters leads to an improvement in the characteristics of the final manufactured component. In the present work, an AI-based system integrated with the control of a resin preheating system allows for improvement of the impregnation stage. A machine learning approach, based on the You Only Look Once (YOLO) algorithm, has been integrated with the visual monitoring system to detect and dynamically track the resin flow front in real time. The flow front position has been compared with the theoretical one, evaluated by using the Darcy's law and based on the mismatch the controller suggests a proper in-time regulation of microwave power. The implemented system is capable of processing images through an AI-based algorithm and extracting the kinematic data of the flow front and integrating the information from the thermocouples and the visual system to control the microwave power.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

In recent years, the use of composite materials for the manufacturing of components has been increasing, justified by their ability to significantly reduce weight; in line with recent findings, this trend is particularly evident in the automotive and EV sectors, where composites contribute not only to lightweight design but also to improved aerodynamic performance, enhanced mechanical strength, greater durability, and overall higher energy efficiency, thus meeting the growing demand for more efficient and sustainable vehicles[1]. Liquid Composite Molding processes have emerged as a versatile and cost-effective class of manufacturing technologies for composite structures, enabling the production of high-performance components through the impregnation of dry fiber preforms. In LCM [2], [3] the flow front position in porous media is controlled by the balance between viscous and capillary forces acting over distinct void scales. Viscosity influences displacement differently across scales, it strongly amplifies macroscopic viscous forces. Therefore, in liquid composite molding processes, the advancement of the flow front assumes great importance, both with regard to the time required to produce the part and the level of quality achieved in terms of defects, such as voids or dry spots. Different systems are used by researchers to evaluate the position of the flow front, some less invasive based on dielectric sensors [4], visual systems[5], and others more invasive[6]. Yu Y. et al. in [7] used embedded fiber optic (FBG) sensors to locally detect resin arrival within different laminate layers, and their measurements, combined with piezoelectric data, enabled accurate real-time reconstruction of the three-dimensional resin flow front during the infusion process. Fernandez Leon et al. [8]present a digital twin for analyzing the resin transfer molding (RTM) process, aimed at detecting non-uniform resin flow and potential defects such as dry spots. The approach uses two deep learning surrogate models trained on synthetic simulation data to enable accurate, real-time monitoring of flow and pressure, achieving prediction errors below 1% and demonstrating good agreement with experimental results. Several authors have exploited the
integration of flow front detection with control, with particular reference to the preheating of the resin. Therefore, by acting on the viscosity and preheating the resin, the infusion time can be reduced[9] [10]. In this work, a digital twin of the Seeman Composites Resin Infusion Molding Processes (SCRIMP), with a resin preheating system using a microwave, has been implemented. The purpose of this digital twin is to control the power to be delivered through the microwave. The system is composed by two environments: a physical one, from which it acquires temperature and visual data [5], and a digital one which evaluates the resin flow front position by means of a machine learning algorithm and compares it with the position obtained by modeling of the infusion phenomenon using Darcy's law. Finally, the system determines the variation in the power delivered by the microwave.

Materials and Methods

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

The vacuum bag is set up by stacking 8 sheets of glass fibers HexForce twill 2/2, with areal density of 390 g/m2 and a sheet of flow medium RDA130V150, with areal density of 130 g/m2, prelaminated with a ELA 20 film; the resin used is SX10EVO, premixed with the Epoxy based hardener in the mixing ratio of 100:26, with a viscosity of 0.8Pas@25∘C. A SCRIMP process was used to manufacture panels of 240×300×2.6 mm3.

[picture]

Fig. 1 Laboratory-scale SCRIMP setup: (a) schematic of the process, showing the microwave resin preheating system, mold, and data acquisition setup; (b) photograph of the mold, highlighting the preheated resin inlet (top-left arrow) and the resin outlet toward the vacuum pump (bottom-right arrow).

Fig. 1. Laboratory-scale SCRIMP setup: (a) schematic of the process, showing the microwave resin preheating system, mold, and data acquisition setup; (b) photograph of the mold, highlighting the preheated resin inlet (top-left arrow) and the resin outlet toward the vacuum pump (bottom-right arrow).

Fig. 1a illustrates the laboratory-scale setup of the SCRIMP process, integrated with a microwave system for resin preheating. A positive pressure applied to the resin catch pot (1) drives the catalyzed resin, at a flow rate of 0.19 L/min, into the resin vessel (2), passing through the microwave (MW) preheating system (3). The resin then flows through the porous medium (4), guided by a vacuum generated by the vacuum pump (5), which is connected to the vacuum bag via a resin trap (6). The fluid is conveyed through PTFE pipes with an inner diameter of 10 mm . The developed digital twin system consists of a virtual replica based on Darcy's law, integrated with the physical environment via three thermocouples: the first (7) positioned before the MW system; the second (8) measuring the temperature at the exit of the MW system, to prevent it from exceeding 39∘C and causing premature polymerization; and the third (9) placed at the mold inlet to monitor the resin temperature for viscosity evaluation. A camera (10) records the process, enabling flow front monitoring through a machine learning approach based on the You Only Look Once (YOLO) algorithm, with data acquisition and processing carried out on a laptop (11). A more detailed description can be found in [5]. A picture of lab scale system is depicted in Fig. 1b.

Fig. 2 shows a scheme of the digital twin, the physical environment is composed by a camera and three thermocouples to acquire information on the resin flow together with a MW system to preheat the resin; the digital environment is made by an Arduino board to read the thermocouples signals, and a python code implemented on a laptop. The frames captured by the camera are first processed using a YOLO algorithm to detect the resin flow front, see Fig. 3. Then, the system evaluates and compares the real flow front position obtained from YOLO with the theoretical position predicted by a Darcy's law model. Moreover, this comparison is used to manage the MW.

[picture]

Fig. 2 Digital twin scheme.

Fig. 2. Digital twin scheme.

[picture]

Fig. 3 Flow front obtained from YOLO elaboration.

Fig. 3. Flow front obtained from YOLO elaboration.

For each frame, the coordinates of the resin flow front are determined. The values corresponding to the mold's centerline (see Fig. 4) are extracted and plotted as the acquired position in Fig. 5. The temperature measured by the thermocouple at the mold inlet is used to estimate the resin viscosity, which is then applied in the Darcy model to predict the flow front, shown as the estimated position in Fig. 5.

[picture]

Fig. 4 Flow front position.

Fig. 4. Flow front position.

The MW Control block of the digital twin monitors, for each frame, both the acquired position obtained via the YOLO algorithm, and the estimated position predicted by the Darcy model. As shown in magnification (a) of Fig. 5, if the acquired flow front lags behind the estimated one, the MW power is increased; otherwise, it is decreased. In the former case, highlighted in (a), a check on the maximum temperature after the MW system is performed to prevent premature polymerization.

[picture]

Fig. 5. Control logic: resin flow front positions-acquired by YOLO and estimated by the Darcy model. (a) Estimated exceeds acquired; (b) acquired exceeds estimated.

Fig. 5. Control logic: resin flow front positions-acquired by YOLO and estimated by the Darcy model. (a) Estimated exceeds acquired; (b) acquired exceeds estimated.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

Fig. 6 shows the results of the laboratory test, specifically in Fig. 6a the acquired positions, evaluated using YOLO, and the estimated positions, using the model based on Darcy's law, are reported.

[picture]

Fig. 6 Results: a) resin flow front positions acquired and estimated; b) temperatures acquired.

Fig. 6. Results: a) resin flow front positions acquired and estimated; b) temperatures acquired.

In Fig. 6b, instead, the temperatures before MW , after MW , and at the mold entrance are shown. Furthermore, in the first one, the value 300 mm is reported, which represents the length of the mold; in the second, there are the two limits in terms of temperature: 39∘C, which represents the maximum value that can occur at the MW outlet, beyond this value premature polymerization may occur and 35∘C which is used to manage power control. Points 1 to 5 shown at the top of Fig. 6b highlight the operation of the DT. In the time between the starting and point 1 , the acquired position of the resin flow front is lower than estimated, and therefore the power is increased. At point 1, although this condition is still met, the temperature has reached the 39∘C limit, which must not be exceeded to prevent premature polymerization. Therefore, the MW power is reduced, resulting in a decrease in T_after MW. Once the temperature reaches 35∘C, the estimated position of the flow front is still ahead of the acquired one. This corresponds to point 2, where the power is then increased. The same discussion applies to points 3 to 5 . The test ends at about 530 s . From Fig. 6b it can be seen that the resin temperature before the MW is about 24∘C and the temperature at the mold inlet varies between a minimum value of 28∘C and a maximum of 33∘C, with an average value of 31∘C.

Conclusions

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

A feedback control system for microwave power has been implemented, based on resin flow front position values evaluated through an AI-based approach, specifically using You Only Look Once (YOLO) algorithm. It is capable of assessing the instantaneous position of the flow front and comparing it with that estimated via a flow model based on Darcy's law. The system monitors the resin flow front positions and the maximum temperature the resin can withstand before premature polymerization occurs.

Acknowledge

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

Funding: This research was funded by the project 'National Centre for Sustainable Mobility' (cod. CN00000023-CUP D43C22001190001)-National Recovery and Resilience Plan PNRR-Italian Ministry of University and Research.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.23.pdf

A. Wazeer, A. Das, C. Abeykoon, A. Sinha, and A. Karmakar, "Composites for electric vehicles and automotive sector: A review," Feb. 01, 2023, Elsevier B.V. doi: 10.1016/j.geits.2022.100043.

T. C. Garrett, Q. S. Allen, and A. R. George, "In-Situ Void Formation During Liquid Composite Molding for Preformed Warp, Weft, and Alternating Orientation RTM Samples," Applied Composite Materials, vol. 33, no. 1, Feb. 2026, doi: 10.1007/s10443-025-10402-9.

V. Esperto, L. Boccarusso, M. Durante, L. Carrino, and P. Carlone, "Permeability analysis of natural and artificial fiber textiles for liquid composite molding process," in Procedia Manufacturing, Elsevier B.V., 2020, pp. 435-439. doi: 10.1016/j.promfg.2020.04.328.

F. Zhang, H. Guo, X. Lu, H. Zhou, Z. Huang, and H. Zhou, "A novel dielectric sensor design for identifying the direction of resin flow front in liquid composite molding," Composites Communications, vol. 53, Jan. 2025, doi: 10.1016/j.coco.2024.102241.

V. Esperto, C. Gallo, S. Lomov, J. Soete, and P. Carlone, "System Integration for Advanced Manufacturing of Composites by Microwave Preheated Resin Infusion: An Experimental Study," J. Mater. Eng. Perform., vol. 34, no. 10, pp. 8759-8767, May 2025, doi: 10.1007/s11665-024-10397-7.

F. Zhang et al., "Designed multifunctional sensor to monitor resin permeation and thickness variation in liquid composite molding process," NDT and E International, vol. 142, Mar. 2024, doi: 10.1016/j.ndteint.2023.103023.

Y. Yu, X. Cui, Z. Liang, X. Qing, and W. Yan, "Monitoring of three-dimensional resin flow front using hybrid piezoelectric-fiber sensor network in a liquid composite molding process," Compos. Sci. Technol., vol. 229, Oct. 2022, doi: 10.1016/j.compscitech.2022.109712.

J. Fernández-León, K. Keramati, L. Baumela, and C. González, "A digital twin for smart manufacturing of structural composites by liquid moulding," International Journal of Advanced Manufacturing Technology, vol. 130, no. 9-10, pp. 4679-4697, Feb. 2024, doi: 10.1007/s00170-023-12637-x.

V. Esperto, M. Durante, P. Carlone, and L. Carrino, "Resin microwave preheating in liquid composite molding process," in AIP Conference Proceedings, American Institute of Physics Inc., Jul. 2019. doi: 10.1063/1.5112650.

F. Rubino, F. Tucci, V. Esperto, and P. Carlone, "Filling Time Reduction in Liquid Composite Molding Processes," Journal of Composites Science, vol. 6, no. 8, Aug. 2022, doi: 10.3390/jcs6080222.

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/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 31-40

doi: 10.4028/p-I0gnEM

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

Submitted:
2026-01-20

Revised:
2026-02-13

Accepted:
2026-02-23

Online:
2026-04-10

Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

Tucci Fausto 1,a*, Viscusi Antonio 2,b, Palmieri Barbara 3,c, Perna Alessia Serena 4, d, Martone Alfonso 5,e and Astarita Antonello 6,f

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

2 Department of Engineering and Sciences, Faculty of Technology and Innovation Sciences, Universitas Mercatorum, Piazza Mattei 10, 00186 Rome, Italy

3 Institute of Polymers, Composite and Biomaterials (IPCB), National Research Council of Italy, 80055, Portici, Italy

4 Department of Chemical, Materials and Industrial Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Naples, 80125, Italy

aftucci@unisa.it, bantonio.viscusi@unimercatorum.it, c  barbara.palmieri@ipcb.cnr.it, d alessia.perna@unina.it, e alfonso.martone@cnr.it, f antonello.astarita@unina.it

Keywords: vitrimer matrix composites, vitrimer flow, cold spray.

Abstract

Aiming to minimize time, energy, and materials-consuming trial and error experimental analyses, a numerical modeling approach of vitrimer flow and cold spray deposition is proposed in this work. The characteristics of vitrimeric matrices were evaluated by elaborating data from previously performed differential scanning calorimetry and dynamic mechanical analysis. The pieces of information related to the transition temperatures and mechanical evolution after curing were exploited to feed the numerical models and to run sensitivity analyses. The flow model is based on prior evaluation of the dry reinforcement permeability at a micro- and meso-scale. The flow model has been implemented using a commercial simulative environment based on the control volumes approach. A single impacting particle was simulated in a finite element environment to analyze, in a focused way, the deposition mechanisms. The objective of this analysis is the integrated implementation of a numerical model for vitrimer flow through carbon fabric reinforcement in infusion processes and single particle deposition on vitrimer matrix composite substrates.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

In current industry, fiber-reinforced polymers represent a relevant solution to achieve high strength and properties customization coupled with low weight [1]. These features made the composite materials particularly appealing for both high performance and sustainability during the in-service life [2]. The mechanical behavior of these multi-phase materials is based on the capability of precisely orienting the continuous reinforcing filaments [3]. Due to this reason, most processes in high-volume production are evolving towards automation and robotization [4], [5], [6], [7]. In this context, research community is devoting relevant efforts towards the development of composites that are reparable, reformable, weldable, and which can be coated by metal and metallic alloy particles.

Vitrimeric resin systems represent a disruptive innovation in polymers. Vitrimers, a novel class of covalently crosslinked polymers capable of network rearrangement through dynamic covalent exchange reactions, combine the mechanical stability of thermosets with the reprocessability of thermoplastics [8]. Their unique viscoelastic and time-dependent mechanical behavior makes them promising candidates for next-generation functional coatings and hybrid composites. This molecular structure enables them to be reprocessed after curing for repairing or to operate further manufacturing steps. In particular, the authors are studying the feasibility of cold spray depositions on vitrimer matrix composites [9], [10].

Cold spray is a solid-state deposition process in which metallic particles are accelerated to supersonic velocities and impact a substrate to form coatings without melting [11]. Over the past two
decades, a substantial body of experimental and numerical research has been devoted to understanding the mechanisms of particle impact, deformation, and bonding in cold spray, particularly in metal-to-metal and metal-to-polymer systems [12]. Despite these advances, most studies have focused on thermoplastic or thermosetting polymer substrates [13], whereas vitrimer materials have received little attention.

To the authors' best knowledge, no previous numerical investigations have addressed the adhesion mechanisms between metallic particles and vitrimer substrates in cold spray conditions.

The present work aims to fill this gap by developing a finite element (FE) model of a single copper particle impacting an epoxy vitrimer substrate. This study represents a first step toward understanding the feasibility and underlying physics of metal-vitrimer deposition via cold spray by numerical approach. This study considers the carbon reinforced vitrimers manufacturing by infusion and the successive coating of their surface by cold spray. In particular, the activity focuses on the numerical modeling of the processes. The numerical approaches, previously implemented and validated on conventional materials, are applied in this study considering an innovative vitrimeric matrix.

Numerical Procedures

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

Modeling of vitrimer infusion.

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

The vitrimer considered is an epoxy-based system enriched with zinc acetil-acetate, and it has been widely described and characterized in previous works [14]. The model implemented aims to simulate the infusion of carbon fiber fabrics (twill 2−2,380 g/m2,12k tow) within a square plant mold having dimensions of 100 mm in length and width and depth of 5 mm . The reinforcement is constituted by 3 layers of carbon fabrics, and it has been concentrated at the lower 3.5 mm of the mold in order to leave a sufficient layer of non-reinforced vitrimer to safely receive the successive cold spray deposition avoiding the erosion of the filaments. Due to this reason, the successive cold spray model can consider a pure vitrimeric substrate, excluding the presence of fibers in the portion of material involved.

The infusion models are based on Darcy's law correlating the vitrimer flow velocity u¯, the permeability tensor of the dry reinforcement K¯―, which in this analysis is assumed to be one unique porous medium, the rheological behavior of the impregnating flow η, and the three-dimensional pressure gradient ∇¯P realized by the vacuum pump into the mold cavity. Darcy's law definition is expressed as:

u¯=−η−1K¯―∇¯P(1)

The evaluation of the permeability is based on the analysis of the average distribution of the fibers in the tow, on their dimensions, concentration and on the geometrical features of the fabrics [15], [16]. Experimental and analytical studies demonstrated that during the infusion, the porosity and the thickness of the fibrous medium undergoes variations due to the absorption of resin by the fabrics [17]. Nevertheless, in the present analysis, this effect has been neglected due to the rigid mold. The fabrics were observed in dry conditions and after impregnation in order to define their geometrical characteristics and the cross-section of the tows. Fig. 1 illustrates the process from geometry acquisition to the digitalization of the fabrics. A dual scale permeability model has been implemented following the procedure described by the scientific literature [18].

The rheology of the vitrimer has been evaluated based on the results of the dynamic mechanical analysis (DMA) reported in a previous publication from the same group [19], by considering in each temperature condition the stress σ*, the strain ε and the testing frequency ω according to the following model:

η=σ*/(εω)(2)

The process simulated is a vitrimer infusion in a rigid mold replicating the process described in a previous work [19]. The initial temperature of 75∘C was set for the entire domain. The temperature of 75∘C has been set as a boundary condition for the lower mold, while adiabatic wall condition has
been set for the upper mold. The resin is infused at a temperature of 80∘C with a pressure gradient of 0,94bar. In conventional infusion processes, the resin preheating is a consolidated practice to improve the reinforcement impregnation and reduce the cycle time [20], [21] The model has been implemented in the numerical environment of the commercial module Ansys CFX.

[picture]

Fig. 1. Observation and digitalization of the reinforcement for permeability prediction.

Fig. 1. Observation and digitalization of the reinforcement for permeability prediction.

Modeling of cold spray deposition.

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

In this section, the authors describe the finite element (FE) modeling of a single copper particle impacting an epoxy vitrimer substrate, conducted using a commercially available FEA software package. Given the novelty of this study, the initial numerical approach assumes the substrate to be unreinforced. The following subsections detail the geometric parameters and material models employed in the simulations.

Both the particle and the substrate were modeled using a Lagrangian reference frame, a common approach in literature for simulating high-velocity impacts while minimizing computational effort [22], [23]. The simulation considered a spherical particle impacting perpendicularly onto a substrate that was at least five times larger than the particle, implemented through a 2D axisymmetric model using explicit dynamic analysis with adiabatic heating effects included. The chosen size ratio ensured that elastic wave reflections from the boundaries did not interfere with the particle-substrate interface during impact [24].

The particle diameter, dp, was set to 18μ m. The computational domain was divided into several regions to achieve a refined mesh with a gradual transition in element size near the particle-substrate interface. Both the particle and the substrate were discretized using 4-node reduced integration elements (CAX4R). The nominal mesh size for the particle was dp/25, and the same mesh density was applied to the substrate interface region to maintain solution accuracy. This mesh configuration was validated through a mesh sensitivity analysis, which is not included here for brevity. The bottom and right edges of the substrate were fully constrained in all degrees of freedom.

The particle's impact velocity and the initial temperatures of both the particle and the substrate were defined as initial conditions. The effects of gravity and air resistance were neglected. Friction and heat generation due to plastic deformation were incorporated into the model. The tangential contact behavior was governed by a friction coefficient using the Surface-to-Surface algorithm, with a value of 0.35 assigned to all contact surfaces [25].

The details of the schematization and the resulting FE model of the impact system are shown in Fig. 2.

[picture]

Fig. 2. Schematization (not in scale) and resulting FE model of single particle deposition.

Fig. 2. Schematization (not in scale) and resulting FE model of single particle deposition.

The impact simulations were carried out by varying the velocity of the particle (Vi) between 50 m/s and 400 m/s, with an increasing step of 50 m/s. In order to capture the different deposition mechanisms on vitrimers, the simulations were performed at temperatures below, slightly above, and significantly above the freezing temperature of the epoxy-based vitrimer ( Tv=170∘C as found in previous work [26]), namely: T1=25∘C,T2=175∘C,T3=220∘C. The percentage penetration depth after the impact was calculated as control parameter, according to Eq. 3. Note that Hs and Hs,i are the substrate height before and after the impact, respectively.

 Penetration depth [%]=HS−HS,iHS×100. (3)

The material modeling of the epoxy vitrimer substrate was performed under the assumption that the material exhibits thermosetting, brittle behavior below the vitrimeric transition temperature and ductile, thermoplastic-like behavior - similar to PMMA polymer - above Tv. Based on this temperature-dependent behavior, the Johnson-Cook (JC) plasticity model was adopted to characterize the mechanical response of both the substrate (above Tv) and the copper particle. The relevant material parameters obtained from the literature are summarized in Table 1 [27], [28], [29].

Table 1. Material parameters for copper and vitrimer.

Material parameter | Copper | Vitrimer
|  | Epoxy (T< Tv) | PMMA (T> Tv)
Density, [kg/m³] | 8960 | 1180 | 1180
Young's modulus, [GPa] | 124 | 3.6 | 3.3
Poisson ratio | 0.34 | 0.3 | 0.35
Tensile strength [MPa] | \\ | 60 | \\
Thermal conductivity, [W/m °C] | 386 | 0.25 | 0.25
Heat capacity, [J/kg·°C] | 383 | 1470 | 1470
Melting temperature, [°C] | 1083 | \\ | 270
A, [MPa] | 90 | \\ | 55
B, [MPa] | 292 | \\ | 312
n | 0.31 | \\ | 0.62
C | 0.025 | \\ | 0.105
Reference strain rate, ε̇₀, [s⁻¹] | 1.0 | \\ | 0.001
Thermal exponent, m | 1.09 | \\ | 0.8
Inelastic heat fraction | 0.9 | \\ | 0.9
Reference temperature, TR, [°C] | 298 | \\ | 170

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

The rheological behavior evaluated from DMA data is reported in Fig. 3.

[picture]

Fig. 3. Rheology of vitrimeric material.

Fig. 3. Rheology of vitrimeric material.

In the specific testing conditions (frequency of 1 Hz and heating rate of 3∘C/min ) the vitrimer curing activation occurs at 79∘C and the viscosity sensibly increases. Once the peak is reached (temperature of 112∘C, viscosity of 0.190 Pa s ) the material exhibits the typical vitrimer resoftening, with a new decrease of viscosity reaching values oscillating around 0.06 Pa s . The rheological behavior of the considered vitrimeric system can be described by the following model:

η={0.0093exp[0.082(T−79∘C)],T<112∘C0.1216exp[−0.049(T−112∘C)],T≥112∘C.(4)

This rheological behavior has been included into Eq. (1) to model the matrix flow through the fibrous preform. The vitrimer infusion simulation evidence that the unsaturated flow crosses the mold length of 100 mm in 64 s , and the full saturation of the reinforcement occurred in 240 s .

This section presents the results of the finite element (FE) modeling. Specifically, when the particle impacts the substrate at 25∘C, the vitrimer exhibits behavior characteristic of a thermosetting, brittle material, as shown in Fig. 4. Particularly, it can be seen that no plastic deformation occurs in either the particle or the substrate, and material damage initiates at an impact velocity of 50 m/s. The von Mises stress distribution and the substrate damaged zone are shown in Fig. 4a and Fig. 4b, respectively, under these conditions.

[picture]

Fig. 4. The von Mises stress distribution (a) and the substrate damaged zone (b) at VI=50 m/s and T1.=25∘C.

Fig. 4. The von Mises stress distribution (a) and the substrate damaged zone (b) at V I = 50 m / s and T 1 . = 25 ∘ C .

With increasing impact velocity, the extent and severity of polymer damage become more pronounced, thereby inhibiting adhesion between the particle and the substrate, as shown in Fig. 5. Notably, at an impact velocity of 250 m/s, severe damage occurs, and the particle tends to fully penetrate the substrate, disrupting its structure. This behavior is clearly illustrated in Figs. 5a and 5b.

[picture]

Fig. 5. The von Mises stress distribution (a) and the substrate damaged zone (b) at VI=250 m/s and T1=25∘C.

Fig. 5. The von Mises stress distribution (a) and the substrate damaged zone (b) at V I = 250 m / s and T 1 = 25 ∘ C .

When the particle impacts the vitrimer substrate at temperatures exceeding the vitrimer transition temperature, a markedly different behavior is observed compared to impacts occurring below this threshold. At relatively elevated temperatures, the substrate exhibits pronounced ductile characteristics, which facilitate the partial or complete penetration of the impacting particle into the polymeric matrix. As a consequence, the particle becomes embedded within the softened polymer network.

Figure 6 illustrates the influence of the substrate temperature on penetration depth as a function of impact velocity. The plot clearly shows that penetration depth increases monotonically with impact velocity for both thermal conditions. However, for any given velocity, the penetration depth achieved at 220∘C is consistently higher than that at 175∘C, with the difference widening as the velocity increases. This trend indicates that elevated substrate temperatures promote deeper material deformation, likely due to enhanced thermal softening and reduced resistance of the substrate to impact-induced flow. The qualitative interpretation is supported by the von Mises stress contours shown on the right side of the figure.

Overall, the combined trend curves and stress maps confirm that substrate temperature is a dominant parameter governing the impact dynamics. The embedding mechanism is strongly temperature-dependent and becomes increasingly significant as the impact temperature rises well above Tv. Under these conditions, the polymeric substrate undergoes localized deformation, allowing the particle to settle or "accommodate" within its surface. This process enhances the formation of a mechanical interlocking interface between the particle and the substrate. Summarizing, the combined effects of increased ductility, particle penetration, and interfacial interlocking at temperatures above Tv. contribute to a more robust and adhesive particle-substrate interaction.

[picture]

Fig. 6. Penetration depth percentage vs. impact velocity.

Fig. 6. Penetration depth percentage vs. impact velocity.

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

A numerical model was successfully implemented to simulate the infusion of vitrimeric resin into carbon fiber reinforcements using Darcy's law and a dual-scale permeability approach. Rheological analysis identified that curing activation occurs at 79∘C, reaching a peak viscosity at 112∘C before the material undergoes a characteristic vitrimer resoftening phase. The simulations showed that the resin flow covers a mold length of 100 mm in 64 seconds, with full reinforcement saturation achieved in 240 seconds.

Finite element (FE) modeling demonstrated that the substrate temperature is the dominant parameter governing impact dynamics and bonding mechanisms. Below the transition temperature the vitrimer behaves as a brittle thermoset; high impact velocities (e.g., 250 m/s ) result in severe structural damage and inhibit particle adhesion. Above transition temperature, the substrate exhibits ductile characteristics that allow the copper particles to penetrate and become embedded within the polymer matrix. Higher temperatures (e.g., 220∘C ) promote deeper penetration and the formation of a mechanical interlocking interface, leading to more robust and adhesive interaction.

The application of high versatility vitrimer matrices in high performance composites will be based on the exploitation of their unique properties combining good flowability and capability to be resoftened. Future studies should improve the manufacturing processes of the coated vitrimeric composites, investigate their surface properties and explore their reparability potentialities.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1182.31.pdf

The authors acknowledge financial support under the National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.1, Call for tender No. 1409 published on 14.9.2022 by the Italian Ministry of University and Research (MUR), funded by the European Union -NextGenerationEU- Project Title "Functionally cold spRayed cOatiNgs for viTrimer composItes in 1Eo-space hybRid Structures - "FRONTIERS" - CUP D53D23018170001 - Grant Assignment Decree No. P2022CP94J adopted on PE8 by the Italian Ministry of Ministry of University and Research (MUR).

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 41-50

doi: 10.4028/p-SiV9h3

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

Submitted:
2026-01-26

Revised:
2026-02-14

Accepted:
2026-02-17

Online:
2026-04-10

Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

Hao Yuan 1,a*, Burak Ogun Yavuz 1,b, Yuncong Feng 1,c, Ian Hamerton 1,d, Byung Chul Kim 1,e, Stephen R. Hallett 1,f and Jonathan P.-H. Belnoue 1, g

¹Bristol Composite Institutes, University of Bristol, Bristol BS8 1TR, United Kingdom

a*Hao.Yuan@bristol.ac.uk, b  Ogun.Yavuz@bristol.ac.uk, c  ol24008@bristol.ac.uk, d lan.Hamerton@bristol.ac.uk, e B.C.Eric.Kim@bristol.ac.uk, f Stephen.Hallett@bristol.ac.uk, g  Jonathan.Belnoue@bristol.ac.uk

*corresponding author

Keywords: aligned discontinuous fibres, forming simulation, in-plane shear.

Abstract

Aligned discontinuous fibre reinforced composites (ADFRC) have demonstrated an improved formability for small to medium sized parts with complex geometries compared to the continuous fibre based prepreg due to their stretchability along the fibre direction. The process simulation tool developed for this class of materials so far mostly concerns their tensile behaviour along the fibre direction. However, neglecting other deformation modes like the in-plane shear in a forming simulation may pose risks for the correct prediction of formed shape. This study verified a strategy which adopts previously developed analytical micromechanical models for tensile and inplane shear deformation of ADFRCs, in a finite element framework. The implementation is validated by comparing results from virtual shear tests against experiments at different temperatures. This was then followed by virtual forming experiments on a doubly curved geometry, in which the tensile and shear properties of the material were varied separately to study the effects of each deformation mechanism on the simulated forming behaviour of the material.

Introduction

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Highly aligned discontinuous fibre reinforced composites (ADFRC) manufactured using HighPerformance Discontinuous Fibre (HiPerDiF) technology [1], originated from University of Bristol, have been shown to retain the mechanical properties comparable to those of continuous fibre-based counterparts when their fibres are longer than critical length and aligned well in the loading direction. Additionally, the possible movement between discontinuous fibres during forming helps reduce the process-induced defects like wrinkling, which enhances the deformability in the forming of complex 3D shapes [2]. Beyond these processing advantages, a notable feature of these materials is their capability to repurpose reclaimed carbon fibres, thereby supporting the circular-economy and reducing the environmental burden associated with composite manufacturing. Coupled with fast snap-cure resin systems, ADFRC prepregs represent promising candidates for high-rate production of lightweight structural components. These developments underscore the need for reliable simulation frameworks capable of predicting deformation behaviour and process-induced defects to guide material and process optimisation at scale.

There have been attempts made to assess the formability of ADFRCs through quantitative experimental studies at specimen [3] and preform levels [4]. However, these approaches only consider the tensile deformation along fibre direction and obtained experimental results are material and layup specific, meaning that new test campaigns are required for different ADFRC materials. Over the past two decades, forming simulation for continuous fibre-based composites has matured and the simulation frameworks for textile composites typically adopt in-plane shear and out-of-plane bending as key input parameters to predict forming behaviour and major defects like wrinkling [5,6]. More recently, the community has begun to adapt these constitutive approaches to highly aligned discontinuous fibre composites [7,8], focussing primarily on their ability to deform along the fibre direction. However, this emphasis risks overlooking the influence of other deformation mechanisms.

In particular, the role of in-plane shear in aligned discontinuous fibre prepregs remains underexplored and inaccurate representation of shear properties may affect defect formation, post-forming shape and fibre orientation.

This study verified an analytical micromechanical model for in-plane shear behaviour of epoxybased ADFRC prepregs [9] and then investigated the effects of in-plane shear deformation on the forming behaviour through a series of virtual tests. In the finite element framework developed in [9], the analytical models which relate both tensile [7] and shear deformations of the ADFRC prepreg to shearing of the matrix and its rheological properties were integrated into a hypoelastic based constitutive model developed for forming of fibrous materials, which were implemented in ABAQUS/Explicit through VUMAT subroutine. While in [9] the matrix viscosity values were directly taken from the supplier's data sheet, rheological properties of the matrix materials investigated in current study were measured via the oscillatory rheology experiment at a range of temperature and shear rates. Furthermore, a ratio between experimentally measured in-plane tensile and out-of-plane bending properties was assigned to the hybrid membrane-shell elements to fully decouple material's in-plane and out-of-plane behaviours while correctly projecting the total stiffness. The shear test simulation was performed to verify the modelling approach for in-plane shear behaviour, and force-displacement results were compared against the experimental curves. The effects of in-plane shear properties on the forming behaviour of ADFRCs were studied using forming simulations with tensile and shear properties from different temperatures.

Material Characterisation

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The ADFRC investigated in this study was a unidirectional tape produced with HiPerDiF technology and made with 3 mm -long carbon fibres and polylactic acid (PLA) matrix. The same HiPerDiF tape has been used in a previous study on its tensile behaviour [7], where material properties of the fibre and matrices were given. In the previous study, the oscillatory rheology experiments were conducted for the PLA matrix material to obtain the viscosity η and storage modulus G based on the Maxwell model (Eq. 1) at different temperatures for both amorphous and semi-crystalline phases:

τ+ητ˙/G=ηγ˙.(1)

where τ˙ and γ˙ are shear stress rate and shear strain rate in the matrix, respectively. In the more recent study [9], the obtained rheological properties of the matrix were also related to the shear behaviour of an epoxy-based tape in the modelling in addition to its tensile behaviour. The manufacture of the prepreg tape with HiPerDiF technology, was described in detail in [1]. The width and thickness of the manufactured tape are 5 mm and 1 mm , respectively. Fig. 1 shows the modified picture-frame test rig [10] used in this study with PLA-based HiPerDiF test specimens before and after the test. The same test procedure as demonstrated in [9] was followed for the PLA-based tape in current study. The tape was clamped on the test rig with fibres oriented in the horizontal direction. As shown in Fig. 1 (b), by pulling up the moving block on each side with the central block fixed, the effective in-plane shearing occurs symmetrically in two 10 mm×5 mm regions. Due to the difficulty in reaching a uniform temperature distribution above 100∘C, the test was performed only at 100∘C and a shear strain rate of 0.001rad/s, and the in-plane shear strain was measured using Stereo DIC with two 16 MP cameras.

[picture]

Fig. 1. Modified picture-frame test setup with PLA-based HiPerDiF test specimens (a) before the test and (b) after the test.

Fig. 1. Modified picture-frame test setup with PLA-based HiPerDiF test specimens (a) before the test and (b) after the test.

Simulation

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

Analytical models for tape deformation.

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

Due to the highly aligned fibres in ADFRCs, the microstructure evolvement during loading of the composite tape can be idealised and the load developed in the composite tape is transferred through the matrix as shearing between aligned discontinuous fibres. The analytical micromechanical models for both tensile [7] and shear deformation [9] of ADFRCs developed by Yavuz et al. adopts the assumption above and relates the mechanical behaviour of the tape to its microstructures and rheological properties of the matrix. As demonstrated in [7], under tensile loading the shear strain rate of matrix material ( γ˙ ) can be calculated from the strain rate of the tape in fibre direction ( ε˙11 ) as:

γ˙=ε11′˙(L−δ)[K−1]/D.(2)

where L,D and K are fibre length, fibre diameter and the geometric factor related to an assumed hexagonal fibre packing ( K=2.64 [11]), respectively. After deriving the matrix shear stress ( τ ) from known rheological properties of matrix and matrix shear strain using Eq. 1, the change of stress in the tape along the fibre direction ( Δσ11 ) can then be calculated from the shear stress change in matrix as:

Δσ11=2Δτfδ/D.(3)

where f is the fibre volume fraction of the uncured tape and δ is the fibre overlap length calculated as a function of strain of the tape along the fibre direction:

δ=(L/2)(a+bε11+cε112).(4)

As proposed in [9], when the tape subject to in-plane shearing, the shear strain of matrix (γ˙) can be derived from the in-plane shear strain rate of the tape ( ε12 ) as follow with same geometric factor of fibre packing:

γ˙=ε12′˙K.(5)

Following the derivation of matrix shear stress (τ) using Eq. 1, the change of in-plane shear stress of the tape ( Δσ12 ) can then be calculated as:

Δσ12=Δτ.(6)

FE Implementation.

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The numerical simulation of the shear test and a virtual double diaphragm forming was performed using Abaqus/Explicit following the similar strategy adopted in [7,9]. The HypoDrape VUMAT, a hypoelasticity-based user material subroutine specially developed for forming of thin fibrous materials [12], was modified to incorporate above analytical micromechanical models for tension and shear deformation of the HiPerDiF tape. The out-of-plane bending properties of the tape was decoupled from its in-plane material properties by the hybrid element consisting of membrane and shell elements sharing common nodes. Instead of applying in-plane properties in shell elements as in [9], the stiffness of shell elements in current study correlates to the bending stiffness of the tape only whereas the sum of the stiffness of shell and membrane elements represents the material tensile stiffness. Table 1 shows the material properties used for both element types for the PLA-based HiPerDiF tape. The analytical micromechanical model for tensile deformation was implemented for both element types for tensile properties along the fibre direction to account for effects of the tape deformation on its bending stiffness. Furthermore, cantilever bending test was performed using DMA (Dynamic Mechanical Analysis) for the material and ratios of its bending stiffness and tensile stiffness were measured as 0.48,0.39, and 0.49 at 80∘C,100∘C and 120∘C, respectively [13]. The discrepancies of these values between different temperatures could be attributed to the variations from the experiment, including differences in strain rates between tensile and bending tests and crystallinity variations due to temperature inconsistencies. As shown in Table 1, these numbers were used as a multiplicative factor during the stress calculation for two types of elements.

Table 1. Material properties used for membrane and shell elements.

Element Type | Density [tonne/mm³] | Fibre-Direction Properties [MPa] | Tensile | Transverse-Direction Tensile Properties [MPa] | Shear Properties [MPa]
Membrane | 7.13E-05 | Micromechanical model*(1-ratio) | 0.1*(1-ratio) |  | Micromechanical model
Shell | 7.13E-05 | Micromechanical model*ratio | 0.1*ratio |  | 0

In the simulation of shear test, only effective shear region on the left was modelled due to symmetry of the rig. To replicate correct boundary conditions in the experiment, the right edge of the material was fixed while the left edge was constrained to a reference point which was connected to another fixed reference point on the right with a rigid link so that one can rotate around another when a vertical displacement is applied. It is worth noting that during experiments at high temperatures there was noticeable tensile deformation in the rig when the test machine pulling up the moving block, resulting in a smaller displacement of the moving edge than prescribed in the testing programme. Therefore, the displacement history obtained from the DIC was used in the simulation of shear tests. As multiple deformation modes (i.e. out-of-plane bending and tension) can be induced during the test in addition to in-plane shear due to buckling and alignment of the material edge and rig's rotation pins, force-displacement results were used to verify the model instead of the shear stress-strain results. Additionally, as shown in Fig. 2 a double diaphragm forming (DDF) process was also modelled to further investigate the effects of shear properties on the forming behaviour of the HiPerDiF preform. The simulation was set up in a similar way to that in [9], in which a two-ply preform ( [0∘/90∘] ) was placed between two diaphragm films under vacuum pressure and then formed over a doubly-curved mould by the vacuum between the bottom diaphragm and mould surface. Diaphragm films were stretched after pressure applied to both films to replicate the slight tension induced by the clamps in the real process.

[picture]

Fig. 2. Double diaphragm forming model setup and boundary conditions.

Fig. 2. Double diaphragm forming model setup and boundary conditions.

Results and Discussion

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Fig. 3 shows the averaged force-displacement curve from shear test at 100∘C and simulation at four temperatures. Error bars on the experimental curve indicate the standard deviation from different test repeats. Note that the matrix rheologic properties at 105∘C was interpolated from the rheology experiment results at 100∘C and 120∘C. The force-displacement from simulation at 100∘C shows an overall good agreement with the experimental curve. For shear test simulation at 80∘C,100∘C and 105∘C, force-displacement curves have a similar characteristic shape with an initial sharp increase dominated by the in-plane shear deformation in the beginning of the test and a slower force increase at larger displacements related to the out-of-plane buckling and fibre direction tension induced by the rig. Additionally, the tension could also lead to potential sliding of the specimen edge within the clamps at larger displacement when tension becomes more prominent. These has led to much greater variations in the measured force after 0.5 mm displacement. However, significant effects of temperature can be seen between 105∘C and 120∘, at which only a slower increase of the force was observed. This was attributed to the reduction of resin properties, leading to overall lower mechanical properties of the specimen (e.g. tensile, shear and bending stiffness) and a different deformation behaviour during the test than that at lower temperatures.

This can be further analysed quantitatively through the shear angle distribution results in Fig. 4, which shows contours from shear test simulation at 1.5 mm crosshead displacement, corresponding to a theoretical shear strain of 0.15 . It can be seen that the material's ability to shear improves with increased temperature and decreased matrix properties as the overall shear strain increases and its distribution becomes more uniform at higher temperatures. At 80∘C, shearing the specimen is barely possible due to restricted relative sliding of fibres imposed by the "stiffer" matrix. As a result, rigid rotation of the specimen can occur, and severe buckling or tensile failure could appear at corners near the clamp due to high compression or tension in fibre direction. In contrast, the decreased tensile and bending stiffness and improved shearing capability lead to minimum wrinkling on the specimen at 120∘C.

[picture]

Fig. 3. Force-displacement results of experimental shear test at 100∘C and numerical shear test simulation at 80∘C,100∘C,105∘C and 120∘C.

Fig. 3. Force-displacement results of experimental shear test at 100 ∘ C and numerical shear test simulation at 80 ∘ C , 100 ∘ C , 105 ∘ C and 120 ∘ C .

[picture]

Fig. 4. Shear angle distribution (unit: rad) at 1.5 mm machine crosshead displacement for shear test specimens at four different temperatures.

Fig. 4. Shear angle distribution (unit: rad) at 1.5 mm machine crosshead displacement for shear test specimens at four different temperatures.

As both tensile and shear deformations of the HiPerDiF prepreg are dominated by the shearing of matrix, it is difficult to study the effect or contribution of each individual deformation mode on the overall behaviour of the material. Therefore, in the virtual forming test the in-plane shear and tensile properties were decoupled in the VUMAT subroutine so that shear and tensile properties can be varied separately without affecting each other. As shown in Fig. 5 (a) and (d), forming simulations with real tension and shear properties were performed at 100∘C and 120∘C whereas Fig. (b) and (c) show the simulation with artificial properties (i.e. shear and tension responses use matrix rheological properties at different temperatures). The colour contour shows the ratio of thickness reduction of the preform Δt/t0 calculated from the in-plane strains ( ε1 and ε2 ) using Eq. (7):

Δt/t0=1−exp(−(ε1+ε2)).(7)

It can be observed that the preform could not conform to the mould at 100∘C as large wrinkling was formed in the diagonals, further stiffening the HiPerDiF preform. At 120∘C the preform exhibited
an improved conformity and less thinning in the centre, however, there was the presence of small wrinkling around the tight radii between the doubly curved surface and flat surface. It is worth noting that forming of PLA-based prepreg is normally performed at 140∘C and the results related to forming simulation are only analysed qualitatively in this study. Increasing the tensile properties by using matrix rheological properties at 100∘C instead (Fig. 5 (c)) shows no noticeable influence on the overall forming behaviour whereas increasing shear properties (Fig. 5 (b)) modifies the conformity of the preform, which is closer to that in the forming simulation with real tensile and shear properties at 100∘C. This suggests that the in-plane shear response dominates the forming behaviour for PLAbased HiPerDiF preform under current process conditions.

Increasing tensile properties

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

[picture]

Fig. 5. Post-forming material thickness reduction ( Δt/t0 ) for PLA-based HiPerDiF preform with different shear and tensile properties.

Fig. 5. Post-forming material thickness reduction ( Δ t / t 0 ) for PLA-based HiPerDiF preform with different shear and tensile properties.

To further explore the influence of these deformation mechanisms, forming simulations were also performed for a HiPerDiF preform consisting of recycled carbon fibres and a snap-cure epoxy resin. Although directional tests (e.g. tensile and in-plane shear characterisation tests) have not been completed for this material, the deformation of this HiPerDiF material is still assumed to be dominated by the shearing of matrix when aligned discontinuous fibres slide against each other. Therefore, the same modelling strategy described in the previous section is followed to obtain the tensile and shear properties of the tape from its matrix rheological properties. Since rheological properties of the snap-cure epoxy are much lower than those of PLA and the deformation of ADFRC tape are dominated by the matrix properties, forming simulation was only performed at much lower temperature (i.e. 25∘C and 40∘C ) for epoxy-based HiPerDiF preform to preserve the material integrity during the process. The same test procedure as in [7] was followed to obtain the storage modulus and viscosity values at varied shear rates for the epoxy resin at 25∘C and 40∘C. However, these values are not presented at this stage as further calibration is required once the test campaign is completed.

Similar to the forming simulations presented previously, two simulations with real shear and tensile properties and two simulations with artificial properties were performed for epoxy-based preform. Fig. 6 shows the results of four forming simulations with colour contours representing the thickness reduction of the preform. Compared to PLA-based preform, a much better conformity can be seen for the epoxy-based material as there was no noticeable wrinkling occurring for both simulations at 25∘C and 40∘C (Fig. 6 (a) and (d)). Nevertheless, the major concern on the defects here lies in thinning of the preform, as the reduction in thickness rises from 12% to above 22% when temperature increased from 25∘C to 40∘C. Increasing only shear properties did not change the resulted material thinning (Fig. 6 (b)) whereas increasing only tensile properties improved the result (Fig. 6 (c)), which is closer to that in a forming simulation at 25∘C. This was attributed to the relatively lower apparent shear stiffness of the epoxy-based material compared to the PLA-based material (shear stresses observed in the preliminary simulations are in the order of ×10−5 to ×10−2MPa ), which was a result of the much lower matrix rheological properties. Due to high stretchability of the ADFRC prepreg, shear strain and shear strain rate of the matrix achieved through material tensile deformation in the fibre direction can be significantly greater than those achieved through shear deformation. Therefore, for this particular epoxy-based system, the increase in material tensile stiffness plays a much significant role in the change of forming behaviour than the increase in its apparent shear stiffness.

Increasing tensile properties

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[picture]

Fig. 6. Post-forming material thickness reduction ( Δt/t0 ) for epoxy-based HiPerDiF preform with different shear and tensile properties.

Fig. 6. Post-forming material thickness reduction ( Δ t / t 0 ) for epoxy-based HiPerDiF preform with different shear and tensile properties.

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

In this study, the finite element modelling approach with an analytical micromechanical model developed previously for shear deformation of ADFRCs has been verified through experimental and numerical tests. The predicted force-displacement curve from simulation agrees well with the experimental ones at 100∘C test temperature, demonstrating that the shear deformation of HiPerDiF tape is also dominated by the shearing of matrix material. Curves show an initial increase corresponding to the prominent in-plane shear deformation followed by a slower increase after out-of-plane buckling occurs. Shear test simulations at different temperatures suggest that increased temperature can improve the material's ability to shear and significantly reduce wrinkling during this type of tests through improved stretchability. The current approach allows the model to be validated, as different deformation mechanisms (i.e. in-plane shear, out-of-plane bending and tension) can be captured during the test. It must be noted, however, that the current approach is insufficient to extract the shear properties due to the early apparition of out-of-plane wrinkling. Therefore, it is still necessary to improve the shear test for this class of materials to promote pure in-plane shear deformations for a range of relevant process conditions while maintaining the material integrity.

Forming simulations were performed for both PLA-based and epoxy-based HiPerDiF preforms to investigate the effects of in-plane shear and tensile properties on their overall forming behaviour. For each type of HiPerDiF material forming simulations were performed with real shear and tensile properties, and two simulations were performed with artificial properties where tensile and shear responses use matrix properties at different temperatures. The PLA-based preform showed a shear dominated forming behaviour with out-of-plane wrinkling as its major defects. In contrast, the epoxybased preform demonstrated a tensile dominated forming behaviour due to relatively lower apparent material shear stiffness caused by low matrix rheological properties compared to PLA. With high stretchability of the material, the matrix shear achieved through material shear deformation can be much lower than that achieved through tension deformation, which further signifies the contribution of tensile properties in the overall deformation during forming for the epoxy-based preform. However, comparison with the results from ongoing experimental work is required to confirm these preliminary findings from the numerical study. Further analysis on the material deformation will also be performed to quantify the contribution of the in-plane shear properties on the forming behaviour of materials investigated.

This study highlights the importance of correct measurement of the matrix properties as well as an appropriate numerical tool that takes into account different deformation modes. Such a tool can be useful in virtual forming trials and help reduce the efforts on material tests if one of the deformation modes plays an insignificant role on the material's overall behaviour.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

This work was supported by the APC (Advanced Propulsion Centre UK)-funded SCALE-UP project (Sustainable Composite for Automotive and Low-Emission UK Production).

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.41.pdf

H. Yu, K.D. Potter, M.R. Wisnom, A novel manufacturing method for aligned discontinuous fibre composites (High Performance-Discontinuous Fibre method), Compos Part A Appl Sci Manuf 65 (2014) 175-185.

T.A. Cender, P. Simacek, J.W. Gillespie, S.G. Advani, Microstructural evolution of highly aligned discontinuous fiber composites during longitudinal extension in forming, Compos Sci Technol 254 (2024).

L.J. Tomlin, T.A. Cender, S. Sauerbrunn, S.G. Advani, Methodology to establish a forming process window for thermoset aligned discontinuous fiber composites, Compos Part A Appl Sci Manuf 180 (2024).

K.S. Morris, T.A. Cender, E.T. Thostenson, S. Yarlagadda, Forming limits of highly aligned discontinuous fiber composite laminates, Compos Part A Appl Sci Manuf 190 (2025) 108683.

P. Boisse, R. Akkerman, P. Carlone, L. Kärger, S. V. Lomov, J.A. Sherwood, Advances in composite forming through 25 years of ESAFORM, International Journal of Material Forming 15 (2022).

P. Harrison, Modelling the forming mechanics of engineering fabrics using a mutually constrained pantographic beam and membrane mesh, Compos Part A Appl Sci Manuf 81 (2016) 145-157.

B.O. Yavuz, I. Hamerton, M.L. Longana, J.P.-H. Belnoue, Modelling the tensile behaviour of aligned discontinuous carbon fibre thermoplastic matrix composites under processing conditions, Compos Sci Technol 269 (2025) 111252.

A. Stack, P. Simacek, A. Ford, K. Morris, T.A. Cender, S. Advani, Modeling the extension behavior of aligned discontinuous fiber prepreg during thermoforming, International Journal of Material Forming 18 (2025) 96.

T. Gordon, B.O. Yavuz, B. Zhang, X. Sun, I. Hamerton, M.L. Longana, S.R. Hallett, J.P.-H. Belnoue, B.C. Kim, Double-diaphragm forming of highly aligned short-fibre preforms for complex composite parts, International Journal of Material Forming 18 (2025) 85.

B. Zhang, B.C. Kim, Experimental characterisation of large in-plane shear behaviour of unidirectional carbon fibre/epoxy prepreg tapes for continuous tow shearing (CTS) process, Compos Part A Appl Sci Manuf 162 (2022).

R.B. Pipes, D.W. Coffin, P. Simacek, S.F. Shuler, R.K. Okine, Rheological Behavior of Collimated Fiber Thermoplastic Composite Materials, in: S.G. Advani (Eds.), Flow and Rheology in Polymer Composites Manufacturing, Elsevier Science B.V., Amsterdam, 1994, pp. 85-125.

A.J. Thompson, J.P.H. Belnoue, S.R. Hallett, Modelling defect formation in textiles during the double diaphragm forming process, Compos B Eng 202 (2020) 108357.

B.O.Yavuz, Forming simulations of aligned discontinuous fibre thermoplastic prepreg: towards right-first-time sustainable composite manufacturing, PhD thesis (2025), University of Bristol.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 51-58

doi: 10.4028/p-jWtIA2

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

Submitted:
2026-01-19

Revised:
2026-02-18

Accepted:
2026-02-20

Online:
2026-04-10

Fabric Patching: A Simple Approach to Mitigate Defects

The original version of this paper is available on https://www.scientific.net/MSF.1182.51.pdf

Siyuan Chen 1,a, Jonathan P-H Belnoue 1, b and Dmitry S. Ivanov 1,c*

1 University of Bristol, University Walk, Queen's Building, Bristol, UK, BS8 1TR

a  siyuan.chen@bristol.ac.uk bjonathan.belnoue@bristol.ac.uk, c  dmitry.ivanov@bristol.ac.uk

(*corresponding author)

Keywords: Forming of Dry Preforms, Defect Mitigation, Embedded element approach

Abstract

Forming of dry textile preforms for liquid moulding processes becomes increasingly challenging for geometries exhibiting strong double curvature and aggressive tapering. While sequential draping can mitigate defects, it is often impractical for high-rate manufacturing and lacks robustness for dry fabrics with limited inter-ply tack. This paper investigates an alternative approach in which locally printed and cured or semi-cured resin patches are used to steer deformation during forming and suppress shear localisation. A numerical framework is developed to model patched preforms using a superposition-based material representation and is applied to an extreme "bow-tie" benchmark geometry. Initial simulations reveal severe shear-strain localisation leading to fibre-path instability. Various patching strategies are explored to identify the dominant drivers governing defect mitigation. The results demonstrate that appropriately placed and sufficiently stiff patches can significantly delocalise shear and eliminate multi-stripe deformation patterns. Based on these findings, key optimisation parameters and practical guidelines for patch placement and stiffness selection are formulated, providing a foundation for future automated optimisation of patch-assisted preform forming.

Introduction

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Forming of textile preforms in the context of liquid moulding processes becomes particularly challenging when complex geometries are involved. Even when fabrics are sufficiently drapable under carefully controlled sequential lay-up operations, they may not be formable in a single-step process using rigid moulds, diaphragm forming set-ups, or thermoforming stations. This is particularly apparent when comparing results of kinematic drape models and mechanical simulations [1,2]. Sequential draping of dry preforms is, however, not always feasible in industrial settings due to the absence of inter-ply tack. Powder binders partially address this limitation, but their thermal activation typically requires large thermoforming stations in which forming must again be performed in a single step, effectively reintroducing the original challenge.
Controlling the draping deformation of delicate dry preforms is therefore a technologically demanding task. Low resistance to compressive stresses, combined with shear limits governed by lateral yarn interactions, makes the process prone to fibre-path defects. Various strategies have been proposed to alter the effective formability of preforms and suppress uncontrolled fibre motion. These include external constraints, such as blank holders [3,4], tensioning systems [5,6], and risers [7], as well as internal modifications of the preform, including tufting [8] and stitching [9]. The common objective of these approaches is to minimise excessive shear and compressive stresses by locally modifying the mechanical response of the preform or constraining critical regions.
Turk et all [10] have was shown that incorporating internal constraints directly into the preform, i.e. specifically by printing resin patches and curing them locally, can effectively protect critical regions from excessive shear and promote delocalisation of forming deformations. This fabric treatment enables more controlled preform deformation while avoiding the complexity associated with manual draping operations or external constraint systems. Importantly, patching does not alter fibre orientation and does not introduce structural disruptions that could degrade material properties. In addition, local patch properties can be tailored, for example by controlling the degree of cure. The viscosity of the printed resin directly governs patch deformability, offering an additional lever for
process control. Thermal conditioning of partially cured printed patches has also been shown to be feasible and well controlled [11].
As with any forming-defect mitigation strategy, determining the optimal placement of patches is nontrivial and requires numerical optimisation. Over-constraining the preform may lead to adverse effects by restricting the degrees of freedom required for the fabric to conform to the tool geometry. The objective of patching is therefore to protect critical areas from excessive deformation, diffuse shear localisation where possible, and steer deformation toward regions with lower defect risk. Employing patches that are not fully rigid (which is achievable by limiting the degree of resin cure) may provide a gentler and more effective constraint strategy. Previous studies have demonstrated that patch material properties can be identified through bespoke characterisation procedures and incorporated into numerical models for process optimisation [12]. One of the promising material for patches is vitrimeric resins that are fully compatible with subsequent infusion resins and can be tuned to create seamless interface with the patch [13].
A range of optimisation techniques has been proposed for forming simulations, such as Bayesian surrogate modelling, which has shown significant efficiency gains in the optimisation of diaphragmforming processes [14]. In this framework, successive simulations are strategically selected to reduce uncertainty in the response space. In the present work, patch optimisation is considered through the lens of such techniques. However, the associated design space is large, as patches may vary in shape, size, position, number, and stiffness. Prior to formal optimisation, it is therefore essential to identify the dominant parameters governing process performance. This paper discusses the key drivers of the patch optimisation problem, presents simulations highlighting the associated constraints, and identifies optimisation metrics relevant to defect mitigation. Finally, initial guidelines are proposed for selecting patch configurations for arbitrary geometries.

Test Case

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The selected test case represents a "bow-tie" geometry, which may be regarded as an extreme variant of a spar featuring a recessed central region. This configuration was chosen because, despite its relatively simple composition of flat segments, it exhibits aggressive tapering that leads to high shear angles (above 50∘ ) and highlights the primary challenges associated with double-curvature forming. The preform is formed within a double-sided rigid mould representative of an RTM process (Figure 1).
A single-ply orthogonal fabric preform is considered, with warp and weft yarns initially aligned with the part edges. The fabric dimensions are 231.4×250 mm, the width of the web 150 mm , the length of the recess area of 70 mm , and the radii of curvature in the web-flange corners are 10 mm . In the simulations, the concave mould is held stationary while the convex mould advances until full tool contact is achieved.

[picture]

Fig. 1. Geometry of the moulds and initial model setting (blue - steel moulds, red - preform prior to compaction).

Fig. 1. Geometry of the moulds and initial model setting (blue - steel moulds, red - preform prior to compaction).

Physical Model and Numerical Implementation

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To represent fabric behaviour, a computational approach differing from conventional forming models is adopted. Instead of defining explicit constitutive relations, the material response is represented through a superposition of several components:
(1) warp yarns with elastic stiffness along the fibre direction and negligible transverse and shear stiffness, (2) weft yarns with analogous properties but initially orthogonal to the warp direction, (3) a connecting "quasi-matrix" medium calibrated to reproduce the fabric shear response in bias extension tests, (4) locally applied rigid patches with stiffness representative of cured composite material. This framework allows accurate calibration of bending and shear behaviour while seamlessly incorporating rigid or semi-rigid patches into an otherwise compliant preform. The bending response of the fabric is controlled by the Young's modulus of fibrous plies in the longitudinal direction, whereas the quasi-matrix media regulates the shear response of the system. Such assembly allows to tune the properties critical for predicting main wrinkling modes. However, in contrast to shell/membrane formulations [16] such approach does not account for decoupling of membrane and bending responses and can only be applicable in the absence of preform stretching and considerable loads in the plane of the fabric. The embedded element approach has previously been shown to be effective for modelling viscoelastic behaviour associated with uncured resin systems [15].
In the present model, shear properties representative of a carbon plain woven fabric are adopted [16]. The connecting medium is implemented using a hyperelastic isotropic formulation, with material input provided in the form of uniaxial test data. The bending stiffness of the material is controlled by the Young's modulus of fibrous plies in the longitudinal direction. Patch properties were calculated using Chamis micromechanical formulas for unidirectional properties in warp and weft direction and then averaged across the two directions. The moulds are modelled as rigid steel surfaces. All simulations are performed using Abaqus/Explicit. The effective material density is adjusted to balance computational efficiency with dynamic stability - a scaling factor of 100 was applied to the densities of all materials in the model.
During the sequence of numerical trials, it was observed that a low flexural stiffness of the fabric occasionally led to convergence difficulties caused by excessive local rotations associated with wrinkle initiation, which in turn resulted in element distortion. This premature wrinkling terminated the simulations prior to full mould closure and altered the redistribution of shear deformation, thereby preventing a consistent comparison between different configurations. To ensure stable mould closure in all trials and to isolate the influence of patching from numerical instabilities associated with earlystage buckling, the bending stiffness of the fabric was temporarily increased by assigning a longitudinal Young's modulus of 3.1 GPa to the fibrous ply. This modification was introduced solely as a numerical stabilisation measure and was not intended to represent the physical behaviour of the material. The increased bending stiffness suppressed premature wrinkling, enabled complete mould closure, and allowed a controlled and consistent comparison between patched and non-patched configurations under otherwise identical conditions. After identifying the optimal patch configuration, the bending stiffness was restored to its physically realistic value (the flexural modulus was reset to 33 MPa [16]) for subsequent simulations and interpretation of the results.

All superimposed material components are modelled using 3D elements with a nominal thickness of 0.5 mm . The fabric was meshed with 8 -node linear hexahedral (brick) solid elements with reduced integration specifically designed for non-linear and large deformation problems. The characteristic mesh size is 5 mm . Frictionless contact is assumed between the fabric and the mould surfaces. Material superposition is implemented using the embedded element technique.

Initial simulations and problem statement

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Simulation of the unpatched preform during mould closure reveals severe localisation of shear strain. Narrow shear bands initiate near the flange-web corner, intersect with bands of opposite sign in the recessed web region, and terminate at the bottom of the part (Figure 2). This behaviour results in abrupt fibre-orientation changes over very short length scales. Although the model does not explicitly
predict out-of-plane wrinkling, the deformation patterns clearly indicate severe fibre-path defects. In practice, such fluctuations would likely lead to yarn buckling, fabric splaying or unacceptable fibre waviness.

[picture]

Fig. 2 (a) Shear strain of formed unpatched material, (b) Compressive stresses in the direction across the length of the spar.

Fig. 2. (a) Shear strain of formed unpatched material, (b) Compressive stresses in the direction across the length of the spar.

It should be noted that the current model does not account for in-plane bending stiffness, which has been shown to play a critical role in predicting certain defect modes under rapidly varying constraints [17]. Nevertheless, whether these multi-stripe shear patterns correspond to in-plane waviness, out-ofplane wrinkling, preform splaying or intra-fabric buckling, they represent severe defects that must be avoided. These observations define the primary objective of patching: to prevent the formation of such shear-localisation bands.

For automated optimisation, suitable quality metrics must be defined. Maximum shear angle alone is insufficient, as a uniform shear band even at high intensity may still correspond to acceptable forming. Compressive stress is also of limited relevance in the present case, as it is largely concentrated near corners and does not correlate well with observed defect locations (Figure 2b). Out-of-plane displacement provides a direct measure of wrinkling but is not informative for the example considered here. The most relevant metric for the present study is therefore the shear-strain gradient, which can provide a quantitative measure of the observed defect severity. Shear strain gradient can be calculated using direct numerical differentiation of shear distribution or, to eliminate the numerical noise, using analytical differentiation of the locally approximated shear field. While no absolute threshold exists for acceptable gradients, minimisation of this measure offers a clear optimisation objective.

Patch optimisation

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To enable numerical optimisation, the design space must be defined and patch parameters such as position, shape, size, and stiffness, must be parametrised. As noted previously, excessive constraint can worsen forming behaviour rather than improve it. Initial trials demonstrate that restricting deformation in regions where shear would naturally develop, such as along the symmetry axis or top flange, can lead to intensified cross-over patterns and alternating shear bands. In some cases, buckling within the patched region is observed, which in practice could result in fibre damage. These results confirm that overly large or overly stiff patch regions are counterproductive.

[picture]

Fig. 3 (a) Shear map of formed bulk-patched material (contour lines show the borders of patches, inner patch area is highlighted, min: -1.68 , max: 1.66 ).

Fig. 3. (a) Shear map of formed bulk-patched material (contour lines show the borders of patches, inner patch area is highlighted, min: -1.68 , max: 1.66 ).

A more effective strategy is therefore required. Based on the initial simulations, a working hypothesis was formulated: preventing multiple shear stripes from developing independently and instead forcing the formation of a single, continuous shear band could mitigate defect formation. This can be achieved by surrounding the high-risk region near the transition to recess area with a frame-like or rail-type patch configuration that suppresses localised shearing.
Several patch lengths and stiffness levels were investigated to assess the viability of this concept. The results (Figure 4) show that, beyond a critical patch length, fibre-orientation variations become significantly more gradual and the violent oscillations observed in the unpatched case are largely eliminated. These findings demonstrate that the proposed strategy is effective. The simulations further indicate that higher patch stiffness is beneficial for suppressing localisation. Figure 4 compares patches with varying stiffness: one assuming a fraction of cured resin stiffness and another is full stiffness (representative to engineering vitrimer or epoxy resins). It can be seen that the stiffer patch appears more effective in the hypothesised railing action and protecting the inner region from disjointed shear stripes.

[picture]

Fig. 4 Shear map of formed rail-patched material (red square show the position of the patch): (a) patch properties assuming 10% of epoxy stiffness, (b) patch properties assuming epoxy stiffness.

Fig. 4. Shear map of formed rail-patched material (red square show the position of the patch): (a) patch properties assuming 10 % of epoxy stiffness, (b) patch properties assuming epoxy stiffness.

Once plausible results had been obtained using the artificially stiffened fabric configuration, the bending rigidity was reduced to more realistic values, consistent with those reported by Thompson et al. [16]. The reduction in flexural stiffness introduced an additional wrinkling mode, characterised by fold formation on the top surface. Once the mould is closed and the fold is squashed, it translates to the violent oscillations of shear deformations - Figure 5a. The shear distribution along the sides also became less regular, and several characteristic shear bands re-emerged even in the presence of rail patches. A pragmatic solution was achieved by introducing additional stabilising patches in the longitudinal direction of the part and by increasing the width of the side rail patches. The latter
modification enhanced their in-plane bending stiffness and helped maintain the continuity of shear deformation within the shear bands (Figure 5b).

[picture]

Fig. 5 Shear map of forming of preform with realistic flexural stiffness (a) without patches, (b) with patches (patches are highlighted in red).

Fig. 5. Shear map of forming of preform with realistic flexural stiffness (a) without patches, (b) with patches (patches are highlighted in red).

Obviously there might be practical limitations to this approach. Fully cured composite patches are exposed to bending around part corners and may bear risk of fibre damage during tool closure. Potential alternatives include using high-viscosity but partially cured materials, terminating patches before sharp corners, or limiting patch length. Overall, the results establish a strong basis for defining a compact and practical design space in which patch length, termination location, and stiffness are the primary optimisation variables. Most importantly, the feasibility of patch-assisted forming is confirmed, offering a cost-effective and pragmatic alternative to complex external constraint systems for dry-fabric preforms.

Conclusions

The original version of this paper is available on https://www.scientific.net/MSF.1182.51.pdf

This study demonstrates that locally applied resin patches can be an effective means of controlling deformation and suppressing defect formation during the forming of dry textile preforms for complex geometries. Numerical simulations of an extreme bow-tie test case reveal that unpatched preforms exhibit severe shear-strain localisation manifested as narrow, alternating shear bands, which are indicative of critical fibre-path defects. Conventional defect indicators such as peak shear angle, compressive stress, and out-of-plane displacement were found to be insufficient for capturing this behaviour, whereas the shear-strain gradient emerged as a robust and physically meaningful optimisation metric.
Systematic exploration of patching strategies shows that over-constraining the preform exacerbates localisation and can introduce additional instabilities, highlighting the necessity of careful patch placement. In contrast, targeted patch configurations that surround critical regions and inhibit independent shear-band formation promote the development of a single, smoothly varying deformation mode. Sufficient patch stiffness is required to achieve this effect; however, fully rigid patches may be impractical due to bending demands near tool corners, suggesting that partially cured or high-viscosity materials provide a more viable compromise. The approach is readily suitable for creating vitrimeric-epoxy multi-matrix hybrids, that can other forming and repair benefits [18], but could also be applicable in the context of liquid printing [19] or solid resin deposition [20].
The findings enable a significant reduction of the patch optimisation design space, identifying patch length, termination location, and stiffness as the dominant parameters governing forming quality. Overall, the results confirm the feasibility of patch-assisted forming as a practical and cost-effective alternative to external constraint systems, and establish a foundation for future automated optimisation frameworks for complex preform geometries.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/MSF.1182.51.pdf

The work has been supported by EPSRC project "Realising Structural Power: Addressing the Manufacturing Challenges", EP/W03526X/1.

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Janzen J.P., Schafer H., Çelik M., Robert C., Bradaigh C.M.O., May D., Neumeyer T. Influencing the draping behaviour of solid epoxy prepregs by applying 3D-printed resin patterns, Materials & Design 259 (2025) 114780.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 59-71

doi: 10.4028/p-zhZXT4

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

Submitted:
2026-01-19

Revised:
2026-02-18

Accepted:
2026-02-18

Online:
2026-04-10

Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

The original version of this paper is available on https://www.scientific.net/MSF.1182.59.pdf

Margoto Olivia H. 1,a*, Batouei Mohammad A. 1,b, Yang Victor 1,c, Abdin Yasmine 2, d* and Milani Abbas S. 1,e

1 School of Engineering, University of British Columbia, Kelowna, Canada

2 Department of Materials Engineering, University of British Columbia, Vancouver, Canada

a * olivia.margoto@gmail.com, b  amin.batouei@gmail.com, c vy@student.ubc.ca, d  yasmine.abdin@ubc.ca, e  abbas.milani@ubc.ca

Keywords: flax woven fabrics, forming-induced defect prediction, 3D scanning, haralick features extraction and prediction, Monte Carlo cross-validation.

Abstract

Natural fiber-reinforced composites offer lightweight and sustainable alternatives for automotive and aerospace applications. However, similar to synthetic composite options, forminginduced defects such as wrinkles can reduce targeted performance. Predicting these defects is particularly challenging for natural fiber reinforcements due to the inherent variability in the fiber geometry and ensuing fabric properties. This study applies a machine learning approach to predict formability in flax woven fabrics ( 2×2 twill and biaxial non-crimp) using a glass fabric as a synthetic fabric reference. The fabrics' shear, bending, tensile, and friction behaviors were experimentally characterized to capture forming-relevant mechanical properties. The fabrics were subsequently formed in single-, dual-, and triple-layer configurations over a square tool, followed by 3D scanning to quantify wrinkle distributions. Forming-induced surface deformations were transformed into grayscale maps, from which Haralick texture features were extracted. Combined with the fabric design parameters such as weave, orientation, number of layers, grammage, and thickness, the mechanical properties features were used to train linear regression models, reliably predicting select Haralick features, cross-validated using Monte Carlo simulations. Results showed that flax twill reinforcements exhibited the lowest formability, while the glass fabric formed smoothly, and biaxial non-woven fabric showed primarily localized folds. Increasing the fabric orientation from 0∘ to 45∘ improved forming performance for most woven reinforcements; but not the biaxial non-woven alternative. Linear regression models accurately predicted the defect severity via homogeneity ( R2= 0.81 ) and dissimilarity ( R2=0.73 ) texture features, demonstrating that integrating texture-based image analysis with fabric parameters and mechanical properties provides a promising machine-learning-based framework for predicting forming performance of fabric-reinforced composites.

Introduction

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Woven and non-woven fabric-reinforced composites are widely used in automotive and aerospace applications, among others, due to their low weight, high strength, and good formability [ 1,2 ]. In Liquid Composites Molding (LCM), this formability is critical, as dry reinforcements must conform to complex tool geometries prior to resin injection [3,4]. Inadequate control of the forming stage can lead to defects such as out-of-plane wrinkling, in-plane waviness, tow buckling, fiber fracture, and slippage, which may ultimately result in part rejection [2,5]. Consequently, detailed characterization of fabric behavior under different deformation modes is essential to understand the mechanisms behind forming-induced defects. During forming, the fabric reinforcements often undergo in-plane shear, biaxial extension, inter-ply and tool-ply friction, bending, and compaction, with intra-, interply shear and ply bending playing dominant roles in enabling the lay-up conformance to single- and double-curvature geometries [2,4,6−9].

Fiber architecture and physical properties further influence the defect formation [10]. For example, biaxial Non-Crimp Fabrics (NCFs) provide high tensile and flexural stiffness but are sensitive to stitching characteristics (e.g., density, pattern, thread, and orientation) [11-14], whereas woven
fabrics introduce crimp that modifies in-plane shear behavior [10]. In natural fiber reinforcements, additional complexity arises from inherent material variability and yarn heterogenous structure. Flax flat yarns, e.g., composed of segmented elementary fibers bonded with adhesives, exhibit high lateral stiffness, making them prone to tow buckling during forming, while removing adhesives after weaving further increases strain and reduces tow strength [15,16]. Physical parameters such as areal density and fiber distribution also affect deformability, with higher-density flax non-woven mats showing improved preforming behavior [17].

Geometrical and processing factors also play a key role in forming outcomes. For instance, forming over square-box tools has been shown to induce severe shear and wrinkling due to sharp corners and quasi-inextensible fiber paths, whereas cylindrical mold geometries distribute deformation more uniformly [4,18,19]. Process defects substantially degrade the mechanical performance of the final part, with wrinkles reaching 20−60% of the nominal laminate thickness reported to reduce cured part strength by 50−70% [20]. Modifications to tool and blank-holder designs can help reduce defects (e.g., adding risers to increase fabric tension), though optimal configurations remain highly case-dependent due to the complex fabric-tool interactions [21].

Understanding and predicting forming behavior is therefore critical for improving fabric composites manufacturability and quality. Machine Learning (ML) approaches guided by experimental and simulation data have only recently shown promise for predicting drapability behavior of different composite materials (including fabrics), enabling faster defect detection, parameter optimization, and quality prediction through data-driven methods [22,23]. For instance, ML approaches have been successfully used to infer optimal forming parameters from laminate images [24], optimize forming parameters through reinforcement learning [22], classify defective parts with high accuracy [25], and support automated inspection and real-time control in advanced manufacturing processes [26-28]. Despite these advancements, most of current ML applications have focused on synthetic fiber-reinforced composites [22-26,28], leaving a gap in applying data-driven approaches to forming-induced defects in natural fiber woven reinforcements.

This study addresses this gap by developing a supervised machine learning framework to predict the formability of a set of commercial flax fiber woven reinforcements, with glass fiber fabric also used as a reference. Fabric geometrical parameters and their mechanical properties serve as model inputs, while forming-induced defects are quantified using Haralick texture metrics, extracted digitally from post-forming wrinkle maps. As a proof of concept, formability is predicted using linear regression due to the limited dataset, and model robustness is evaluated through Monte Carlo crossvalidation.

Methodological Details

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Materials.

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Three commercial flax reinforcements were selected: a 250 g/m22×2 twill fabric from Lingrove (FTW250), a 367 g/m22×2 twill fabric from Rock West Composites (FTW367), and a 350 g/m2 ampliTex® biaxial non-crimp fabric from Bcomp (FBX350). A 280 g/m22×2 twill glass fiber fabric from Easy Composites was included as a synthetic reference material for comparison. The twill flax fabric is made from flat tows, the biaxial NCF from spun yarns, and the glass fabric from rovings. The main physical properties of these test materials are listed in Table 1.

Table 1. Specifications of the tested flax fabrics.

Fabric code | FTW250 | FTW367 | FBX350 | GTW280
Material (type) | Flax | Flax | Flax | Glass
Weave (type) | 2×2 Twill | 2×2 Twill | Biaxial NCF | 2×2 Twill
Areal weight (g/m²) | 250 | 367 | 350 | 280
Thickness (mm) | 0.78 ± 0.03 | 1.29 ± 0.05 | 0.97 ± 0.03 | 0.29 ± 0.01
Tow orientation (°) | 0/90 | 0/90 | ± 45 | 0/90
Stitch Orientation (°) | - | - | 90 | -
Number of warp yarns per cm | 4 | 3.5 | 14 | 7
Number of weft yarns per cm | 4 | 3.5 | 8 | 8

An overview of the designed workflow for predicting fabric formability is presented in Fig. 1, illustrating the sequence from the material selection and mechanical characterization, through 3D forming and post-forming surface mapping via a handled scanner, to wrinkle quantification, Haralick feature extraction for regression modeling.

[picture]

Fig. 1. Overall workflow for the formability prediction, summarizing materials, mechanical characterization, 3D forming, data acquisition, and Haralick feature extraction for machine learning modeling.

Fig. 1. Overall workflow for the formability prediction, summarizing materials, mechanical characterization, 3D forming, data acquisition, and Haralick feature extraction for machine learning modeling.

Mechanical characterization of the reinforcements.

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Mechanical characterization of the selected reinforcements included friction, bending, tensile, and shear behavior, reflecting the deformations these fabrics undergo during complex 3D forming [3].

Friction Characterization.

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Ply-ply, ply-tool, and ply-holder friction coefficients were measured using a Friction Tester (Labthink International Inc., USA). For ply-ply tests, fabric specimens ( 250×130 mm on the bed, 63.5×63.5 mm on the sled) were used. Ply-tool and ply-holder tests employed aluminum and acrylic plates on the bed, respectively. Tests were conducted at 4 mm/min under ~5 N force and repeated five times per configuration for consistency.

Effective out-of-plane bending.

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The bending stiffness of flax and glass fabrics was measured using a Peirce cantilever tester (Taber Industries, USA) on nine specimens per fabric ( 200×25 mm ) [29]. Each fabric's ability to bend under its own weight was evaluated by sliding strips over a platform edge until they bent at approximately 41.5∘. Overhang length and fiber width were recorded, and bending length and flexural rigidity, D( N.mm), were calculated following ASTM D1388 [30]. Then, the effective out-of-plane bending ( Deff  ) at specific fabric angles θ (as illustrated in Fig. 2) was calculated as per Eq. 1 [31]:

Deff=Dcos2θ(1)

[picture]

Fig. 2. Schematic of fabric orientation used to calculate effective mechanical properties. The orientation angle 250 mm×75 mm is measured relative to the tool square corner, and relative to the loading direction for tension.

Fig. 2. Schematic of fabric orientation used to calculate effective mechanical properties. The orientation angle 250 m m × 75 m m is measured relative to the tool square corner, and relative to the loading direction for tension.

Effective in-plane tension. Five specimens ( 5 mm/min ) for each fabric configuration were tested in uniaxial tension using an Instron 5969 at 2×2 with a 150 mm gauge length, and waveprofile jaws were used to prevent slippage [32-34]. The 0/90∘ twill fabrics were tested at

Eeff=(cos4θ+sin4θ)E(2)

, and the biaxial non-crimp fabric with its stitch direction aligned to the loading axis. The effective modulus for each fabric orientation was calculated from the initial linear region of the stress-strain curve [3537] as per Eq. 2:

θ

where Eeff  is the fiber (or stitch) orientation relative to the loading direction, E is the unidirectional fiber modulus and 210×55 mm is the effective in-plane modulus in the loading direction, assuming a balanced fabric architecture.

In-plane shear stiffness.

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The in-plane shear behavior of the textile reinforcements was evaluated using bias extension tests. Rectangular specimens ( 45∘ ) with yarns at 5 mm/min[4,32] to the fiber (local) tension direction were clamped in flat rubber-coated jaws with a 110 mm gauge length and tested three times per fabric on an Instron 5969 at Fsh( N/mm). Normalized shear forces γ(∘) and shear angles 40∘ were calculated as described in [38]. The shear modulus was taken at a 45 cm×45 cm shear angle, consistent with [4].

3D forming setup.

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An experimental 3D forming setup was developed in-house for rapid yet repeatable data collection on the forming behavior of the woven fabrics, as shown in Fig. 1. The setup consisted of a squarebox tool ( 112 mm width) and a transparent acrylic fabric holder ( 25 mm thick). Surface geometry and forming-induced defects were captured using a Handyscan Black Elite 3D scanner (Creaform Inc., Canada) with an accuracy of 0.025 mm . Fabric specimens ( 0∘,15∘,30∘ ) were cut according to predefined fiber orientations ( 45∘, and 20in·lb ) and layer configurations ( 1,2 , and 3 layers).

During forming, the fabric holder was manually displaced at an approximately constant speed to drape the fabric over the tool and subsequently clamped under a controlled torque of

|x−ara|n+|y−brb|n=1(3)

.

Haralick feature extraction for predictive models.

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3D scanned surface after each forming experiment was imported as point clouds using the Open3D Python library. Individual layers were extracted by selecting points within a defined tolerance of the target planes (e.g., all x-coordinates within 0.1 mm of the target), reducing the 3D data to 2D representations for surface analysis. To isolate forming-induced deformations, the scanned formedfabric surface was decoupled from the underlying square-box tool geometry. The ideal tool surface, representing the nominal geometry in the absence of wrinkles, was modeled using the Superellipse Lamé curve (Eq. 3) [39]:

x

where the y and a=b=0 are the Cartesian coordinates of points on the tool surface. The tool is centered at the origin ( 112 mm(ra=rb=12 ), has a width of ) width n=12 mm, and a corner roundness defined by α.

The Cartesian coordinates of both the scanned surface and the ideal tool geometry were converted into polar coordinates with respect to the tool center. In this representation, r parameterizes the position along the tool perimeter and α represents the radial distance from the tool center, as shown in Fig. 3. Forming-induced deformations were obtained by subtracting the ideal radius from the measured radius at each α, producing a one-dimensional deformation profile that captures local forming-induced surface deviations. The use of 30% provides a natural ordering of points along the surface, enabling the generation of structured 1D profiles suitable for Haralick feature analysis.

[picture]

Fig. 3. Polar representation ( 70% ) of the square tool, converting the 2D scanned surface into a structured 1D profile suitable for Haralick texture analysis.

Fig. 3. Polar representation ( 70 % ) of the square tool, converting the 2D scanned surface into a structured 1D profile suitable for Haralick texture analysis.

To visualize these deformations across the lateral surfaces, 2D maps were generated by compiling unfolded vertical face profiles into grayscale images, where intensity represents deviation magnitude. The top surface was excluded for simplicity. These deformation maps, at each surface of the formed box, were processed into Gray Level Co-Occurrence Matrices (GLCMs) and normalized to extract Haralick features, including ASM, Contrast, Correlation, Dissimilarity, Energy, and Homogeneity [40,41]. Combined with fabric geometrical parameters (weave, orientation, number of layers, grammage, thickness) and mechanical properties (Table 2), these features were used to train linear regression models to predict fabric formability, with Haralick features representing wrinkle patterns.

The linear regression dataset comprised 48 samples. Given this relatively small dataset and the need for interpretable relationships between fabric parameters and texture-based defect metrics, linear regression method was selected as a baseline/preliminary supervised learning approach due to its simplicity and prior literature use in composite defect detection prediction [23]. An independent test
set corresponding to R2 of the data was held out for final model evaluation. The remaining 0/90∘ of the samples were used for model training and assessed using Monte Carlo cross-validation with 10 random resampling iterations to evaluate model robustness [42]. Model performance was quantified using the coefficient of determination ( 2×2 ) and the Mean Absolute Error (MAE).

Results and Discussion

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Mechanical characterization of the reinforcements.

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The mechanical properties of the flax and glass fiber reinforcements are summarized in Table 2 for the [6,18,43] orientation, and the arrows indicate literature-supported trends associated with reduced forming-induced wrinkles. For the two 0∘ twill woven flax fabrics, the increase in areal weight from FTW250 to FTW367 resulted in a higher Young's modulus, consistent with the presence of more load-bearing fibers per unit area in FTW367. The glass fiber reinforcement (GTW280) remained substantially stiffer ( 3.29 GPa ) than all flax reinforcements. As reported in the earlier literature [4], lower tensile stiffness promotes greater in-plane elongation, which can facilitate draping over complex geometries by lowering the induced shear angle.

It is important to emphasize that the continuous fiber textile reinforcements investigated in this study are composed of relatively stiff yarns compared to knitted reinforcements or stretch-broken fibers [4]. Achieving a double-curved geometry therefore necessitates substantial in-plane shear deformation, as shear is one of the dominant mechanisms enabling the transition from twodimensional plies to three-dimensional formed components 15∘. Consistent with this, FTW367 (higher areal weight) exhibited higher shear stiffness than FTW250. This trend aligns with observations in jute fabrics, where low-density architectures allow greater yarn mobility and rotation, enabling larger deformations under lower axial forces [44]. Interestingly, the shear stiffness of the glass reinforcement GTW280 was similar to that of FTW250, despite the significant difference in tensile modulus.

Table 2. Mechanical properties of the tested fabric reinforcements at θ orientation.

Fabric (type) | downward arrow Young's Modulus (GPa) | downward arrow Shear Stiffness at 40° (N.mm⁻¹) | upward arrow Bending Stiffness (N.mm) | downward arrow Friction Ply/Mold Dynamic coefficient
FTW250 | 0.24 ± 0.08 | 0.008 ± 0.001 | 1.47 ± 0.16 | 0.17 ± 0.00
FTW367 | 0.46 ± 0.11 | 0.021 ± 0.002 | 1.61 ± 0.47 | 0.16 ± 0.00
FBX350 | 0.57 ± 0.15 | 0.069 ± 0.035 | 1.04 ± 0.09 | 0.15 ± 0.00
GTW280 | 3.29 ± 0.34 | 0.012 ± 0.002 | 0.07 ± 0.01 | 0.22 ± 0.01

Arrows indicate literature-supported trends associated with reduced forming-induced wrinkles [2-4].

Regarding bending behavior, the flax twill fabrics displayed comparable flexural rigidity, while the biaxial NCF (FBX350) exhibited lower bending stiffness. The glass fabric showed the lowest bending stiffness despite its high tensile modulus, which was also observed by Bai et al. [4]. Literature indicates that higher bending stiffness generally contributes to improved drapability and reduced wrinkling in dry textiles, as the ply with the lowest bending stiffness tends to wrinkle first during forming [4,45,46].

For ply-tool friction, all flax reinforcements showed similarly low dynamic and static coefficients, whereas the glass fabric exhibited a noticeably higher coefficient. When considering forming-induced wrinkling in dry reinforcements, low friction between the ply tool can facilitate smoother deformation as the dry reinforcement shapes around complex tooling geometries, reducing the likelihood of wrinkles.

3D forming Experiments.

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The experimental evaluation of single- and triple-layer reinforcements formed into the square shape involved analyzing 3D surface deformations across multiple orientations. The results, summarized in Fig. 4, highlight clear material- and orientation-dependent differences in formability. In the singlelayer condition, the woven reinforcements FTW250, FTW367, and GTW280 exhibited their most
severe forming-induced defects at the 0∘ orientation, where large out-of-plane wrinkles and distortions were consistently observed.

[picture]

Fig. 4. 3D surface deformation of the reinforcements formed into a square shape and scanned: single-layer configuration (left) and three-layer configuration (right). Colors indicate the deformation magnitude in millimeters, as shown by the scale below each image.

Fig. 4. 3D surface deformation of the reinforcements formed into a square shape and scanned: single-layer configuration (left) and three-layer configuration (right). Colors indicate the deformation magnitude in millimeters, as shown by the scale below each image.

For the biaxial NCF (FBX350), the poorest performance occurred at 45∘. Among all materials, the flax twill reinforcements showed the lowest formability, displaying bulky, highly pronounced wrinkles with amplitudes reaching up to 15 mm across the five evaluated faces. In contrast, the glass fiber reinforcement formed more efficiently (with minimal defects) under the same conditions. Although the biaxial NCF exhibited surface deformation of similar magnitude to the flax twills, the resulting defects were primarily localized folds rather than large-scale out-of-plane distortions.

Increasing the fabric orientation from 30∘ to 45∘ markedly improved the forming response of most woven reinforcements in the single-layer setup. FTW367 showed the greatest improvement at 0∘ and 30∘, where the formed shapes were noticeably smoother and exhibited fewer wrinkles. By comparison, the FBX350 NCF showed little variation in deformation across the tested orientations. This relative orientation independence is likely due to its higher in-plane stiffness, lower bending compliance, and reduced inter-ply friction, which together restrict its ability to conform to doublecurved shapes [4].

When comparing single-layer to three-layer configurations, the forming behavior of GTW280 remained largely unchanged across all orientations, indicating a low sensitivity to layer count. For FTW250 at 45∘, the deformation patterns also remained similar between one- and three-layer forming. In most other cases, however, FTW250, FTW367, and FBX350 formed more effectively in the threelayer configuration. The thicker laminate generated greater clamping tension during forming, which helped stabilize the fabric and reduce defect severity. Among all reinforcements, FTW367 again demonstrated the best performance at R2 and R2, producing the smoothest surfaces with the smallest wrinkles. Localized fiber compression was observed at the corners of the formed shape, visible as concentrated regions of deformation. Notably, while folds and other surface defects were much more pronounced in single-layer flax NCF compared to the glass fabric, the difference between the two materials diminished substantially in the three-layer configuration.

Haralick feature extraction for predictive models.

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The Haralick features extracted from the deformation maps (Fig. 4) were used to assess the predictive capability of linear regression models for fabric formability. Table 3 summarizes the model performance in terms of R2 and MAE, reported as average ± standard deviation across the 10 Monte Carlo cross-validation runs. For completeness, texture features such as Contrast and ASM were evaluated in the methodology but did not contribute meaningfully to model predictability and are therefore not included in the remaining sections of this study.

Table 3. Average linear regression models' performance obtained across Monte Carlo crossvalidation runs for the prediction of different Haralick texture features (dependent variables).

Haralick Features | Correlation | Dissimilarity | Energy | Homogeneity
R-square (R²) | Training | 0.74 ± 0.03 | 0.86 ± 0.03 | 0.76 ± 0.03 | 0.90 ± 0.03
Testing | 0.57 ± 0.16 | 0.73 ± 0.12 | 0.67 ± 0.11 | 0.81 ± 0.10
All dataset | 0.71 ± 0.01 | 0.84 ± 0.01 | 0.75 ± 0.01 | 0.88 ± 0.01
Mean Absolute Error (MAE) | Training | 0.00 ± 0.00 | 0.03 ± 0.00 | 0.01 ± 0.00 | 0.01 ± 0.00
Testing | 0.00 ± 0.00 | 0.04 ± 0.00 | 0.01 ± 0.00 | 0.01 ± 0.00
All dataset | 0.00 ± 0.00 | 0.03 ± 0.00 | 0.01 ± 0.00 | 0.01 ± 0.00

Among the evaluated texture features, dissimilarity and homogeneity were predicted most accurately by linear regression, with Monte Carlo-averaged testing R2 up to 0.81 , compared to 0.57 0.67 for correlation and energy. Fig. 5 shows a prediction plot from a single Monte Carlo iteration along with the R2 values from all 10 cross-validation runs, illustrating both model performance and stability under repeated resampling.

[picture]

Fig. 5. Linear regression for Haralick features: (a) actual vs. predicted dissimilarity, (b) actual vs. predicted homogeneity, (c) Monte Carlo R2<0.57 per iteration for dissimilarity, (d) Monte Carlo 0∘ per iteration for homogeneity.

Fig. 5. Linear regression for Haralick features: (a) actual vs. predicted dissimilarity, (b) actual vs. predicted homogeneity, (c) Monte Carlo R 2 < 0.57 per iteration for dissimilarity, (d) Monte Carlo 0 ∘ per iteration for homogeneity.

Theoretically, the homogeneity measures how similar neighboring pixel intensities are, based on the gray-level co-occurrence matrix [40,41]. Values close to the GLCM diagonal indicate a uniform texture, while lower values indicate more variation. Consequently, accurate prediction of homogeneity provides valuable insight into the consistency of wrinkle formation on the formed surface. In this study, a trend was observed in which lower homogeneity values corresponded to pronounced wrinkles (mainly formed along the square-tool sides), suggesting that this Haralick
feature can provide a quantitative indicator of surface quality and forming consistency in flaxreinforced composites.

Dissimilarity measures the average intensity difference between a pixel and its neighbors across the image, thereby capturing variations in gray-level pairs. Higher dissimilarity values indicate greater texture variation, and hence more severe surface defects [47-49]. Accurate prediction of this metric enables direct comparison of wrinkle intensity between different forming materials. Notably, dissimilarity was found to capture both defect severity and fabric architecture effects: draping of glass fiber reinforcement was associated with lower dissimilarity values, whereas higher values corresponded to the FBX350 reinforcement. This dissimilarity feature provided the second-best prediction accuracy, with an average 15∘ of 0.73 on the test sets over 10 Monte Carlo cross-validation runs.

The FBX350 forming was observed to be clustered by low Haralick correlation values. Although the R2 for correlation was relatively low ( R2 for testing dataset), it still shows potential to capture differences in wrinkle-pattern progression across the forming surface, where long, narrow folds dominate. This reflects how intrinsic material properties influence wrinkle formation.

The energy among Haralick features also exhibited a clear relationship with fabric orientation and forming-induced defects. Lower energy values at smaller orientation angles ( mathematical formula and superscript number ) were associated with increased defect severity, whereas higher values corresponded to minimal defect formation. This trend highlights the sensitivity of the energy metric to ordered texture patterns and underscores its relevance for assessing forming quality as a function of fabric angle.

Finally, although forming-induced wrinkling is governed by nonlinear mechanical phenomena such as buckling and shear-tension coupling [50], the primary objective of this study was to assess whether macroscopic wrinkle severity metrics could be statistically predicted from experimentally measured fabric parameters. The observed predictive performance (test superscript number up to 0.81 for dissimilarity and homogeneity) indicates that, within the investigated parameter space, first-order linear relationships provide an accurate approximation given the limited dataset. Exploration of more advanced nonlinear models will be conducted in future work as the dataset expands.

Conclusion

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This study demonstrated a machine learning-based framework to predict forming-induced defects in flax woven fabrics using 3D scanning and Haralick texture analysis. By combining fabric geometrical parameters, mechanical properties, and wrinkle distribution quantification, the approach provided a reliable assessment of formability (namely, the surface quality upon forming). Experimental results showed that flax twill fabrics exhibited the lowest formability, while glass fiber and biaxial NCF fabrics formed more smoothly, with orientation and layer count significantly influencing wrinkle severity.

Linear regression models achieved high predictive accuracy, with an average test set superscript number of 0.81 across 10 Monte Carlo cross-validation iterations, demonstrating that integrating image-based texture analysis with fabric geometrical and mechanical parameters enables quantitative and consistent prediction of forming performance. Among the Haralick features, lower homogeneity values corresponded to pronounced wrinkles along the square-tool sides, highlighting its ability to indicate surface quality and forming consistency. Dissimilarity feature captured both defect severity and fabric architecture effects, with glass reinforcements showing lower values and the FBX350 reinforcement higher values.

It should be noted that the in-plane tension stiffness measured in this study reflects small-strain behavior, representing a limitation of this work. During forming, fabrics may experience larger strains, particularly near high-curvature or sharp-edged tools, where nonlinear effects such as fiber reorientation, strain-rate dependency, and microstructural characteristics can significantly influence the reinforcement response. These effects were not explicitly accounted for and should be incorporated in future investigations.

Future work will extend the proposed modeling framework by incorporating additional natural fiber types and advanced machine learning strategies to improve predictive accuracy. Generalization
to complex tool geometries is currently under investigation through integration of 3D-scanned point cloud reference meshes, replacing tool-specific analytical formulations. Scaling up to industrial forming scenarios and implementing real-time defect monitoring strategies can further enhance the applicability and robustness of this approach for sustainable composite manufacturing.

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The original version of this eBook is available on https://www.scientific.net/book/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 73-82

doi: 10.4028/p-C1cyX0

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

Submitted:
2026-01-25

Revised:
2026-02-15

Accepted:
2026-02-20

Online:
2026-04-10

Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

Kari D. White 1,a* and James A. Sherwood 1, b

¹Department of Mechanical Engineering, University of Massachusetts, Lowell, One University Ave., 01854, Lowell, MA, USA.

a  Kari_White@uml.edu; b  James_Sherwood@uml.edu

Keywords: Composites, Finite Element, Thermoplastic, Thermoforming, Consolidation.

Abstract

Thermoforming of thermoplastic fiber-reinforced composites enables cost-effective production of complex, high-volume components, yet wrinkling and shear-induced thickness variations remain persistent challenges in compound-curvature geometries, often leading to nonuniform consolidation. This work presents a predictive virtual process simulation that integrates discrete mesoscopic finite element modeling with targeted blank design strategies to address these limitations. The approach, developed by the Sherwood Group and implemented in LS-DYNA, is applied to the thermoforming of a UHMWPE unidirectional cross-ply composite system (DSM ® Dyneema ® HB210). A thickness-stretch shell formulation (SHELL ELFORM25), coupled with a user-defined material model, is employed to simultaneously capture in-plane shear, through-thickness deformation, and frictional interactions during forming. A parametric study is conducted to evaluate the combined effects of tooling geometry and strategically introduced slits in the blank, including side- and corner-oriented configurations. The results demonstrate that the proposed formulation provides an effective balance between computational efficiency and predictive accuracy while explicitly reducing shear-induced thickening. Notably, corner-oriented slits at 45∘ to the fiber directions significantly reduced thickness variability and wrinkle severity compared to unmodified blanks and side-slit configurations. These findings highlight the novelty of integrating thicknessaware forming simulations with geometric blank modification as a robust pathway for achieving nearuniform thickness and improved preform quality in thermoformed composite parts.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

Wrinkling is a persistent defect when forming textile-reinforced composite blanks into doublecurvature geometries, because the continuous sheet must accommodate incompatible in-plane strain states as it conforms to a hemispherical or helmet-like surface. Much of the composites forming literature has addressed wrinkle mitigation through process-level strategies, such as adjustments to forming pressure, tooling temperature, blank-holder conditions, or laminate architecture, while retaining continuous, uncut blanks. Although these approaches can delay the onset of wrinkling or reduce wrinkle severity, they do not fundamentally resolve the geometric incompatibility between a planar blank and a compound-curvature surface, and residual wrinkling in flange regions or along principal fiber directions is frequently observed. A review of military composite helmet manufacturing similarly identified wrinkling and fiber distortion as enduring challenges when forming highly curved structures from textile-based composites using continuous blanks [1]. From a mechanics perspective, numerical studies have further shown that wrinkling arises from global kinematic constraints governed by the interaction of tensile, in-plane shear, and bending stiffness, rather than purely local material response [2].

Intra-ply shear is the dominant mode of deformation during the forming process, and various degrees of material shearing are what allow the material to conform across a compound curvature part. Adding complexity to the forming process outcome is the increase in thickness of the lamina due to conservation of volume during in-plane shear. Dangora et al. [3] documented the incompressibility phenomenon with micrographs taken of laminates of DSM Dyneema® HB80
sheared to 0∘,20∘, and 60∘ showing the associated thickness increases corresponding to conservation of volume. Based on that research, the resulting thickness in an area of the formed part can be correlated to the degree of shear in that area. The implications of thickness changes during the process are two-fold: (1) thickness variations in the preforms and (2) effects on tool/material friction during the forming.

Consider a two-step forming process. In Step 1, stacks of multiple plies are preformed one at a time. In Step 2, heat and pressure are applied in combination with matched dies to consolidate a stack of preforms and to cure the part. Figure 1 depicts how thickness variations in individual preforms can lead to poor-quality consolidation and voids due to pressure variations. Therefore, these thickness changes must be considered in a forming simulation. Ideally, a "uniform" thickness preform would resolve these manufacturing-induced defects associated with the consolidation step.

[picture]

Fig.1 Variations in preform thickness lead to inconsistent/poor consolidation [14].

Fig.1. Variations in preform thickness lead to inconsistent/poor consolidation [14].

During the preforming step, the friction between the binder ring and the blank introduces in-plane tensile stresses that mitigate the wrinkling associated with shear deformation, but do not eliminate the change in thickness associated with shear. The resulting shear-induced thickness variations influence which areas of the material remain in contact with the binder ring during forming. Prior studies have shown that friction at sliding interfaces can lead to undesirable effects, including distortion of the final part geometry, residual stresses, and the formation of wrinkles [4-8]. Conversely, when binder rings are employed, controlled friction combined with appropriate binderring pressure can be used beneficially to restrain material flow and suppress wrinkle formation [3, 913]. In particular, hemispherical preforming trials conducted by Dangora et al. [3] demonstrated the strong dependence of wrinkle size and morphology on binder-ring pressure during the forming of a unidirectional cross-ply thermoplastic laminate (DSM Dyneema® HB80).

In a previous study by the authors [14], simulations of the experimental performing setup were completed to validate the material properties and friction values used in the simulations. Measured punch force, shear angle distribution, draw-in profile, and visual wrinkle distribution were metrics used in the evaluation. All simulations showed good correlation with the experimental results, and it was concluded that the modeling approach was valid to proceed with a parametric study of the tooling. The simulations were then used to find processing and tooling configurations that worked well in mitigating wrinkles and providing "uniform" thickness [15]. In that study, it was shown that tooling and blank shape also contribute to the uniformity of preform thickness, the development of wrinkles, and the overall quality of the preformed part. The gap between the binder ring and the punch, the gap between the die and the punch, and the radii of both the binder ring and the die are parameters that can be altered to influence the preform results. All simulations used flat blanks without slits or darts.

Classical textile mechanics establishes that darts and gores are a geometric necessity for draping flat woven fabrics over spherical surfaces without wrinkling [16]. Past works by others have demonstrated that blank segmentation, through the introduction of strategic slits, relief cuts, or dartlike features, can address the geometric constraints that lead to wrinkling by locally releasing in-plane compressive stresses. In the context of thermo-hydroforming of composite helmets, Ahn et al. [17] explicitly treated the blank shape and the relief cuts made in the blank as design variables in a numerical optimization framework aimed at minimizing wrinkle density and wrinkle height, showing that appropriately designed V-shaped relief cuts significantly reduced wrinkling and improved
thickness uniformity. Related studies by Ahn et al. [18] further emphasized the importance of integrating considerations of forming kinematics, material architecture, and blank design in helmetlike thermo-hydroformed components. Experimental work by Hu et al. [19] on hemispherical forming of continuous fiber-reinforced textile preforms demonstrated that precision slitting in high-shear regions reconfigured deformation paths, delayed the onset of shear locking, and suppressed global wrinkling. Similar geometric modification strategies were also reported by Kim et al. [20] in doublediaphragm forming, where pre-cut prepregs were employed to improve part quality in complex geometries.

In contrast to prior works that optimize relief-cut geometry primarily through numerical or process-level studies, the present work implements and evaluates slit/dart strategies directly within the thermoforming of fiber-reinforced composite blanks of DSM ® Dyneema ®  HB210, with the dual objectives of mitigating wrinkling and reducing thickness variations across the surface of the formed part. One of the promising configurations from the previous research [15] was used as a baseline for modifying the blank in the current research. The results of this investigation lay the foundation for using the proposed methodology to design tooling and incorporate strategic cuts in the blank to mitigate wrinkling and reduce thickness variations during the forming of compound curvature parts.

Methodology

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

Modeling Approach. The Sherwood Group [21] developed a discrete modeling approach that has been shown to simulate the forming of a plain-weave hemisphere shape with good accuracy. Conventional elements available in commercial finite element software are used in the unit cell approach shown in Figure 2. Fiber directionality is described and tracked by beam elements that represent the tensile and flexural properties of the laminate. In the current research, which uses LSDYNA, the shear load is carried by thickness-enhanced shell elements (thick-thin shell), SHELL ELFORM25, that capture the evolution of the in-plane shear stiffness as a function of the degree of shear, as well as linear strain through the thickness. The initial thickness is prescribed in the section definition keyword card set. In the case of woven materials, the horizontal and vertical beams represent the warp and weft tows with a bilinear modulus for the beam elements to capture wrinkling behavior [22]. In the case of the 0/90 cross-ply considered in the current research, the horizontal and vertical beams can be assigned tensile and flexural properties of the 0∘ and 90∘ layers.

[picture]

Fig. 2. Unit cell configuration for mesoscopic laminate material model [14].

Fig. 2. Unit cell configuration for mesoscopic laminate material model [14].

[picture]

Fig. 3. Hemisphere preform simulation in LS-DYNA [15].

Fig. 3. Hemisphere preform simulation in LS-DYNA [15].

The hemisphere preform model as shown in Figure 3 was built to replicate the experimental setup; the tooling geometry was then modified to represent the binder ring and die sizes. The friction coefficients for the material were calculated from data recorded using the UMass Lowell friction tester, as redesigned by Campshure et al. [14, 23, 24].

The composite laminate system investigated in this research is DSM ® Dyneema ® HB210. This material system is a thermoplastic cross-ply containing four unidirectional layers oriented in a ( 0/90)2 fiber configuration with each ply comprised of UHMWPE fibers and a thermoplastic polyurethane (TPU) based matrix [25]. The tensile, shear and bending properties at 100∘C for Dyneema ® HB 210 are provided from previous testing [5, 26, 27] and shown in Table 1, where γ is defined as the shear strain of the composite lamina. The friction values are averages of fiber orientation and resin condition, as the hemisphere is symmetrical and each condition is represented equally.

Table 1. Material Properties for Hemisphere Preforming Simulations (MPa)

Shear Stiffness as a Function of Shear Strain

Tensile

(MPa)

Compressive

Modulus

(MPa)

Tool/Ply

(MPa)

Static

Friction

Tool/Ply

Dynamic

Friction

superscript number | 19300 | 5000 | 0.110 | 0.077

Parametric Study. Tooling Geometry Parameters. Specific geometry attributes were identified to be relevant to the preforming outcomes. Figure 4 shows the upper gap as the distance between the inner radius of the binder ring and the outer radius of the punch. The lower gap indicated the distance between the inner radius of the die and the punch. The lower radius is a measure of the fillet, or curvature, of the die.

[picture]

Fig. 4. Tooling parameters analyzed in study [15].

Fig. 4. Tooling parameters analyzed in study [15].

The experimental preform setups had the geometric values listed in Table 2, and the simulations were created to reflect these values. An initial parametric study was conducted that used combinations of the existing tooling to evaluate the sensitivity of the model to parameter changes. A binder pressure of 300 kPa was used to replicate the experimental pressure used with the four layers of laminate with the redesigned tooling. All simulations were performed with the properties of DSM ® Dyneema ® HB 210 at a processing temperature of 100∘C. One set of tooling that showed promising results for wrinkle mitigation, in terms of wrinkle distribution and average wrinkle height, and uniform material thickness in the hemispherical area had tooling dimensions listed in Table 2.

The preform quality and thickness profile are shown in Figure 5.
Figure 5(a) is a uniform color to allow a clear view of the wrinkle distribution in the part and their heights.

Figure 5(b) shows the final thickness distribution in the part. The thickest areas are in the ±45∘ regions.

Table 2. Geometric Properties of Baseline Tooling

Upper Gap

Lower Gap

Lower Radius

mathematical formula | 3.18 | 10.2

[picture]

Fig. 5. Baseline tooling configuration used for blank slit study:
(a) Formed part showing distribution of wrinkles (b) Thickness variation denoted by color contours

Fig. 5. Baseline tooling configuration used for blank slit study: (a) Formed part showing distribution of wrinkles (b) Thickness variation denoted by color contours

Blank Slit Study. One method of reducing wrinkles is to remove part of the blank material, allowing the fibers to move freely in local areas. The next set of investigations was planned to determine whether adding relief areas, via slits in the material, would not only aid wrinkle mitigation but also reduce thickness variations. Two types of slits were introduced to the square blank material: slits that extended horizontally and vertically from the midsides of the square blank and slits that extended at 45∘ into the blank from the corners of the square. Eight slit sizes were investigated for each type of slit. For each slit size, the square "Area between slits", as denoted in Figure 6, was kept the same to be able to compare side and corner slits. The dimensions and mean values for each of the slit configurations that were investigated are provided in Table 3.

[picture]

Fig.6. Blank configurations: (a) Baseline [no slits], (b) Blank with slits from sides of square blank, and (c) Blank with slits from corners of square blank.

Fig.6. Blank configurations: (a) Baseline [no slits], (b) Blank with slits from sides of square blank, and (c) Blank with slits from corners of square blank.

Three metrics were used in comparing the results from the study, i.e., (1) Thickness distribution, (2) Wrinkle Height, and (3) In-plane shear angle distribution. The thickness distribution over the hemispherical portion of the preform gives guidance on how well the preform can be consolidated into a uniform part. As controlling thickness uniformity is a goal of this project, measures of thickness variation were used as a quantitative comparison. Wrinkle heights were quantified by outputting the location of every shell node within the hemispherical portion of the preform, then determining the distance of each node from the surface of the punch. Finally, the in-plane shear angle distribution contributes to both the thickness uniformity, and an indication of how well the binder ring can engage appropriate shearing of the laminate into the hemispherical shape.

Results and Discussion

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

The initial thickness of one ply of the DSM ® Dyneema ® HB210 material was 0.72 mm , and the final thicknesses of the elements over the hemisphere portion of the preform were normalized to this initial thickness to evaluate the relative change in thickness. Box-and-whisker plots were used to visualize the distribution of element thickness across the part. Figure 7 shows normalized thickness results for all 16 slit configurations that were analyzed, as well as the baseline square blank. The box for each
configuration represents the middle 50% of the data, while the lines extending to the top and bottom represent the max and min data values.

In addition to thickness uniformity, wrinkle height provides a complementary measure of out-ofplane defect severity and is presented here immediately following the thickness results for direct comparison. Wrinkle height is a critical quality metric, as fewer, smaller wrinkles than in the baseline configuration are desirable. However, quantifying wrinkles is more complex than discerning the thickness variations. Figure 8 shows the wrinkle heights for all configurations, with the X marking the mean height. Note that the wrinkle height was defined as the distance of the node from the punch, which means that if the material is in contact with the punch, then the wrinkle height would be half the thickness of the material at that point. Mean wrinkle height is used here as a scalar metric to evaluate the average size of wrinkles over the part. Alternative geometry-based wrinkle metrics have been reported in the literature, such as the wrinkle index introduced by Chen et al. [28], which quantifies wrinkle severity using local surface normal variation extracted from finite element simulations. While conceptually different from the wrinkle-height definition adopted in the current research, both approaches aim to capture out-of-plane deformation associated with forming-induced defects.

[picture]

Fig. 7. Normalized thickness variation for all slit configurations.

Fig. 7. Normalized thickness variation for all slit configurations.

[picture]

Fig. 8. Wrinkle height for all slit configurations.

Fig. 8. Wrinkle height for all slit configurations.

The goal is to minimize thickness variation. Therefore, the tighter (or narrower) the box and the smaller the whiskers, i.e., the range between the maximum and minimum, the better in Figure 8. The mean normalized thickness of the baseline blank was 1.22(SD=0.16), indicating moderate variation.

Again, this tooling geometry was selected based on the quality of the preform. Adding side slits reduced variation in two configurations ( 1 S and 2 S ) relative to the baseline, as indicated by a decrease in standard deviation; however, these configurations have the least material in the center of the blank without slits, so the slits will extend into the hemispherical portion of the preform. The other side slit configurations did not improve the thickness uniformity. Discontinuities in the material are undesirable in most applications due to a loss of strength. The corner slits performed remarkably well at maintaining uniform thickness, even with small slits applied to the blank material. The average normalized thickness of configuration 8 C , which has the largest intact central material, is 1.07 , with a standard deviation of 0.10 , an improvement over the baseline configuration. Figure 9 shows the thickness distribution across the part for configurations 1 S,8C, and the baseline. The slight asymmetry observed in the thickness distribution in Figure 9a is attributed to a numerical effect associated with the use of an explicit time-integration solver rather than a physical asymmetry in the model.

Table 3. Sample Dimensions and Mean Values

Fig. 9. Thickness variations over the hemisphere portion of the preform for configurations (a) 1 S , (b) 8 C , and (c) baseline configurations.

The baseline configuration has a mean wrinkle height of 1.20 mm , while the best side-slit configuration has a mean height of 1.34 mm(1 S), and the corner-slit configuration has a mean height of 1.26 mm(4C). As in the thickness study, the best side-slit configuration is also one with very long slits that would extend into the material. Although the corner-slit configuration with the smallest average is not the one with the smallest slits, the improvements in slit size from 8C are minimal.

Future work on wrinkle height should include subtracting the material thickness at the location, or employ another method of normalizing the data for comparison.

Summary

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

In this research, hemisphere preforming simulations were performed on a unidirectional thermoplastic cross-ply material system, DSM Dyneema® HB210. A parametric study was performed to evaluate the role of the binder gap (space between the punch and the binder) and the die radius (the curvature of the die that the material is pushed through). Results showed corner slits outperform side slits in wrinkle control and thickness uniformity, with smaller slits outperforming larger ones. Side slits show increasing wrinkle height and thickness variability with smaller slits, indicating potential process challenges. Future studies will normalize the wrinkle distribution for better quantification.

Acknowledgements

The original version of this paper is available on https://www.scientific.net/MSF.1182.73.pdf

This work was performed under Cooperative Agreement W911NF-18-2-0033 with the US Army Research Lab. The material was donated by DSM, and LS-DYNA was donated by ANSYS.

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White KD, Campshure B, Sherwood JA. Effects of Thickness Changes and Friction during the Thermoforming of Composite Sheets. ESAFORM 2021 24th International Conference on Material Forming; Liège, Belgique2021.

White KD, Sherwood JA. An investigation into the relationship between hemisphere tooling parameters and thickness changes during the thermoforming of a thermoplastic composite. Materials Research Proceedings. 2024;41:513-22.

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Ahn H, Kuuttila NE, Pourboghrat F. Effects of pressure, boundary conditions, and cutting reliefs on thermo-hydroforming of fiber-reinforced thermoplastic composite helmet based on numerical optimization. Journal of Thermoplastic Composite Materials. 2021;34(2):181-202.

Ahn H, Kuuttila NE, Pourboghrat F. Thermo-hydroforming of a fiber-reinforced thermoplastic composites considering fiber orientations. AIP Conference Proceedings. 2018;1960(1):020002.

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Kim S, Shin H, Lee K, Ha S. Enhancing Product Performance via a Modified Double-Diaphragm Forming (mDDF) Preform Method for Prepreg Compression Molding of Fiber-Reinforced Polymer Composites. Polymers. 2025;17(11):1489.

Jauffres D, Sherwood J, Morris C, Chen J. Discrete mesoscopic modeling for the simulation of woven-fabric reinforcement forming2010. 1205-16 p.

Dangora LM, Mitchell CJ, Sherwood JA. Predictive model for the detection of out-of-plane defects formed during textile-composite manufacture. Composites Part A: Applied Science and Manufacturing. 2015;78:102-12.

Fetfatsidis KA, Gamache LM, Gorczyca JL, Sherwood JA, Jauffrès D, Chen J. Design of an apparatus for measuring tool/fabric and fabric/fabric friction of woven-fabric composites during the thermostamping process. International Journal of Material Forming. 2013;6(1):1-11.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 83-90

doi: 10.4028/p-JwxQ3e

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

Submitted:
2026-01-20

Revised:
2026-02-15

Accepted:
2026-02-17

Online:
2026-04-10

Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

Elias DELSOL 1,2,a, Philippe OLIVIER 1, b*, Bruno CASTANIE 1,c, Wiyao AZOTI 1, d and Léon RATSIFANDRIHANA 2,e

¹University of Toulouse, UT3, CNRS, ICA, UMR 5312, ECA, 3 Rue Caroline Aigle, 31400

Toulouse, France

2 SEGULA TECHNOLOGIES Immeuble EQUINOX, Bat-1, 24 Boulevard Déodat de Séverac, F-31770 Colomiers

a  edelsol@insa-toulouse.fr, b  philippe.olivier@univ-tlse3.fr, c  bruno.castanie@insa-toulouse.fr, d  azoti@insa-toulouse.fr, eleon.ratsifandrihana@segula.fr 

Keywords: Process induced deformations, spring-in, compensated mould design, warpage

Abstract

This work investigates the formation and control of residual deformations in composite Lshaped parts manufactured by autoclave curing. An experimental study is first conducted to characterize spring-in for different stacking sequences. Dimensional measurements are performed using stereo digital image correlation to quantify spring-in and to assess the presence of warpage along the flanges. A numerical study is then carried out to develop a simulation method for processinduced deformation prediction. The influence of the main mechanisms involved is analyzed, and a modeling strategy for the tool-part interaction is proposed. Finally, compensated mould design is addressed. The convergence of the optimization problem is investigated, and an optimized mould geometry is determined for each part considered in this study.

Introduction

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

Composite materials play a key role in the aerospace industry. They account for more than 50% of the mass of modern commercial aircraft and constitute a large proportion of primary structural parts. In this context, reducing manufacturing costs represents a major industrial challenge [1]. The total cost of high-performance composite structures is strongly linked to the manufacturing process. Beyond raw material costs and the autoclave curing cycle [2], mould design and manufacturing represent a significant expense. Indeed, the fabrication of composite parts inevitably leads to the development of residual deformations, which generate spring-in and warpage of the part and may compromise geometric tolerances [1].
The autoclave curing of thermoset composite parts involves multiphysics mechanisms due to the polymerization of the resin in a constrained environment [3], [4]. The heterogeneous nature of the composites generates intrinsic residual stresses [5]. The main mechanisms involved are thermal expansion, chemical shrinkage of the resin [6], and the development of thermal gradients during the cure [7]. In addition, the part interacts with the mould, release films, and peel plies under the autoclave pressure. These phenomena are referred to as extrinsic mechanisms. The main extrinsic mechanism is the tool-part interaction [8], which plays a significant role for thin composite parts [9]. Depending on the manufacturing method used process-induced deformation can be linked to other phenomenon as shown for example in refs. [13,14] with pultruded L-shaped composites.
As a consequence, the final geometry of a composite part never exactly matches that of the mould. To address geometrical tolerances, the best way is to design a compensated mould [10]. This designing process can be time-consuming and costly, as it often relies on successive experimental trial-and-error iterations. In a competitive industrial environment, reducing the number of experimental iterations is a key objective [1]. To this end, a digital mould design method must be implemented, and accurate numerical tool has to be developed. The objective of this study is to develop a numerical method for the design of a compensated mould for composite L-shape parts, with a particular focus on spring-in compensation.

The paper is organized as follows. First, the experimental study of process-induced deformations is presented. Then, the numerical methodology for predicting residual deformations is detailed and validated. Finally, a compensated mould design approach is introduced, and the convergence of the associated optimization problem is studied.

Experimental Study of Process Induced Deformations

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The first part of this work focuses on the experimental investigation of residual deformations in composite L-shaped parts. Two stacking sequences are considered: [0,90]2 s and [0,90]4 s. The material used is a unidirectional carbon/epoxy prepreg (AS4/8552). The L-shaped parts have dimensions of 150×50 mm, with a fillet radius of 2 mm . The vacuum bagging is illustrated in Figure 1.

[picture]

Fig.1. Vacuum bagging and mould used for this study

Fig.1. Vacuum bagging and mould used for this study

The aluminum mould is treated with a release agent, and two peel plies are placed on both sides of the laminate to avoid additional spring-in effects by layup asymmetry during curing. The laminate coordinate system is defined such that the x-direction is parallel to the fillet axis of the part. Curing is performed in an autoclave according to the composite manufacturer's recommended cycle. For each stacking sequence, three identical specimens are manufactured. The manufactured parts are dimensionally characterized using Digital Image Correlation (DIC). This technique provides fullfield displacement measurements over the entire upper surface of the part, allowing accurate determination of the fillet radius, the spring-in value and possible warpage along the flanges. The experimental setup is shown in Figure 2 as well as the displacements measured by DIC on an Lshaped part.

[picture]

Fig. 2. Experimental setup for the dimensional monitoring. Displacements measured by DIC on a L-shaped part.

Fig. 2. Experimental setup for the dimensional monitoring. Displacements measured by DIC on a L-shaped part.

After dimensional inspection using DIC, the point cloud corresponding to the upper surface of the L shaped part is extracted. A post-processing procedure based on a least-squares fitting algorithm is used to compute the spring-in angle and the fillet radius. Additionally, thanks to this control method, the presence of warpage along the flanges is investigated. For the parts considered in this study, no significant warpage is observed. The final geometry of the L -shaped part can therefore be accurately described by the spring-in angle only. The results are reported in Figure 3. For each part, three measurements are performed:

With both peel plies in place,

With only a single peel ply in contact with the mould,

After removal of both peel plies.

[picture]

Fig. 3. Experimental spring-in angle measurements of [0,90] laminates

Fig. 3. Experimental spring-in angle measurements of [ 0 , 90 ] laminates

Figure 3 first shows that no significant difference is observed between the spring-in angle measured with both peel plies in place and the angle measured after their removal. This observation indicates that when two peel plies are placed on both sides of the part, no significant asymmetry is introduced
in the shear stresses transmitted to the part under these configurations. This effect is therefore neglected in the remainder of this study, and peel plies are no longer considered. In addition, a larger spring-in angle is observed for the thinner part, highlighting the influence of part stiffness on the magnitude of residual deformations.

Numerical Study of Process Induced Deformations

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

Beyond the prediction of process-induced deformations, which constitutes the primary objective of this section, understanding the influence of the underlying mechanisms is essential. To this end, a progressive increase in model complexity is adopted. A first simplified model, accounting only for intrinsic mechanisms, is introduced and its limitations are discussed. The influence of the mould is then added, first by considering geometric constraint effects, and subsequently, by introducing the frictional interaction between the part and the mould. Owing to the small thickness of the manufactured parts, thermal gradients are neglected in the present modelling framework. The numerical simulations are performed using Abaqus and reproduce a portion of the vacuum bagging configuration presented in Figure 1. Based on the experimental observations regarding the peel plies, only the mould and the composite part are modelled.
The interaction between the mould and the composite part is described using a frictional contact interaction, with properties evolving as a function of the degree of cure. The curing cycle is applied uniformly to all components; therefore, no coupled thermal analysis is performed. An autoclave pressure of 0.7 MPa is applied to the upper surface of the L-shaped part. The material properties are taken from the literature [11], [12]. Resin curing is modelled using the CHILE (Cure Hardening Induced Linear Elastic) model. A known limitation of this approach is the neglect of viscoelastic effects, particularly in the rubbery stage. The CHILE model is implemented through a dedicated UMAT subroutine.
During the cure, minimal boundary conditions are applied to the mould to suppress rigid body motions. For the demoulding, the mould is removed, and isostatic boundary conditions are applied to the L-shaped part to eliminate rigid body motions without generating additional stresses. Twentynode quadratic brick elements (C3D20) are used. The mesh is locally refined in the fillet region to accurately capture bending effects in this critical area (see Figure 4).

[picture]

Fig. 4. Example of the numerical simulation on ABAQUS for the curing of a L -shaped laminate.

Fig. 4. Example of the numerical simulation on ABAQUS for the curing of a L -shaped laminate.

The simulation results (Figure) obtained without accounting for mould effects are first examined. Thermal deformations alone account for around 30% and 34% of the experimentally measured spring-in for the 8 plies and 16 plies L-shaped parts, respectively. The introduction of the chemical shrinkage significantly improves the prediction accuracy, leading to predicted values corresponding to 78% and 87% of the total spring-in, respectively. Nevertheless, this initial study shows the necessity of accounting for extrinsic mechanisms, in particular the autoclave pressure and mould effects such as the interactions between the mould and the part.

[picture]

Fig. 5. Comparison between experimental spring-in values and numerical predictions accounting for intrinsic mechanisms

Fig. 5. Comparison between experimental spring-in values and numerical predictions accounting for intrinsic mechanisms

The mould effect is then introduced, and a first analysis focuses on the influence of the friction coefficient during the rubbery stage. Figure shows that the introduction of friction between the mould and the laminated part bottom surface leads to an increase in spring-in for both configurations. It is observed that the influence of friction becomes more pronounced as the part stiffness decreases. It can be seen in Figure 6 that calculating the spring-in angle value without considering any friction ( f =0 ) leads to slightly underestimated values. Using higher values of f such as f=0.25 or f=0.5 gives theoretical values overestimating the experimental ones. A friction coefficient of f=0.15 provides a satisfactory prediction for 16 -ply L-shaped part. In contrast, if keeping f=0.15 for the 8 -ply configuration, the spring-in is clearly overestimated. It therefore does not appear possible to identify a single friction coefficient that is numerically admissible for both configurations. This observation suggests that accounting for friction only during the rubbery stage is insufficient, and that a non-zero friction coefficient must be applied during the viscous stage.
By considering a friction coefficient of 0.1 during the viscous stage and 0.15 during the rubbery stage, the prediction is improved, with predicted spring-in angle values of 1.80∘ and 1.64∘ for 8 -ply and 16 ply parts, respectively. This result indicates that shear stress transfer occurring during the viscous stage contributes to a reduction in spring-in. This behaviour is not unexpected in the present configuration, since the ply adjacent to the mould is a 0∘ ply, which is mainly loaded in longitudinal tension. Through Poisson's effect, transverse compressive strains are stored, which are released during demoulding and result in a reduction of the spring-in.
This numerical study makes it possible to identify a set of parameters that account for the dominant mechanisms governing spring-in and to achieve predictions consistent with the experimental results. The magnitude of the shear stresses generated at the tool-part interaction interface is consistent with values reported in the literature [11]. However, this analysis also highlights the difficulty of unambiguously identify the influence of individual mechanisms. While some mechanisms tend to increase spring-in, others contribute to its reduction, and experimental data required for parameter identification remain difficult to access. Further investigations are therefore required to improve the understanding of these mechanisms, notably by considering additional stacking sequences and different part shapes.

[picture]

Fig. 6. Comparison between experimental spring-in values and numerical predictions including rubbery friction interaction effects

Fig. 6. Comparison between experimental spring-in values and numerical predictions including rubbery friction interaction effects

Compensated Mould Design

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

The validation of the prediction approach makes it possible to consider the use of the model for compensated mould design. The objective is to design the mould geometry such that the final shape of the manufactured part matches the desired geometry after demoulding. For the composite L-shaped parts in this work, this consists in determining the mould angle that leads to a final angle equal to 90∘. To this end, the configuration using the friction coefficients identified as optimal in the previous section is retained. The same numerical model is employed, and the initial mould angle is parameterized in order to identify the optimal mould angle.
Figure presents the evolution of the angular error of the L-shaped part as a function of the initial mould angle. The relationship is found to be linear, indicating that the optimization problem is straightforward for L-shaped parts without warpage. Only two simulations are required to identify the optimal angle. The optimal angle is 91.83∘ for 8-ply, and 91.65∘ for the 16-ply part.

[picture]

Fig. 7. Linear relationship between angular error and initial mould angle for compensated mould design

Fig. 7. Linear relationship between angular error and initial mould angle for compensated mould design

Conclusion

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

This study led to the development of a numerical prediction method for previously manufactured composite L-shaped parts. The progressive numerical analysis made it possible to assess the influence of the dominant mechanisms involved in spring-in formation and to identify a set of parameters allowing tool-part interaction to be accounted for. The numerical tool was then applied to the design the compensated moulds for the two configurations investigated. The convergence analysis showed that the angular error varies linearly with the mould angle.
This analysis also highlights the inherent difficulty of reliably modelling curing-induced deformation mechanisms. Some effects contribute to an increase in spring-in, while others tend to reduce it, making the individual validation of each mechanism challenging. Additional experimental investigations are required to better isolate and quantify these effects. For example, the use of male and female moulds, variations in the orientation of the ply in contact with the mould, or the study of flat laminates would provide valuable insight. A numerical approach validated over such a range of configurations could then be considered sufficiently reliable for the individual modelling of the main mechanisms.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.83.pdf

B. Castanie et al., «Review of monolithic composite laminate and stiffened structures in aeronautic applications », Compos. Part C Open Access, vol. 17, p. 100585, juill. 2025, doi: 10.1016/j.jcomc.2025.100585.

J. Zhang, G. Lin, U. Vaidya, et H. Wang, « Past, present and future prospective of global carbon fibre composite developments and applications », Compos. Part B Eng., vol. 250, p. 110463, févr. 2023, doi: 10.1016/j.compositesb.2022.110463.

L. Moretti, P. Olivier, B. Castanié, et G. Bernhart, «Experimental study and in-situ FBG monitoring of process-induced strains during autoclave co-curing, co-bonding and secondary bonding of composite laminates », Compos. Part Appl. Sci. Manuf., vol. 142, p. 106224, mars 2021, doi: 10.1016/j.compositesa.2020.106224.

L. Moretti, B. Castanié, G. Bernhart, et P. Olivier, «Characterization and modelling of curedependent properties and strains during composites manufacturing », J. Compos. Mater., vol. , p. 3109-3124, sept. 2020, doi: 10.1177/0021998320912470.

M. R. Wisnom, M. Gigliotti, N. Ersoy, M. Campbell, et K. D. Potter, « Mechanisms generating residual stresses and distortion during manufacture of polymer-matrix composite structures », Compos. Part Appl. Sci. Manuf., vol. 37, no 4, p. 522-529, avr. 2006, doi: 10.1016/j.compositesa.2005.05.019.

C. Li, K. Potter, M. R. Wisnom, et G. Stringer, «In-situ measurement of chemical shrinkage of MY750 epoxy resin by a novel gravimetric method», Compos. Sci. Technol., vol. 64, 1, p. 55-64, janv. 2004, doi: 10.1016/S0266-3538(03)00199-4.

T. A. Bogetti, «Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates ».

G. Twigg, A. Poursartip, et G. Fernlund, « Tool-part interaction in composites processing. Part I: experimental investigation and analytical model », Compos. Part Appl. Sci. Manuf., vol. 35, n 1, p. 121-133, janv. 2004, doi: 10.1016/S1359-835X(03)00131-3.

A. Lerdwongpaisan, «Experimental and numerical study of springback of composite structures : considering mould/laminated part interaction. », Theses, INSA de Toulouse, 2023. accessed January 2026 on:

E. Kappel, «Compensating process-induced distortions of composite structures: A short communication», Compos. Struct., vol. 192, p. 67-71, mai 2018, doi: 10.1016/j.compstruct.2018.02.059.

N. Ersoy, T. Garstka, K. Potter, M. R. Wisnom, D. Porter, et G. Stringer, « Modelling of the spring-in phenomenon in curved parts made of a thermosetting composite », Compos. Part Appl. Sci. Manuf., vol. 41, n 3, p. 410-418, mars 2010, doi: 10.1016/j.compositesa.2009.11.008.

N. Ersoy et al., «Development of the properties of a carbon fibre reinforced thermosetting composite through cure», Compos. Part Appl. Sci. Manuf., vol. 41, 3, p. 401-409, mars 2010, doi: 10.1016/j.compositesa.2009.11.007.

A. Vedernikov, F. Tucci, P. Carlone, S. Gusev et al. «Effects of pulling speed on structural performance of L-shaped pultruded profiles », Composite Structures, vol. 255, January 2021, paper 112967, DOI: 10.1016/j.compstruct.2020.112967

A. Vedernikov, A. Safonov, F. Tucci, P. Carlone et al. « Modeling spring-in of 1-shaped structural profiles pultruded at different pulling speeds », Polymers, 2021, vol. 13(16), 2748 2021, DOI: 10.3390/polym13162748

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/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 91-102

doi: 10.4028/p-Nfg58d

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

Submitted:
2026-01-19

Revised:
2026-02-16

Accepted:
2026-02-17

Online:
2026-04-10

Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

The original version of this paper is available on https://www.scientific.net/MSF.1182.91.pdf

WAROQUIER Pierre 1,2,a*, LEVY Arthur 1, b, LE CORRE Steven 1,c, BAILLEUL Jean-Luc 1, d, SERRA Joël 2,e, BERTEVAS Erwan 2,f

1 Nantes Université, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR6607, F-44000, Nantes, France

2 Institut de Recherche Technologique Jules Verne, 1 Mail des 20000 Lieues, 44343 Bouguenais, France

a* pierre.waroquier@univ-nantes.fr (*corresponding author), b arthur.levy@univ-nantes.fr, c  steven.lecorre@univ-nantes.fr, djean-luc.bailleul@univ-nantes.fr, e  joel.serra@irt-jules-verne.fr, f erwan.bertevas@irt-jules-verne.fr

Keywords: Composites, Thermoplastic, Welding, Intimate Contact, Adhesion, Squeeze Flow

Abstract

High-performance thermoplastic polymers paved the way for new fast manufacturing processes, including welding. In order to obtain optimal bonding of the substrates, an adhesion step is required, governed by two main phenomena: intimate contact and healing. While healing has been widely explored, theorized, and is starting to be understood, prediction and characterization of the degree of intimate contact is still a challenge. After a review of squeeze flow models for intimate contact, along with the expressions of the analytical solutions for a Newtonian and a shear-thinning fluid modeled by power law, a finite element model is presented in order to observe the influence of asperity geometry, fluid behavior, and other assumptions on the evolution of the degree of intimate contact.

Introduction

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The use of thermoplastic resins in carbon fiber-reinforced polymer (CFRP) materials has received increasing interest over the years due to promising mechanical and chemical properties. In addition to simple storage conditions prior to processing, thermoplastics can also be remelted, offering reprocessability, repairability, and potential recyclability. This asset allowed new consolidation processes and joining techniques [1, 2]. In any thermoplastic composite manufacturing or joining process, adhesion is critical to obtain the best mechanical properties for the final composite part. In this work, adhesion is considered at a thermoplastic composite interface. This adhesion can be between unidirectional tapes as in the Automated Fiber Placement (AFP) process, or between neat polymer and composite substrate (overmolding), or even between composite substrates (welding). With increasing demand for CFRP, manufacturing processes are becoming fast or even continuous. For instance, the characteristic process times of AFP, overmolding, and conduction welding are approximately, 200 ms,1 s, and 10 s , respectively.

For fast manufacturing processes, adhesion has only a short time to occur. Adhesion can be decomposed into two phenomena: intimate contact and healing. At the beginning, two molten substrates (whether unidirectional tapes, raw polymer films, etc...) with initial surface roughness are considered. The first step consists in flattening the surface asperities by applying pressure to the substrates. This aims to attain optimal surface contact, defined as "intimate contact". The degree of intimate contact Dic  is thus defined as the ratio between the area of contact and the total area of the substrate surface. Dic  is highly dependent on the pressure applied, processing temperature, and contact time. If asperities do not flatten sufficiently, contact will be limited and remain incomplete as the temperature at the interface decreases rapidly.

As soon as some asperities come into contact, interdiffusion of macromolecular chains can occur by "reptation" movements of the chains, as originally theorized by De Gennes in 1971 [3]. The
healing phase corresponds to the progressive recovery of the strength of the interface as a result of the interdiffusion of the chains across this newly created interface. Wool and O'Connor [4] introduced the degree of healing, Dh=σ/σ∞, where σ is the strength of the interfacial fracture and σ∞ the strength of the interfacial fracture of the virgin material. The degree of healing enables the evaluation of strength recovery at the interface. For thermoplastic polymers, the degree of healing is modeled according to the polymer diffusion theory as

Dh∝(ttw)1/4(1)

where tw is the welding time, which corresponds to a full recovery of interface strength.
Although healing theory has been extensively studied for long adhesion times [5], intimate contact, which is predominant for fast processes [6], remains difficult to predict accurately. The most common analytical models for evaluating the degree of intimate contact are based on squeeze flow [7, 8, 9]. More recently, alternative intimate contact models, based on Darcy flow [10,11] have shown a new way to consider the intimate contact phenomenon with resin "percolation" of the interfacial voids. Other models considering bubble or void growth in molten thermoplastics may also be useful to predict intimate contact [12, 13]. The development of intimate contact can also be limited by surrounding gas or degassed chemicals from molten resin or fiber sizing that can remain trapped between asperities.

In fast manufacturing processes, intimate contact and healing are coupled; Butler et al. [14] define the degree of bonding, Db, to evaluate the resulting bond strength. Assuming that Dic  is a sufficient parameter to calculate the adhesion strength, the expression of Db is given by

Db(t)=Dic(0)Dh(t)+∫0tDh(t−τ)Dic˙(τ)dτ(2)

When Db is equal to 1 , interface properties are fully recovered. Fig. 1 represents the different stages of a fast adhesion with regard to these phenomena. The aim of this work is to obtain a realistic intimate

[picture]

Fig. 1: Mechanisms governing short-time adhesion.

Fig. 1. Mechanisms governing short-time adhesion.

contact model. The methodology consists in numerically solving the flow of an asperity at the interface. A FreeFEM++ numerical finite element model based on Newtonian and non-Newtonian squeeze flow for different geometries is developed. It is then compared to common intimate contact squeeze flow analytical solutions.

Review of Intimate Contact Models with Squeeze Flow

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Squeeze flow models have historically been the first to be used in predicting intimate contact for thermoplastic composites. In 1985, Dara and Loos [7] first considered the initial roughness of a unidirectional tape as a succession of non-uniform rectangles representing the tows of a unidirectional tape.

This first model was then simplified two years later by Lee and Springer [8], who replaced the rectangles of different shapes with evenly spaced and uniform rectangles. This model is the most commonly used in the literature due to the low number of input parameters required for it to give an estimation of the degree of intimate contact. The model was then updated by Mantell and Springer [15] to consider time-dependency of pressure, temperature, and viscosity. In order to describe the geometry of squeezed asperities more precisely, Yang and Pitchumani [9] developed a new rectangle model based on a Cantor set fractal description of roughness. Although these models are widely used in the field of thermoplastic polymers, they are based on strong hypotheses:

The asperities are rectangles, wider than they are tall, in order to comply with the lubrication assumption. Squeezed rectangles are thus supposed to remain rectangles at every time.

The rheological behavior of the thermoplastic polymer fluid is considered to be Newtonian, but its real behavior tends to be non-Newtonian (shear-thinning fluid), depending on the interface squeezing velocity.

Other physical and chemical aspects such as wetting and air-trapping are not taken into account while modeling the phenomenon.

Governing equations of squeeze flow. In order to describe the evolution of intimate contact, asperities are modeled as rectangles, as schematized in Fig. 2. An incompressible two-dimensional fluid is considered. Instead of working with the roughness of the two surfaces, only the asperity of a single surface is represented. This equivalent asperity is squeezed onto a flat rigid surface. This assumption is common in the literature and is based on Greenwood and Williamson's work [16]. The asperity is assumed to be composed only of resin, an assumption made based on the fact that studied substrates have a polymer film at their surface in order to enhance adhesion when welded. It is supposed that the body and gravitational forces are neglected, with the prevalence of viscous forces. With a Reynold number, Re, much smaller than unity, inertia effects can also be neglected. No-slip boundary conditions on the upper and lower sides of the rectangle is considered. Additionally, the lubrication assumption is expressed, hence, the height h(t) of the rectangle is supposed to be smaller than the width L(t), at every time. The Navier-Stokes equations (i.e. the momentum and incompressibility equations) are written

[picture]

Fig. 2: Schematic of the squeeze flow problem for intimate contact. The domain of the problem is Ω.

Fig. 2. Schematic of the squeeze flow problem for intimate contact. The domain of the problem is Ω .

in this case as

{∇→·σ―→=0→ on Ω∇→·u→→=0 on Ω∮Γu(σ――·n→)·ey→=Papp(3)

with σ――=2μD――−pI―― the two-dimensional stress tensor of the fluid, where D―― is the strain rate tensor, μ is the viscosity modeled by the Ostwald-de Waele power law μ=Kγ˙n−1―, where K and n are the flow consistency and behavior indices, respectively. p and u→ are the pressure and the velocity vector of the studied fluid. The third equation is used to consider the constant lineic load Papp  applied onto the substrate. The upper boundary Γu moves at h^ velocity and is obtained thanks to the lineic load Papp .

The solutions of this Stokes problem for a Newtonian and a power law fluid can be found and are summarized in Fig. 3 with free-slip and no-slip boundary conditions.
Analytical solutions for intimate contact. In the case of the squeeze flow models, the degree of intimate contact Dic  is defined as

Dic=L L∞(4)

where L∞ is the spatial period between asperities. For simple compression and squeeze flow, if the lubrication assumption is considered, mass conservation gives L=L0 h0 h, where L0 and h0 are the initial height and width of the rectangle, respectively. L can thus be replaced in Eq. 4:

Dic=L0 h0hL∞(5)

From Eq. 5 and the solutions expressed in Fig. 3, it is possible to find an evolution law for the degree of intimate contact for each case. For non-isothermal processes, it is more convenient to adopt an instantaneous approach. The rate of intimate contact Dic  is expressed as a function of the degree of intimate contact Dic, along with the geometrical and process parameters. The corresponding expression of Dic ˙ is

Dic˙=−L0 h0 L∞h˙ h2=−h˙ L∞Dic2 L0 h0(6)

The evolution law of the simple compression of a rectangle with a shear-thinning fluid is

Dic˙=Dic1−1n(−Papp L∞2n+1 K)1n∝(−Papp K)1nDic1−1n(7)

If the fluid is Newtonian, the flow behavior index n is equal to 1 and Dic ˙ does not depend on Dic . Similarly, the evolution law of the degree of intimate contact for the squeeze flow of a rectangle with a shear-thinning fluid is

Dic˙=Dic−(n+3)n L∞L0 h02nn+1[( L0 h02 L∞)1+2nn(1−n1+2n)]((n+1)Papp2μ1( L∞2)n+2(1n+2−1))1n(8)

In this case, Dic ˙ is proportional to (Papp /K)1nDic −(n+3)n and when n=1, the result is the same as reported in the literature [8], with Dic ˙∝(Papp /K)1nDic −4. For both simple compression and squeeze flow configurations, Dic ˙ appears to be proportional to a power of Dic  and (Papp /K)1n. A generalized evolution model is thus suggested with

Dic˙∝(Papp K)1n(Dic)α(9)

where α is an evolution index that may vary with asperity geometry and boundary conditions.

[picture]

Fig. 3: Solutions of the Stokes problem for a rectangle with free-slip (1) and no-slip (2) boundary conditions for Newtonian and non-Newtonian fluids. The velocity of the upper boundary is h .

Fig. 3. Solutions of the Stokes problem for a rectangle with free-slip (1) and no-slip (2) boundary conditions for Newtonian and non-Newtonian fluids. The velocity of the upper boundary is h .

Shear-thinning fluid:

{ux=(hx˙2( h2)1+2nn(1−n1+2n))[(−y+h2)1+nn−(h2)1+nn]uy=h˙ hyp=−Kn+1(−h˙(n+1)2n1( h2)1+2nn(1−n1+2n))n(xn+1−(L0 h02 h)n+1)h˙=−2nn+1[( h2)1+2nn(1−n1+2n)]((n+1)Papp2μ1( L0 h02 h)n+2(1n+2−1))1n

Finite Element Model for Intimate Contact

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In order to determine the missing constant α in the evolution law given by Eq. 9, a finite element study of the flow is investigated.
Resolution domain and numerical implementation. An updated Lagrangian approach is considered. The Stokes problem in Eq. 3 is solved with an explicit iterative time integration scheme for u→,u on domain Ω and h˙. Space integration is handled with standard P2/P1 finite element method in

FreeFEM++. The mesh is then moved explicitly according to the displacement field u→δt where δt fulfills the Courant-Friedrichs-Lewy convergence condition. Fig. 4a illustrates the initial full shape of an example geometry, in this case a triangle asperity. Fig. 4b presents the computed symmetry that is solved numerically. The mesh is composed of triangular elements.

[picture]

Fig. 4: (a) Resolution domain for a triangular asperity with a central axis of symmetry represented by Γ1. (b) Simplification of the domain using symmetrical considerations. The effective length of Γu is twice as small even if the visual ratio is conserved in this schematic.

Fig. 4. (a) Resolution domain for a triangular asperity with a central axis of symmetry represented by Γ 1 . (b) Simplification of the domain using symmetrical considerations. The effective length of Γ u is twice as small even if the visual ratio is conserved in this schematic.

Contact between the asperity and the origin surface y=0 is handled by implicit penalization over Γσ with the penalization force vector fpen → defined as

{fpen →=0→ if y+uydt>0fpen →=A(y+uydt)2·y→ otherwise (10)

A is a penalization constant that needs to be chosen wisely in order to reach convergence. The problem becomes nonlinear with penalization. An iterative Newton-Raphson method is used to solve for u→,p, and h .
Numerical model validation. The FEM model is validated on two test cases with existing analytical solutions. The first one is a case of simple compression for a Newtonian and a shear-thinning fluid. The second test case is a Newtonian squeeze flow of a rectangular asperity. The numerical degree of intimate contact is calculated from the evaluation of the length in contact with the surface at y=0. For these two test cases, it is considered that L∞=2 L0 thus Dic (t=0)=12.

For the simple compression case, the asperity geometry is a square ( h0=L0 ). Fig. 5 shows agreement between the analytical and numerical solutions of Dic  and h˙ for simple compression whether the fluid is considered Newtonian or non-Newtonian. For the second test case, in order to compare the numerical solution with Lee and Springer's analytical solution, the dimensions of the rectangle must comply with the lubrication assumption. This implies that the aspect ratio h(t)/L(t) is smaller than unity at each timestep. In this example, the initial width of the rectangle L0 is equal to 5 and the initial height h0 is equal to 1 . Fig. 6 shows the results for Dic  and h .

In addition, it is possible to determine the numerical evolution index α of Eq. 9 by identifying the slope of the curve of Dic  as a function of Dic  in a log-log graph, represented in Fig. 7a. In order to find the numerical D˙ic, the curve of Dic is first fitted with a polynomial regression. The order of the polynomial fit is determined with the minimization of the residual sum of squares (RSS). The polynomial fit is then differentiated to get the numerical Dic˙.

In Fig. 7a, the first part of the logarithm curve represents only a few computed points. These points represent the initial contact-and-penalization phase and thus differ from the expected slope. The slope of the main part of the fitted curve is close to the analytical one ( α=−4 ), validating this test case. The decrease of the slope at the end of the graph stems from fitting artifacts. By considering that the beginning of the squeeze flow takes place when the evolution index gets close to α=−4, at log(Dic )=−0.25, which means at Dic =0.56, the curve of Dic  is closer to the analytical solution, as presented in Fig. 7b.

[picture]

Fig. 5: (a) Simple compression test case: evolution of Dic as a function of time for different flow behavior index. (b) Simple compression test case: evolution of h as a function of time for different flow behavior index.

Fig. 5. (a) Simple compression test case: evolution of D i c as a function of time for different flow behavior index. (b) Simple compression test case: evolution of h as a function of time for different flow behavior index.

[picture]

Fig. 6: (a) Squeeze flow test case: evolution of Dic  as a function of time for a Newtonian fluid. (b) Squeeze flow test case: evolution of h as a function of time for a Newtonian fluid.

Fig. 6. (a) Squeeze flow test case: evolution of D ic as a function of time for a Newtonian fluid. (b) Squeeze flow test case: evolution of h as a function of time for a Newtonian fluid.

Results and Discussion

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Impact of the aspect ratio of a rectangular shape on the prediction of the degree of intimate contact. To describe the material roughness as rectangles, geometrical parameters representing a statistical height and width have to be measured, commonly by profilometry analyses [17, 18, 19]. This section investigates the impact of the aspect ratio (i.e. the ratio between height and width of the statistical rectangle) on the predicted value of Dic  compared to analytical solution based on lubrication assumption. It has been observed that for high aspect ratios (h0≈ L0), the solved velocity h˙ differs from the analytical solution, as presented in Fig. 8a. Consequently, Dic  will also vary. They differ at the start of the squeeze flow: when the rectangle get squeezed, the aspect ratio decreases and the numerical solution thus tends toward the analytical solution. The comparison of numerical and analytical his done by calculating the average relative error, e―, for multiple aspect ratios. The average relative

[picture]

Fig. 7: (a) Evolution of the logarithm of Dic ˙ as a function of the logarithm of Dic . (b) Adjusted evolution of Dic as a function of time for a Newtonian fluid.

Fig. 7. (a) Evolution of the logarithm of D ic ˙ as a function of the logarithm of D ic . (b) Adjusted evolution of D i c as a function of time for a Newtonian fluid.

error is defined as

e―=1tsim ∫0tsim |h˙num (t)−h˙ana (t)||h˙num (t)|dt(11)

where tsim  is the time reached at the end of the simulation for each case. The results are presented in Fig. 8b.

[picture]

Fig. 8: (a) Evolution of h˙ as a function of time for a rectangular Newtonian squeeze flow with an aspect ratio of 1: L0=h0=1. (b) Average relative error with corresponding analytical solutions for aspect ratios between 0.2( L0=5 h0) and 1( L0=h0).

Fig. 8. (a) Evolution of h ˙ as a function of time for a rectangular Newtonian squeeze flow with an aspect ratio of 1: L 0 = h 0 = 1 . (b) Average relative error with corresponding analytical solutions for aspect ratios between 0.2 ( L 0 = 5 h 0 ) and 1 ( L 0 = h 0 ) .

This section shows that the error on h˙, and thus on Dic, increases with respect to the aspect ratio, compared to the analytical solution of Lee and Springer's model. When using this analytical model, one must choose a small aspect ratio. Additionally, high incertitude is present when measuring experimentally h0 and L0, which may also lead to errors in the prediction of the degree of intimate contact if the aspect ratio is too high, typically above 0.3 .

Influence of asperity geometry on the establishment of the degree of intimate contact. Rectangles may not be representative of the real roughness of molten polymers. The finite element model enables to evaluate the establishment of the degree of intimate contact for different asperity geometries, such as trapeze, triangle, half-circle, or even real roughness extracted from profilometry.

In this section, the influence of the asperity geometry is studied by comparing the evolution index α found for a circular shape to the theoretical analytical evolution index given for a rectangular shape, which can be found using Eq. 7 and Eq. 8. Fig. 9a shows the variation of Dic  for different flow behaviors. The same procedure as described above in the model validation part is used to fit and find the numerical Dic ˙. The log-log graph is presented in Fig. 9b. The evolution index is equal to the slope in the log-log graph.

[picture]

Fig. 9: (a) Evolution of Dic  as a function of time for different flow behavior indices. The geometry considered is a half-circle. (b) Evolution of the logarithm of D˙ic  as a function of the logarithm of Dic . The linear fits are plotted as a reference for n=1.

Fig. 9. (a) Evolution of D ic as a function of time for different flow behavior indices. The geometry considered is a half-circle. (b) Evolution of the logarithm of D ˙ ic as a function of the logarithm of D ic . The linear fits are plotted as a reference for n = 1 .

For this particular case, three stages are identified for each curve, based on Fig. 9b. Only the slopes with negative values will be considered; the third one, at the end of the plot, is due to fitting artifacts. Two evolution indices are then identified for each curve. Table 1 summarizes the obtained evolution indices compared to analytical theory for a rectangle. During the first stage, half-circle flow tends to behave closer to a rectangular simple compression ( α1 index). During the second stage, the flow behavior changes to reach an evolution index ( α2 ) closer to rectangular squeeze flow.

For each type of asperity geometry, the variation of the evolution index enables to estimate a critical transition time, tcrit , at which flow behavior changes. This change is accompanied by a switch of morphology for the geometry: from its nearly initial form to a quasi-rectangular constrained shape, as shown for a Newtonian squeeze flow of a triangle in Fig. 10.

In this section, results show that asperities with non-rectangular geometry behave differently than the analytical models. For the two non-rectangular geometries (half-circle and triangle) studied, it is possible to see that the evolution index decreases during the flow. This can be interpreted as a transition from a behavior similar to rectangular simple compression to an intermediate rectangular squeeze flow behavior.

Conclusion

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This paper has focused on the study of the intimate contact phenomenon in fast manufacturing processes of thermoplastic composites. Typically, strong hypotheses are made to obtain rectangular squeeze flow analytical models for intimate contact. A more realistic finite element model has been developed based on Stokes flow for Newtonian and shear-thinning fluids in 2D. This numerical model was

Table 1: Evolution indices for rectangular analytical simple compression and squeeze flow. These indices are compared to those from numerical results of the flow of a semi-circular geometry. The field displayed for the semi-circular asperity is the horizontal velocity of the fluid.

flow index | rectangular simple compression diagram rectangular simple compression | rectangular squeeze flow diagram rectangular squeeze flow | semi-circular flow diagram semi-circular flow
n = 1 | α = 0 | α = −4 | α₁ = −0.56 α₂ = −1.14
n = 0.8 | α = −0.25 | α = −4.75 | α₁ = −0.63 α₂ = −1.32
n = 0.6 | α = −0.67 | α = −6 | α₁ = −0.82 α₂ = −1.77

[picture]

Fig. 10: Transition of the evolution index for a Newtonian triangular flow. A visual representation of the triangle is presented for each evolution index. Similar to the semi-circular flow, the two phases describe two different behaviors during the flow. The field displayed for the triangular asperity is the horizontal velocity of the fluid.

Fig. 10. Transition of the evolution index for a Newtonian triangular flow. A visual representation of the triangle is presented for each evolution index. Similar to the semi-circular flow, the two phases describe two different behaviors during the flow. The field displayed for the triangular asperity is the horizontal velocity of the fluid.

validated on test cases. The first section presents the impact of the asperity aspect ratio on the final degree of intimate contact. As the aspect ratio increases, the error with the uniform rectangle model also grows. Geometrical dependency was shown by comparison of theoretical and numerical evolution indices. This approach appears useful to analyze the flow behavior and could potentially help build a metamodel. Future work will focus on the addition of other physical and chemical phenomena, such as air trapping and wetting. The influence of shear-thinning fluid behavior and the impact of real geometries must be studied further. The intimate contact model must also be experimentally validated.

Acknowledgments

The original version of this paper is available on https://www.scientific.net/MSF.1182.91.pdf

The authors would like to acknowledge the funding of the PERFORM program by IRT Jules Verne (French Institute for Advanced Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic, and Hybrid Structures), which made this work possible. The authors also wish to thank the industrial partners of PERFORM for this project: Airbus, Chantiers de l'Atlantique, Daher, Naval Group, and Safran.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.91.pdf

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 103-112

doi: 10.4028/p-VmX8fD

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

Submitted:
2026-01-16

Revised:
2026-02-17

Accepted:
2026-02-17

Online:
2026-04-10

Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

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Mouadh BOUBAKER 1,a*, Arthur CANTAREL 1, b, Gérald DEBENEST 2,c

1 Institut Clément Ader, Université de Toulouse, CNRS UMR 5312, IMT Mines Albi, UPS, INSA, ISAE-SUPAERO, Toulouse, France

2 INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Université de Toulouse, Allée Camille Soula, 31400, Toulouse, France

aMOUADH.BOUBAKER@iut-tarbes.fr, barthur.cantarel@iut-tarbes.fr, c  gerald.debenest@toulouse-inp.fr

Keywords: Liquid Composite Molding; Unsaturated flow; Capillary effects; Process simulation.

Abstract

Liquid Composite Molding (LCM) processes, used for producing high-quality, complex composite parts, rely on the uniform infiltration of liquid resin into fibrous fabrics. These fabrics possess a dual-scale structure: highly porous inter-tow spaces surrounding denser fiber tows. The resulting disparity in permeability and flow rates is a primary cause of defect formation, such as voids. To minimize these defects, accurate simulation, incorporating the critical influence of capillary pressure on resin infiltration within the fiber tows, is essential. This work presents a robust numerical model developed to simulate the two-phase resin flow and impregnation dynamics within a digitized, real plain-weave E-glass reinforcement obtained via X-ray micro-computed tomography (CT). The simulation utilizes the open-source multiscale multiphase solver, hybridPorousInterFoam, which employs a Darcy-Brinkman approach, transitioning between Darcy's law in porous regions and Navier-Stokes in free space. A key methodological enhancement involved modifying the advection algorithm using the isoAdvector scheme to mitigate numerical instabilities caused by the high viscosity ratio between the resin and air. Capillary effects at the mesoscale are incorporated through multiscale parameters, specifically the drag and surface tension forces. The key findings demonstrate that the modified solver successfully handles the fluid-fluid interface advection for high viscosity ratios. A parametric study highlighted the significant effect of capillary pressure on multiphase flow within the dual-scale porous media. The numerical results for flow front advancement showed very good agreement when compared against dedicated experimental validation data, confirming the model's high predictive accuracy and its potential for optimizing LCM injection conditions.

Introduction

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The global demand for lightweight, high-performance composite materials necessitates highly efficient manufacturing techniques, with Liquid Composite Molding (LCM), including RTM and VARTM, being key processes [1]. A critical challenge in LCM is void formation during resin impregnation, which severely compromises structural integrity; even a 5% void content can cause a 20% reduction in interlaminar strength, leading to part rejection [2].
The primary mechanism of void creation is linked to the Capillary number (Ca), which is the ratio of viscous forces to capillary forces :

Ca=μUγ(1)

where μ is the injected liquid resin viscosity, U is its velocity and γ is the surface tension between resin and air.
This force balance governs the flow distribution within the dual-scale fabric's macro- and micropores. Accurate modeling of capillary pressure, which significantly assists in filling the micro-scale fiber tows, is essential for optimizing saturation [3].

Conventionally, LCM flow modeling often relied on single-phase approaches, but recent work highlights the necessity of multiphase flow models to capture phenomena like capillary effects and void formation accurately [4]. However, standard interface-capturing methods (like VOF) suffer from spurious currents at the fluid-fluid interface, especially with the extremely high viscosity ratio (e.g., 104 to 105 ) characteristic of resin/air systems [5]. These numerical artifacts corrupt surface tension calculations, limiting the model's reliability.
Furthermore, the validation of high-fidelity models based on X-ray micro-computed tomography (CT) often lacks the rigorous multi-scale experimental confirmation needed to verify underlying dualscale flow physics (e.g., unsaturated permeability) [6].
This study presents a novel, stabilized, two-phase numerical model for simulating resin flow in dualscale fabrics. It utilizes the open-source, multiscale, multiphase hybridPorousInterFoam solver [7], fundamentally modified to eliminate spurious currents and enhance robustness for typical resin viscosities. The stabilized solver is used to examine the effects of capillary pressure on the multiphase flow in dual-scale porous media, simulate resin impregnation directly within realistic 3D CT-scanned geometries and perform rigorous multi-scale experimental validation against flow front advancement. This research aims to provide a reliable predictive tool for process optimization, contributing to higher saturation levels and reduced part rejection in high-performance composite manufacturing.
The remainder of this paper is structured as follows. Section 1 details the essential modification made on the multiphase multiscale hybridPorousInterFoam solver, focusing on the method used to effectively reduce spurious currents caused by high viscosity ratios. Section 2 presents a parametric study that highlights the significant impact of capillary pressure on multiphase flow within dual-scale porous media. Section 3 presents the numerical simulation of resin flow within realistic scanned geometries and its subsequent validation against experimental results, including comparisons of flow front positions and shapes. Finally, the concluding section summarizes the key findings and outlines future research directions.

Solver Modification for Spurious Currents Reduction

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Accurate multiphase flow simulations, particularly those with sharp differences in fluid properties (like liquid resin and air in Liquid Composite Molding - LCM), are difficult. The main problem is spurious currents: non-physical fluid movements near the interface caused by an imbalance between the discrete calculation of capillary forces and pressure jumps. These currents are amplified with extreme property ratios (e.g., density and viscosity) and prevent simulations from reaching a stable state (equilibrium).
Volume Of Fluid (VOF) methods are widely used Eulerian approaches for directly simulating unsteady, incompressible multiphase flows. However, like all numerical methods, they have limitations particularly when capillary forces dominate. VOF methods reconstruct interfaces using a volume fraction field on a fixed grid, and the Continuum Surface Force (CSF) model is often employed to represent surface tension. However, the discrete nature of this representation, coupled with finite difference approximations of the volume fraction field, leads to significant errors in calculating interface normal and curvature. These errors, in turn, produce spurious currents that become problematic when surface tension dominates. Different methods have been attempted in the literature to minimize spurious currents and enhance surface tension modeling in different contexts [8, 9]. Comparative studies highlight that the effectiveness of different methods and reduction techniques depends on the specific flow scenario and fluid properties (such as density and viscosity ratios) and the desired level of accuracy [10].
Liquid resin used in LCM processes typically exhibits a viscosity ranging from 10−2 to 1 Pa· s and a density around 1000 kg/m3. In contrast, the displaced air within the dry textile preform has a significantly lower viscosity, approximately 1.76·10−5 Pa· s and a density of about 1.2 kg/m3. Simulating the multiphase resin flow through a dual-scale porous domain using the hybridPorousInterFoam solver, in conditions similar to those found in LCM processes, resulted in pronounced numerical instabilities at the fluid-fluid interface. These instabilities, characteristic of
spurious currents, are directly attributed to the substantial disparities in fluid properties, presenting a significant challenge to numerical stability. Initial attempts to mitigate these instabilities included mesh refinement, time step reduction, as well as modifications of the discretization schemes yielded no observable improvement which demonstrates that a fundamental modification of the solver's structure is needed, particularly in the interface tracking method used which is the VOF method. VOF schemes can be categorized into algebraic and geometric schemes. Algebraic VOF schemes (like Multidimensional Universal Limiter with Explicit Solution MULES [11]) are computationally efficient but may lack accuracy for complex interfaces and often fail to predict surface tension accurately in low capillary number flows, leading to spurious currents. Geometric schemes, in contrast, explicitly reconstruct the interface within each cell using local volume fraction data enabling more precise fluid volume flux calculations and enhancing interface sharpness and accuracy. The isoAdvector algorithm is a robust geometric VOF method designed for sharp interface advection in incompressible multiphase flows. It offers higher accuracy and better interface sharpness compared to algebraic methods like MULES, making it particularly advantageous for complex geometries and situations where surface tension effects are significant. It also excels in volume conservation and overall accuracy [12]. A key advantage of the isoAdvector algorithm is its enhanced interface sharpness. By geometrically reconstructing the fluid interface within each surface cell, it achieves a more distinct phase separation, reducing numerical diffusion at the interface. This sharper representation is crucial in simulations where surface tension and curvature effects are significant [13]. Benchmark tests and applications confirm the promising accuracy of isoAdvector in standard interface advection problems like notched disc and sphere transport in shear flow and show that it excels in volume conservation, boundedness, interface sharpness and overall accuracy compared to algebraic methods like MULES [14]. Inspired by these successful benchmark tests, we aimed to replace the MULES advection method with isoAdvector in the hybridPorousInterFoam solver to eliminate spurious currents in our simulations.
To achieve this, we developed a multi-step algorithm inspired from existing research [14], to modify hybridPorousInterFoam's advection scheme. We then conducted several tests to evaluate the modified solver's performance in maintaining a sharp and stable interface, particularly in scenarios like those encountered in Liquid Composite Molding (LCM) processes. As an example, Figure 1 showcases the solver's ability, when using isoAdvector, to effectively eliminate numerical instabilities at the fluidfluid interface. In this test, a fluid with a viscosity of μ=1 Pa· s (shown in red in Fig. 1) is injected into a dual-scale domain (Fig. 1(a)), which is initially saturated with air (blue in Fig. 1), under a constant velocity of 1 mm/s.

[picture]

Fig. 1. MULES and isoAdvector performance in simple porous media geometry.

Fig. 1. MULES and isoAdvector performance in simple porous media geometry.

We successfully demonstrated the feasibility of integrating the geometric VOF algorithm isoAdvector into OpenFOAM's multiphase, multiscale solver hybridPorousInterFoam. This modification allows for the accurate simulation of test fluid injection into a dual-scale porous domain. The enhanced solver consistently produced sharper and smoother interfaces, leading to more stable simulations across various porous geometries and significantly reducing spurious currents.

Parametric Study of Capillary Effects on Mesoscale Impregnation

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The hybridPorousInterFoam solver rigorously incorporates capillary effects through relative permeability, which describes the change in permeability due to the presence of a second fluid, and capillary pressure pc, which describes the pressure difference between the two phases resulting from surface tension [7].
To assess the impact of capillary effects on resin flow simulations at the mesoscale, we will simulate the flow of a test fluid within the Representative Elementary Volume (REV) presented in Fig. 2 representing a 2×2 tow structure of a plain weave textile (Fig. 2). The porous tows have a fiber volume fraction of 0.6 and a transversal and longitudinal permeabilities estimated using Gebart model assuming a fiber radius of 12μ m. The global fiber volume fraction of the REV is 0.67 . Fluid injection is driven by a pressure gradient applied between the inlet and outlet, with the REV initially saturated with air. The resin is considered as the wetting phase and the air as the non-wetting phase. This section focuses on analyzing how variations in the entry capillary pressure amplitude pc0 influence the resin flow dynamics, where the capillary pressure dependence on saturation is modeled using the Van Genuchten model :

pc=pc0(αl,pc−1 m−1)1−m(2)

with α1,pc is the effective wetting fluid saturation and m is a non-dimensional coefficient dictated by porous media properties.
The pressure difference between the inlet and outlet was set to ΔP=100kPa and 4 cases were investigated:

Case 1: Neglecting the capillary effects ( pc0=0 Pa ).

Case 2: Considering the capillary effects using Van Genuchten model for the capillary pressure (Eq. 2) with low value of pc0=10 Pa and m=0.8.

Case 3: Considering the capillary effects with pc0=100 Pa and m=0.8.

Case 4: Considering the capillary effects with higher entry capillary pressure value pc0= 1000 Pa and m=0.8.
The comparison was performed by analyzing the saturation profiles and the global domain saturation. The saturation comparison is illustrated in the cross-section shown in Fig. 2.

[picture]

Fig. 2. Location of the cross-section used for results representation.

Fig. 2. Location of the cross-section used for results representation.

Due to the very low value used in Case 2, the results were similar to those obtained when capillary effects were negligible (Case 1), both saturation curves coincide and the curve for pc0=10 Pa was cut in Figures 4 and 5 for visualization. Conversely, Fig. 3 demonstrates the significant effect and importance of capillary forces for a higher entry capillary pressure value in impregnating the fibrous tows by comparing Case 1 and Case 3 at t=2.28 s.

[picture]

Case 3: Saturation of the cross-section α1=0,998

Figure 3. Case 3: Saturation of the cross-section α 1 = 0 , 998

Fig. 3. Comparison of liquid injection patterns between Case 1 and Case 3. (In both cases, red indicates the injected liquid, blue represents the initially present air, and clear zones denote the porous tows).

Figures 3 and 4 clearly shows a significant difference in global domain saturation between the two cases. The figures clearly show an increase in saturation when the entry capillary pressure is raised from pc0=0 Pa to pc0=100 Pa.

[picture]

Fig. 4. Effect of pc0 on the domain saturation for ΔP=100kPa.

Fig. 4. Effect of p c 0 on the domain saturation for Δ P = 100 k P a .

For this pressure difference value, ΔP=100kPa, no significant difference is observed when the value of the capillary pressure is increased to pco=1000 Pa as evident in the saturation vs time plot (Fig. 4). Notably, using this higher value of entry capillary pressure drastically increases the computational time without significantly impacting the domain saturation. Consequently, the fourth test was stopped at t≈1 s.
A second case was investigated by reducing the pressure difference controlling the flow to ΔP= 20 kPa , in order to examine the dependence of the entry capillary pressure's effect on the applied pressure. The same four values of pc0 used in the first example were tested. As observed in Figure 8, a higher capillary pressure results in increased saturation within the fibrous tows. This test demonstrates also that even with an entry capillary pressure of pc0=1000 Pa, the domain does not reach full saturation (achieving a maximum saturation of around 0.8 ). This contrasts with the first case, which used a higher applied pressure, and indicates that higher capillary pressure values are necessary to achieve full saturation when lower applied pressure values are used.

[picture]

Fig. 5. Effect of pc0 on the domain saturation for ΔP=20kPa.

Fig. 5. Effect of p c 0 on the domain saturation for Δ P = 20 k P a .

The influence of capillary pressure on the impregnation of dual-scale porous media, and its dependence on the applied pressure magnitude, has been demonstrated. Capillary forces can be particularly significant in driving resin flow, notably during the initial impregnation stages and within densely packed fiber tows. This can be explained by the fact that at high capillary pressures, capillary effects become significant, aiding in pulling resin into the fiber tows and saturating them. However, the achievable capillary pressure is limited in this model; modeling high values of pco requires a finer mesh and necessitates longer computational time. Future research will investigate the influence of fiber volume fraction on these capillary effects and leverage the numerical model to determine the optimal injection pressure required to achieve full saturation as a function of specific flow parameters.

Simulation of Resin Flow in Realistic Scanned Geometries

The original version of this paper is available on https://www.scientific.net/MSF.1182.103.pdf

To validate the capability of our numerical model in capturing the flow front positions and shapes, a dedicated experimental setup was developed. This new setup utilizes a microscope to closely monitor the flow front's advancement and shape, allowing for a precise validation and identification of the model's limitations. Experimental flow front data is crucial for the validation and optimization of simulation models. Precise monitoring provides data that can be compared against reinforcement filling simulations, helping in identifying discrepancies and allowing for the refinement of simulation models by incorporating real complexities of real reinforcements, such as varying fiber volume fraction. This leads to more accurate predictions of flow front position, fill time, and potential defect formation.
In this study, we chose to simulate liquid resin flow in a 3D scanned geometry obtained using μCT. The textile reinforcement scanned is an E-glass plain weave with a tow linear density of 2400 g/km and a nominal areal weight of 800 g/m2. The greyscale image datasets of the multi-layer textile sample have been acquired using a laboratory-scale GE Phoenix Nanotom μCT scanner [15]. A fourlayer specimen with a diameter of 40 mm was prepared to fit the in-situ compaction fixture of the scanner. The μCT data was processed in MATLAB R2023b, to accurately distinguish between intertow space, warp tows, and weft tows. There are two primary tasks: image segmentation and individual tow identification. Image segmentation, based on grayscale thresholding, differentiated between air and tow pixels. Three STL files, corresponding to warp tows, weft tows, and inter-tow space, were generated post-segmentation.
The experimental setup (Fig. 6) is designed for the unidirectional injection of a test fluid into a fourlayer specimen placed in a circular mold. The mold consists of a 17 mm thick lower plate and a 4.8 mm thick transparent plexiglass upper plate, enabling visual tracking of the flow front. The mold itself is circular, with a 100 mm diameter and an inner circular cavity of 63 mm diameter where the
specimen is seated. The fluid is injected through a 5.5 mm circular injection port, connected via a silicone pipe to a syringe. This syringe is operated by a syringe pump, allowing for precise control of the injection flow rate. A second pipe is connected to the mold's outlet to evacuate the test fluid once the textile is saturated.

[picture]

Fig. 6. Overview of the experimental setup.

Fig. 6. Overview of the experimental setup.

Circular specimens, each consisting of four layers of the described plain weave textile, were prepared with a 63 mm diameter using a laser cutting machine. The specimen is seated in the mold's inner cavity and the mold is then closed with the upper plate and clamped using bolts to achieve the desired thickness, which corresponds to the target fiber volume fraction. The distance between the upper and lower plates h , measured using a caliper, is linked to the fiber volume fraction Vf through Eq. 3:

Vf=mρAh(3)

where m is the mass of the sample, ρ is the fiber density characteristic of the used fabric and A is the sample's planar area.
Once closed, the mold is connected to the pipes and the test fluid is injected through the inlet at a constant flow rate controlled using the syringe pump. The test fluid used is rapeseed oil, with a viscosity of 7.78·10−2 Pa· s, a surface tension of approximately 0.032 N/m at 25∘C and a density of 916 kg/m3. The impregnation process is observed and filmed using a KEYENCE VHX 7000 microscope. An overview of the entire experimental setup is illustrated in Fig. 6.
The syringe pump enables control over the injection volumetric flow rate, ranging from 0 to 1500ml/h. For a fiber volume fraction of 0,5 , the computed sample thickness, derived using Eq. 3, is 2.68 mm (measured using a caliper). We assume the flow to be established and unidirectional once it reaches the half-way point of the mold.
A numerical simulation was conducted to model the flow in the experimental conditions, (Fig. 7). The inlet velocity was set to 1.64 mm/s, consistent with the established flow velocity imposed experimentally. Van Genuchten model (Eq. 2) was used to model the capillary effects also in these simulations for the three fiber volume fractions with pc0=1000 Pa and m=0.8. These values were chosen to approximate the capillary pressure values found in the experimental studies of the composites applications [16].

[picture]

Fig. 7. Correspondence between experimental and numerical domains.

Fig. 7. Correspondence between experimental and numerical domains.

The numerical-experimental comparison encompassed both the flow front shapes and positions. Images captured using the microscope were binarized to clearly identify the flow front shapes, enabling direct comparison with simulations.

[picture]

Fig. 8. Comparison between experimental and numerical flow front shapes.

Fig. 8. Comparison between experimental and numerical flow front shapes.

From Fig. 8, we can observe that our numerical model is able to model the experimental flow front shapes. In Fig. 8 (a) and (b), the numerical simulation exhibits the same faster flow in the inter-tow spaces and slower flow inside the longitudinal weft tows and transversal warp tows. However, Fig. 8 (c) shows a limitation of the numerical geometry used in these simulations: it over-represents the inter-tow space size in the upper surface. In the numerical domain, this zone is considered a free-flow space with a larger size than the actual compacted inter-tow space on the upper surface of the real specimen, which explains the shape difference observed between the binarized and the numerical simulation images in Fig. 8 (c).

[picture]

Fig. 9. Comparison between experimental and numerical flow front positions.

Fig. 9. Comparison between experimental and numerical flow front positions.

The numerical flow front advancement at different time steps, depicted in Fig. 9, shows overall good agreement with the experimental positions (Mean Absolute Percentage Error (MAPE) of 6%). Differences between model predictions and experimental results can stem from experimental errors or data manipulation. Experiments are susceptible to uncontrollable factors like variations in material properties and handling effects. These discrepancies can also indicate limitations in the model's underlying assumptions or the need to incorporate additional physical phenomena for greater accuracy. Numerical models inherently simplify reality by making assumptions and neglecting certain complexities (e.g. homogeneous tow permeability and porosity). Discretization errors, arising from mesh quality and time step choices, also contribute to the differences. Furthermore, manual extraction of experimental results can introduce some uncertainty.

Conclusions

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This study presents the development and rigorous validation of a robust numerical multiphase, multiscale model essential for simulating resin infiltration in dual-scale composite reinforcements, specifically addressing and stabilizing the numerical instabilities caused by the extreme viscosity ratio between resin and air. This refined model demonstrated that capillary pressure significantly enhances impregnation into fiber tows, and that its impact is dependent on the applied injection pressure. By applying the solver to 3D realistic scanned geometries, the study eliminated the predictive inaccuracies of idealized configurations, achieving very good agreement against experimental data, including flow front positions and shapes. This integration of advanced computational stabilization techniques with highly accurate geometric representation provides important insight into LCM flow behavior, enabling the optimization of process parameters for the production of high-quality composite parts. Future research will focus on the influence of fiber volume fraction and extend the model to account for additional phenomena, such as tow deformability induced by resin flow and the resulting changes in local permeability. By incorporating these fluid-structure interactions, the numerical model can be leveraged to determine optimal injection parameters for achieving full domain saturation across varying textile architectures.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.103.pdf

Facciotto, S., Simacek, P., Advani, S.G., Pickett, A., & Middendorf, P. (2023). Modeling formation and evolution of voids in unsaturated dual scale preforms in Resin Transfer Molding processes. Composites Part A: Applied Science and Manufacturing, 173, 107675.

Park, C. H., & Woo, L. (2011). Modeling void formation and unsaturated flow in liquid composite molding processes: A survey and review. Journal of Reinforced Plastics and Composites, 30(12), 957-977.

LeBel, F., Ruiz, E., & Trochu, F. (2019). Void content analysis and processing issues to minimize defects in liquid composite molding. Polymer Composites, 40(1), 109-120.

Gascón, L., García, J.A., LeBel, F., Ruiz, E., & Trochu, F. (2016). A two-phase flow model to simulate mold filling and saturation in Resin Transfer Molding. International Journal of Material Forming, 9(2), 229-239.

Raeini, A.Q., Blunt, M.J., & Bijeljic, B. (2012). Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method. Journal of Computational Physics, 231(17), 5653-5668.

Adhikari, D., Lisegaard, J.J., Pierce, R.S., Mikkelsen, L.P., Hattel, J. H., & Mohanty, S. (2025). Meso-scale permeability prediction from the multi-block 3D reconstruction of fiber reinforced polymer composite with experimental validation. Composites Science and Technology, 111290.

Carrillo, F. J., Bourg, I. C., & Soulaine, C. (2020). Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach. Journal of Computational Physics: X, 8, 100073.

Tong, A. Y., & Wang, Z. (2007). A numerical method for capillarity-dominant free surface flows. Journal of Computational Physics, 221(2), 506-523.

Renardy, Y., & Renardy, M. (2002). PROST: A parabolic reconstruction of surface tension for the volume-of-fluid method. Journal of Computational Physics, 183(2), 400-421.

Inguva, V. (2020). On methods to reduce spurious currents within VOF solver frameworks. Part 1: A review of the static bubble/droplet. Chemical Product and Process Modeling, 1.

Deshpande, S. S., Anumolu, L., & Trujillo, M. F. (2012). Evaluating the performance of the two-phase flow solver interFoam. Computational Science & Discovery, 5(1), 014016.

Roenby, J., Larsen, B. E., Bredmose, H., & Jasak, H. (2017). A new volume-of-fluid method in OpenFOAM. In Marine vi: Proceedings of the vi International Conference on Computational Methods in Marine Engineering (pp. 266-277).

Roenby, J., Bredmose, H., & Jasak, H. (2019). IsoAdvector: Geometric VOF on general meshes. In OpenFOAM (pp. 281-296). Springer International Publishing.

isoAdvector.(2025). isoAdvector/isoAdvector[C++]. GitHub.

Wijaya, W., Ali, M. A., Umer, R., Khan, K. A., Kelly, P. A., & Bickerton, S. (2019). An automatic methodology to CT-scans of 2D woven textile fabrics to structured finite element and voxel meshes. Composites Part A: Applied Science and Manufacturing, 125, 105561.

Pucci, M. F., Liotier, P-J., & Drapier, S. (2015). Capillary wicking in a fibrous reinforcement - orthotropic issues to determine the capillary pressure components. Composites Part A: Applied Science and Manufacturing, 77, 133-141.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 113-123

doi: 10.4028/p-H1MHkN

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

Submitted:
2025-12-22

Revised:
2026-02-16

Accepted:
2026-02-17

Online:
2026-04-10

Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

The original version of this paper is available on https://www.scientific.net/MSF.1182.113.pdf

Manoj. R. Gongati 1,2,a*, Laurent Warnet 1, b, Francesco Rondina 2,c, Edwin T. J. Klompen 2, d and Remko Akkerman 1,2,e

¹Chair of Production Technology, Faculty of Engineering Technology, University of Twente, Drienerlolaan 5, 7622 NB Enschede, the Netherlands

2 ThermoPlastic composites Research Center, Palatijn 15, 7521 PN Enschede, the Netherlands

a  m.r.gongati@utwente.nl, b  l.warnet@utwente.nl, c  francesco.rondina@tprc.nl, d  edwin.klompen@tprc.nl, e  r.akkerman@utwente.nl

Keywords: residual stress, unsymmetric laminates, thermoplastic composites.

Abstract

Residual internal stresses arise during thermal processing of thermoplastic composites due to differential shrinkage of stacked orthotropic plies and can lead to defects such as shape distortion, microcracking or delamination. In the current study, a comprehensive thermomechanical model for predicting residual stresses and strains in semicrystalline thermoplastic composites is presented with specific application to unidirectional Carbon fiber reinforced LM-PAEK composite laminates. The model is based on an incremental Classical Laminate Theory (CLT) framework that incorporates temperature-dependent material properties and accounts for both thermal and crystallization-induced shrinkage effects. Material characterization is performed to measure key temperature-dependent properties: thermomechanical analysis (TMA) is used to measure the transverse thermal expansion coefficient (CTE) and crystallization shrinkage upon cooling from melt state, dynamic mechanical analysis (DMA) to obtain the transverse modulus ( E22 ). The stress-free temperature ( TSF ), the temperature at which residual stresses begin to develop, is identified through curvature evolution measurements of unsymmetric laminates using image analysis. The model validation is performed via curvature measurements of unsymmetric cross-ply laminates using laser scanning techniques, demonstrating good agreement between model predictions and experimental measurements.

Introduction

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Polymer composites provide a promising alternative to traditional materials like metals or alloys, thanks to their favorable properties and potential for lightweighting. Thermoset composites, which are mostly used, rely on polymer curing during production, which is usually time-consuming due to long curing times. In addition, the circular use of such thermoset composite materials is known to be challenging. In contrast, thermoplastic composites (TPC) offer several advantages, including shorter processing cycles, superior toughness, and improved recyclability. Moreover, TPC are particularly well suited for automated manufacturing and structural integration through techniques such as welding and overmolding, enabling the efficient production of large-scale, lightweight composite structures [1]. Process-induced residual stresses are inevitable in the manufacturing of thermoplastic composites, and they directly affect the shape of composite parts (warpage and spring-in), which are critical for the dimensional tolerance. Besides, residual stresses also affect the strength of the composite [2]. The sources of shrinkage in semi-crystalline thermoplastic composites can be separated into two components, namely crystallization shrinkage and thermal shrinkage or expansion, which is a result of applied change in temperature. During crystallization, the thermoplastic undergoes an increase in density and a corresponding reduction in volume, referred to as crystallization shrinkage. The residual stresses in composites arise from constrained deformation of the thermoplastic matrix due to thermal & crystallization shrinkage and the presence of fibers. The magnitude of microscopic residual stresses is determined by the mismatch between the thermo-elastic material properties of the matrix and the fiber. Furthermore, macroscopic residual stresses are developed in the laminate with a multidirectional stacking sequence as a result of anisotropic
properties of laminae. The presence of residual stresses, both micro and macro scales, has an implication on the strength of the composite, specifically on the transverse failure of laminates [3]. The present study focuses on predicting process-induced warpage and residual stresses in thermoplastic composite laminates at the macroscopic scale. At this scale, residual stresses primarily arise from mismatch in thermomechanical properties, such as the CTE and stiffness, between plies of different fiber orientations. In cross-ply laminates, the 90∘ plies undergo greater transverse thermal shrinkage than the 0∘ plies in fiber direction. During cooling from the processing temperature, the shrinkage of each ply is restricted by adjacent plies with different fiber orientations. The resulting mismatch in thermal deformation, and constraint imposed by neighboring plies, leads to compressive stresses in the 0∘ plies and tensile stresses in the 90∘ plies. In semicrystalline thermoplastic composites, an additional source of residual stress arises from the mismatch in crystallization shrinkage in the 90∘ and 0∘ plies during cooling [3,4]. Accordingly, this work aims to develop a thermomechanical model capable of predicting the macroscopic residual stress state and the associated laminate warpage in composite laminates.
The prediction of residual stresses in CF/LM-PAEK laminates requires reliable temperaturedependent thermomechanical properties, including the E22, CTE, crystallization-induced shrinkage and TSF. In previous studies on residual stress development in semicrystalline thermoplastic composites, the stress-free temperature ( TSF ) has commonly been assumed based on crystallization temperatures obtained from differential scanning calorimetry (DSC), such as the onset of crystallization [5], the peak crystallization temperature [6], or the end of crystallization [7]. Because multiple assumptions exist regarding the definition of the TSF, this work proposes an experimental technique to determine the TSF directly. Accordingly, this work focuses on the experimental characterization of the temperature dependent E22, transverse CTE, and crystallization shrinkage of CF/LM-PAEK composites together with the determination of TSF. The model validation is performed using a straightforward approach based on the fabrication of unsymmetric laminates, which undergo measurable warpage due to process-induced residual stress. The resulting curvatures are experimentally measured and compared with numerical predictions, avoiding the complexity and limitations associated with alternative residual stress measurement techniques such as layer removal method, first-ply failure and hole drilling methods.

Thermomechanical Modelling

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The CLT provides a theoretical framework for predicting the evolution of thermomechanical residual stress and strains in laminated composites on a macroscopic scale. The CLT is formulated based on the Kirchhoff plate hypothesis, which assumes a state of plane stress and neglects transverse shear deformation, making it applicable primarily to thin, plate-like structures [8]. In the present work, an incremental formulation of CLT is adopted to capture the evolution of residual stresses during cooling, explicitly accounting for the nonlinear temperature dependence of material properties. The residual stresses are evaluated by integrating stress increments over successive temperature steps as expressed in:

σt+dt=σt+Δσ(1)

where the stress increment is determined from the incremental form of Hooke's law:

Δσi=Q―ij(Δεjtot−αjΔ T−Δεjcrys)(2)

where Q―ij is the reduced stiffness matrix, αj is the CTE and Δεjcrys  is the crystallization strain increment [9]. The reduced stiffness matrix in the material coordinate system is defined as:

Q―ij=[E111−v12v21v21E111−v12v210v21E111−v12v21E221−v12v21000G12](3)

The total increment strain at a distance z from the laminate mid-plane can therefore be expressed as:

Δεjtot=Δεj0+zΔκj0(4)

The mid-plane strains and curvatures are then obtained from the laminate constitutive relation:

[Δε0Δκ0]=[A B BD]−1[ΔNth +ΔNcrys ΔMth +ΔMcrys ](5)

where A,B and D denote the laminate extensional, coupling, and bending stiffness matrices, respectively. The ΔNth ,ΔNcrys ,ΔMth  and ΔMcrys  are the thermal and crystallization-induced inplane forces and bending moments [9]. In agreement with available literature, and specifically for APC-2 thermoplastic composites [10,11], the fiber-dominant material properties (e.g., stiffness and CTE along the fiber direction) of the CF/LM-PAEK composite are assumed to be temperatureindependent over the processing temperature range, with values reported in Table 1. This assumption is justified by the close similarity between APC-2 and CF/LM-PAEK composite, as both are carbon fiber-reinforced, high-performance semicrystalline thermoplastic composites with comparable fiber architectures and processing temperature ranges. In contrast, matrix-dominated properties, such as the transverse modulus and the CTE, exhibit significant temperature dependence and are therefore defined as temperature-dependent. Although the in-plane shear modulus ( G12 ) is also matrix dominated, the present study is restricted to cross-ply laminates, in which no shear strains or torsional curvatures are generated during consolidation. Consequently, G12 does not affect the predicted curvature or residual stress state of the laminate. Therefore, G12 is assumed to be temperature independent, with a constant value of 4.3 GPa measured at room temperature [12]. The experimental procedures used to measure the transverse CTE, and modulus are described in the following section.

Table 1. Fiber-dominant material properties [11].

Property | Values
E₁₁ | 135 GPa
α₁₁ | 0.1 × 10⁻⁶ 1/°C

Material Characterization

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This section presents an overview of the experimental characterization of material properties, including the temperature-dependent transverse CTE), crystallization-induced shrinkage, transverse modulus, and determination of the stress-free temperature. The material investigated in this study is a unidirectional carbon fiber (T700)-reinforced low melting poly(aryl-ether-ketone) (PAEK) thermoplastic, manufactured by Toray Advanced Composites and is known as Toray Cetex TC1225. The composite exhibits a fiber volume fraction of 59%, and the melting temperature (Tm) and glass transition temperatures ( Tg ) are 305∘C and 147∘C respectively [12]. The unidirectional laminates of the CF/LM-PAEK composite for the material characterization were manufactured using a pressconsolidation process. The prepreg tapes were heated to a processing temperature of 365∘C (above Tm ) at a heating rate of 10∘C/min and held for 40 min to ensure complete melting. Subsequently, the laminates were cooled to room temperature at a rate of 5∘C/min under a consolidation pressure of 15 bar.
Thermal and Crystallization Shrinkage. The temperature-dependent transverse linear thermal expansion and crystallization-induced shrinkage of the CF/LM-PAEK composite are characterized using TMA. The measurements are performed in accordance with ASTM E831 [13] for the determination of the linear CTE. In the first set of experiments, referred to as Method A, the specimens are heated to 250∘C, remaining within the solid-state temperature range of the composite, to determine the transverse linear CTE following the standard ASTM E831 procedure. In the second set of experiments (Method B), the test methodology is extended by heating the specimens above the melting temperature of the composite to determine the crystallization shrinkage. During the subsequent controlled cooling from the melt, both the crystallization shrinkage and transverse CTE are evaluated.

The rectangular specimens with nominal dimensions of 3×3×6 mm3 are prepared in accordance with the recommendations of ASTM E831. The TMA analysis consists of two successive heatingcooling cycles: the first cycle is used to eliminate prior thermal history and process-induced effects, thereby establishing a reproducible reference condition, while the second cycle is used to determine the material properties. A constant heating and cooling rate of 3∘C/min is employed to minimize temperature gradients and thermal lag between the specimen and the furnace environment. The change in specimen length as a function of temperature is continuously recorded, and the transverse linear CTE ( α22 ) is calculated according to

α22=1Δ TΔ L L0(6)

The results of the thermomechanical analysis of the CF/LM-PAEK composite in the in-plane transverse direction obtained using Method A, during heating to 250∘C within the solid-state temperature regime, are presented in Fig. 1a. The results shown in Fig. 1a indicate thermal expansion during the first heating cycle, with a contraction observed prior to the glass transition temperature. This contraction is attributed to the partial release of tensile residual stresses in this temperature range [14], which are likely introduced during the press-consolidation process. During the second heating cycle, the thermal expansion and contraction behavior is repeatable and consistent with the expected thermomechanical response of the material. The linear strain is observed to vary linearly with temperature below Tg whereas above Tg the slope increases and the strain-temperature relationship becomes nonlinear at higher temperatures. In the present study, the linear strain above Tg is approximated using a quadratic fit, and the transverse CTE is evaluated by calculating the slopes of the fitted curves below and above Tg and is shown in Fig 1b.

[picture]

Fig. 1. (a) Linear strain vs temperature results measured using TMA;
(b) Second cooling experimental and fitting results.

Fig. 1. (a) Linear strain vs temperature results measured using TMA; (b) Second cooling experimental and fitting results.

To determine the crystallization-induced shrinkage using Method B, the CF/LM-PAEK composite is heated above its melting temperature and subsequently cooled under controlled conditions. The TMA results obtained during cooling from the melt are presented in Fig. 2. At the onset of cooling, the molten specimen exhibits a non-linear contraction. However, a pronounced decrease in shrinkage is observed during the solidification phase, corresponding to crystallization. After further cooling, the composite undergoes nonlinear shrinkage as it transitions from the rubbery to the glassy state, followed by a region of nearly constant strain below Tg. The α22 is evaluated in a manner consistent with the procedure described previously and is illustrated in Fig. 1b. To incorporate crystallizationinduced shrinkage into the analysis, a linear fit is applied over the crystallization temperature range, and the slope of this segment is interpreted as an effective CTE during crystallization [15]. This approach combines thermal expansion and crystallization shrinkage into a single apparent linear strain-temperature relationship. The approach is justified because the CTE measurements were performed at a cooling rate of 3∘C/min representative of the cooling rate considered pressconsolidation process ( 5∘C/min ), under which the laminate attains near-maximum crystallinity.

Consequently, crystallization shrinkage is approximated as primarily temperature dependent and not on degree of crystallinity. The limitation of this approach is that it is valid primarily for processes involving similarly low cooling rates where the composite reaches to the near to maximum degree of crystallinity and will not be applicable to process where the cooling rates are higher.

The evaluated α22 values from both the solid-state and crystallization regimes are summarized in Table 2. The onset ( Tonset  ) and end ( Tend  ) crystallization temperatures are identified as 268∘C and 256∘C, respectively, while the Tg is measured as 133∘C and Tr is the room temperature.

Table 2. CTE values measured from different methods.

Temperature range (°C) | α₂₂ (x 10⁻⁶ 1/°C) Method A | Method B
[Tr: Tg] | 36.82 | 33.74
(Tg : Tend] | 0.47 T + 5.16 | 0.59 T - 27.59
(Tend: Tonset] | N/A | 600.56

[picture]

Fig. 2. TMA analysis showing crystallization shrinkage during cooling.

Fig. 2. TMA analysis showing crystallization shrinkage during cooling.

Temperature-dependent Transverse Modulus. The temperature-dependent transverse stiffness (E22) of the thermoplastic composite is measured using DMA. A three-point bending DMA specimen geometry is selected in accordance with ASTM D5023 [16] with a fixed span length of 40 mm is used in the experiments. Based on the span-to-thickness ratio and overhang requirements, specimens with nominal dimensions of 56×13×2.24 mm3 are prepared. The static and dynamic displacement amplitudes are set to 15μ m and 7.5μ m, respectively, with the static displacement exceeding the dynamic displacement to ensure continuous contact between the specimen and the fixture. A thermocouple is embedded within the specimen to directly monitor the specimen temperature during testing. The temperature is ramped from 25 to 250∘C at a constant rate of 3∘C/min. The transverse storage modulus is calculated from the measured dynamic force amplitude and phase angle using Euler-Bernoulli beam theory.

E′=Faua Ls34bh3cos(δ)(7)

where Fa is the dynamic force amplitude, ua is the dynamic displacement amplitude, Ls is the span length, b is the width of specimen, h is the thickness of specimen, and δ is the phase lag angle. The variation of the transverse storage modulus with temperature is shown in Fig. 3a. The initial heating cycle exhibits a response that differs from the subsequent thermal cycles (cooling-heating-cooling).

To validate the DMA measurements, quasi-static three-point bending tests are performed at room temperature, yielding a transverse stiffness of 8.65 GPa . This value is in close agreement with the transverse modulus obtained during the first cooling cycle and the second heating and cooling cycles in the modulus-temperature response. A significant reduction in transverse stiffness is observed beyond T , with the modulus decreasing from 8.76 GPa at 25∘C to approximately 1.3 GPa at 250∘C. The Tg values determined from the inflection point of the modulus drop and from the peak of tanδ are 137∘C and 162∘C, respectively. To incorporate this temperature-dependent behavior into the numerical analysis, the transverse modulus data is fitted using a Boltzmann function [17].

E22=∑i=12(Ei1+exp[T−Tg+ΔTiτi])(8)

with the corresponding parameters provided in Table 3.

[picture]

Fig. 3. (a) Temperature-dependent storage modulus;
(b) Fitted model for temperature-dependent transverse modulus.

Fig. 3. (a) Temperature-dependent storage modulus; (b) Fitted model for temperature-dependent transverse modulus.

Table 3. Fitting parameters for temperature-dependent transverse modulus.

Fitting parameters | E₁ (MPa) | E₂ (MPa) | ΔT₁ (°C) | ΔT₂ (°C) | τ₁ (°C) | τ₂ (°C) | Tg (°C)
Values | 3915 | 4995 | -77.39 | -15.75 | 50.76 | 6.52 | 137

Stress-free Temperature. The stress-free temperature ( TSF ) is defined as the temperature at which residual stresses begin to develop during the cooling process from the initial processing temperature. As reported in the literature [11, 12], TSF is commonly determined by monitoring the curvature evolution of unsymmetric laminates during a controlled heating cycle, with the temperature corresponding to zero curvature identified as the stress-free condition. A similar approach is adopted in this study, wherein the curvature of unsymmetric composite strips is measured using image-based analysis during thermal cycling. The stress-free temperature is determined by extrapolating the curvature-temperature response to the point of zero curvature. Unsymmetric composite strips with a stacking sequence of [ 04/904 ] and in-plane dimensions of 300×90 mm2 are used for the TSF measurement. The composite strips are placed inside an Instron testing oven as shown in Fig 4. Their lateral profiles are oriented to face the observation window of the oven. A monochrome IDS camera is positioned in front of the oven window to capture high-contrast images of the laminate's lateral
profile. Camera and lens calibration is performed using a checkerboard pattern and the calibration images are analyzed using MATLAB's Computer Vision Toolbox to obtain the lens distortion parameters and to determine the pixel-to-mm conversion factor. Following calibration, the images of the laminate profile are acquired continuously during both heating and cooling, with thermocouples attached to the specimens for temperature measurements. A custom MATLAB routine is developed to extract edge points from the images, after which a circular fitting procedure is applied to the extracted profile, and the laminate curvature is calculated as the inverse of the fitted radius.

Fig. 4. Experimental setup for the temperature dependent curvature analysis.
The laminates are subjected to two heating cycles heating to the temperature of 250∘C, consistent with the procedures adopted for the TMA and DMA measurements. The evolution of curvature as a function of temperature is shown in Fig. 5a. The curvature-temperature response exhibits a distinct change in slope across Tg, reflecting the different thermomechanical behavior of the laminate in the glassy and rubbery regimes. A noticeable increase in curvature is observed following the first cooling cycle, which may be attributed to annealing effects at elevated temperatures that promote further development or redistribution of residual stresses within the laminate [12]. At higher temperatures, the curvature response tends to stabilize, showing minimal variation with further temperature increase. To determine the stress-free temperature, a linear regression is applied to the curvaturetemperature data in the range of 160−230∘C, where the response is approximately linear. The stressfree temperature is identified as the extrapolated temperature at which the curvature becomes zero, corresponding to a state of negligible thermally induced internal stress, and is determined to be 255∘C.

[picture]

Fig. 5. a) Temperature-dependent curvature results of CF/LM-PAEK composite laminates; b) Extrapolation of TSF.

Fig. 5. a) Temperature-dependent curvature results of CF/LM-PAEK composite laminates; b) Extrapolation of T S F .

Results

The original version of this paper is available on https://www.scientific.net/MSF.1182.113.pdf

The current section presents the validation of numerical prediction of curvatures for two different unsymmetric cross-ply laminates with layup [04/904] and [02/902]2 fabricated via press consolidation. The temperature-dependent curvatures are predicted using the incremental CLT incorporating the material properties characterized in the preceding section. The post-fabrication curvature of the laminates was experimentally measured using a laser scanning technique. In this method, the out-ofplane ( z ) displacement was recorded while the specimen was scanned along the x and y-directions. The z-displacement was captured using a non-contact laser displacement sensor with a 20 mm measurement range and a position-sensing laser triangulation sensor device (LTS). The laminate curvature was determined by performing circular fits on all centerline z-profiles across the scanned surface and reporting the mean curvature, defined as the inverse of the average fitted radius obtained from all valid data lines. The experimentally obtained curvatures are compared with the predicted values for the two unsymmetric laminates and are shown in Fig 6. The curvature measured using the LTS method for the [O4/904] and [O2/902]2 unsymmetric laminates are 5.45 m−1 and 1.34 m−1 respectively. Additionally, for the [04/904] laminate, the predicted temperature-dependent curvatures are compared against the experimentally measured curvatures reported in the previous section. At room temperature, the deviations between the predicted and experimentally measured curvatures (LTS method) for the [O4/904] and [O2/902]2 unsymmetric laminates are 9.81% and −4.47%, respectively. The discrepancy of curvatures is likely attributable to the free-cooling assumption inherent in classical laminate theory (CLT) and neglecting effects of processing history on the material properties.

[picture]

Fig. 6. Comparison between experimental and analytical curvature results for UD unsymmetric cross-ply laminates.

Fig. 6. Comparison between experimental and analytical curvature results for UD unsymmetric cross-ply laminates.

Discussion

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In the present work, commonly adopted assumptions of TSF which are introduced in the introduction section are critically evaluated. The temperature-dependent curvatures of the laminates are predicted using each of the aforementioned TSF definitions and comparing the results with the experimentally determined TSF obtained from curvature measurements, as described in the previous section. The DSC measurements were conducted at a cooling rate of 5∘C/min to determine the crystallization onset temperature ( Tonset  ), peak crystallization temperature ( Tpeak  ), and end crystallization temperature ( Tend  ), and the results are presented in Fig. 7a. The corresponding curvature predictions based on these different TSF assumptions are presented in Fig. 7b and compared against the experimentally measured response.

[picture]

Fig. 7. a) DSC analysis of CF/LM-PAEK composite during cooling at a rate of 5∘C/min;
b) Comparison of the temperature dependent curvatures with different assumptions of Stress-free temperatures.

Fig. 7. a) DSC analysis of CF/LM-PAEK composite during cooling at a rate of 5 ∘ C / m i n ; b) Comparison of the temperature dependent curvatures with different assumptions of Stress-free temperatures.

The predictions based on the experimentally determined TSF show close agreement with those obtained by assuming the Tend  as the TSF. This consistency is physically justified, as semicrystalline polymers transition to a solid state only when crystallization is complete, accompanied by a significant increase in stiffness [14]. The transverse stiffness results are presented in section of material characterization, where E22 was measured over a temperature range of 30−250∘C using a three-point bending setup, which limits testing to temperatures above the melting point ( Tm ). Although melting is not reached within this range, torsional dynamic mechanical analysis (DMA) during cooling from Tm, as reported by Donderwinkel et al. for a GF/PA6 [0/90]4 woven composite [17], indicates that G12 begins to increase at the onset of crystallization and approaches a stable value at Tend , once crystallization is complete. Therefore, the end-of-crystallization temperature provides a reasonable and physically meaningful estimate of the TSF, as the primary development of stiffness occurs during the crystallization process.

Conclusion

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This study successfully developed and validated a thermomechanical model for predicting residual stresses in semicrystalline thermoplastic composites, with specific application to CF/LM-PAEK laminate systems. The transverse material properties, including E22,α22 and crystallization shrinkage are experimentally characterized using DMA and TMA, respectively, and the TsF is determined experimentally using image analysis. The TMA results revealed nonlinear strain-temperature behavior above the glass transition temperature, as well as an initial contraction during the first heating cycle, indicative of the release of manufacturing-induced residual stresses. The curvatures are predicted using an incremental CLT-based model, incorporating temperature-dependent material properties. The validation of unsymmetric cross-ply laminates resulted in a good comparison between predicted and measured curvatures at ambient temperature.

Acknowledgment

The original version of this paper is available on https://www.scientific.net/MSF.1182.113.pdf

This research was conducted within the Perspectief research program Enlighten, funded by the Dutch Research Council (NWO). The authors also sincerely thank the industrial and academic partners of the ThermoPlastic Composites Research Center (TPRC) for their valuable in-kind contributions and technical support.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.113.pdf

Ageorges, C., & Ye, L. (2012). Fusion bonding of polymer composites. Springer Science & Business Media.

Baran, I., Cinar, K., Ersoy, N., Akkerman, R., & Hattel, J. H. (2017). A review on the mechanical modeling of composite manufacturing processes. Archives of Computational Methods in Engineering, 24(2), 365-395.

Parlevliet, P. P., Bersee, H. E. N., & Beukers, A. (2006). Residual stresses in thermoplastic composites-A study of the literature-Part I: Formation of residual stresses. Composites Part A: Applied Science and Manufacturing, 37(11), 1847-1857.

Shokrieh, M. M. (Ed.). (2021). Residual stresses in composite materials. Woodhead publishing.

Lawrence, W. E., Seferis, J. C., & Gillespie, J. W., Jr. (1992). Material response of a semicrystalline thermoplastic polymer and composite in relation to process cooling history. Polymer Composites, 13(2), 86-96.

Péron, M., Barasinski, A., Krawczak, P., & Chinesta, F. (2020). Measurement and prediction of residual strains and stresses during the cooling of a glass fiber reinforced PA66 matrix composite. Composites Part A: Applied Science and Manufacturing, 137, 106039.

Parambil, N. K., Chen, B. R., & Gillespie, J. W., Jr. (2024). Process-induced residual stress in a single carbon fiber semicrystalline polypropylene thin film. Composites Part A: Applied Science and Manufacturing, 178, 107969.

Daniel, I. M., Ishai, O., Daniel, I. M., & Daniel, I. (1994). Engineering mechanics of composite materials (Vol. 3, pp. 256-256). New York: Oxford university press.

Péron, M., El Bayssari, A. M., Barasinski, A., Jacquemin, F., Daghia, F., & Guillon, D. (2025). Residual stresses and strains during laser assisted tape placement of thermoplastic composite: Multi-physical modelling and experimental validation. Composites Part A: Applied Science and Manufacturing, 109478.

Jeronimidis, G., & Parkyn, A. T. (1988). Residual stresses in carbon fiber-thermoplastic matrix laminates. Journal of Composite Materials, 22(5), 401-415.

Barnes, J. A., & Byerly, G. E. (1994). The formation of residual stresses in laminated thermoplastic composites. Composites Science and Technology, 51(4), 479-494.

Toray Advanced Composites. Toray Cetex TC1225 LMPAEK product data sheet aminates/Toray-Cetex-TC1225_PAEK_PDS.pdf.

ASTM, E. (2006). 831-06; Standard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis. ASTM International: West Conshohocken, PA, USA.

Lebrun, G., & Denault, J. (2010). Effect of annealing on the thermal expansion and residual stresses of bidirectional thermoplastic composite laminates. Composites Part A: Applied Science and Manufacturing, 41(1), 101-107.

Golzar, M., Sinke, J., & Abouhamzeh, M. (2022). Novel thermomechanical characterization for shrinkage evolution of unidirectional semi-crystalline thermoplastic prepregs (PPS/CF) in melt, rubbery, and glassy states. Composites Part A: Applied Science and Manufacturing, 156, 106879.

ASTM International. (2015). ASTM D5023-15: Standard test method for plastics: Dynamic mechanical properties in flexure (three-point bending).

Kravchenko, O. G., Kravchenko, S. G., & Pipes, R. B. (2016). Chemical and thermal shrinkage in thermosetting prepreg. Composites Part A: Applied Science and Manufacturing, 80, 72-81.

Donderwinkel, T. G., van Drongelen, M., & Akkerman, R. (2016). Stamp forming optimization for formability and crystallinity. In Proceedings of the 19th International ESAFORM Conference on Material Forming (ESAFORM 2016). AIP Publishing.

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Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 125-134

doi: 10.4028/p-2Og3qz

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

Submitted:
2026-01-14

Revised:
2026-02-13

Accepted:
2026-02-20

Online:
2026-04-10

Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

Nihad Siddig 1,a*, Mohamed Mtibaa 1, b and Marie Coupé 1,c, Alexandre Guinoiseau 1, d

1 Nantes Université, IRT Jules Verne, 1 Mail des 20000 Lieues, 44340 Bouguenais, France

a* nihad.siddig@irt-jules-verne.fr, b mohamed.mtibaa@irt-jules-verne.fr, c  marie.coupe@irt-jules-verne.fr, d  alexandre.guinoiseau@irt-jules-verne.fr

Keywords: Composites, Liquid Resin Infusion (LRI), Simulation, Particle-filled Resins

Abstract

This work primarily focuses on the development and simulation of the Liquid Resin Infusion (LRI) process for particle-filled resins, aiming to impart additional functionalities to composite parts. The paper presents both the simulation development and the experimental tests used to establish physics-based models. The main challenge lies in understanding how particle addition affects the resin flow process. The introduction of particles increases resin viscosity, which in turn influences flow behaviour. Moreover, particle filtration by the fibrous medium changes its permeability, thereby impacting both flow dynamics and particle distribution. The materials used in the infusion process are experimentally characterised, and the resulting parameters served as inputs for the LRI process simulations. Constitutive behavior laws are implemented within the simulation tool. Simulations are then conducted using all characterized inputs and models for validation purposes. These validated models are subsequently employed to assess the infusion process performance.

Introduction

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The European project PAIRAMID aims to transform the design, development, and certification of aerostructures through an AI-driven digital framework that integrates virtual testing at every level of the certification pyramid, from material to coupon, element, and full aerostructure (Figure 1). By leveraging advanced simulations and data-driven insights, this approach reduces the reliance on costly and time-consuming physical tests, enabling a more efficient and integrated certification process. The project focuses on the fabrication of aeronautical parts using two manufacturing processes: Liquid Resin Infusion (LRI) and Fused Deposition Modelling (FDM). This paper concentrates on the former. The LRI process in the PAIRAMID project includes adding particles to improve the electrical conductivity of composite components, such as the wing front edge and the aerostructure door skin. This functionality is essential for applications such as lightning strike protection and electrostatic discharge mitigation, allowing for the integration of electrical performance directly into the composite structure. Model particles are used herein to investigate the particle-filled LRI process.

[picture]

Fig. 1. The pAIramid project approach

Fig. 1. The pAIramid project approach

Context of the study

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

This study focuses on developing and simulating the Liquid Resin Infusion (LRI) process [1] for particle-filled resins. The paper details both the simulation framework and the experimental work carried out to build physics-based models [2-4]. The materials involved in the infusion process are experimentally characterized. Simulations based on all characterized inputs and models are then performed and compared to infusion experiments with particle-filled resins [5-9].

Experimental Method

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The project investigates the infusion process with particle-filled resin with different particle sizes and percentages. The different percentages are tested to evaluate their influence on the process and to verify if the model can predict the process behaviour in the presence of these particles.

Material characterization

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The main materials used for the infusion trials are unidirectional glass fibre reinforcements from Owens Corning, fibre diameter of about 17μ m, oriented at the flow direction for all the experiments. The epoxy resin Infugreen SR 8100/SD 8822 is used for the fabrication of composites. The ATH particles M15B and M20B from LKAB, with three concentrations ( 10%,15% and 20% ), respectively, were added to study the influence on the process. The particles are rigid and polydisperse with narrow distribution, where the vast majority of particles are on the order of 15μ m for M15B and 20μ m for M20B, respectively. They are characterized as non-deformable. Figure 2 shows a microscopic observation of the fabricated composite, functionalised with the grade M20B, showing particles, fibre bundles and stitching.

[picture]

Fig. 2. Microscope observation of the composite

Fig. 2. Microscope observation of the composite

The viscosity of neat resin was measured by Sicomin. The permeability of the reinforcements was measured by TENSYL in the in-plane and out-of-plane directions and the values are used as input for simulations. The permeabilities and viscosities will be modified by particle addition. Previous studies have shown the influence of particles on both resin and fabric [6-9]. The variation in permeability during infiltration is modelled (by Eqs. 7 and 8) as being a result of particle filtration and clogging of the fibrous medium. A key assumption revolves around the fact that the rigid particles do not mechanically compress or permanently displace the fibre preform. While the particles modify the permeability of the medium and are intended to impart functional properties (e.g., electrical conductivity) to the final composite, they may modify the architecture of the fibrous medium but not the individual glass fibres.

Process conditions

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The process is pressure-controlled, as governed by Darcy's law (Eq. 2). The resin enters the part at atmospheric pressure (on the left of Figure 3), and vacuum pressure is applied and controlled at the resin outlet (on the right of Figure 3). A pressure gradient of 0.8 bar is driving the flow. The extended infusion time is a direct consequence of this low driving pressure gradient combined with the significant increase in suspension viscosity and the progressive reduction in reinforcement permeability due to particle filtration, as described by the constitutive models in Section 4.

Infusion tests

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Several infusion trials are conducted to improve the understanding of the process and to provide input parameters for the process simulation [6]. The infusion trials are illustrated in Figure 3 for three different configurations, with a stacking of 7 plies of unidirectional reinforcement having the same in-plane dimensions as illustrated by the figure, giving a thickness of about 4 mm , and a fibre volume fraction of approximately 50%.

[picture]

Fig. 3. Infusion trials with different particle sizes and percentages

Fig. 3. Infusion trials with different particle sizes and percentages

Figure 3 presents three infusion trials carried out simultaneously under identical process conditions, using two particle sizes ( 15μ m and 20μ m ) and two particle concentrations ( 10% and 20% ), observed 1 h after the start of the infusion. The figure shows that the lowest particle concentration resulted in the most successful infusion among the tested cases. At a given concentration, particle size governs the infusion behaviour, as the 15μ m case exhibited a more advanced flow front than the 20μ m case at the same instant of time.

Modelling and simulation

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To simulate the flow of a particle-filled resin through a porous medium, it is necessary to adopt physical models capable of representing the main phenomena involved, in particular, fluid flow, the filtration of particles within the reinforcement [7]. This simulation is based on the coupling of two fundamental models:

The fluid flow in the fibrous medium model

The particle filtration model

The suspension concentration evolution model

Material behaviour laws (permeability and viscosity)

On the one hand, filtration leads to changes in the local particle concentration, partial retention of these fillers within the fibrous reinforcement, and progressive modifications of the porosity and permeability of the medium. On the other hand, the resin flow is directly influenced by these changes, in particular the reduction in permeability due to progressive clogging (particle accumulation) and variations in viscosity, which itself depends on the local particle concentration [8].

The flow is governed by the continuity equation (Eq. 1) and Darcy's law (Eq. 2).

∇·U→=0(1)

where U→ is the velocity vector.

U→=−Kμ∇p(2)

where K is the permeability tensor, μ is the viscosity and ∇p is the pressure gradient.

The porosity ε of the fibrous medium is described by equation (Eq. 3). It represents the change in porosity as a result of particle retention.

ε=ε0−σ(3)

where ε0 is the initial porosity and σ is the retention, which is governed by the equation (Eq. 4).

∂σ∂t=αU→C(1−σσu)(4)

where α is the filtration coefficient, a measure of the medium's efficiency at capturing particles, with m−1 unit, C is the concentration, and σu is the ultimate particle deposit at which the clogging of the porous medium occurs, representing the maximum particle retention capacity of the porous medium. It is the value of σ at which the retention rate ∂σ∂t becomes zero [6,8]. The equation considers that the retention rate is proportional to the flux of suspended particles, represented by the term U→C. The proportionality constant is called the filtration coefficient α. This coefficient represents the probability of particle capture; it depends on its initial value α0, the porosity and the permeability. The filtration coefficient changes according to this relation (Eq. 5).

α=α0[(KK0)−12(εε0)32(1−ε1−ε0)−1]a1(5)

where K0 is the initial permeability and a1 is an empirical positive constant [7,8].
The concentration is governed by this conservation equation (Eq. 6) [6, 8]. This equation is the resulting mass balance after applying mass conservation on the three species involved: the fluid, the retained and suspended particles.

∂[εC]∂t+∇·{U→C}+∂σ∂t=0(6)

The change in medium permeability K is governed by the electrical analogy equation, Eq. 7, applied to the initial filter permeability K0 and the deposit permeability Kd[6].

K=K0·KdK0+Kd(7)

The deposit permeability Kd is estimated by the Kozeny-Carman relation given in Eq. 8 .

Kd=d2(1−σ)336hKσ2(8)

where d is the particle diameter and hK is the Kozeny constant (Eq. 8).
The viscosity is modelled by equation 9. This model was proposed by Erdal [7], and it assumes that the viscosity depends uniquely on the particle concentration. In this equation, the suspension is assumed to be Newtonian and the viscosity change occurs at a constant shear rate [8].

μ=μ0[1−CA]−2(9)

where A is the packing fraction.

Simulation

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The simulation is realized by COMSOL Multiphysics to model the coupling of suspension flow and particle retention, leading to a coupling between the linear and non-linear equations presented in this section. The continuity equation (1), along with Darcy's law (2) are implemented in the tool to
compute the flow of suspensions. In addition, two user-defined partial differential equations (PDEs) are defined to model the filtration kinetics and the concentration conservation equations. A timedependent study with Phase initialization is introduced to solve the problem [8]. The calculation loop is illustrated in Figure 4.

[picture]

Fig. 4. Calculation loop in COMSOL Multiphysics

Fig. 4. Calculation loop in COMSOL Multiphysics

The model developed is used for simulating the suspension flow through the fibrous medium in LRI process. The initial conditions (at time t=0 ), at any point of the preform, pressure P(x,0)=PVacuum , retention σ(x,0)=0, porosity ε(x,0)=ε0 and particle concentration C(x,0)=0. For the boundary conditions, at the inlet (x=0), during infusion P(x=0,t)=P0,C(x=0,t)=C0, while at the front (x=L(t)),P(x=L(t),t)=PVacuum  and σ(x=L(t),t)=0.

The parameters used for this simulation are presented in Table 1.

Table 1. Parameters used in the models and their corresponding values

Vf0: Fibers' volume fraction (%) | 50%
α₀: Initial filtration coefficient (m⁻¹) | 1 [10]
P₀: Atmospheric pressure (Pa) | 1.01325x10⁵
PVacuum: Vacuum pressure (Pa) | 0.2x10⁵
σu: Ultimate specific deposit | 0.5
A: Empirical constant | 0.68 [10]
a₁: Parameter model | 1 [10]
L₀: Length (m) | 0.5
L₁: Width (m) | 0.2
H₀: Height (m) | 0.004
μ₀: Initial viscosity (Pa.s) | Characterisation
K₀: Initial permeability (m²) | Characterisation

Simulation results and correlation

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

The simulation model was first developed using pure resin, without including the filtration models, and then compared with the experimental results. Figure 5 presents the experimental and numerical flow front positions. The filling model shows good agreement with the experimental data.

[picture]

Fig. 5. Flow front advancement, comparison between experimental and numerical results with pure resin

Fig. 5. Flow front advancement, comparison between experimental and numerical results with pure resin

Figure 4 presents the cases studied, both experimentally and numerically. Two different particle sizes were considered ( 15μ m and 20μ m ). As described in Section 2, the numerical model incorporates particle size through its effect on deposit permeability. The images present the flow front position at 16 minutes from the beginning of the infusion for the experiments with 15μ m resin suspensions.

[picture]

Fig.6. Correlations between numerical and experimental results with particle-filled resin

Fig.6. Correlations between numerical and experimental results with particle-filled resin

Figure 6 shows that the predictions provided by the simulation present deviations from experimental measurements. The figure shows that, numerically, the 10% suspension concentration advances further than the higher concentrations ( 15% and 20% ). This can be explained by the increase in particle content at higher concentrations, which consequently increases viscosity and decreases permeability, thereby delaying the flow front. However, experimentally, the flow front positions for 10% and 15% are very close. This may result from process variability, the suspension preparation method, potential particle sedimentation and resin transfer to the part, all of which can introduce errors in the actual particle concentration [11].

[picture]

Fig. 7. Flow front advancement, comparison between experimental and numerical results with particle-filled resin

Fig. 7. Flow front advancement, comparison between experimental and numerical results with particle-filled resin

Figure 7 illustrates the comparison between numerical and experimental results for front advancement over time, considering three different initial particle concentrations ( 10%,15%, and 20% ) at the same particle size ( 15μ m ). The results indicate a discrepancy between the numerical predictions and the experimental data, which is likely due to insufficient control of the initial particle concentration entering the part during the experimental tests because of potential sedimentation. Although the suspension is prepared with a nominal concentration of 20%, the effective concentration during infusion may differ and may either be higher or lower than the theoretical concentration. However, the numerical model could approximate the overall filling time for the 10% and 15% concentration cases, but the evolution of the flow front remains different from the experiment for all the concentrations. This observation supports the hypothesis that the effective concentration infused during the experimental tests may differ from the nominal concentration.

[picture]

Fig. 8. The final particle distribution in the part

Fig. 8. The final particle distribution in the part

The particle quantity evolution along the length is shown in Figure 8. As expected, increasing the initial particle concentration leads to an increase in the particle quantity in the composite. In the case of a 20% concentration and 15μ m particle size, the selected maximum infusion time ( 6000 s ) is not
sufficient to fill the part. As a result, the particle quantity drops to zero in the unfilled (dry) area. In addition, the influence of particle size on the evolution of the amount of particles in the composite was examined, and no significant effect was observed. This may be attributed to the model's limited ability to accurately represent particle-size-dependent filtration mechanisms. In the governing equations, the retention does not depend directly on permeability, but rather on the filtration coefficient, which itself is a function of permeability. However, the variation of α is very limited; therefore, the resulting difference is not significant, either in terms of retention or concentration.

Multiple criteria were tested to investigate the infusion limit of clogging. In Figure 9, the criterion developed by [6] is tested.

[picture]

Fig.9. The clogging criterion

Fig.9. The clogging criterion

This clogging criterion allows for determining whether the part can be fully filled or whether clogging prevents complete impregnation (Figure 9). For the three experimental tests considered, the criterion was evaluated by multiplying the particle size (d=15μ m) by the initial particle concentration (C0=10%,15% and 20% ), with a fiber volume fraction of 50%. The results show that for an initial concentration of 10% and a particle size of 15μ m, the part can be filled experimentally. In contrast, for 15% and 15μ m, progressive clogging occurs, which is consistent with the experimental observations, as filling becomes increasingly difficult toward the end of the process. Finally, in the case of 20% and 15μ m, complete clogging is observed; experimentally, after a certain time, the particle-filled resin no longer advances.

Conclusion and Perspectives

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

The article presented the main models describing particle-filled resin infusion through fibrous media. Key results included LRI process infusion trials performed with different particle sizes and concentrations. Numerical simulation results were presented and correlated with experimental tests. The simulations showed good agreement with the experiments in terms of flow-front advancement and present a prediction of particle content; however, the models are not very sensitive to particle size and mainly depend on particle concentration. The models should be validated using CNT suspensions, with systematic correlation to experimental results. The performed infusion trials are
consistent with the clogging criterion. Future developments should focus on comparing experimental and numerical particle content and on predicting the LRI process for complex particle-filled components.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

This project has received funding from the European Union's Horizon Europe research and innovation programme under grant agreement No 101192736.

References

The original version of this paper is available on https://www.scientific.net/MSF.1182.125.pdf

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

The original version of this eBook is available on https://www.scientific.net/book/modeling-and-numerical-approach-in-composites-forming-processes/978-3-0357-3774-5

Materials Science Forum, ISSN: 1662-9752, Vol. 1182, pp 135-146

doi: 10.4028/p-hZfPy4

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

Submitted:
2026-01-19

Revised:
2026-02-16

Accepted:
2026-02-17

Online:
2026-04-10

A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

Miro Duhovica 1,a*, Lukas Handl 1, b, Martin Müller 1,c, Dominic Schommer 1, d, Thomas Hoffmann 1,e, Jens Schlimbach 1,f, Thomas Neumeyer 1, g

1 Leibniz-Institut für Verbundwerkstoffe GmbH, Erwin-Schrödinger-Straße 58, 67663

Kaiserslautern, Germany

a  Miro.Duhovic@leibniz-ivw.de, b  Lukas.Handl@leibniz-ivw.de, c  Martin.Mueller@leibniz-ivw.de,

d  Dominic.Schommer@leibniz-ivw.de, e  Thomas.Hoffmann@leibniz-ivw.de,

f Jens.Schlimbach@leibniz-ivw.de, g Thomas.Neumeyer@leibniz-ivw.de

*corresponding author

Keywords: process simulation, thermoforming, spring-angle prediction, digital process chain.

Abstract

This paper presents a comprehensive fully integrated polymer composite thermoforming process simulation chain developed in ANSYS LS-DYNA®, covering the full manufacturing sequence from automated preform creation to final part cooling. The entire simulation consists of three distinct phases, namely, thermoforming, cooling (within the tool) and manufacturing-induced dimensional distortion after demolding (spring-back), where distortions develop as the part is removed from the tooling and finally cools to room temperature. The simulation framework employs a modular model structure consisting of tooling, a preform holding system, and a detailed preform representation based on a semi-discrete unit cell approach. Individual laminate plies are modeled using a combination of beam, solid, and shell elements and simple material models to accurately capture temperature-dependent bending, shear, and thermal behavior of the preform. To ensure industrial applicability, an automated preform meshing strategy has also been developed, utilizing tape placement path planning data exported from the automated tape laying process to generate simulation models with minimal manual effort. The simulation results enable the prediction of springangle distortions (spring-in or spring-back) and can be validated against experimental distortion measurement data from manufacturing trials of several different representative CFRTP components. The presented approach demonstrates the capability of the newly developed simulation chain to support thermoforming process development, tool geometry compensation, and robust manufacturing of complex thermoformed CFRTP structures.

Introduction

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The absence of efficient manufacturing routes for fiber-reinforced thermoplastics (FRTPs) has led to the continued use of aluminum or labor-intensive thermoset-based construction methods for the manufacture of structural aerospace components. Within several German Federal Aviation Research projects, the Leibniz-Institut für Verbundwerkstoffe GmbH (Leibniz Institute for Composite Materials) and its project partners have been developing an efficient process chain for the costeffective production of complex carbon fiber-reinforced thermoplastic components (CFRTPs). This effort combines the key processes of automated tape laying/placement (ATL/ATP), thermoforming, co-consolidation, and over-molding. In this manufacturing route, unidirectional tapes are first converted into customized, material-efficient 2D preforms using a high-speed multiaxial tape-laying machine. Both straight and curved fiber paths can be produced in-line with the part's load bearing directions. Using the thermoforming process, these 2D preforms are reshaped into their final 3D geometry. The preform is first heated by IR-radiation to temperatures above 400∘C depending on the polymer to achieve drapeability and is then formed into the desired shape using a press equipped with the corresponding matched die tooling [1]. More complex integrated structures can be achieved through additional over-molding via injection molding channels and cavities or joining steps via coconsolidation functionality. This process chain offers numerous advantages, including high
production rate, fully integrated manufacturing structural components from hybrid materials, a high degree of automation, and improved damage tolerance. In addition, the inherent weldability of thermoplastics enables the efficient joining of additional parts and repair of components, while recyclability provides a clear advantage over thermosets. However, during the manufacture of such complexly curved or angled CFRTP components, undesirable component deformations and distortions may occur, particularly during thermoforming at high processing temperatures, cooling within the tool, and further cooling of the part to its working temperature. These deformations can pose major challenges during subsequent assembly processes. To support the development of parts produced using this manufacturing process, CAE tools such as finite element simulations are used to model the entire process chain, predict distortion effects, and adjust the required tool geometry accordingly to compensate for these effects. This minimizes the need for costly production trials, tool rework, and the trial-and-error determination of optimal process parameters.

State of the Art

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

Thermoforming.

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The thermoforming of fiber-reinforced thermoplastics is a highly efficient manufacturing process that leverages the ability of thermoplastic polymers to soften and become moldable when heated, and to solidify again upon cooling. Unlike thermosetting composites, this reversible phase change enables very short cycle times and the use of forming techniques similar to those used in metalworking [2, 3]. Thermoforming describes the reshaping of flat, pre-consolidated laminate structures (also known as preforms) into complex two- or three-dimensional components under the influence of heat and pressure. An essential factor in the processing of continuous fiber-reinforced thermoplastics is that the reinforcing fibers (in particular carbon fibers) are practically inextensible during forming. Therefore, the matrix must be molten during deformation to enable deformation processes such as inter-ply slip and intra-ply shear to occur, allowing the fibers to conform to the tool geometry without kinking or breaking [2,4]. The process is often performed using stamp forming in a mechanical or hydraulic press. In the considered process chain, tailored preforms are first produced using the ATP or ATL method. Individual ply layers with the desired fiber orientation are laid down using preconsolidated preform laminate [1,2]. However, other types of preforms can also be used, such as fabric fiber-reinforced preforms, film stacked prepregs, or commingled yarns [2]. The preform is then heated in an external heating device (e.g., by contact heat, infrared radiation, or convection) above melt temperature, Tm for semi-crystalline polymers or well above the glass transition temperature, Tg for amorphous polymers. In this state, the material is flexible and deformable. The hot laminate is then quickly transferred (within a few seconds) to the forming tool to prevent premature cooling. Once positioned in the tool, the press closes and shapes the preform by pressing it between the tool cavities. The component cools under pressure within the tool to well below Tm or Tg. Once a uniform temperature is reached and any recrystallization effects have occurred, the finished part is removed from the tool [1,2,4]. When thermoforming CFRTP components, undesired deviations from the intended part geometry often arise during cooling. Components with curvature or angled surfaces are particularly prone to these distortions [5,6]. These distortions are usually due to internal stress states caused by the forces involved in the thermoforming process, differences in thermal expansion of the reinforcing fibers and polymer matrix, crystallization effects and the anisotropic properties of CFRTP laminates [3, 5]. As a result, two main phenomena are observed: spring-in and spring-back. The extent of each effect is influenced by the material combination (fiber types/reinforcing structures and polymer), processing parameters and the component design. An overview of these parameters and some general trends indicating the potential impact on distortion (spring-angle) behavior is presented in Table 1. Detailed modeling of the entire process chain has already been demonstrated in the physics-based virtual-twin stamp-forming simulation workflow of Pipes [7].In many current approaches, including that of Pipes, the forming simulation and the subsequent distortion (spring-angle) simulation are often carried out in two separate simulation/software environments.

This can make it challenging to fully carry over the process-induced forces and stress states from the forming phase into the distortion simulation.

Table 1. General trends in the influence of processing parameters and component design on springangle distortion, according to [1,2,3,4,5,6,8,9,11].

Parameter | Spring-Angle Δφ | Explanation
|  | Spring-In Spring-in diagram showing inward angle | Spring-Back Spring-back diagram showing outward angle
Processing temperature T | T↗ Δφ ↘ | Spring-in is proportional to the temperature difference between processing temperature and ambient temperature after demolding [4]. | Higher tool and component temperatures reduce spring-back, as improved matrix flow and reduced material elasticity decrease stress build-up [9].
Press force F | F↗ Δφ ↘/↗ | Higher tool pressure leads to stronger transverse matrix flow and increased fiber waviness, which can result in smaller end angles in bending zones [6, 9]. | Higher pressing force leads to greater spring-back due to higher residual stress caused by stretching of the molecular chains [1, 2].
Closing velocity v | v ↗ Δφ → | High velocity is necessary to maintain the laminate temperature above the critical level required for inter-ply slip and kink-free shaping [1, 4]. | -
Holding time t | t ↗ φ → | Longer holding times allow the matrix to fix the fibers more firmly during cooling, which reduces the elastic recovery (spring-back) of the fibers and results in a more consistent and uniform final angle [1, 2]. | Longer holding time reduces spring-back, as the matrix has more time to solidify and fix bent fibers in place [1, 2].
Laminate thickness d | d ↗ Δφ → | Thinner components tend to exhibit more spring-in than thicker ones. Measurements on L-profiles showed a 64% higher spring-in rate for 1 mm laminates compared to 12 mm laminates [6, 9]. | Very thin laminates (1–3 layers) exhibit spring-back due to low stiffness against residual stresses [9].
Laminate structure | Change from UD to quasiisotropic | Δφ ↘ | Quasi-isotropic laminates exhibit greater spring-in than UD laminates due to the stronger Poisson effect and the resulting contraction in the thickness direction [6]. | -
Fabric instead of UD Tape | Δφ ↗ | No spring-in effect observed | Fabric-reinforced laminates tend to cause spring-back [2], [10].
Form radius r | r ↗ Δφ → | Studies suggest that radius size has only a minor influence [2, 6]. | Spring-back decreases with increasing mold radius, as local deformation becomes less pronounced [2, 4].
Flange length l | l ↗ Δφ ↘ | Measured total deformation increases with the length of the flat sections, especially in thin laminates. This is largely due to the distortion of the flat sections [6]. | -

The simulation framework developed here provides a unified environment that enables the study of the influence of all important parameters throughout the entire thermoforming process chain. In the current implementation, strain-rate and cooling-rate effects have not yet been included, as simplified material models were used initially; however, more sophisticated models can be incorporated in future enhancements. In addition, the material models account for volume changes due to both thermal expansion and crystallization through a temperature-dependent "crystallinity-adjusted" thermal expansion coefficient.

Spring-In-Effect.

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The spring-in effect (also known as the spring-forward phenomenon) is a phenomenon of shape distortion that can occur during thermoforming at high processing temperatures of angular or curved CFRTP components [5, 6]. It manifests itself in the reduction of the included angle of a molded component when it cools from processing temperature to operating temperature. The main cause of this phenomenon is the anisotropy of the thermal properties of fiber-reinforced composites. The thermal out-of-plane expansion coefficient (radial) is significantly higher than in the in-plane direction (tangential). This situation arises because the carbon fibers have an extremely low (close to zero) coefficient of thermal expansion (CTE) in the fiber direction, while the matrix has a comparatively much higher CTE. This causes the material to contract more in the thickness direction than in the fiber direction, causing the two curved sides to move closer together due to the greater contraction in the thickness direction, thus increasing the sector angle, which leads to a reduction in the enclosed angle [1,2,3,4]. Studies have shown that partially crystalline thermoplastic matrices undergo anisotropic thermophysical phase-change shrinkage during crystallization, which promotes the spring-forward effect; additionally, in semi-crystalline thermoplastics, the glass transition temperature may be crossed during cooling, leading to a pronounced change in the coefficient of thermal expansion [6,7]. In addition to material anisotropy, other mechanisms also contribute to this phenomenon. For example, the complexity of the component also plays a significant role. In complex geometries, such as a "top hat" component, the inherent boundary conditions lead to stress build-up and additional warping, such as the dishing effect and curving of the flat base [3,6]. Furthermore, during thermoforming, the wrinkling of the fiber bundles in the bending area can contribute to a reduction in the end angle, especially if the pressure leads to axial compression of the fibers [1,2,8]. In addition, thickness reductions due to transverse matrix flow or resin percolation can also influence the end angle and depend on the laminate structure [1].

Spring-Back-Effect.

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The spring-back effect (also known as spring-backward) in thermoforming CFRTPs describes the increase in angle in a curved component after cooling from the processing temperature to the usage temperature [2, 4, 9]. In general, the spring-back effect occurs less frequently in the thermoforming of CFRTPs than the spring-in effect described above, as the deformations resulting from thermal anisotropy often predominate [9]. Typically, the effect is observed primarily in fabric-reinforced laminates compared to unidirectional tapes, which often exhibit spring-in [2,4]. One of the main causes is residual mechanical stress in the laminate. When the laminate is formed, elastic energy is stored in the fibers, which causes the component to spring-back to its original shape after it is removed from the tool [2]. The effect is also enhanced by the residual yield strength present even at high temperatures, which leads to elastic recovery of the material [8, 9]. Spring-back can also occur as recovery after initial spring-in. The viscoelastic recovery of the matrix over a long period of time (up to three years) causes molecular rearrangement, which in turn leads to the release of residual stresses [12].

Methodology

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

To provide computer-aided support and optimization for the CFRTP manufacturing process chain described above, a methodology was developed in ANSYS LS-DYNA ® that simulates the entire thermoforming process, from tape-laying to final forming. The simulation model consists of three
main components: the preform, the preform holder system, and the tooling. These components were developed modularly to ensure a high degree of flexibility, allowing, for example, different tool cavities or preforms with varying properties and geometries to be easily interchanged within the model. The process chain is divided into five steps (two model generation steps and three simulation phases), each representing a different stage of the process supporting real-world operations. A complete overview of the simulated process chain is shown in Fig. 1.

[picture]

Fig. 1. Flowchart of the simulated process chain, where the first two steps correspond to preform generation and the remaining three steps represent the actual simulation phases.

Fig. 1. Flowchart of the simulated process chain, where the first two steps correspond to preform generation and the remaining three steps represent the actual simulation phases.

Reverse Thermoforming Simulation.

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The first step in the simulation process chain does not correspond to an actual manufacturing operation but serves to support the planning of preform production using the ATP/ATL method. This helps minimize costly and time-consuming trial-and-error procedures required to generate a geometry suitable for later manufacturing via ATP/ATL. LS-DYNA® includes a feature that allows simple profiles to be converted into a flat component through a simplified reverse forming simulation, which still preserves the outer contour of the original part. This reverse forming simulation requires minimal input data. A 3D model of the component, in a common CAD format such as ".STEP," is loaded into LS-PrePost as the input file. An automated meshing tool is then used to generate a shell mesh on the outer surface, and the material behavior can be assigned from a predefined selection of material data. With minimal computational effort and processing time, the software converts the 3D part shape into a flattened preform mesh geometry (see Fig. 1 I.). The resulting boundary of the mesh can then be converted into a geometric format such as ".IGES", which is then used as input for programming the tape-laying machine.

Preform Generation.

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To capture the complex deformation behavior of CFRTPs during thermoforming, a semi-discrete solid mechanics approach based on the unit cell concept of Duhovic and Schommer [13] is used to model the preform (see Fig. 2). Instead of representing an incremental section with a single element type, the deformation behavior is modeled through a combination of interacting elements within the so-called unit cell. Beam, shell, and solid elements are employed for this purpose. Beam elements capture fiber orientation and define the bending stiffness of each layer, while solid elements define shear stiffness. Shell elements, also referred to as "null elements", do not possess any mechanical properties but serve to establish thermal contact between the beam and solid elements. Each ply of the laminate is modeled individually using this three-element approach, with individual plies connected to one another via sliding contact conditions. *MAT_ELASTIC_PLASTIC_THERMAL and *MAT_THERMO_ELASTO_VISCO _PLASTIC_CREEP are applied to the beam and solid elements, respectively. The former assigns temperature-dependent values for stiffness, Poisson's ratio, thermal expansion coefficient, yield stress, and tangent modulus to the beam elements representing the fiber behavior. The latter enables the definition of temperature-dependent stressstrain curves and a temperature-dependent thermal expansion coefficient assigned to the solid elements representing the polymer behavior. Additionally, an averaged, temperature-independent, Coulomb-based contact friction is applied between the laminate plies during the thermoforming phase, which is then locked during the subsequent holding and cooling phases (Figure 1 IV and V). The same constitutive models are applied throughout all simulation phases. Therefore, the abovementioned material properties must be available over a broad temperature range, from the forming process down to room temperature.

[picture]

Fig. 2. Preform generated in LS-PrePost and the corresponding unit cell concept.

Fig. 2. Preform generated in LS-PrePost and the corresponding unit cell concept.

As a result, forming induced fiber stresses are included in the shape-distortion predictions. The required material model parameters can be obtained from material property data sheets and the characterization tests shown in Figure 3.
Since generating the preform mesh is labor-intensive, an automated meshing technique has been developed. A JSON file from the multiaxial tape-laying machine, which contains the exact planned placement paths of the preform tapes, is used by a Python script to generate macros that are later imported into LS-PrePost® to construct the mesh along the correct paths, following the unit cell modeling approach described above. The beam elements are precisely aligned with the tape-laying
direction, corresponding to the fiber orientation. Solid elements are generated along the placement paths and across the tape width, with adjustable element sizes to allow increased mesh resolution and simulation accuracy - albeit at the cost of longer computation times. Null elements are defined per layer based on the nodal points generated by the beam elements. The complete preform mesh is then assembled layer by layer according to this principle. A preform created using this method is shown in Fig 2. Once generated, the mesh can be trimmed to the desired final contour using the specified geometry data (see Fig. 1 II). Contact conditions within each unit cell, as well as between individual layers, are automatically established by the script. After all model components including the preform, the preform holder system and the tooling are assembled in 3D space, process parameters can be defined using the appropriate keywords and boundary conditions.

Material Characterization.

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The forming and draping behavior of the preform is defined using standard material models already available within LS-DYNA ®. For this purpose, the bending and shear behavior over the relevant processing temperature range was experimentally characterized.

[picture]

Fig. 3. Processing temperature material characterization using three-point bending and shear frame test.

Fig. 3. Processing temperature material characterization using three-point bending and shear frame test.

The characterization data presented in Fig. 3 were obtained for the high-performance carbon-fiberreinforced thermoplastic polymer LM PAEK (TC1225) from Toray. Temperature-dependent threepoint bending and shear-frame tests were conducted-typically at a minimum of three temperatures within the recommended forming range, with at least five repetitions at each temperature-to determine the corresponding stiffness values. These experiments were then reproduced numerically, and the bending and shear stiffness parameters were iteratively calibrated until good agreement with the experimental results was achieved. Additional preform material properties, including the temperature-dependent coefficient of thermal expansion (CTE), thermal conductivity, and heat capacity, were taken from the material data sheets.

Forming Simulation.

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This step represents the first of three stages of the thermoforming process. Initially, a structured master model is generated, consisting of three primary components: the tool cavity, the preform holder, and the preform described in the preceding simulation step. The modular design of the overall model enables the straightforward exchange of different tools and preforms, as well as the efficient adjustment of process parameters with minimal modeling effort. The tool is represented solely by the tool cavities using a shell mesh and is assumed to behave as a rigid body. The preform is positioned centrally between the upper and lower tool and is accurately aligned within the plane. In accordance with the real manufacturing setup, positioning is achieved using aluminum strips and holding springs/wires. The aluminum strips are also modeled using shell elements and are connected to the preform via tied contact definitions on the preform side. At their opposite ends, the springs/wires are represented by appropriate boundary conditions, which are fixed either in space or to a corresponding frame. The initial state of the simulation corresponds to a preform that has already been heated above the glass transition temperature and positioned correctly within the open tool. Accordingly, both the preform and the tool are assigned initial temperatures reflecting the actual thermal conditions at this stage of the process. In this model, the temperature distribution within the tool is assumed to be homogeneous and remains constant throughout the simulation. However, non-uniform steady-state temperature distributions can also be prescribed and simulated. Upon initiation of the simulation, the tool begins to close and presses the preform into the tool cavity. The closing movement can be controlled either by a prescribed motion, defined by a target gap width, or by a force-controlled approach until a specified maximum forming force is reached. In both cases, the motion is governed by a smooth curve in time. From the onset of the simulation, the preform cools via free convection to the surrounding air, which is defined through appropriate thermal boundary conditions. Once contact between the tool and the preform is established, contact definitions prevent element penetration and simultaneously enable heat transfer between the interacting bodies, thereby replacing the free convection boundary condition. As the tool components are modeled as rigid bodies, these interactions result in the preform conforming to the cavity geometry while gradually cooling toward the tool temperature. Fig. 1 III illustrates the forming process, showing how the preheated preform is pressed into the cavity during tool closure. Once the tool is fully closed, the termination criterion for this simulation step is reached, thereby completing the first stage of the thermoforming simulation. Dividing the thermoforming simulation into discrete phases provides significant advantages. A restart capability allows the simulation to be resumed at any completed stage, facilitating efficient parameter studies. Furthermore, this approach enables the modification of all time- or temperature-dependent parameters individually within each simulation step.

Holding Time/Cooling Simulation.

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In this simulation step, the holding phase is modeled, during which the tool remains closed either at a constant press force or at a constant gap, depending on the control strategy. During this phase, the preform gradually cools to the tool temperature. At present, no explicit crystallization kinetics are included; instead, the effects of crystallization on shrinkage and distortion are captured through the temperature-dependent, "crystallinity-adjusted" thermal expansion coefficient. More detailed models-such as Avrami, or Nakamura-type formulations-can be incorporated in future enhancements to account for the time- and temperature-dependent evolution of crystallinity and its influence on mechanical behavior. Care will be taken however to avoid excessive increases in simulation time, with the most computationally efficient models being tested first.

Spring-Angle Simulation.

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In this simulation step, the tool is reopened after the prescribed holding time has elapsed. This is achieved by modifying the existing time-dependent smooth control curves in the restart file so that the two tool cavities return to their initial open positions. Once contact between the tool and the preform is fully released, the preform is again exposed to free convection with the surrounding air and continues to cool until it reaches ambient temperature. To prevent movement of the preform upon
removal from the tool, fixation boundary conditions are applied to selected nodes of the preform. These constraints restrict specific translational degrees of freedom while still allowing the component to deform freely. Through their connection to the remaining nodes, the three nodes with the minimum required translational constraints ensure that the preform maintains its central position within the tool. When selecting these nodes, only regions that experience minimal deformation during forming are considered. Nodes located in areas with radii or sharp edges are deliberately avoided to minimize their influence on the subsequent spring-in or spring-back behavior. Upon tool opening, the residual stresses accumulated within the preform become effective and induce deformation of the component, depending on their magnitude. This enables the spring-in and spring-back phenomena described previously to be captured within the simulation. The simulation results are evaluated using the postprocessing tools provided by the LS-PrePost® software. For example, temperature and stress distributions can be visualized over time using iso-contours. In addition, angular changes -particularly at radii or inclined sections of the component - can be quantified as a function of time or position.

[picture]

Fig. 4. Angular evolution of a thermoformed V-profile at several locations along the component length.

Fig. 4. Angular evolution of a thermoformed V-profile at several locations along the component length.

Fig. 4 illustrates the angular evolution of a thermoformed V-profile at several locations along the component length. The nominal enclosed angle is 90∘. Throughout the simulation, the individual phases of the thermoforming process can be clearly distinguished. Starting from an initially flat preform ( 180∘ ), the angles decrease during tool closure as a result of forming, reaching the target angle of 90∘ once the closing operation is completed. After the holding time and during tool opening, deviations from the nominal angle occur at the measurement locations due to residual stresses within the preform. In some cases, pronounced angular differences between individual measurement positions along the component length can be observed possibly resulting from the preform holding positions. Following partial stress relaxation through material deformation, a residual angular deviation remains relatively constant, the magnitude and direction of which depend on the specific application. Depending on whether the angle increases or decreases relative to the nominal value, the behavior is referred to as spring-back or spring-in, respectively.

Summary and Outlook

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Using this modeling approach, the entire process chain - from preform manufacturing to thermoforming - can be simulated, providing systematic support for each individual process step. This enables substantial reductions in both time and cost during the planning and manufacturing of CFRTP components. In particular, preform generation can be efficiently supported by a simplified reverse thermoforming simulation, in which the target component geometry is used to derive a planar preform configuration. The thermoforming simulation itself provides early insight into the draping behavior and potential wrinkle/folding defect formation during the initial stages of forming. This allows corrective measures, such as preform post-processing through trimming operations, to be planned and implemented at an early stage. Following completion of the thermoforming simulation, the model enables prediction of component deformation caused by residual stresses introduced during forming. Based on these results, the press tool geometry can be adjusted to compensate for the simulated spring-in or spring-back effects.
A key advantage of this modeling approach is its high degree of flexibility and adaptability to a wide range of component geometries and process conditions. The modular structure of the overall model, combined with the unit-cell-based preform modeling strategy, enables flexible generation and exchange of preforms with arbitrary layup configurations, as well as efficient substitution of tool cavities and clamping frame concepts. The level of model complexity can be increased progressively as required. Fig. 5 illustrates several application cases to which the simulation methodology has already been successfully applied. These include simple geometries such as V-profiles, components of increased complexity such as profiles with closed edges, and highly complex double curvature geometries, for example S-shaped profiles combined with advanced clamping frame concepts. The primary limiting factors are the component geometry itself, which - analogous to real manufacturing conditions - must remain feasible to produce. In addition, increasing model size and complexity lead to a substantial rise in computational cost. As shown in Fig. 5, even relatively simple geometries currently require several days of computation on high-performance computing systems. Using a single computing node equipped with 32 AMD EPYC 9135 processors and the MPP (Massively Parallel Processing) version of the LS-DYNA solver, approximately 110 hours ( 4.5 days) are required to complete the entire simulation process chain for an axisymmetric v-shaped profile. This is despite the application of a thermal and gravity speed-up factor of 100, introduced specifically to reduce overall simulation times. Increasing this factor further leads to undesirable thermal and mechanical inertial effects and necessitates a reduction of the thermal and mechanical time steps, thereby eliminating any additional computational speed-up. In the most complex example shown in Figure 5, 24% of the total computational time is devoted to the thermoforming simulation phase, 44% to the holding phase, and the remaining 32% to the springback simulation phase. This distribution of computational effort among the different phases of the simulation remains largely consistent, irrespective of the specific part geometry. With further increases in model size and complexity, computation times may even extend to several weeks. However using several HPC cluster nodes (e.g. 512 or 1024 CPUs) can help decrease the computation time back to hours. Furthermore, the models enable unprecedented levels of detail and individual ply-level information.
In future work, additional process steps, such as overmolding and co-consolidation, may be incorporated into the simulations as subsequent stages within a single, unified simulation environment. This framework represents the complete process chain described above for the manufacturing of CFRTP components and is capable of predicting distortions arising throughout the entire thermoforming process.Owing to its high degree of adaptability, it can simulate a wide range of component geometries, providing effective support for both component development and
manufacturing process design. The simulation methodology will be validated by comparing predicted distortions with 3D scan measurements of the manufactured parts and their target CAD geometries.

[picture]

Fig. 5. Indication of model sizes and resulting simulation times (using 32 CPUs and MPP LSDYNA mathematical formula solver) for composite part geometries of various complexity.

Fig. 5. Indication of model sizes and resulting simulation times (using 32 CPUs and MPP LSDYNA solver) for composite part geometries of various complexity.

Acknowledgement

The original version of this paper is available on https://www.scientific.net/MSF.1182.135.pdf

The authors gratefully acknowledge the collaboration and R&D support provided by Aerospace Industrial Development Corporation (AIDC), Taiwan, in the development of the simulation technologies presented in this work. This work is also supported by the project ZEUS-Zero Emission Aircraft with Sustainable Fuselage Concept and Technology, funded by the Federal Ministry for Economic Affairs and Climate Action, following a decision of the German Bundestag (funding reference 20W2106F).

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Keywords Index

#

3D Scanning Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

A

Adhesion Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Aligned Discontinuous Fibres Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

B

Bending The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

C

Cold Spray Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Compensated Mould Design Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Composites Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes; Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part; Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints; Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

Consolidation Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

D

Defect Mitigation Fabric Patching: A Simple Approach to Mitigate Defects

Digital Process Chain A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Digital Twin Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

E

Embedded Element Approach Fabric Patching: A Simple Approach to Mitigate Defects

F

Finite Element Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

Finite Element Analysis (fea) Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

Flax Woven Fabrics Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Forming Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

Forming Of Dry Preforms Fabric Patching: A Simple Approach to Mitigate Defects

Forming Simulation The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics; Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Forming-induced Defect Prediction Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

H

Haralick Features Extraction And Prediction Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

I

In-plane Shear Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

In-process Measurement Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

Intimate Contact Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

L

Liquid Composite Molding; Unsaturated Flow; Capillary Effects; Process Simulation Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

Liquid Resin Infusion (lri) Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

M

Machine Learning Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

Monte Carlo Cross-validation Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

N

Non-crimp Fabric The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

P

Particle-filled Resins Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

Process Induced Deformations Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Process Simulation Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling; A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

R

Residual Stress Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

S

Simulation Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

Spring-angle Prediction A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Spring-in Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Squeeze Flow Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

T

Thermoforming Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part; A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Thermoplastic Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part; Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Thermoplastic Composites Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

U

Unsymmetric Laminates Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

V

Validation Techniques Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

Vitrimer Flow Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Vitrimer Matrix Composites Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

W

Warpage Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Welding Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Authors Index

A

Abdin, Y. Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Akkerman, R. Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Astarita, A. Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Azoti, W. Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

B

Bailleul, J. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Batouei, M. Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Belnoue, J. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions; Fabric Patching: A Simple Approach to Mitigate Defects

Bertevas, E. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Boubaker, M. Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

C

Cantarel, A. Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

Carlone, P. Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

Castanié, B. Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Chen, S. Fabric Patching: A Simple Approach to Mitigate Defects

Corre, S. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Coupé, M. Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

D

Debenest, G. Numerical Simulation of Liquid Resin Impregnation in a Real Digitized Reinforcement during Liquid Composites Molding Processes

Delsol, E. Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Duhovic, M. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

E

Esperto, V. Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

F

Feng, Y. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

G

Gongati, M. Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Guinoiseau, A. Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

H

Hallett, S. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Hamerton, I. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Handl, L. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Hoffmann, T. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

I

Ivanov, D. Fabric Patching: A Simple Approach to Mitigate Defects

K

Kim, B. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Klompen, E. Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Kärger, L. Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling; The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

L

Levy, A. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

M

Margoto, O. Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Martone, A. Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Milani, A. Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Mitsch, J. Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling; The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

Mtibaa, M. Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

Müller, M. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

N

Neumeyer, T. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

O

Olivier, P. Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

P

Palmieri, B. Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

Perna, A. Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

R

Ratsifandrihana, L. Process-Induced Deformations on Composite L-Shaped Part: Numerical Prediction and Compensated Mould Design

Rondina, F. Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Rubino, F. Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes

S

Schlimbach, J. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Schommer, D. A Unified Simulation Environment for Thermoforming and Distortion Prediction of CFRTP Aircraft Components

Schäfer, B. The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

Serra, J. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

Sherwood, J. Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

Siddig, N. Simulation and Experimental Investigation of the LRI Process for Particle-Filled Resins in Aerostructure Applications

T

Tucci, F. Microwave Resin Preheating Integrated with AI-Based Flow Front Monitoring for Liquid Composite Molding Processes; Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

V

Villing, L. The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

Viscusi, A. Numerical Approach to the Simulation of Vitrimer Matrix Composites Manufacturing by Infusion and Coating by Cold Spray

W

Wank, J. Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling; The Influence of Side-Dependent and Nonlinear Bending Behavior in Forming Simulation of Non-Crimp Fabrics

Warnet, L. Prediction of Residual Stress in Carbon Fiber Reinforced LM- PAEK Composites

Waroquier, P. Numerical Modelling of Intimate Contact for Thermoplastic Composite Joints

White, K. Application of a Discrete Finite Element Modeling Approach to Form a Near-Uniform Thickness Compound Curvature Composite Part

Würth, T. Validation of Thermoforming Simulation Models Prior to Parameterization Using Covariance-Based Input-Output Statistics Assessing the Role of Thermomechanical Material Modeling

Y

Yang, V. Machine Learning-Based Prediction of Forming-Induced Defects in Flax Woven Fabrics Using 3D Scanning and Haralick Texture Features

Yavuz, B. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions

Yuan, H. Numerical Investigation of the In-Plane Shear Behaviour of Aligned Discontinuous Fibre Composites under Processing Conditions