# Finite element modeling of buckle defects formation during RTM preforming of dry woven reinforcements

Zakariae El-Alami, Audrey Hivet, Gilles Hivet

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## To cite this version:

Zakariae El-Alami, Audrey Hivet, Gilles Hivet. Finite element modeling of buckle defects formation during RTM preforming of dry woven reinforcements. Material Forming - ESAFORM, May 2025, Paestum, Italy. pp.458-467, 10.21741/9781644903599-50. hal-05244171

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Submitted on 8 Sep 2025

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# Finite Element Modeling of Buckle Defects Formation During RTM Preforming of Dry Woven Reinforcements

EL-ALAMI Zakariae¹,ª*, HIVET Audrey¹,ᵇ and HIVET Gilles ¹,ᶜ

¹Univ. Orléans, Univ. Tours, INSA-CVL, LaMé (EA 7494), 28000 Chartres, France

azakariae.el-alami@univ-orleans.fr, baudrey.hivet@univ-orleans.fr, cgilles.hivet@univ-orleans.fr

**Keywords:** Buckle defects formation, dry woven reinforcements, RTM, Finite Element Modeling.

**Abstract.** Mesoscopic defects, such as buckles and yarn sliding, arise in dry woven reinforcements during the preforming step of processes like the Resin Transfer Molding process. To study these defects, the LaMé laboratory developed an experimental device based on the Pullout test, which replicates the conditions leading to defect formation but does not fully explain the underlying mechanics. To address this, a Finite Element Model (FEM) is proposed to complement experimental data by providing detailed insights into stress, strain, and friction. While the model offers preliminary predictions of buckle defects, a full identification of the remaining parameters, including friction and those related to the fixed jaws, is essential for accurate parametric studies on their formation.

**Introduction**

Woven reinforcements exhibit multi-scaled properties, allowing their study on three distinct levels: macroscopic, microscopic, and mesoscopic (see Fig. 1). At the macroscopic scale, these reinforcements are modeled as uniform materials, offering simplicity in modeling but omitting finer structural details. The microscopic scale zooms into individual fibers and their complex interactions, providing a high level of detail. The mesoscopic scale focuses on the analysis of yarns, or bundles of fibers, representing them as homogeneous materials that reflect the collective behavior of fiber assemblies. This scale bridges global results, such as the deformed state of the woven reinforcements, with local results, such as yarn strains and variations in their cross-sectional shapes.

<figure><img src="image_3.png" /><figcaption>**Fig. 1:** The three characteristic scales of the studied glass-fiber woven reinforcements.</figcaption></figure>

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
The preforming of dry woven reinforcements, which is the initial step in shaping processes such as RTM (Resin Transfer Molding), can lead to the formation of defects. These defects are distinguished by their scale of observation: wrinkles are macroscopic defects visible at the level of woven reinforcements, while buckle and yarn sliding defects (see Fig. 2), identified as mesoscopic, are noticeable at the yarn scale.

The mesoscopic defects include the formation of buckle defects, where yarns bend in-plane, creating curves. At the peak of these curves, out-of-plane deformations occur to accommodate the excess length between the inside and outside of the yarn [1]. Another defect is yarn sliding, which results from a loss of cohesion within the woven reinforcements due to sliding between the yarns, which leads to a localized deficit of material [2,3].

<figure><img src="image_5.png" /><figcaption>**Fig. 2:** The two types of mesoscopic defects observed in glass-fiber woven reinforcements.</figcaption></figure>

## Experimental setup

To reproduce mesoscopic defects in a laboratory setting, an experimental device called Pull-out [4] was developed to generate these defects under RTM-like conditions and allows for the analysis of their behavior and potential interdependence between them [4,5]. This device uses a square sample held on three edges with fixed jaws applying a controlled pressure, similar to a blank holder's role in RTM forming process (as indicated in Fig. 3).

<figure><img src="image_6.png" /><figcaption>**Fig. 3:** Pull-out test bench developed by LaMé laboratory.</figcaption></figure>
In the Pull-out Test, we pull on several yarns to induce changes in internal cohesion of the woven reinforcements. This pull results in transverse yarns adhering and sticking to the extraction of longitudinal yarns, leading to the shearing of the woven reinforcements. This shearing generates transverse tensile forces causing the transverse yarns to bend in-plane until they reach a maximum shear angle. At this point, the transverse yarns become locked in their in-plane curvature and begin transitioning to out-of-plane curvature, which corresponds to Buckle defects (see Fig. 4).

<figure><img src="image_7.png" /><figcaption>**Fig. 4:** Illustration of buckle defect formation during the Pull-out test.</figcaption></figure>

As the cohesion governed by weaving and friction between transverse and longitudinal yarns becomes insufficient to support the in-plane bending of transverse yarns, these yarns start sliding relative to the longitudinal yarns being pulled out. This behavior leads to decohesion within the woven structure and the occurrence of yarn sliding defects. Interestingly, the occurrence of premature yarn sliding defects prevents buckle defects from forming, revealing a possible interdependence between these two types of mesoscopic defects [4,5].

By comparing the behavior of yarns in the Pull-out Test to their behavior in defect zones during a forming test, which uses a complex pyramid-shaped punch with double curvature designed to ensure defect formation [6,7] (see Fig. 5), demonstrates that the Pull-out Test effectively replicates the conditions responsible for mesoscopic defect formation.

The Pull-out test provides valuable insights into the kinematics of the woven reinforcements as mesoscopic defects form, through images taken during the test. Additionally, it offers information on the cohesion and resistance of the woven reinforcements to yarn extraction, by analyzing the force-displacement curve of the pulled-out yarns. This test is particularly advantageous because it allows for the control of key variables, such as:

* the extraction speed,

* the pressure applied by the fixed jaws on the sample,

* the number of the pulled-out yarns.

This control enables the isolation of each parameter to assess its impact on mesoscopic defect formation.

The current study focuses on buckle defects, as they emerge early and may influence the development of yarn sliding defects. Experiments address two key questions: where and when these defects manifest during the Pull-out test (see Fig. 6). Findings confirm that buckle defects typically form in the center of the transverse yarns, away from the edges, and reach their peak
amplitude simultaneously with the peak force on the force-displacement curve of the pulled-out yarns [4,5].

<figure><img src="image_8.png" /><figcaption>**Fig. 5:** Comparison of yarn behavior in the Pull-out test and forming test with double curvature punch. [6,7]</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6:** Localization and peak amplitude of buckle defects in transverse yarns during the Pull-out test.</figcaption></figure>

## Finite element modeling

While the Pull-out experimental test offers valuable insights into the kinematics of buckle defect formation, it does not fully capture the underlying physics that explains the interactions involved. A more complete understanding involves analyzing both the movements and the mechanics driving their appearance. To achieve this, a Finite Element Model of the pull-out test will be developed and validated against experimental results, offering in-depth details of strain distribution, stress fields, and frictional interactions that experiments alone cannot provide.

Selection of Explicit Procedures over Implicit Methods. The preforming of woven reinforcements and the Pull-out test are quasi-static processes that can be effectively modeled using either implicit or explicit finite element methods [8]. Although the implicit method is generally preferred for such processes, it becomes computationally expensive when the model involves significant material and geometric nonlinearities, and frequent changes in contact conditions. For instance, a plate undergoing in-plane bending will shift to out-of-plane bending once a critical flexure threshold is surpassed. The explicit method allows for modeling this transition, whereas the implicit method
remains limited to in-plane bending without capturing the out-of-plane shift (as demonstrated in Fig. 7).

<figure><img src="image_10.png" /><figcaption>**Fig. 7:** Comparison of explicit and implicit methods in modeling the transition from in-plane to out-of-plane bending of a plate.</figcaption></figure>

**Yarn Material Behavior.** Yarns exhibit significantly higher rigidity along their longitudinal direction compared to other directions, with their transverse behavior often assumed to be isotropic. (see Fig. 8-b) [9]. This significantly higher rigidity along their longitudinal direction requires precise tracking of the longitudinal direction to avoid accumulating errors in stress updates, especially during finite strain scenarios like fabric shearing, where preserving good material directions is crucial for accurate numerical simulations [10].

Consequently, a transversely isotropic elastic model implemented in a VUMAT subroutine is employed, treating the yarn as a homogeneous equivalent solid material. This approach utilizes hypo-elastic constitutive modeling under finite strain, incorporating an objective stress rate that consistently aligns with the yarn's waviness throughout the simulation [11,12].

The necessity of using this objective stress rate arises from the limitations of the Green-Naghdi and Jaumann frames available in Abaqus, which fail to preserve accurate material directions for materials with highly oriented orthotropic behavior, such as yarns [13].

<figure><img src="image_11.png" /><figcaption>**Fig. 8:** a- Tracking the direction of longitudinal rigidity along the yarn's undulations. b- The planes within the yarn that display isotropic behavior.</figcaption></figure>
Geometry Modeling, Contact and Meshing. The geometry of the woven reinforcements used in this model is generated using GEOFAB [14], an internal software developed in the LaMé laboratory, ensuring that their experimental dimensions match perfectly and that contact surfaces are carefully defined without overlaps or interpenetrations between the yarns.

The model is meshed using standard 3D solid finite elements with reduced integration, assigning two elements across the yarn's thickness (see Fig. 9). Because the yarns being studied are wavy and their midline follows an undulating path, Abaqus's standard mesh element orientation does not allow for a tangent reference frame to be defined along these undulations. Instead, it assigns a constant reference frame that moves in a straight-line translation between elements without adapting to the wave pattern (see Fig. 8-a). To resolve this, GEOFAB was employed to create a mesh with element orientations adapted to the yarn's undulations.

<figure><img src="image_12.png" /><figcaption>Fig. 9: a- Geometry of the analyzed woven reinforcement meshed in Abaqus. b- Close-up view of the overlap-free contact surfaces.</figcaption></figure>

To reduce computational time, a general contact strategy was adopted instead of contact pairs. The properties assigned include a "hard" pressure-overclosure model, which allows no contact pressure until nodes come into contact and then applies pressure once contact is established, paired with an isotropic Coulomb friction model with equal static and dynamic coefficients.

Rig Simplifications. Instead of fully modeling the fixed jaws, which would be computationally expensive, their roles are analyzed and simplified in the analysis (see Fig. 10). The longitudinal jaw and the two transverse jaws serve distinct purposes: the longitudinal jaw applies minimal pressure, sufficient only to keep the yarns straight and prevent gravity-induced bending, while the transverse jaws exert more significant pressure.

In the simulation, the longitudinal jaw's role is modeled by constraining all movements except along the extraction axis for the pulled-out yarns, complemented with a light tension force derived from the tangential forces resulting from the longitudinal jaw's pressure.

The two transverse jaws apply balanced, relatively higher pressure, and the friction they generate with the woven reinforcements enables the transverse yarns to resist the tangential forces induced by the applied pressure. This resistance occurs during in-plane bending and continues as the transverse yarns transition to out-of-plane bending. To model this behavior, the two transverse jaws were simplified as springs. These springs initially prevent displacement below a specific force threshold, representing the static friction phase. Beyond this threshold, controlled displacement occurs with a defined stiffness (k), simulating the dynamic friction phase.
<figure><img src="image_13.png" /><figcaption>Fig. 10: Simplification of the jaws used in the Pull-out test bench.</figcaption></figure>

## Results and discussion

The finite element model incorporates several input parameters, including the geometric configuration of the woven reinforcements; the material properties defining the stiffness tensor in the hypo-elastic constitutive law; the friction coefficient between yarns; the threshold force and the stiffness of the springs representing the effect of the fixed transverse jaws on an individual yarn. Additionally, the tension applied to the extracted yarns is crucial, as it replicates the influence of the longitudinal jaw during the pull-out test.

The primary objective is to construct a model that can provide insightful preliminary findings on buckle defect formation. At this stage, the geometric configuration and the material parameters identified for the glass fibers yarns in Hivet's work [10] are available. However, the friction between the yarns still needs to be characterized, as well as the parameters associated with the simplified fixed jaws. These fixed jaw parameters are under identification by measuring the reaction force generated when a yarn is extracted from fiberglass woven reinforcements under fixed jaw pressure. This reaction force should be reflected in the behavior of the springs attached to the yarns. In the meantime, a friction coefficient of 0.3 is used, along with a tension of 5 N applied on the side of the longitudinal jaw, a threshold function for the springs set to 0.07 N, and a stiffness of 0.9 N/mm.

An indicative comparison of simulation and experimental force-displacement curves during the pull-out of five yarns is presented in Fig. 11, providing an order-of-magnitude estimate of the simulation force relative to experiment. The simulation confirms buckle defects appearing at the expected location, in the center of the sample, and at the predicted timing, aligning with the peak in the force-displacement curve of the pulled-out yarns. Currently, the simulation curve shows lower cohesion compared to the experimental curve. Ideally, high cohesion should be indicated by a higher maximum force at a smaller displacement, as the maximum force typically appears at the start of the curve, which is not yet fully reflected in the simulation.

The deformed state observed at the maximum pull-out force of five yarns from fiberglass woven reinforcements is compared between simulation and experimental results, as illustrated in Fig. 12. A visual inspection reveals noticeable similarities in overall deformation and average shear angles during buckle defect formation. Although the simulation currently uses approximated parameters for the fixed jaws and friction coefficient, the promising findings indicate that the simplified finite element model is progressing toward becoming a valuable tool for studying buckle defect formation.
<figure><img src="image_14.png" /><figcaption>**Fig. 11:** a- Experimental force-displacement curve for the Pull-out test of five yarns. b- Finite element analysis result at 4mm displacement of the pulled-out yarns. c- Finite element analysis result at the peak force on the force-displacement curve of the pulled-out yarns.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 12:** Preliminary comparison of the deformed state of fiberglass woven reinforcements at the peak of the force-displacement curve for five pulled-out yarns: experimental (a) vs. simulation (b).</figcaption></figure>

**Summary**

This research focused exclusively on buckle defects, as they emerge early and may influence the evolution of yarn sliding defects. Although the finite element model effectively simulates the appearance of buckle defects in terms of their location and timing, it predicts lower cohesion in the force-displacement curve compared to experimental data. While the comparison with experimental findings remains preliminary until the finite element model's parameters are fully identified, once calibrated, the model will subsequently be used in parametric studies. These studies will evaluate the impact of variations in the number of pulled-out yarns, the pressure applied to the fixed jaws, the geometric configuration of the woven reinforcements, and the fiber type on buckle defect formation.

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