Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2024.48.0056 Acta Polytechnica CTU Proceedings 48:56–60, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague CHARACTERIZATION OF WOVEN COMPOSITE MATERIAL UNDER MULTIAXIAL LOADING REGIMES USING FE-BASED STEREOCORRELATION Andrija Zaplatića,b, Zvonimir Tomičevića,∗, François Hildb a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 10002 Zagreb, Croatia b Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS – Laboratoire de Mécanique Paris-Saclay, 91190 Gif-sur-Yvette, France ∗ corresponding author: zvonimir.tomicevic@fsb.unizg.hr Abstract. In this paper, woven glass fiber composite samples were subjected to three different cyclic loading histories (i.e., tensile, shear and combined loading at 45° via the Modified Arcan Fixture. During the experiments, the samples were monitored by a stereovision system. Finite Element based stereocorrelation was used to measure the displacement and strain fields. The analysis of the experiments revealed different damage mechanisms. Furthermore, for the 45° experiment, the highest strain levels were reached, whereas for the tensile test, the highest stress levels were achieved. Keywords: Stereocorrelation, woven composite, Arcan fixture, multiaxial loading. 1. Introduction The mechanical characterization of various materials is essential for designing and optimizing engineering com- ponents. In modern engineering, traditional materials like steel and alloys are increasingly being replaced by fiber-reinforced polymer (FRP) composites [1]. These composites are highly sought after for their excellent strength-to-weight ratio. An additional advantage of FRPs is their customizable architecture, which can be tailored to meet specific workload conditions. How- ever, predicting the ultimate failure and degradation of these components remains challenging due to their complex architecture. Predicting their lifetime is also challenging due to their heterogeneity, which makes composites susceptible to various damage mechanisms that may degrade their stability [2]. Therefore, ex- tensive experimental investigations are necessary to study the composite behavior under different loading regimes [3]. Since uniaxial mechanical tests do not ad- equately simulate real-world conditions, more complex loading configurations are required. However, these tests often demand high-cost and specialized testing machines, which may not be readily available. To address this issue, specially designed loading apparatuses for uniaxial testing machines have been developed. One popular setup is the Modified Ar- can Fixture (MAF) [4–6], which applies three distinct loading regimes (i.e., tensile, shear, and their varied combinations at several angles) to butterfly-shaped specimens. The MAF allows for testing a variety of materials, including wood [7] and composite joints [8], although it was originally designed for composite ma- terials [9]. Due to the complex geometry of the Arcan samples, which features two V-notches in the ligament area, classical contact measurement equipment is highly impractical. As a result, contactless optical measure- ment methods like Digital Image Correlation (DIC) are more suited [10, 11]. DIC utilizes visible light cam- eras to perform full-field measurements, and in recent years, the global DIC approach has gained popular- ity [12]. This approach incorporates Finite Element (FE) features in such a way that displacement mea- surements are performed on meshes. Consequently, the resulting outputs are nodal displacements, from which strain fields are determined. Additionally, this method provides correlation residuals, which highlight damaged areas during the experiment [13]. An added advantage of FE-based approaches is the continuity assumption of the displacement fields, eliminating the need for interpolation as required in local ap- proaches [14]. If out-of-plane motions are expected or a complex 3D sample is being tested, multiple cameras are em- ployed within a stereovision framework [15, 16]. The finite element method has also been integrated into stereocorrelation environments [17–19]. By utilizing the known FE geometry of the observed object, it is possible to perform camera calibration directly on the object itself [19, 20] and then measure 3D surface displacements. 2. Materials and methods In this section, the woven composite samples, exper- imental setup, and investigation are presented. Ad- ditionally, the FE-based stereocorrelation method is briefly introduced. 2.1. Material The investigated composite samples were manufac- tured by reinforcing a vinylester resin with woven glass fibers. The 3 mm thick samples were composed 56 https://doi.org/10.14311/APP.2024.48.0056 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 48/2024 FE-based stereocorrelation for woven composites (a) (b) (c) (d) Figure 1. Experimental setup. (a) Testing machine and optical system protected by black fabric. Loading configurations: (b) tension, (c) shear and (d) combined tension and shear at 45°. of 7 layers of woven fabric, where the yarns were 0°/90° oriented. Additionally, the fabric layers were stacked identically on top of each other. Due to the complex geometry of the samples and the use of glass fibers, conventional machining meth- ods were sub-optimal for processing the composite plates. Therefore, water jet technology was used to cut the samples from the composite plates. To ensure sample failure during the experiment, two additional V-notches were cut for each sample. These additional notches were 2 mm long and 0.5 mm wide, thereby re- ducing the net section area to approximately 48 mm2. 2.2. Experimental investigation The experimental setup (Figure 1a) consisted of the MAF and the optical system. The MAF allows for different loading conditions to be applied to the Arcan sample by rotating the fixture relative to the load- ing axis. In this research, three Arcan specimens were tested and three loading configurations were pre- scribed, namely tension (WF00) (Figure 1b), shear (WF90) (Figure 1c), and their combination at 45° (WF45) (Figure 1d). For each experiment, the sample was loaded at a velocity of 2µm s−1 in displacement control mode on the Messphysik Beta 50-5 uniax- ial testing machine, each experiment consisting of eight loading/unloading cycles. The testing speed was chosen according to previous research [13, 20]. The samples were intermittently taken out of the MAF to perform X-ray computed tomography scanning to obtain any micro-structural changes inside of the ma- terial. Therefore, cyclic loading regimes were defined. To minimize external lighting influences that could affect brightness and contrast conditions, the exper- imental and optical setups were covered with black fabric (Figure 1a). The optical system included two identical visible light cameras that monitored the sur- faces of the samples during the experiments. Further- more, two light sources were employed to illuminate the sample surface. 2.3. FE based stereocorrelation In this work, FE-based stereocorrelation [5, 21] was performed to measure 3D surface displacement fields using FE meshes [17–19], which correspond to the observed sample geometry. Additionally, strain fields were calculated from the measured displacement fields. Stereocorrelation consists of two main steps, namely, calibration and correlation. In the calibration step, the projection matrix [π] for each camera is deter- mined, allowing the FE mesh to be projected onto both camera images, defining the same Region of In- terest (ROI). The projection matrix [π] can be built if the intrinsic and extrinsic camera parameters are known. However, usually they are unknown and are determined with the calibration. The calibration can be defined as a least square minimization between the two camera images ρ2({P}) = ∑ ROI ∥f1 (x1) − f2(x2)∥2 , (1) where {P} is a vector that gathers all the sought intrinsic and extrinsic parameters, xc are the projected physical points defined over the FE mesh X xc = xc (X, [πc]) . (2) In the correlation step, the nodal-wise displacement field U(X, t) is measured for any given time-step t. The new cost function can be written as U(X, t) = arg min Nc∑ c=1 ∑ ROI (g̃c (xc, t) − fc (xc))2 , (3) 57 A. Zaplatić, Z. Tomičević, F. Hild Acta Polytechnica CTU Proceedings where fc are the respective camera reference images, g̃c the corrected deformed image at time t by the kinematic field U(X, t) for each respective camera and Nc is the camera number. The regularity of the kinematic field U(X, t) in space is ensured by using a set of spatial shape functions ψi(X) U(X, t) = DOF∑ i=1 ui(t)ψψψi(X), (4) where DOF is the number of degrees of freedom, ui(t) are the nodal displacements for the time t. In these analyses, the FE meshes consisted of three-noded elements (T3) [19]. Furthermore, the camera-wise gray level residuals ϕc can be computed for each physical point xc ϕc = g̃c (xc, t) − fc (xc) . (5) Both the calibration and correlation are performed by resorting to the iterative Gauss-Newton scheme. For more detailed information, the reader is referred to Zaplatić et al. [20], Chang et al. [16, 21]. 3. Results In this section, the stereocorrelation results are pre- sented for all three experiments. The major principal strain (Figure 2) and stereocorrelation residual (Fig- ure 3) fields are displayed for the maximum achieved stress level σmax for each experiment respectively (Ta- ble 1). From Table 1, it is concluded that the highest stress level was achieved for the tensile test (WF00), whereas the lowest was reached for the shear test (WF90). In Figure 2 the major principal strain fields are displayed for all three experiments for the maximum stress levels (Table 1). First, for the tensile test (Fig- ure 2a), two concentrated strained bands emanating from the notches are observed. Furthermore, four additional strain concentrations are distinguished on the peripheral areas of the sample. Since the yarns were parallel to the tensile load, the middle part was the most rigid part of the sample, whereas the periph- eral areas were not. Hence, they were more prone to damage. In the shear experiment (Figure 2b), a single strained band is visible in the gauge region, parallel to the loading direction. At the roots of the notches, the strain levels were the highest, whereas the top and bottom parts exhibited very small strain values. For the WF45 experiment, a single strained band developed between the V notches (Figure 2c), simi- larly to WF90 test. However, it was slightly inclined compared to the WF90 strained band. Two strain concentrations are visible at diagonal peripheral areas of the sample, depicted by the green circles. Using the stereocorrelation residuals, it is possi- ble to reveal if surface damage developed. For the tensile test (Figure 3a), three cracks formed around the root of the left notch. Four cracks also devel- oped in peripheral areas, which were also visible in (a) (b) (c) Figure 2. Major principal strain fields for (a) test WF00, (b) test WF90 and (c) test WF45 at the ul- timate stress. The blue squares depict the virtual gauges where the nodal strain values were extracted and averaged. The green circles highlight strain con- centrations outside of the virtual gauge. Experiment σmax WF00 300 MPa WF90 78 MPa WF45 178 MPa Table 1. Ultimate stress levels for each experiment. the corresponding strain field (Figure 2a). Several small horizontal cracks are observed on the surface of the sample, which corresponded to surface matrix cracks [20]. In the residual field of the shear experiment (Fig- ure 3b), a major crack is distinguished, which em- anated from the root of the left notch. The entire gauge region displayed increased residuals, which fur- ther indicated damage on the surface. Last, for the 45° experiment, increased residuals are present across the entire middle gauge region of the sample (Figure 3c). The residual levels are higher than in the previous two experiments (Figure 3a, b). Similarly to the strain field, increased residuals spread out diagonally on the opposite ends of the gauge area. 58 vol. 48/2024 FE-based stereocorrelation for woven composites (a) (b) (c) 20 -20 0 20 -20 0 20 -20 0 Figure 3. Stereocorrelation residual fields for (a) WF00, (b) WF90 and (c) WF45 tests for the ultimate stress. The residuals are expressed as a percentage of the dynamic range of the camera reference images. 4. Discussion In this section, the stress-strain responses (Figure 4) of the three experiments are compared and discussed. The stresses were calculated as the applied force di- vided by the net section area of each sample. The average strain levels were determined from virtual strain gauges defined for each experiment in Figure 2. As previously noted, the tensile test exhibited the highest stress levels, while the shear experiment showed the lowest. When examining the stress-strain curves, it is observed that the tensile test resulted in the lowest strain levels, whereas the combined tensile and shear experiment achieved the highest strain lev- els. This difference is attributed to the orientation of yarns with respect to the loading direction. The tensile test corresponded to the highest rigidity due to the aligned yarn orientation, whereas shear exhibited the lowest rigidity. The WF45 experiment had yarns oriented at 45° with respect to the loading direction; thus it had increased rigidity compared to the shear experiment. 5. Conclusion In this work, FE based stereocorrelation was applied to characterize the mechanical response and behavior of woven glass fiber composite samples under three 0 50 100 150 200 250 300 0 5 10 15 20 25 30 S tr e ss [ M P a ] Principal strain [%] WF00 WF45 WF90 Figure 4. Stress-major principal strain curves for all three experiments. distinct loading configurations. The main conclusion are as follows: • The sample orientation with respect to the loading direction had a major influence on the stress-strain response, in particular its rigidity. • The tensile test reached the highest stress level, whereas the shear experiment achieved the lowest. • The highest strain and stereocorrelation residual levels were reached for the 45° experiment, thereby indicating the most accumulated damage on the investigated surfaces. The experimental setup presented herein is not lim- ited to composite materials. It was designed to be robust and versatile. Since the experimental protocol was established for different loading regimes, it is possi- ble to introduce additional modalities in the stereocor- relation procedure, such as infrared and X-ray spectra for a more comprehensive material characterization. Acknowledgements This work was performed within the FULLINSPECT project supported by the Croatian Science Foundation (UIP-2019-04-5460 Grant). 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