Experimental and numerical investigation of mechanical behavior of plain woven CFRP composites subjected to three-point bending

Qiaoli ZHAO, Yuliang HOU, Weihan WANG, Yutong LIU, Cheng LI

School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou 450001, China

KEYWORDS Equivalent Cross-Ply Laminate (ECPL) cell;Local homogenization;Multiscale modeling;Plain woven CFRP composites;Three-Point Bending (TPB)behavior

Abstract The mechanical behavior of plain woven Carbon Fiber-Reinforced Polymer (CFRP)composites under Three-Point Bending (TPB) is investigated via experimental and numerical approaches.Multiscale models,including microscale,mesoscale and macroscale models,have been developed to characterize the TPB strength and damages.Thereinto, Representative Volume Elements(RVEs) of the microscale and mesoscale structures are established to determine the effective properties of carbon-fiber yarn and CFRP composites, respectively.Aimed at accurately and efficiently predicting the TPB behavior, an Equivalent Cross-Ply Laminate (ECPL) cell is proposed to simplify the inherent woven architecture,and the effective properties of the subcell are computed using a local homogenization approach.The macroscale model of the TPB specimen is constructed by a topology structure of ECPL cells to predict the mechanical behavior.The TPB experiments have been performed to validate the multiscale models.Both the experimental and numerical results reveal that delamination mainly appears in the top and bottom interfaces of the CFRP laminates.And matrix cracking and delamination are identified as the significant damage modes during the TPB process.Finally, the quasi-static and dynamic behaviors of plain woven composites are discussed by comparing the results of Low-Velocity Impact (LVI) and TPB simulations.

1.Introduction

Due to the high specific stiffness and strength,excellent fatigue performance and corrosion resistance, advanced Carbon Fiber-Reinforced Polymer (CFRP) composites have been widely used in aerospace1,2and aeronautical3,4structures, carbodies,5etc.Among these CFRP composites, plain woven composites having inherent fabric architectures exhibit better in-plane and out-of-plane properties than conventional Unidirectional (UD) ones.Therefore, more and more highperformance structural components are designed and manufactured by plain woven CFRP composites, e.g., aeroengine cases,6airframes7,8and automotive B-pillars.9These composite components are usually required to bear bending loads during their service life.However, the fabric architectures make plain woven composites behave deformation and damages with multiscale features, posing noteworthy challenges to accurately and efficiently capture the bending behavior of these components.Thus, there are necessities to comprehensively study the mechanical behavior of plain woven CFRP composites subjected to bending loads.

Recently,the bending behavior of woven fabric composites has been explored via experimental and numerical approaches.10–14Zhang et al.15presented an experimental investigation on the failure mechanisms of Hybrid 3D Textile Composites (H3DTCs) subjected to quasi-static Three-Point Bending (TPB).Three different hybrid architectures were obtained by varying the percentages and lay-ups of the constituent fiber yarns.Then, they were examined to understand the effect of hybridization on the performance enhancement,such as the bending modulus and the strain to failure.It was found that the failure strain obviously increases with the rise of the specimen thickness.Zhao et al.16investigated the bending strength and damages of plain woven CF/PA6 composites with different layers.Several groups of step-by-step interrupted TPB tests were performed on composite laminates.Optical micrographs had been taken within the damaged regions to analyze the damage mechanisms.The results showed that a combination of matrix cracking between the fiber yarns (i.e., intralaminar and interlaminar cracks),debonding in the fill and warp yarns, buckling of the warp yarns, and delamination are characterized as the predominant failure modes.Dong17developed a Finite Element(FE)model to study the flexural properties of hybrid carbon-glass-fiberreinforced composites.Via the FE model, various stacking sequences were used to study the effect of hybridization on the flexural properties.The numerical results revealed that the hybrid composites containing half carbon/epoxy plies and half glass/epoxy plies possess the highest flexural strength,which coincided with the experimental measurements.

The experiments and numerical simulations usually focus on the macroscale structure of woven fabric composites.The effects caused by the microscale structure containing carbon fibers and matrix, and the mesoscale one containing warp and fill yarns are ignored.Hence, multiscale modeling frameworks have been developed to predict the mechanical properties of plain woven composites.18–23Hou24and Zhao25et al.investigated the Low-Velocity Impact (LVI) behavior of plain woven composites via multiscale models.The multiscale models containing microscale, mesoscale and macroscale models are used to predict the mechanical properties of CFRP composites, and the reliability of these models was verified by LVI experiments.Udhayaraman and Mulay26established a multiscale model to predict the microscale and mesoscale failure modes, and the ultimate strength of Plain Woven Textile Composites (PWTC) under in-plane loads.Zhou et al.27presented a multiscale stochastic fracture model to study the nonlinear mechanical behavior of Two-Dimensional (2D) woven C/SiC composites under uniaxial tension.And tensile tests had been conducted to verify the numerical predictions.It can be found that the presented model provided an efficient tool for evaluating the mechanical properties of woven composites.

According to the aforementioned literature,it can be found that the multiscale modeling strategies have the capacity to capture the mechanical properties of plain woven composites.The advantage of these methods is that they construct internal relations among microscale,mesoscale and macroscale models.The effective properties of the yarn used in the mesoscale model are obtained from the microscale model.The macroscale model is established by the mesoscale model based on local homogenization approach.Mechanical parameters and data crossing different scales can be either passed from one hierarchical level to another, or shared simultaneously in the multiscale models.The computational efficiency is significantly improved, and the global–local mechanical behavior is wellcaptured via multiscale modeling.However, this class of approaches is rarely introduced to predict the mechanical properties of plain woven CFRP composites under bending load.28,29Therefore,the correlative research on this issue is significative and necessary.

In this study,multiscale models are proposed to predict the TPB behavior of plain woven CFRP composites.The experimental TPB process is presented in Section 2.The multiscale models of plain woven CFRP composites are demonstrated in Section 3, including the construction of the microscale and mesoscale Representative Volume Element (RVE) models,the Equivalent Cross-Ply Laminate (ECPL) cell and the macroscale TPB model.Section 4 exhibits the experimental and numerical results, and analyzes the bending behavior and damages of plain woven composites.Besides,the comparison between LVI and TPB is performed to explore the dynamic and quasi-static behaviors of plain woven composites.Ultimately,the findings and insights obtained are concluded in Section 5.

2.Experimental work

2.1.Materials and specimen preparation

The studied plain woven CFRP composites are provided by Weihai Guangwei Co., Ltd.The composites consist of carbon fibers T300/3K and epoxy resin 7901, and their mechanical properties provided by the supplier are listed in Table 1.The tensile and compressive fracture toughnesses are obtained by experimental measurements.The diameter and density of the carbon fiber are 7 μm and 1.78 g/cm3, and the density of the epoxy resin is 1.20 g/cm3.The composites contain 8 plies of plain woven fabrics,and the thickness of each fabric is around 0.25 mm.The total thickness is obtained as 2.0 mm.The weight and volume fractions of carbon fibers are approximately 62.4% and 54% within the CFRP composites,respectively.

The multiscale structures of the plain woven composites are illustrated in Fig.1.Thereinto, the micro-structure(Fig.1(a)) and meso-structure (Fig.1(c)) are obtained by a Scanning Electron Microscope (SEM) FEI QUANTA FEG 250 and an Optical Microscope (OM) Keyence VHX-6000,respectively.Microscale and mesoscale RVEs are constructed based on these micrographs.As shown in Fig.1(b), the microscale RVE model consists of carbon fibers and matrix,and the geometrical dimension (7.45 μm × 7.45 μm ×12.91 μm) is at the micro scale.The mesoscale RVE model is composed of warp and fill yarns and matrix, and the geometrical dimension (4 mm × 4 mm × 2 mm) is at the millimeter scale, as illustrated in Fig.1(d).For experimentally investigating the bending behavior, the plain woven composites are cut into individual TPB specimens (dimension is 150 mm × 100 mm × 2 mm) by a waterjet cutting machine HSQ1210.

Table 1 Mechanical properties of carbon fiber T300/3K and epoxy resin 7901.

Fig.1 Schematic diagram of multiscale structures obtained for the studied plain woven CFRP composites.

2.2.Three-point bending test

In order to experimentally characterize the bending behavior of the plain woven CFRP composites, a TPB testing setup is constructed according to the ASTM D7264/D7264M-15 standard,30as shown in Fig.2.The TPB test is carried out at room temperature using a WDW300 tensile testing machine.Fig.2(b) shows the fixture used to prescribe the bending load on the specimen during the TPB testing process.The radius of the loading nose and the base supports is 15 mm,and the support span is 100 mm.The specimen is freely placed on the two base supports,and a transverse displacement is imposed on the middle of the specimen to perform the TPB test by the loading nose.The displacement rate is set as 0.5 mm/min,ensuring that quasi-static testing results are obtained.

Prior to each TPB test, a reference point is marked on the middle of the specimen, as shown in Fig.2(c).Throughout the bending process, the transverse displacement of the reference point is recorded by a high-speed camera I-speed 221,regarded as the deflection of the specimen.Meanwhile, the bending load is directly recorded by the testing setup.Hence,the displacement-force curve of each TPB test is obtained by the combination of these displacement and force data.Within these experimental curves,the sudden drop of the bending load is considered as the onset of the final failure.According to the displacement-force curve of the composites, the bending strength σb31is calculated by

where P is the ultimate failure force; Lbis the support span; b and t are the width and thickness of the specimen,respectively.And the bending modulus Ebis computed bywhere m is the slope of the initial linear portion of the load–displacement curve.

In addition, three specimens are tested to ensure the reproducibility of the experimental results, and the variations are around 10%.After the TPB tests, damage morphologies of each specimen are analyzed via OM photographs to study the bending behavior and damage mechanisms, as presented in Section 4.

3.Multiscale modeling of plain woven CFRP composites subjected to TPB loads

3.1.Microscale and mesoscale RVE models

A microscale RVE model is developed to estimate the effective properties of the carbon fiber yarn, which are difficult to be directly characterized via experimental approaches.Based on the experimental observation of the micro-structure(Fig.1(a)), a microscale RVE model is generated accordingly.During the microscale RVE construction process, the carbon fiber yarn is treated similar as UD composites, in which the carbon fiber is located parallel to each other.The carbon fibers possess circle cross-sections and are embedded into the resin matrix in a hexagonal manner,as shown in Fig.3(a).The connection between the carbon fibers and the matrix is simplified as perfect bonding.It means that the carbon fibers and the matrix are bonded directly.Moreover, the carbon fibers are transversely isotropic materials, and the resin matrix is a fully isotropic material.Hence, a microscale RVE model with a cubic shape, is constructed to represent the micro-structure,as illustrated in Fig.3(b).

Fig.2 Experimental TPB setup.

Fig.3 Schematic diagram of microscale RVE model for plain woven CFRP composites.

In addition, the geometrical parameters,32,33such as the length l, width w and height h, of the microscale RVE model are 7.45 μm,7.45 μm and 12.91 μm,respectively.24The radius r of the carbon fiber is set as 3.5 mm,and the volume fraction Vfis 80%.Consequently,as the Periodic Boundary Conditions(PBCs)34,35are employed to perform the different loads on RVEs, a periodic FE mesh generated by HyperMesh36is used to discretize the microscale RVE model.Besides,the maximum principal stress failure criteria are employed to determine the damage initiation of the microscale RVE model.Once the damage criterion is satisfied, the damage initiates and the material properties are degraded following a damage evolution law based on fracture toughness.

To compute the effective properties of plain woven composites, a mesoscale RVE model is established using the software TexGen,37according to the actual inherent woven architectures.For the mesoscale RVE model, the crosssection of the yarn is considered as elliptical, and the profile curve is assumed to include straight lines and sinusoidal curves,as depicted in Fig.4.Thereinto,L and H are the length and height of the mesoscale RVE model, whose values are 4.00 mm and 0.25 mm,respectively.For the carbon fiber yarn,the major and minor axes of the cross section, namely W and H,are set as 1.62 mm and 0.11 mm,respectively.Moreover,A0and A1are the lengths of the straight and sinusoidal parts,which are equal to 0.40 mm and 1.20 mm,respectively.Subsequently, to meet the demand of prescribing PBCs, a periodic mesh is employed to discretize the mesoscale model by HyperMesh.36During the numerical simulation, 3D Hashin and maximum principal stress failure criteria are employed to determine the damage initiation of the yarn and matrix.The progressive degradation model is used to govern the damage evolution.

3.2.ECPL cell and macroscale model of TPB test

The multiscale features of plain woven CFRP composites have been captured by the microscale and mesoscale RVE models,and a macroscale model is subsequently constructed to study the bending behavior.To improve the computational efficiency without reducing the prediction accuracy, an ECPL cell consisting of 0° and 90° subcells is established to transform the mesoscale RVE model into a regular manner, via a local homogenization approach.24,38

In the mesoscale model,plain woven CFRP composites are considered as a sequence of cross-ply laminates with 0°and 90°plies alternating their positions, as shown in Fig.5(a).The assumption is that, the warp and fill yarns, as well as the matrix attached on the yarns,are converted to equivalent subcells.In this way, the 0° and 90° plies are transformed into 0°and 90° subcells, as illustrated in Fig.5(b).Consequently, the ECPL cell is established through staggering the 0° and 90°subcells along the warp and fill directions, as illustrated in Fig.5(c).The effective properties of each subcell are obtained from the simulation results of mesoscale RVE model through a local homogenization method, as listed in Table 2.The geometrical parameters of the subcell are 2 mm × 2 mm × 0.12 5 mm (length × width × thickness).And the dimension of the ECPL cell is 4 mm × 4 mm × 0.25 mm(length × width × thickness).More information about the construction process of the ECPL cell is given in our previous studies.24,39,40

Fig.4 Illustration of OM photograph of meso-structure, mesoscale RVE model and geometrical parameters for studied plain woven CFRP composites.

Fig.5 Flowchart of ECPL cell construction.

In order to further understand the bending behavior of plain woven CFRP composites, a macroscale TPB model is established,as illustrated in Fig.6.The model of the specimen is constructed by 8 plies,and each ply is created by periodically arranging the ECPL cells along x and z directions,as shown in Fig.6(a).Ply-1, namely the top surface, corresponds to the bending side.The front and back sides correspond to the sides of the specimen along x direction, as shown in Fig.6(b).The plies are meshed by hexahedral eight-node reduced integration elements.The length and number of the element are 1 mm and 236800, respectively.To capture the intralaminar damages,zero-thickness interface is introduced between the adjacent plies.The interface is discretized by eight-node 3D cohesiveelements (element type is COH3D8), and the element number is 103600.

Table 2 Effective properties of 0° and 90° subcells within ECPL cell.

As illustrated in Fig.6(c), the coordinate system is marked in the left corner of the figure, and x, y and z directions are along the length, thickness and width directions, respectively.During the numerical TPB test, the specimen is freely placed on the two supports according to the experimental testing standard.These supports possessing cylinder shapes with a radius of 15 mm,are set as rigid bodies.And all the Degrees of Freedom(DOFs)associated with these supports are fixed.Furthermore, the loading nose is built using the actual geometrical dimension of the TPB test setup, and it is regarded as rigid body.Then a displacement of 20 mm is prescribed on the loading nose along the y direction.Besides,the interaction between all the contact pairs, especially the one between the loading nose and specimen, are defined using general contact.

In the TPB simulation,3D Hashin criteria are implemented to capture the intralaminar damage initiation.41–43The bending behavior of the composites is obtained from the multiscale simulations.And then the results of TPB experiments are used to validate the multiscale models.

4.Results and discussion

4.1.Bending behavior

To validate the multiscale models,numerical simulations have been performed to analyze the bending behavior of plain woven CFRP composites subjected to TPB loads.The bending properties,such as the ultimate failure force and displacement,as well as the bending modulus and strength, are computed and depicted in Fig.7.Additionally, three specimens are used in the experimental TPB tests, and the average values of these results are plotted in Fig.7.Besides, the variations of the ultimate failure force and displacement are 1.93%and 3.78%,and the values of the bending modulus and strength are 3.36%and 1.77%, as illustrated in Fig.7.

Fig.6 Schematic diagram of TPB simulation.

Fig.7 Experimental and numerical results of ultimate failure force,displacement,bending modulus and strength of plain woven CFRP composites.

As shown in Fig.7(a), the ultimate failure forces obtained from the experimental and numerical results are 1.87 kN and 1.95 kN, and the relative error is 4.10%.Besides, the ultimate failure displacements are identified as 15.32 mm and 16.15 mm for the experimental and numerical results, respectively.The difference between them is 5.14%.The numerical results obtained from the multiscale model are consistent with the experimental ones.

Based on the recorded force and displacement data, the bending modulus are calculated as 36.75 GPa and 40.31 GPa for the experimental and numerical cases,respectively.The difference between them is 8.83%.Moreover, the bending strengths are 703.13 MPa and 732.38 MPa, and the relative error between them is 4.00%,as shown in Fig.7(b).According to these results, it can be found that both the experimental bending modulus and strength are lower than the predicted values.The dissimilarities of the mechanical properties are attributed to the fact that the numerical process is idealized,and there is no energy loss caused by TPB setup during the numerical simulation.Furthermore, Fig.7(b) exhibits that the differences between the predicted and experimental bending properties are within a reasonable range.These comparisons clarify that the multiscale models have the ability to predict the bending behavior of plain woven CFRP composites subjected to TPB loads.

Fig.8 shows the primary damage processes of plain woven CFRP composites under TPB loads.It is found that delamination occurs at the displacement of 4.73 mm, and is considered as the initial damage.As the displacement increases to 6.38 mm, intralaminar damages (fiber breakage and matrix cracking) appear along the y direction, and delamination extends in a progressive manner.Finally, the specimen fully fails as a result of delamination, fiber breakage and matrix cracking until the transverse displacement rises to 15.32 mm.It can be concluded that the interlaminar damage (delamination) emerges prior to the intralaminar damages (fiber breakage and matrix cracking) during the bending process, and then both of them contribute to the final failure of the specimen.

4.2.Bending damage morphology analysis

To further understand the damage mechanisms of plain woven CFRP composites, the damage morphologies have been analyzed by experimental and numerical approaches.Fig.9(a)gives the damage morphology of the specimen, and Figs.9(b)–(g) highlight the local damages corresponding to Points B–G (marked in Fig.9(a)).Thereinto, Points B–D and E–G are located on the front and back sides of the specimen,respectively.Through observation, the delamination on the back side mainly concentrates in Zones E–F and F–G.And Points E & G are identified as the boundaries of the damage zone.In order to comparatively analyze, Points B & D are selected on the front side corresponding to Points E & G.

As shown in Figs.9(b)–(d), it is found that a large amount of matrix cracking and delamination obviously concentrate within the middle and bottom plies, while the fiber breakage mainly appears in the fracture location.It reveals that the ability of compression resistance of each ply is better than the tension resistance.However, the matrix cracking and delamination on the back side exhibit in a pretty limited amount and they mainly focus within the middle plies,as illustrated in Figs.9(e)–(g).This is attributed to the TPB setup, in which the loading nose is not absolutely parallel to the supports.The front side of the specimen starts to bear the bending load prior to the back side during the TPB process.In addition, it is worth noting that the fiber breakage no matter on the front or back sides is always significant.

Fig.8 Morphologies of bending damages at different displacements.

Fig.9 Experimental damage morphologies of specimen subjected to TPB.

Subsequently, the delamination (interlaminar), fiber-based and matrix-based (intralaminar) damages of each interface and ply within the specimen are obtained from the numerical simulations, as illustrated in Figs.10–12.In Fig.10,Interface-1 corresponds to the one nearest to the top surface.The cohesive elements fully fail as the damage variable(SDEG) reaches 1.Comparing the interlaminar damage of each interface,it is found that the delamination area gradually decreases from Interface-1 to 4, and then increases from Interface-5 to 7.Furthermore, in order to accurately capture the damage trend,Fig.11 shows the interlaminar damage energies dissipated by each interface and the whole specimen during the TPB process.The total interlaminar damage energy finally reaches 1.65 J.Thereinto, Interfaces-1 and 2 dissipate 54%of the total energy,and Interfaces-6 and 7 dissipate 29%.However,the middle interfaces (Interfaces-3,4,and 5)are not significantly damaged by the bending load.The results indicate that the delamination mainly occurs in the top and bottom interfaces.And this discovery concurs with the experimental observations.

Fig.10 Projected delamination (interlaminar damage) of each interface within numerical TPB specimen.

Fig.11 Predicted interlaminar damage dissipation energy of whole specimen and each interface,obtained from numerical TPB simulation.

Fig.12 shows the intralaminar (fiber-tensile, fibercompressive, matrix-tensile and matrix-compressive) damages of each ply within the specimen.Ply-1 is located on the top surface and the red areas represent the damage regions.In Fig.12(a), the fiber-tensile damages mainly appear from Plies-5 to 8,and the damage area increases as the ply is located nearer to the bottom surface.However, the fiber-compressive damages only appear in Plies-1,2 and 3,and the area progressively decreases, as shown in Fig.12(b).It is attributed to the fact that the top plies mainly bear compressive loads while the bottom plies carry the tensile loads.

Figs.12(c) and (d) show the matrix-based (matrix-tensile and matrix-compressive) damages of each ply.In Fig.12(c),it is found that the area of the matrix-tensile damage in Ply-8 is the largest one, and the distribution from Ply-1 to 8 exhibits in an increasing trend.In Fig.12(d),the distribution of the matrix-compressive damages from Ply-1 to 5 continuously decreases, while the damage suddenly increases from Ply-6 to 8.The largest area of the matrix-compressive damage occurs in Ply-1 and the smallest one appears in Ply-5.

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By comparing these intralaminar damage distributions(Figs.12(a)–(d)), it can be found that the fiber-based damage areas are smaller than the matrix-based damage ones.These results demonstrate that the matrix-tensile and matrixcompressive damages are the primary damage modes during the TPB process.In addition, as shown in Fig.12, there are some discontinuous areas of the intralaminar damages emerging within the plies.This phenomenon is due to the inhomogeneous features of the composites, and stress concentration inevitably occurs in the vicinity of the intersection between the warp and fill yarns, and then brings these discontinuous damages.

According to the results illustrated in Figs.10 and 12, the damage morphologies obtained from the multiscale modeling are consistent with those in the experimental measurements.Consequently, it indicates that the multiscale models possess sufficient reliability and accuracy to predict the bending behavior of plain woven CFRP composites.

Fig.12 Projected intralaminar damages of each ply within numerical TPB specimen.

4.3.Comparison of quasi-static and dynamic behaviors of plain woven CFRP composites

To investigate the quasi-static and dynamic damage behaviors of plain woven CFRP composites, a comparative study of the mechanical responses caused by TPB and LVI loads is given.In addition, the impact tests are carried out using a WLJ300 drop-weight testing machine which provides the impact energy from 4 J to 12 J.However,the impact damage morphologies of the specimen are difficult to be characterized when the impact energy is below 6 J.Hence,the impact energies of 8 J,10 J and 12 J are selected for the LVI testing plan.

Fig.13 shows the experimental force–displacement curves of the plain woven CFRP composites extracted from the experimental TPB and LVI tests.The maximum impact forces are 2.17 kN, 2.40 kN, and 2.91 kN for the impact energy E of 8 J, 10 J, and 12 J, respectively.When the impactor contacts the specimen, the displacement and force increase fiercely and the specimen performs elastoplastic deformation.Then as the impact force increases, the impactor penetrates into the specimen.Meanwhile, the curve enters an oscillation stage until the impact force comes to the maximum value.Eventually, the impactor rebounds and the curve drop rapidly.In the TPB test, the specimen exhibits brittle fracture behavior,and it carries out elastoplastic deformation until the specimen completely fails.In comparison, it can be found that the specimen has no oscillation stage during the quasi-static loading process.

Fig.13 Comparison of force–displacement curves between TPB and LVI obtained from experiments.

Fig.14 shows the interlaminar damage of each interface predicted by the numerical LVI simulation with the impact energy of 8 J.As illustrated in Figs.10 and 14, the delamination distributions are different between TPB and LVI specimens.In comparison, the delamination area of Interface-4 is larger than other interfaces within the LVI specimen.Moreover,it can be found that the top and bottom interfaces within the specimen are easily damaged under quasi-static bending condition, while the middle interfaces are more sensitive to the dynamic impact loads.

Fig.15 shows the intralaminar damages of each ply predicted by the numerical LVI simulation, where Ply-1 is the impacted side.The intralaminar fiber-tensile, matrix-tensile and matrix-compressive damages are clearly observed in the numerical simulation, but the fiber-compressive ones barely emerge.In the LVI simulation, the intralaminar damages primarily occur around the impact point.The damage areas are close to an elliptical shape in top three plies,and then turn into a cross in the back plies.This phenomenon is different from the numerical TPB simulation.During the TPB process, all the four interlaminar damage modes (fiber-tensile, fibercompressive, matrix-tensile and matrix-compressive) appear within the specimen.And the intralaminar damages distribution exhibits in a linear manner along the y direction.

As shown in Fig.15, the fiber-tensile and matrix-tensile damage areas in Ply-8 are the largest, while the matrixcompressive damage in Ply-1 is the most significant.The damage distribution of the specimen under LVI is similar to that under TPB loads.From Figs.12 and 15, it is demonstrated that not only under the quasi-static conditions but also under dynamic conditions, the compressive damages mainly concentrate in the top plies,and the tensile damages mostly distribute in the bottom plies.

On the other hand,Fig.15 shows that the fiber-tensile damages are obviously smaller than the matrix-tensile and matrixcompressive ones.Meanwhile, during the TPB process, the fiber-based damages are much smaller than the matrix-based damages,as illustrated in Fig.12.These numerical results confirm that the matrix-based damages (namely matrix cracking)are identified as the major damage modes under both quasistatic and dynamic loading conditions.

Fig.14 Interlaminar damage of each interface obtained from numerical LVI simulation with the impact energy of 8 J.

Fig.15 Intralaminar damages of each ply obtained from numerical LVI simulation with the impact energy of 8 J.

5.Conclusions

This study concentrates on the experimental and multiscale numerical investigations onthe bending behavior of plain woven CFRP composites.Multiscale models including microscale and mesoscale models are used to predict the effective properties of the yarn and CFRP composites.An ECPL cell is developed via local homogenization of mesoscale RVE modeling.And then,the macroscale TPB model is established using ECPL cells,to characterize the bending behavior and to identify the damage mechanisms.Some conclusions can be drawn as follows:

(1) The macroscale model has been employed to numerically predict the bending behavior of plain woven composites.The differences of the ultimate failure force and displacement between the experimental and numerical results are 4.10% and 5.14%, respectively.And the relative errors of the bending modulus and strength are 8.83% and 4.00%, respectively.

(2) During the TPB process, both experimental and numerical results reveal that the interlaminar damages appear prior to the intralaminar damages,and the matrix cracking and delamination are identified as the principal damage modes.Besides,the delamination concentrates in the top and bottom interfaces.And the matrix-based damages are more significant than the fiber-based damages.

(3) The quasi-static and dynamic behaviors of plain woven CFRP composites are investigated through TPB and LVI experiments and simulations.In comparison, the specimen has no oscillation stage during the quasi-static process.Moreover,the middle interfaces within the composites are sensitive to the dynamic loads, while the top and bottom interfaces are easily failed under quasi-static loading conditions.The fiber-based damages within the composites are more significant in the quasi-static loading case than those in the dynamic loading case.

Overall, the presented multiscale models provide useful tools for predicting the bending behavior of plain woven CFRP composites,and offer a possibility for virtually evaluating the bending damage mechanisms of plain woven CFRP composites.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors acknowledged the financial supports from the National Natural Science Foundation of China (No.52005451) and the China Postdoctoral Science Foundation(No.2022M712876).This study was also supported by the Joint Fund of Research and Development Program of Henan Province, China (No.222301420033) and the Foundation of Henan Center for Outstanding Overseas Scientists, China(No.GZS2021001).