A novel numerical simulation method for predicting compressive properties of 3D multiaxial braided composites considering various defects

Ruixin LEI, Ho DOU, Yn SUN, To LIU, Wei FAN,b,*,Chenyng SONG, Shujun WANG, Yo LU, Xue YANG, Dinsen LI

a School of Textile Science and Engineering, Xi’an Polytechnic University, Xi’an 710048, China

b Key Laboratory of Functional Textile Material and Product (Xi’an Polytechnic University), Ministry of Education,Xi’an 710048,China

c School of Chemistry, Xi’an Jiaotong University, Xi’an 710049, China

d Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology, Ministry of Education, School of Chemistry,Beihang University, Beijing 100191, China

KEYWORDS

Abstract This paper reports a novel manufacturing process of preparing the Three-Dimensional Multiaxial Braided Composites(3DMBCs)and the effects of various defects generated in the manufacturing process on the compressive mechanical properties of 3DMBCs through the experimental and numerical methods.The five-step fabrication process of the 3D multiaxial braided preform was firstly introduced in detail.Then,the influences of various defects such as voids,waviness,and fiber breakage defects on the compressive properties of 3DMBCs were discussed.It is found that the fiber breakage defect and waviness defects were the two primary factors on the decrease of compressive properties of 3DMBCs.However,void defects in the resin and interface had little effect on the composites.When the fiber breakage defect content was 25% and the waviness was 7°, the composite compressive modulus decreased by 51%.The progressive damage process and failure mechanism of the composite under 90°compressive loading confirmed the validity of the numerical model by comparing with the experiments.

1.Introduction

Three-Dimensional (3D) reinforcement composites have been widely applied into aerospace and high-tech energy fields because they solve the shortcomings of easy delamination for 2D laminated composites.1–3However, for loadbearing structural parts such as wings and wind turbine blades that simultaneously bear multi-directional tensile and compressive stresses, the composite structural parts need to have excellent mechanical properties in all directions.4,53D multiaxial composites thereby attract more and more attention since they can effectively improve the in-plane properties of composites by changing the direction and distribution of yarns and increasing the specific gravity of each direction.6,7

The preparation steps of 3D multiaxial composites are mainly divided into two parts: manufacturing the braided preform and curing the preform to form the composites.The methods of preparing the preforms can be divided into 3D weaving, 3D knitting, and 3D braiding.Bilisik and Mohamed8proposed two 3D weaving methods of tube rapier and tube carrier.The modified tubular rapier loom could be used to prepare 3D multiaxial woven fabrics.However, the weaving process was too complicated.Guo et al.9developed a guiding mechanism to enable the lateral displacement of the oblique yarn and simplify the weaving process.Li et al.10adopted the 3D knitting technique to prepare 3D multiaxial warp knitted fabrics by bonding unidirectional tows stacked at 0° and 90° in the thickness direction using warp knitting needles.Fan et al.11used the substitution method to pass the yarns through a glass plate filled with steel needles to complete the preparation of multiaxial braided preform.This kind of manual braiding method was error-prone and inefficient.Therefore, a novel manufacturing process with high efficiency to prepare the 3D multiaxial fabrics needs to be supplemented.

To understand the mechanical properties and failure mechanism of 3D multiaxial composites, researchers have carried out in-depth research using experiments and numerical simulations.12,13Labanieh et al.14found that biased yarns could improve the off-axis tensile strength of the composites.Zhang et al.15established a full-scale model to simulate the progressive damage process of open-celled 3D multiaxial woven composites.They found the orientation of the yarn affects the stress distribution and damage pattern around the hole.However,most current numerical models are based on ideal conditions of the composites.16,17In fact,many defects exist widely,and seriously affect mechanical properties of the composites.18,19Hang et al.20found that buckling defects reduced the effective modulus and strength of woven composites.Ge et al.21established a Representative Unit Cell (RUC) model with pore defects to predict the elastic constants of the braided composites.The compressive behavior is also a key factor in the design of composites.Up to now, the compressive behaviors of 3D multiaxial composites considering the various defects have not been investigated.

In this work, a novel manufacturing process of preparing the 3D Multiaxial Braided Composites(3DMBCs) were firstly reported.Then the effects of various defects generated in the manufacturing process on the compressive properties of 3DMBCs were discussed through the finite element simulations.The results found the different effects of various defects on the compressive behaviors of the 3DMBCs.The analysis methods and conclusions obtained can be extended to other braided composites prepared by the similar manufacturing process.

2.Materials and experiments

2.1.Braiding processing technology of 3DMBCs

The manufacturing process of 3DMBCs mainly consists of two parts, one is the preparation of 3D Multiaxial Braided Preforms (3DMBP), the other is the curing process with the Vacuum-Assisted Resin Transfer Molding(VARTM)method.The 3DMBP is prepared by a new 3D five-step braiding method, as is shown in Fig.1(a).It is a further improvement based on the patents published in the previous research work.22

The specific braiding steps are as follows:

Step 1.Move the columns where the body yarn is located upward by a distance of the yarn guide.

Step 2.Move the rows where the edge yarn is located to the right by a distance of the yarn guide.

Step 3.Move the columns where the body yarn is located down by a distance of the yarn guide.

Step 4.Move the rows where the edge yarn is located to the left by a distance of the yarn guide.The yarn in 0°direction is introduced between the two fiber layers +θ/90° layer and 90°/–θ layer.

Step 5.Exchange the Z yarns, ensuring that Z yarns are perpendicular to the body yarn.

Figs.1(b) and (c) respectively shows the microstructural schematic and real image of the 3DMBP.The 3DMBP was then cured by the VARTM process to form the 3DMBC as is shown in Fig.1(d).

According to Fig.1(b), the fibers in 3DMBCs manufactured by 3D five-step braiding method are oriented along with many primary directions such as 0°, 90°, and ±θ (θ is about 42°).This kind of structure makes 3DMBCs stronger in mechanics than the braided composites prepared by the traditional 3D four-step braiding technique.However, the manufacturing process of the five-step method is also more complicated.

2.2.Various defects generated in manufacturing process

Fig.1(c)indicates that many fiber breakage defects exist in the preform because of the continuous intertwining and friction of the yarns during the braiding process.During the molding and curing process of the composites, the viscous flow of the resin is difficult to eliminate the voids and the extrusion of the interlayer yarns.Void defects and waviness defects are then generated in the composites as shown in Fig.1(d).Therefore, it is necessary to explore the effects of various defects introduced in the manufacturing process on the compressive properties of 3DMBCs.

2.3.Compression test and results in discussion

Fig.1 Manufacturing process of 3DMBCs.

According to the multiaxial structure of the preform,the compression tests were performed along with the 90°, 0°, and ±θ directions, respectively, following the ASTM 3410 compression standard.Considering the discreteness of the experimental results, 5 samples in each compression direction with the size of 10 mm × 10 mm × 4 mm were prepared, respectively.The hydraulic servo universal testing machine was used to carry out the compression experiment.The test fixture is shown in Fig.2(a).The loading speed was set to 2 mm/min.The composites prepared in the same batch were selected for the compression experiment, and the results showed good consistency.

Fig.2(b) shows the stress–strain curves of the 3DMBC in different directions.It can be seen that the trends of all curves are roughly the same,showing prominent nonlinear characteristics.This is due to the micro-buckling of the yarns inside the composites.The yarns deviated from the loading direction can also continue to carry the load.Besides, compared with the compression along with 90° direction, the results of the other three directions are apparently different.This is mainly attributed to three reasons:

(1) 90° yarns have fewer defects such as fiber breakage and waviness.

Fig.2 Compression tests and results.

(2) Z yarns are also arranged along with the 90° direction,which has a certain reinforcing effect on the 90° direction of the composites.

(3) θ = 42°, which leads to a higher enhancement effect in the 90°compression direction than in the other compression directions.

When the composites are compressed in the 90° direction,the 90° yarns and resin primarily bear the compressive load.As the compressive load increases, the 90° yarns are crushed and the strain reaches the plastic point, and the slope of the curve decreases gradually.Fig.2(c) shows the plastic initial of the composite (the plastic point is shown in Fig.2(b)) and Fig.2(d) shows the failure morphologies.Fig.2(d) shows the obvious 45° shear-cracks on the surface of the composite,which is primarily due to the compressive-shear coupling effects.The tendency of the curves is similar when the composites are compressed along with the 0°and±θ directions.However, compared with the compression in the 90° direction, the composite enters the plastic stage earlier and form a plastic platform.The main failure mode of compression composites along the 0° direction is crushing except the matrix cracking and shear failure.When the composites are compressed in the±θ direction,the failure of the composites is mainly caused by yarn breakage and shear failure.

3.Numerical methodology

3.1.Geometrical morphology characterization

Based on the actual morphological and structural uniform properties of 3D braided composites, we adopted computeraided engineering software CATIA V5R20 and commercial finite element analysis software ABAQUS to build the geometrical model of 3DMBCs.The cross-sectional areas of the fiber bundles in different layers were photographed using a superdepth-of-field microscope.The geometric parameters used for model construction,such as the length,width of the fiber bundle and the height of the model h, could be obtained.In the image analysis, at least 10 characteristic images were selected for the geometric parameter values of each layer of yarn.According to the real morphology of each component shown in Fig.3(a), Tables 1 and 2 list the structural parameters and geometric relationships of 3DMBCs.

Table 1 Proportion of each yarn orientation.

3.2.Assumptions for different types of defects

According to the defects shown in Figs.1(c) and (d), some assumptions were made for each type of defects.

3.2.1.Assumptions for voids in resin and interface

This work assumed that some micro or invisible void might exist in the resin and interfaces between the fiber and resin.This kind of void defects randomly existed, and could not be inevitable in the experiments.Therefore, the Monte Carlo method was adopted to randomly select the ‘void defect’elements on the resin and the interface,23,24as shown in Fig.3(b).This is because this kind of method was more consistent with the real defects in the experiments.To generate the void defects, the following assumptions were made:

(1) The fiber bundle was fully impregnated with the resin.

(2) The void defects existed at the resin and the interface randomly.

(3) The void defects were micro-scale defects that were not resulted from the failure curing process.

To ensure the convergence of the numerical calculation,25the elastic modulus Evand Poisson’s ratio νvfor each voidelement were set to a very small value (Ev= 10–6Pa and νv= 10–6).

Table 2 Geometric relationship of RUC model.

3.2.2.Assumptions for waviness defect

Fig.1(d)shows the waviness defect of the fiber in the composite.The waviness defect is determined by the local deflection angle φ of the yarns relative to a specified horizontal reference line.26The waviness calculation formula is as

where (xi, zi) and (xi+1, zi+1) are the pixel coordinates of the feature points at the peaks and valleys of the yarn extracted from the microscope image, respectively.The waviness of 90°yarns is determined by the formula to be 7°.

In fact,this kind waviness defect was random and irregular.It was difficult to create the real geometrical model for the yarn with waviness defect structure.Therefore, the waviness defect was introduced into the material model by modifying the elastic parameters of the yarn.The details would be described in Section 3.3.1.

3.2.3.Assumptions for fiber breakage defect

The fiber breakage defect is apparent according to Fig.1(c).Many previous research introduced this kind of defect into the model through assigning the weak mechanical properties to some elements.Here,the fiber damage caused by the braiding process should not be considered as the void.It was because that area was also composed of some fibers and resin.Therefore,the fiber breakage defects were also introduced into the material model by modifying the elastic parameters of the yarn.

3.3.Material model

The carbon fiber was regarded as transversely isotropic material, and the resin was defined as an isotropic material.The elastic properties of the constituent materials, including T700 carbon fiber and JC-02A epoxy resin, were shown in Table 3,where the subscript ‘‘t” and ‘‘c” mean tension and compression.

3.3.1.Mechanical properties of fiber tow

As the elastic modulus formula of fiber bundles with certain fiber breakage defects could not be accurately determined,the improved Chamis formula27and spherical defect theory28were adopted to evaluate the effect of fiber breakage on the elastic modulus of carbon fibers:

The effective longitudinal elastic modulusof carbon fiber bundles affected by the fiber waviness effect was mainly related to the four independent elastic constants and ply orientations in the principal coordinate system of the material.30The longitudinal elastic modulus can be obtained by transforming the off-axis unidirectional composite compliance matrix.The derived formula was

where E33,G13and ν13are the transversal modulus,shear modulus and Poisson’s ratio of the linear fiber bundle,respectively.

The strengths of the fiber bundles were determined by the tensile test of intact Toray T700s-12k fiber bundles and damaged fiber bundles extracted from 3D multiaxial braid fabrics,respectively.The modulus and strength of the intact fiber bundles measured experimentally were basically consistent with the Toray Company’s parameter table.However,the modulus and strength of damaged fiber bundles decreased significantly,the fiber bundle modulus decreased by about 54.1%, and the strength decreased by about 66.1%.The specific experimental details could be referred to the Supplementary material.

At present, there was no scientific method to characterize the defect content of fiber breakage.31Here,the breakage content of the fiber bundle was estimated to be 25%, combining the fiber bundle tensile test and the elastic modulus formula Eq.(2) of the carbon fiber.

3.3.2.Constitutive relations of resin

An elastic–plastic constitutive relation obeying the J2-isotropic hardening plasticity theory was assumed for the resin.Ductile and shear damage criteria32–35were used to define the damage initiation of the epoxy resin.The equivalent plastic strain at the onset of ductile damage was assumed to be a function of stress triaxiality and strain rate.The equivalent plastic strain at the onset of shear damage was assumed to be a function of shear stress and strain rate.The criterion for damage initiation was met when each of the following condition was satisfied:

Table 3 Mechanical properties of fibers and resin.

3.3.3.Definition of interface

The fracture energy is composed of

where Gn, Gs, and Gtare the current energy release rates of pure mode n,s,and t,respectively.The maximum relative displacement in the loading process is defined as

where δmis the effective relative displacement.

The interface also adopts linear damage evolution, and the damage variable d is determined by

3.4.Elements descriptions and boundary conditions

The total number of mesh elements was 595239 and the corresponding number of nodes is 125313.In order to explain the interfacial debonding mechanism, a zero-thickness cohesion element (COH3D6) was created at the coincident nodal coordinates between the fiber bundle and the resin.The fiber bundles and resin adopt four-node three-dimensional tetrahedral elements (C3D4) with a mesh size of 0.15.

Considering the boundary effects in the unit cell structure,the Periodic Boundary Conditions (PBCs)39,40was adopted to calculate the compressive behaviors of the 3DMBC along with 90° direction.The general expressions of the PBCs were described as

where uiandare the displacement field and global average strain tensor, respectively;is the periodic part of displacement components on boundary surfaces.

The macroscopic uniform deformation uion each pair of relatively parallel boundary surfaces can be written as

where the superscript ‘‘j+” and ‘‘j-” denote the positive and negative directions of the periodic displacement field,respectively.

The periodic displacement applied on the opposite faces should comply with

4.Results and discussion

4.1.Influence of different defects on mechanical properties of composites

Fig.4(a) shows that the elastic modulus of the composites hardly decreased when the void defect content increased from 2% to 15%.The reason is that the yarns in the compression direction were mainly subjected to unidirectional load, and the stress on the yarns was much higher than the microstress at the voids.The uncertainty effects of void defects on the mechanical properties of composites were further analyzed in the Supplementary material to verify the tiny influence of void defects on the 3DMBCs.

Table 4 Interface strengths and fracture toughness.

Fig.4 Numerical results of RUC model with different defects.

Fig.4(b)shows that the compressive properties of the composites reduced significantly after considering the effect of waviness.The increase of φ means the fiber orientation gradually deviated from the compressive direction.Therefore, fiber waviness defects could significantly affect the mechanical properties of the 3DMBC.Fig.4(c) shows that the compressive properties of the composites decreased continuously with the increase of fiber breakage defect content.This is because the area of the fiber breakage defect could not effectively undergo the compressive deformation.

By comparing the numerical results of different defect types, it could be found that the fiber breakage defect had the greatest influence on the compressive properties of the 3DMBC.When the fiber breakage defect was 25%, the composite compressive modulus decreased by 40%.The 7° waviness defect could cause the compressive modulus drop by 27%.The void defects had the least influence.Furthermore,the numerical results were within 5% error by incorporating the measured 7°waviness defect and 25%fiber breakage defect into the ideal model, indicating that the model considering some defects were more reliable and efficient.

4.2.Compressive failure mechanism of 3DMBC

Table 5 shows the progressive damage process of yarns, resin,and interface under 90° direction compressive load for the RUC model with 25% fiber breakage defects and 7° waviness defects.The entire damage process was divided into three stages: the initial damage, the propagation of damage, and the final damage.When the 3DMBC was compressed in the 90°direction,the yarns parallel to the direction of compression bore the load primarily.When the strain ε=0.33%,as shown in Table 5 A1, the 90° yarn damaged at 1/4 and 3/4 of the yarns.The straight section of the Z direction yarn parallel to the loading direction also played a certain bearing role.When the strain reached 0.55% and 0.85%, the interface and the resin damaged sequentially as shown in Table 5 C1 and D1.For both the interface and the resin, the main damage areas were concentrated at the ±θ yarn/resin interlacing point and the Z yarn bend section.This could be attributed to the stress concentrations effect at the yarn interleaving point, where the damage was most likely to occur.In addition,under the action of compressive stress and shear stress,an apparent shear bandalong with 45° direction also occurred in the surface of resin.The 0°yarns and±θ yarns damaged later due to the existence of a certain angle with the loading direction.As the failure propagated along the interface, the damaged area of the 0°yarn appeared at the yarn/resin interface as shown in Table 5 E1.The ±θ yarns were mainly subjected to shear force, and the damage appeared on the top of the yarns, as shown in Table 5 F1.

Table 5 Progressive damage of 3DMBC.

The next stage was the damage propagation of the composites.The 90°yarn continued to play the main bearing role,and the damaged area extended to both ends of the yarns,showing an apparent shear band.This indicated that the yarns of this layer were also subjected to the shearing force of the remaining interlayer yarns.With further loading,the damaged area of the interface expanded continuously, but could still transmit the stress.Under the action of ±θ yarn shearing force, the damaged area of the resin spread around the yarn interlacing point and the shear band,and simultaneously penetrated along with the thickness direction.After that, the composite entered the final damage stage.When the strain was 1.75%, the 90° yarn yielded as shown in Table 5 A3.From the scanning experimental fracture morphology, the yarn showed obvious shear fracture characteristics at 3/4 of the composite.The stress–strain curve at this point was flattened by the breakage of the 90°yarn,but the value did not arrive at the peak stress.The damage of the yarn in the Z direction accumulated continuously at the root, resulting in breakage.When the total strain was increased to 2.34%, as shown in Table 5 C3, the interface was severely damaged and completely debonded,accompanied by the breakage of the 90°load-bearing yarn.The resin yielded at 2.45% strain and exhibited significant shear failure under compressive and shear stress.Therefore, the failure of the interface was earlier than the failure of resin.Finally,the composites showed obvious large cracks at the 0° yarns due to the transversal damage of the 0° yarns and interfacial debonding.The ±θ yarn was mainly subjected to shear stress during the whole compression process, exhibiting 45° shear failure and bottom crush.

According to the analysis of Table 5, the main failure modes of composites were the breakage of bearing fibers,interface debonding, and resin cracking.In addition, the different load-bearing degrees of multidirectional yarns were the main reason for the nonlinear stress–strain curve result, causing the composites to exhibit ductile failure.By comparing the progressive damage process with the fracture morphology of composite materials, the mesoscopic model established could accurately reveal the progressive damage process of the 3DMBCs.

5.Conclusions

3DMBCs were prepared by a novel five-step braiding manufacturing process.The compressive properties and failure mechanisms of the composites in different directions were investigated.In addition, the effect of different defects on its compressive properties was studied by numerical methods.The validity of the RUC model was confirmed by comparing experimental failure morphology and the Mises stress distribution of the numerical simulation.Through detailed analysis,the following conclusions were drawn:

(1) The compression properties of 3DMBCs mainly depended on the mechanical properties and volume content of fiber bundles in the compression direction.The yarns along with 90°direction have fewer fiber breakage defects and waviness defects, making the compressive performance in this direction significantly better than in other directions.

(2) The fiber breakage and waviness defects were two primary defects generated in the manufacturing process of the 3DMBCs.The composites with 25%volume fractions of fiber breakage defects and 7° waviness defects could cause the composite compressive modulus decreased by 51%.The void defects in the resin and interface have barely effects on the compression properties of 3DMBCs.

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

This work was supported by the National Natural Science Foundation of China (Nos.52073224, 52173080, and 12002248), the Key Research and Development Program of Xianyang Science and Technology Bureau, China (No.2021ZDYF-GY-0035), the Local Transformation Program of Major Scientific and Technological Achievements of Xi’an Science and Technology Bureau,China(No.2021SFGX0003),the Technology Innovation Guidance Special Program of Shaanxi Province, China (No.2022CGBX-10), the Young Talent Fund of University Association for Science and Technology in Shaanxi, China (No.20210509).

Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cja.2023.07.011.