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Abstract

The main goal of this study was to investigate the effect of tow tension and related internal micro-structure on the damage behavior of 3D orthogonal woven composites under tensile loading. For representing the internal micro-structure of the composite with respect to varying tow cross-section and the unregulated undulated path which are introduced by Z-binder tension, a dynamical method at filament level which simulates an interlacing process was used to obtain the fabric architecture. Then, an element recognition algorithm was proposed to convert a representative unit cell of 3D woven fabric architectures into a finite element model with 8-node solid elements consisting of four kinds of sets in terms of warp, weft, Z-binder tows and resin matrix. In addition, filament trajectory was also extracted from fabric architecture to serve as a local material orientation. Comparative simulations under tensile loading were conducted on the FEA models generated by this work and texgen software, respectively. An experiment was also carried out to verify the simulation results. The stress–strain curve in the proposed model was found to be closer to the experiment data. The results show that the tensile modulus and strength reduce due to the diverged warp tow path which is induced by the interaction between the tows during the weaving process. Moreover, the irregularity and compressed weft tow cross-sections nearby the intercross point are more likely to generate the transverse damage which would result in the non-linear tensile behavior of the composite material.

Keywords

3D orthogonal woven composite micro-structure representative unit cell tow tension damage behavior

Introduction

Attributing to its advantages of high stiffness, high strength-to-weight ratios and impact resistance, 3D woven composites are becoming increasingly attractive in various industrial fields [1]. The Z-binder tow in the 3D woven composites was used to couple the transverse reinforcement and obtain significant out-of-plane performance [2]. Therefore, the mechanical properties of 3D woven composites are strongly anisotropic due to the architecture of 3D woven fabric reinforcement [3 –6].

In order to characterize the complex fabric architecture of 3D woven fabric, many geometric models have been developed by the experimental and numerical methods. The well-known textile modeling software packages such as TexGen and WiseTex provided a description of internal architecture of fabric reinforcements integrated with mechanical models of 2D and 3D woven fabrics [7 –11]. However, the irregular tow cross-section and crimped tow path were simplified in these geometry models. Due to the existence of Z-binder tow through thickness of fabric, tow crimps are introduced in the warp and weft during the manufacture process. Several numerical models based on the CT technology have been proposed to replicate the internal micro-structure of 3D woven composites [12 –14]. However, the experimental-based models are non-predictive and significant cost. Therefore, geometric models based on the numerical method were introduced to generate the fabric architecture [15 –23]. Typical micro-structure features such as local waviness and resin pockets at pinching area were captured. Then, algorithm converting the fabric architecture to finite element models was implemented to investigate the mechanical behaviors of 3D woven composite [24 –26].

The tow crimp leads to non-linear stress–strain relationship of dry fabric under uni-axial tension load [27 –29], and further influences the mechanical properties of corresponding reinforced composites [3,30 –32]. Green et al. [24] and Joglekar and Pankow [26] carried out a numerical simulation at representative unit cell level for 3D woven fabric composite and suggested that the geometric imperfections have a significant effect on the damage initiation and evolution. Mahadik and Hallett [31] and Mahadik et al. [33] investigated the effect of increasing level of compaction on the internal tow crimp and on the compressive properties of a 3D woven interlock fabric. In fact, these tow crimps are determined principally by the fabric architecture and adjusted by the tow tension during the weaving process [34,35]. Therefore, a further investigation on how the tow tension and internal micro-structure affect the damage behavior of 3D woven composite is necessary.

The paper is organized as follows. The next section presents a dynamical method at filament level for the 3D orthogonal woven fabric architecture. In the subsequent section, an element recognized algorithm is developed to discriminate each mesh to build four element sets involving warp, weft, Z-binder and resin. The local material orientation of the tow elements is assigned according to the filament trajectory. Then, strain-based continuum damage model and maximum stress instantaneous damage model are applied to impregnated tows and resin, respectively. Then in the following section, the stress–strain curves predicted by the proposed model (considering Z-binder tension and internal micro-structure) and texgen model are compared and analyzed, while the conclusions are presented in the last section.

Dynamical method

The principle of weaving process for 3D orthogonal woven fabric is presented in Figure 1. Because the fabric architecture is formed during the weaving process, two stages namely initial weave and interlacing process are proposed. In the first stage, there is no interlacing between the warp and weft tows, and they are straight and perpendicular to each other with a certain tension load. Then, the Z-binder tension is applied to simulate the interlacing process to pinch the warp and weft tows. The fabric sample is produced on a home-made 3D woven machine as shown in Figure 1(c). The tow tension is measured by a tension meter which is provided by Shimpo (Figure 1(d)). The primary weaving parameters are listed in Table 1.

Figure 1.

The principle of weaving process for 3D orthogonal woven fabric. (a) Schematic views of the 3D weaving prototype, (b) applied Z-binder tension according to the actual weaving process, (c) home-made machine, (d) tension meter.

Table 1.

Weaving parameters.

Tow set	Material	Tow density (mm)	Tow tension (cN)
Warp	Carbon T700, 24 K	2	200
Weft	Carbon T700, 24 K	3	–
Z-binder	KELLAR-29, Type 950	–	50

Initial weave

The fabric architecture is assigned loosely at initial state as shown in Figure 2(a). Three sets of tow are oriented in Cartesian coordination system. The warp direction, weft direction and through-the-thickness direction are referred to as x-direction, y-direction and z-direction, respectively. The warp and weft are non-interweaving and are locked by the Z-binder tows. The Z-binder tows are also assembled loosely with vertical sections at the crossover points initially.

Figure 2.

The assembly of 3D orthogonal woven textile, (a) initial loose textile, (b) fiber filament represented by truss element chain, (c) Z-binder tow.

Due to the large length-to-diameter ratio of fiber, the bending stiffness is too small to take into account. One-dimensional truss element in three-dimension space that results in a fiber-like behavior is used as individual fiber filament at near microscale resolution. The fiber filaments are in a certain straight condition initially. Circular and rectangular cross-sections had been compared in the multi-chain digital element analysis by Wang et al. [19] and they found that the initial configurations of tow cross-section shape had no obvious influence on the final geometry of the tow. Therefore, a circular and rectangular cross-section was adopted as the initial shape of warp and weft tows, Z-binder tows, respectively. The high numbers of interactions among numerous filaments give rise to high computational cost. As the statement in Miao's work [19], the increasing filament number in a tow contributes to improve the numerical accuracy at the cost of higher computational time. In this work, the filament number in warp and weft tow is 61 and that in Z-binder tow is 25. The parameters of these three sets of fiber filaments are listed in Table 2.

Table 2.

The parameters of the filaments.

Filaments	Diameter (mm)	E (GPa)	υ
Warp filament	0.18	230	0.2
Weft filament	0.18	230	0.2
Z-binder filament	0.10	70	0.2

Interlacing process

The Z-binder tensiles are applied to each fiber ends and that have the effect of straightening the Z-binder tows. The initial cross-section assemblies of fiber bundles are collapsed into diverse shapes seen in the sectioned textile samples as shown in Figure 3. The deformation of cross-section is caused by the interaction between the tows which further induce the contact among fibers. Therefore, the interactions between fibers play a significant role in the forming process.

Figure 3.

Cross-section shapes of tows after deformation processes.

This forming process is implemented in commercial software Abaqus. Finite-sliding contact algorithms have been considered in this model and classical Amonton–Coulomb law with a constant isotropic frictional coefficient is used. If contact occurs between fibers, the physical condition would be either sticking or sliding. Sticking would happen if

μ \cdot f_{x} > f_{y} + f_{x}

(1)

where μ is the frictional coefficient,

f_{x}

is the compression force,

f_{y}

and

f_{z}

are the element nodal forces. It is now necessary to determine the magnitude of compression force between the two fibers. As shown in Figure 4, two fibers

T_{1}

and

T_{2}

intersect each other. Two points

C_{1}

and

C_{2}

are defined as closest on the centerlines of the fiber

T_{1}

and

T_{2}

, respectively. The penetration depth h is defined as

h = (r_{1} + r_{2}) - | C_{1} - C_{2} |

(2)

where

r_{1}

and

r_{2}

are the radius of the fiber

T_{1}

and

T_{2}

, respectively. The magnitude of compression force

f_{x}

required to prevent the penetration is expressed as

f_{x} = kh

(3)

where k is a constant.

Figure 4.

Intersection between two fiber filament in 3D space.

Sliding would happen if

μ \cdot f_{x} \leq f_{y} + f_{z}

(4)

There are six different contact pairs for the textile including warp-to-weft, warp-to-binder, weft-to-binder, warp-self, weft-self and binder-self. Carbon fiber is used as warp and weft tow, and Kevlar fiber is used as Z-binder tow. The contact frictional coefficients are presented in Table 3. This interlacing process needs about 5 h using a workstation with an intel(R) Xeon(R) CPU E3-1230 v3 3.30 GHz and 24 Gb RAM.

Table 3.

Contact frictional coefficients of each contact pairs.

Contact kinds	Contact pairs	Frictional coefficients
Carbon to carbon	Warp-to-weft	0.24
	Warp-self
	Weft-self
Carbon to Kevlar	Warp-to-binder	0.26
Carbon to Kevlar	Weft-to-binder	0.26
Kevlar to Kevlar	Binder-self	0.29

After interlacing process, these three sets of tow achieve a dynamic balance and a 3D woven fabric architecture is obtained as shown in Figure 5. However, this fabric architecture which is at the scale of filament cannot directly use for the mechanical prediction of 3D woven composite. Therefore, a further treatment is needful to convert the fabric architecture into a finite element model.

Figure 5.

3D woven fabric architecture.

Finite element model

Voxel mesh generation

The periodicity of the fabric architecture is taken into account for the definition of the mesoscale representative unit cell (meso-RUC). Therefore, the entire fabric architecture can be represented as a continuous assemblage of the meso-RUC. The fabric architecture is trimmed by four planes normal to the X-direction and Y-direction as shown in Figure 6. Homogeneous voxel meshes are generated according to the dimensions of the meso-RUC.

Figure 6.

Definition of a unit cell. (a) Top view of the 3D woven textile. (b) Textile unit cell. (c) Homogeneous voxel meshes.

Then, it is necessary to determine that each voxel mesh belongs to either tows or resin matrix for the heterogeneous material. An element recognition algorithm is proposed to identify the mesh effectively. The main principle of this algorithm is to judge whether the voxel mesh includes fiber points. If there is no fiber point in the voxel mesh, it would be regarded as a resin matrix element. Otherwise, it would be regarded as a tow element. The fiber body is described by the fiber trajectory points and corresponding cross-section contours in the textile model. However, the fiber trajectory points are too sparse to identify all meshes in the fiber body and misjudgments can be induced as shown in Figure 7(a). Therefore, it is required to fill the fiber body with enough points. Two steps are carried out to generate fiber points to avoid misjudgments. The first one is that several interpolated points are inserted between the two trajectory points to obtain intensified trajectory points. The second one is that circumferential points with uniform distribution in the cross-section contour which corresponds to those intensified trajectory points are generated as shown in Figure 7(b). Besides, all fiber points distributing in a cross-section are attached with a direction property which is equal to the orientation of corresponding intensified trajectory points. The density of fiber points is controlled according to the voxel mesh size.

Figure 7.

Fiber points amending for the mesh identification. (a) Before amending. (b) After amending.

However, a scenario that fiber points belongs to more than one tow set appear in the same voxel mesh, which is illustrated in Figure 8. The distance between fiber point and mesh center point is calculated and the point with minimum distance is used to determine the element type. The procedure described above is successfully used to generate the finite element model of 3D orthogonal woven-reinforced composite.

Figure 8.

Scenario that fiber points belonging to more than one tow sets appear in the same voxel mesh happens in the critical contact areas.

Local material orientation

As shown in Figure 9, the fiber orientation would diverge from tow path due to the pinching effect at crossover points. A local material orientation for an accurate and reliable calculation of highly anisotropic composite materials is proposed in the present model. There is a fiber point inside voxel element belonging to tows as mentioned in ‘Voxel mesh generation’ section. The major principal axis of local material coordinate for the voxel element is defined by the unitization of the direction of fiber point. The second principle axis is taken in arbitrary vertical direction to the major principle axis. The third principle direction requires no manual configuration which is calculated as the vector product of the first two. The assignations of the local material orientations for each voxel element which belong to tows are exhibited in Figure 10.

Figure 9.

Non-parallel fiber orientations in the 3D woven textile model. (a) Warp tow. (b) Weft tow. (c) Z-binder tow.

Figure 10.

The assignations of the local material orientations for each voxel element which belongs to tow: (a) warp tow, (b) weft tow, (c) Z-binder tow.

Material property

Material constitutive relationship

Elements in the composite unit cell belong to either pure resin or impregnated tows. The resin phase is prescribed by the property of isotropic, while the impregnated tows are assumed to be transversely isotropic property. To determine the mechanical properties of the impregnated tows, a micro-scale representative unit cell (micro-RUC) model is constructed with fiber volume fracture of 50.0% as shown in Figure 11. The material properties of carbon fiber and resin are summarized in Table 4. The predicted effective properties of impregnated tows are listed in Table 5.

Figure 11.

Geometry of micro-scale repeating unit cell model (micro-RUC).

Table 4.

The material properties of carbon fiber and resin (from manufacturer's data-sheets).

Material	E (GPa)	υ	Strength (MPa)
Carbon T700	231	0.2	4558
Kevlar 29	70.3	0.2	2923.4
Resin	2.9	0.35	75

Table 5.

Predicted effective properties of impregnated tows.

Tows	$E_{11}$ (GPa)	$E_{22}$ (GPa)	$G_{12} = G_{13}$ (GPa)	$G_{23}$ (GPa)	$υ_{12} = υ_{13}$	$υ_{23}$
Weft	115	15.7	6	6.3	0.25	0.25
Warp	115	15.7	6	6.3	0.25	0.25
Z-binder	36	13.6	5.5	5.2	0.22	0.22

Damage initiation criteria

The damage initiation criteria for the impregnated tows are based on a strain-based continuum damage formulation [36]. The impregnated tow is assumed to be linearly elastic before damage occurs. In this case, two modes of damage in term of transverse matrix damage and longitudinal fiber damage are considered for the impregnated tows.

The damage state in transverse direction is given by

\begin{matrix} f_{22}^{m} = \sqrt{\frac{ɛ_{22}^{t}}{ɛ_{22}^{c}} {(ɛ_{22})}^{2} + (ɛ_{22}^{t} - \frac{{(ɛ_{22}^{t})}^{2}}{ɛ_{22}^{c}}) ɛ_{22} + {(\frac{ɛ_{22}^{t}}{ɛ_{22}^{c}})}^{2} {(ɛ_{12})}^{2}} \\ f_{33}^{m} = \sqrt{\frac{ɛ_{33}^{t}}{ɛ_{33}^{c}} {(ɛ_{33})}^{2} + (ɛ_{33}^{t} - \frac{{(ɛ_{33}^{t})}^{2}}{ɛ_{33}^{c}}) ɛ_{33} + {(\frac{ɛ_{33}^{t}}{ɛ_{33}^{c}})}^{2} {(ɛ_{13})}^{2}} \end{matrix}

where

ɛ_{22}^{t}

(

ɛ_{33}^{t}

) and

ɛ_{22}^{c}

(

ɛ_{33}^{c}

) are the damage strains in tension and compression respectively.

ɛ_{12}^{t}

is the damage shear strain. Damage occurs when

f_{22}^{m}

f_{33}^{m}

exceed its threshold value

ɛ_{22}^{t}

ɛ_{33}^{t}

The damage state in longitudinal direction is given by

f_{f} = \sqrt{\frac{ɛ_{11}^{t}}{ɛ_{11}^{c}} {(ɛ_{11})}^{2} + (ɛ_{11}^{t} - \frac{{(ɛ_{11}^{t})}^{2}}{ɛ_{11}^{c}}) ɛ_{11}}

where

ɛ_{11}^{t}

and

ɛ_{11}^{c}

are the damage strains in tension and compression respectively. Damage occurs when

f_{f}

exceeds its threshold value

ɛ_{11}^{t}

. On the other side, the damage of pure resin is assessed using maximum principle stress criterion and instantaneous damage. Damage initiation is assumed when the principle stress exceeds the value of fracture strength. The strength properties for the damage initiation criteria are listed in Table 6.

Table 6.

Damage initiation properties of impregnated tows and resin (MPa).

	$S_{11}^{T}$	$S_{11}^{C}$	$S_{22}^{T}$ = $S_{33}^{T}$	$S_{22}^{C}$ = $S_{33}^{C}$	$S_{12} = S_{13}$	$S_{23}$
Weft	3212	670	65	175	105	105
Warp	3212	670	65	175	105	105
Z-binder	2070	430	50	160	50	50
Resin	75	–	–	–	–	–

Damage evolution law

For the transversely isotropic constitutive property of impregnated tows expressed, the modulus stiffness can be written as follows

\begin{matrix} C_{11}^{0} = \frac{E_{11} (1 - v_{23}^{2})}{a} \\ C_{22}^{0} = \frac{E_{22} (1 - v_{12}^{2})}{a} \\ C_{33}^{0} = \frac{E_{22} (1 - v_{23}^{2})}{a} \\ C_{12}^{0} = \frac{E_{22} (v_{12} + v_{12} v_{23})}{a} \\ C_{13}^{0} = \frac{E_{22} (v_{12} + v_{12} v_{23})}{a} \\ C_{23}^{0} = \frac{E_{22} (v_{23} + v_{12} v_{23})}{a} \\ C_{44}^{0} = G_{12} \\ C_{55}^{0} = G_{13} \\ C_{66}^{0} = G_{23} \\ a = 1 - 2 v_{12}^{2} - v_{23}^{2} - 2 v_{12}^{2} v_{23} \end{matrix}

The transverse and longitudinal damage indicators $d_{22}^{m}$ , $d_{33}^{m}$ and $d_{f}$ are calculated as follows

\begin{matrix} d_{22}^{m} = 1 - \frac{ɛ_{22}^{t}}{f_{22}^{m}} e^{(- C_{22} ɛ_{22}^{t} (f_{22}^{m} - ɛ_{22}^{t}) / G_{m})} \\ d_{33}^{m} = 1 - \frac{ɛ_{33}^{t}}{f_{33}^{m}} e^{(- C_{33} ɛ_{33}^{t} (f_{33}^{m} - ɛ_{33}^{t}) / G_{m})} \\ d_{f} = 1 - \frac{ɛ_{11}^{t}}{f_{f}} e^{(- C_{11} ɛ_{11}^{t} (f_{f} - ɛ_{11}^{t}) / G_{f})} \end{matrix}

Here

G_{m}

and

G_{f}

are the fracture energy for transverse matrix failure and longitudinal fiber failure, respectively. The fracture energies in Table 7 were obtained from Li et al. [37]. Then, the reduced modulus stiffness matrix of impregnated tow can be calculated by

\begin{matrix} C_{11} = (1 - d_{f}) C_{11}^{0} \\ C_{22} = (1 - d_{22}^{m}) C_{22}^{0} \\ C_{33} = (1 - d_{33}^{m}) C_{33}^{0} \\ C_{12} = (1 - d_{f}) (1 - d_{22}^{m}) C_{12}^{0} \\ C_{13} = (1 - d_{f}) (1 - d_{33}^{m}) C_{13}^{0} C_{23} = (1 - d_{f}) (1 - d_{22}^{m}) (1 - d_{33}^{m}) C_{23}^{0} \\ C_{44} = (1 - d_{f}) (1 - d_{22}^{m}) C_{44}^{0} \\ C_{55} = (1 - d_{f}) (1 - d_{33}^{m}) C_{55}^{0} \\ C_{66} = (1 - d_{22}^{m}) (1 - d_{33}^{m}) C_{66}^{0} \end{matrix}

Table 7.

Impregnated tow fracture energy (J/mm²).

	Warp	Weft	Z-binder
$G_{m}$	1.0	1.0	1.0
$G_{f}$	12.5	12.5	12.5

The damage model is implemented using the user defined material subroutine (UMAT) and is connected with a commercial software packaged named as ABAQUS/Standard.

Results and discussion

Internal geometry comparing

In order to validate the finite element model, three cross-sections of the model are compared with microscope images of the composite sample. The cross-section views of the composite are shown in Figure 12. The cross-section images reveal that the upper and button layers of weft tows have some out-of-plane waviness at crossover points. The reason is that the adjacent weft tows at the crossover points sustain lateral force and experience significant shifting through the thickness.

Figure 12.

Comparing of samples and voxel mesh model results at three mentioned cut plane, (a, b) along weft tow, (c, d) along warp tow, (e, f) along Z-binder tow.

In addition, the tow cross-sectional shapes are well visualized by the model. The warp tow cross-section could be considered as convex shape. The cross section of weft tows in the upper and button layers are arch and those in the middle layer are shaped as rectangle as shown in Figure 12(c) and (d). In Figure 12(e) and (f), the cross-section of weft tow in middle layer is shaped into trapezoid to fit the waviness of Z-binder tow. The tow cross-sectional area, width and thickness are measured by ImageJ software on the graphs and the values are listed in Table 8. The differences of warp and weft tow area between experiment and numerical model are less than 6%. The difference of tow width is around 4% and that of tow thickness is lower than 10%. Therefore, the composite sample has semblable cross-section characters compared to the numerical model.

Table 8.

Mean values of the cross-sectional area, two main dimensions of yarns (width and thickness) and aspect ratio.

	Area (mm²)		Width (mm)		Thickness (mm)
	Model	Experiment	Model	Experiment	Model	Experiment
Warp	1.906	1.965	3.096	2.957	0.698	0.756
Weft	1.743	1.651	2.484	2.417	0.843	0.768
Z-binder	0.237	0.229	1.235	1.248	0.272	0.285

Mesh dependency analysis

Five models with different mesh density are employed to clarify the mesh dependency. The detail fiber volume fractions of each set of tows in the model are listed in Table 9. It is found that the fiber volume fraction decreases along with the increase of mesh density, which can be attributed to the element recognition algorithm that over mesh identifications may happen on the circumference of the fiber filaments. Therefore, more accurate and relative lower fiber volume fraction would be obtained with higher mesh density. The tensile modulus in warp direction for five models is similar and the differences are lower than 2.5% as shown in Figure 13. The accuracy of those models has little mesh density dependence. Therefore, Model-I was adopted to obtain a higher computational efficiency, which has less than 90,000 elements and 0.13 (mm) mesh size.

Table 9.

Detail fiber volume fractions of each set of tows in the model.

Models	Elements	Ele-fvf (warp)	Ele-fvf (weft)	Ele-fvf (Z-binder)	Ele-fvf	Fvf (50%)
I	85,668	25.1	53.7	3.8	82.6	41.3
II	176,400	24.6	51.7	3.5	79.8	39.9
III	271,440	24.5	51.8	3.4	79.6	39.8
IV	348,740	24.0	50.4	3.3	77.7	38.8
V	447,678	24.4	50.6	3.2	78.2	39.1

ele-fvf: element fraction of impregnated tow; fvf: effective fiber fraction in the composite material.

Figure 13.

Tensile modulus with different mesh density.

Damage behavior

For further understanding of the damage behavior of 3D orthogonal woven composite, two finite element models are generated by the texgen and the proposed method, respectively. The same material parameters and similar fiber volume fractions are set for the two models. The predicted tensile properties of both models are summarized in Table 10. Stress–strain curves from two models and experiment data in tensile loading along the warp direction are shown in Figure 14. Although these curves have similar trend, three obvious differences about the tensile response can be observed for the two models. Firstly, the texgen model overestimates the tensile modulus by around 15%, while proposed model had a slightly higher modulus than experimental results by 3%. Secondly, the tensile strength predicted by texgen model was higher than the experimental results for almost 40%. Thirdly, the stress–strain curve of the proposed model deviated from the linear-line at about 0.01 strain while that of the texgen model still keep linear until 0.015 strain.

Table 10.

Predicted tensile properties of both models.

Models	Modulus (GPa)	Strength (MPa)
By texgen	27.21	597.15
By proposed method	24.41	439.13
Experiment	23.71	421.11

Figure 14.

Stress–strain curves for each model alongside experiment for tensile warp loading.

Because of the heterogeneous nature of the textile reinforced composites, the stress distribution inside 3D woven composite is uneven. It can be seen from Figure 15(a) and (b) that the largest stresses areas concentrate on the warp tows. One of the warp tows in the unit cell is extracted from both the texgen model and the proposed model as shown in Figure 15(c) and (d). The stress distribution at about 0.005 strain for these two models is significantly different because of the different paths of warp tow. Warp tow longitudinal fractures are outlined as shown in Figure 15(e). We can find that the fiber ruptures of warp tow are jagged. This phenomenon reflects the difference load conditions which are induced by the misalignment of fiber filament in the warp tow. The warp tow path diverged at edges of tow for the proposed model. It is attributed to the lateral squeezing with up-layer weft tow that is originated from Z-binder tension. This lateral squeezing results in fiber misalignment which would reduce the carrying capacity of warp tows. However, the warp tow in the texgen model is constantly straight as shown in Figure 15(d) and all the filaments in the warp tow have the same reinforcement effect under the tensile loading. This is the reason for overestimation of tensile modulus and strength in the texgen model.

Figure 15.

Stress distribution of the meso-RUCs and warp tows for each model. (a, b) The proposed model, (c, d) the texgen model, (e) damage morphology.

Although the warp tow sustains most of tensile loading, the weft tow which is perpendicular to the loading direction also plays a noticeable role during the loading process. The transverse damage indicator (SDV2) at 0.01 strain mainly distributed in the weft tows is shown in Figure 16. The element damages can be divided into two kinds in terms of intra-tow crack and interface debonding. Several resin cracks on the surface of the sample can be found in Figure 16(c). These resin cracks in the intercross regions of weft and Z-binder tows result in interface debonding, and that lead to intra-tow crack of weft in addition. Not only the areas occupied by the element in transverse damage state, but also the values of SDV2 in the proposed model are significantly larger than that in the texgen model. Therefore, the damage in the weft tow would progressively weaken the tensile response of the 3D woven composite. It may be the reason for the non-linear tensile behavior of the composite material in Figure 13. The most obvious weft tow structure difference between the two models could be the neglect of up-layer weft tow crimp at intercross point. This tow crimp is determined by the Z-binder tension and lead to various cross-section shapes. One of the weft cross-sections nearby the intercross point from two models was extracted and compared in Figure 16. The cross-sectional shape of the proposed model is irregular and more flattened which would result in more contact area with the warp tow. In addition, stress concentration is more likely to appear in the edge of the flattened weft tow edges, which would induce the weft tow transverse damage under the tensile load along the warp direction.

Figure 16.

The distribution of transverse damage indicator (SDV2) for the meso-RUCs at 0.01 strain. (a) The proposed model, (b) the texgen model, (c) damage morphology.

Conclusions

The 3D woven fabric architecture was obtained by a dynamical method at filament level and an element recognition algorithm was proposed to convert a representative unit cell (RUC) into a finite element model. The comparison between cross-sections of numerical model and images of manufactured sample indicated that the tension (50cN) on Z-binder would cause internal micro-structure which includes diverged tow path and irregularity tow cross-sections. The stress–strain curves offered by the proposed model were found to be closer to the experimental data (error is within 5%) than that produced by texgen model (error is over 15%).

The tensile modulus and strength reduced due to the diverged warp tow path which is induced by the interaction between the tows during the weaving process. Moreover, the irregularity and compressed weft tow cross-sections around the intercross point are more likely to generate the transverse damage in the weft tow which would result in the non-linear tensile behavior of the composite material. The comparison of these two models can clearly demonstrate the effect of internal micro-structure on the damage behavior of the 3D orthogonal woven composites.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Science Foundation of China (Grant No.51775514) and Zhejiang Provincial Natural Science Foundation of China (Grant No.LR18E050001).

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Effect of Z-binder tension and internal micro-structure on damage behavior of 3D orthogonal woven composite

Abstract

Keywords

Introduction

Dynamical method

Initial weave

Interlacing process

Finite element model

Voxel mesh generation

Local material orientation

Material property

Material constitutive relationship

Damage initiation criteria

Damage evolution law

Results and discussion

Internal geometry comparing

Mesh dependency analysis

Damage behavior

Conclusions

Footnotes

Declaration of conflicting interests

Funding

References