Numerical simulation and experimental study of the bursting performance of triaxial woven fabric and its reinforced rubber composites

Abstract

In this paper, the bursting performance of triaxial woven fabric and its reinforced rubber composites are studied by the finite element method and the experimental approach, and compared with plain woven fabric and its reinforced rubber composites. The bursting morphologies and load–displacement curves of the specimens during the bursting process are obtained. The results indicate that the rubber matrix has a protective and consolidation effect on the inner fabric, significantly improving the bursting strength of the fabric. Triaxial woven fabric shows a steeper load–displacement slope, higher maximum bursting load, and smaller initial damage displacement than plain woven fabric. The bursting morphologies of the specimens indicate that the structure of triaxial woven fabric is more stable and exhibits good expansion resistance to bursting damage. The bursting process of triaxial woven fabric can be divided into four stages: yarn straightening, yarn slippage, yarn breakage, and breakage extension.

Keywords

bursting performance rubber composites finite element method triaxial woven fabric bursting strength

Triaxial woven fabric (TWF) is formed by three sets of yarns interlacing at 60 or 120 degrees with each other in a planar,¹ leaving hexagonal voids between adjacent interlacing points, as shown in Figure 1.² When the three sets of yarns are the same and the ratio of the yarn diameter to the yarn pitch is 0.33, the cover factor of the fabric is 0.67. Regardless of the direction in which the fabric is stressed, it has a relatively uniform tensile and shear-resistant strength and rigidity. Due to its quasi-isotropic and low cover factors, TWF has been applied to lightweight high-performance industrial fabrics, especially as composite reinforcements for highly isotropic requirements. The bursting performance can reflect the characteristic information of the multi-directional tensile strength of a material.³ For this reason, the bursting test is an alternative method for measuring strength, and is especially suitable to evaluate the mechanical properties of materials for which the maximum strength does not have distinct directions, such as knitted materials, lace, or TWF. In addition, the bursting performance directly affects the practical application of a fabric and its reinforced composites.

Figure 1.

(a) Triaxial woven fabric. (b) Plain weave fabric.

During the last decade, numerous studies had been conducted to study the mechanical properties of TWF and TWF-reinforced composites using experimental, theoretical, and numerical methods. The structural model of TWF and the biaxial-extension theory were presented to predict the biaxial tensile properties of TWF, and the theory was in good agreement with the experimental results.⁴ Analytical solutions were also developed to predict the tensile and shear moduli of TWF-reinforced composites, which showed fairly good accuracy.^5,6 The tensile, bending, shearing, compressive, and thermal deformation properties of single-layer carbon fiber TWF-reinforced composites were also studied by experiment and finite element analysis (FEA), and the FEA results agreed well with the experimental results.^7–10 The influence of tows waviness and anisotropy effects on the effective Mode I/II fracture toughness of TWF composites were also investigated by means of numerical and experimental methods.^11,12 Some new theoretical analysis models have also been developed for the bending and tensile properties of TWF-reinforced composites, the results of which were compared with the results of experiments.^13–15

Although many studies have investigated the application of TWF and its reinforced composites, these have largely focused on resin-based composites. The quasi-isotropic mechanical properties of TWF make it more suitable for the reinforcement of flexible composites that are simultaneously stressed in multiple directions during service, such as rubber diaphragms. The bursting performance directly reflects the durability of deformation and fracture of these composites under external force, and provides characteristic information on their multi-directional tensile properties.

Several scholars have studied the bursting property of TWF and traditional fabrics (such as plain woven fabric (PWF)),^16–18 and showed that TWF was more suitable for multi-axial force than traditional fabrics during service. An investigation was also carried out into the stab resistance of single and multilayer TWFs for soft body armor.¹⁹ The results showed that TWF improved the impact resistance property and exhibited better energy absorption capacity than other fabrics. A measuring device has also been developed to estimate the uniformity of force distribution in woven multi-axial structures.²⁰

Numerous studies have been conducted on the bursting performance of fabrics and reinforced flexible composites, using both experimental and numerical methods. The puncture behaviors of three kinds of woven fabric have also been explored through both experimental and FEA simulation methods.²¹ The results showed that the load–displacement curves and damage morphologies of the woven fabrics obtained from FEA agreed well with the experimental results. The bursting properties of warp-knitted long-lasting mosquito-proof net was shown to depend on the fiber property, yarn count, and fabric weight.²² FEA and experimental methods were also used to study the effects of impactor shape and structural parameters of fabrics on the puncture damage of the composites, and the FEA results were in good agreement with the experimental results.^23–25 A study into the puncture resistance of high-strength nonwoven natural rubber latex (NRL)-coated fabrics and uncoated fabrics showed that coating NRL onto the fabric improved the puncture performance of flexible unidirectional (UD) fabric by offering higher frictional effects.²⁶ These UD NRL-coated fabrics also had higher puncture resistance than uncoated fabrics. A geometric model of polyester woven fabric-reinforced thermoplastic urethane composites was established and the load was calculated according to the strain energy principle. Meanwhile, the puncture morphologies and failure mechanism of the employed flexible woven fabrics and the composites reinforced by them also were analyzed. It was found that owing to the protection of the matrix and the consolidation effect on the inner fabric, the flexible composite exhibited much greater bursting strength than that of the reinforced woven fabric.²⁷ The stab failure behavior of coated and uncoated woven fabrics was studied by experimental and FEA approaches. It was found that the stab strength obtained from FEA agreed well with experimental results.²⁸

At present, however, understanding of the bursting performance of TWF and reinforced triaxial woven fabric (TWFR) is limited. Considering this, in this article, the bursting performances of TWF and TWFR are discussed in comparison with PWF and its reinforced rubber composites (reinforced plain woven fabric (PWFR)). The bursting morphologies and load–displacement curves are evaluated by FEA and the experimental approach. Moreover, the failure mechanism of fabrics and their reinforced rubber composites are investigated.

Experimental details

Materials

The TWF and PWF used in this study are made of polyamide-66 filaments (supplied by Wuxi Taiji Industry Co., Ltd). The properties of the polyamide-66 filaments are as follows: yarn count of 186.67 tex, twists of 70 T/m, breaking strength of 530 MPa, elongation of yarn of 16.12%, and average tensile elastic modulus of 5980 MPa. The construction parameters of the TWF and PWF are given in Table 1. The butadiene-acrylonitrile rubber resin is supplied by Xinxiang Dingcheng Rubber Plastic Co. Ltd. Chemlok402 is used as the adhesive to bind the rubber and fabric, which is manufactured by the LORD Corporation.

Table 1.

Parameters of triaxial woven fabric (TWF) and plain woven fabric (PWF)

Construction	Warp 1 /10 cm	Warp 2 /10 cm	Weft /10 cm	Density g/m²	Thickness /mm	Cover factor /%
TWF	33	33	33	194.04	0.43	62.57
PWF	51		51	199.90	0.36	69.14

Coating methods

Fabric-reinforced rubber composites are made by hot pressing, as shown in Figure 2. Fabrics are firstly coated with adhesive. After drying, the fabrics are placed in the middle of the rubber compound, and then put into molds. Finally, the molds are placed in a CARVER 4128 (maximum pressure 30 T, pressure plate diameter 30 cm × 30 cm) hot pressing machine at a temperature of 145℃ and pressure of 18 MPa for 20 minutes. The prepared fabric-reinforced rubber composites have a weight of 3431 g/m² and fiber mass fraction of 5.8%.

Figure 2.

Preparation process for the fabric-reinforced rubber composites.

Bursting test

The bursting tests are conducted using a universal testing machine (Instron-3385H) as specified in GB/T 19976-2005 (China Standard),²⁹ as shown in Figure 3. The cylindrical impactor has a 25.4 mm diameter with a spherical tip, and the top of it is polished. Specimens are mounted between two annular clamps that have a 45 mm diameter hole in the center, on the surface of which there are concentric grooves to prevent sample slippage. The test rate is 300 mm/min. If the specimen slips out of the annular clamps during the testing process, the result is discarded. Load–displacement curves are obtained from the test. Super-eyes digital zoom electron microscopy (B008) and a scanning electron microscope (SEM; SU1510) are used to observe the damage morphologies of yarns in the fabrics and fabric-reinforced rubber composites, respectively.

Figure 3.

Setup of the bursting test system.

Finite element model

FEA has been reported to be the most effective simulation method to study the bursting performance of fabrics.^30,31 Therefore, the commercial FE package of ABAQUS/Explicit version 6.14 is used for the current study.

Geometric model

TWF is interlaced by three sets of yarn interweaving at angles of 60 degrees with each other, as shown in Figure 1(a), while PWF is made by warp and weft yarns interlacing at an angle of 90 degree, as shown in Figure 1(b). In this study, the models of fabrics are established according to the yarn cross-section and path by Solidworks® 2015,³² as shown in Figure 4.

Figure 4.

Solid modeling of specimens: (a) triaxial woven fabric; (b) reinforced triaxial woven fabric.

Material properties

The FE model considers polyamide-66 filaments as continuous solids with a lenticular section, whose surface is assumed to be uniform and smooth. The yarns are assumed to be transverse isotropic material,³³ showing isotropy on the Y–Z sides, as shown in Figure 5, and the relation of stress and strain is expressed as given by Equation (1)

\begin{matrix} {\begin{matrix} ɛ_{11} \\ ɛ_{22} \\ ɛ_{33} \\ ɛ_{12} \\ ɛ_{13} \\ ɛ_{23} \end{matrix}} = {\begin{matrix} 1 / E & - μ' / E' & - μ' / E' & 0 & 0 & 0 \\ 1 / E' & - μ / E' & 0 & 0 & 0 \\ 1 / E' & 0 & 0 & 0 \\ Symmetry & 0 & 1 / G' & 0 & 0 \\ 1 / G' & 0 \\ 1 / G \end{matrix}} \times {\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{12} \\ σ_{13} \\ σ_{23} \end{matrix}} \end{matrix}

(1)

Figure 5.

Yarn material coordinate diagram.

The material parameters in the formula satisfy the following relationship (2)–(4)

G' = E' / 2 (1 + μ')

(2)

- 1 < μ' < 1 - 2 μ E' / E

(3)

- \sqrt{\frac{E}{E'}} < μ < \sqrt{\frac{E}{E'}}

(4)

In this equation, E′ is the elastic modulus in the transversely isotropic plane (YZ plane); E is the elastic modulus in the direction of the perpendicular transversely isotropic plane (the direction of the X-axis); μ′ is the transverse isotropy in-plane Poisson's ratio; μ is the Poisson's ratio in the direction of the perpendicular transverse isotropic plane; G′ is the shear modulus in the transversely isotropic plane; an G is the shear modulus in the direction of the perpendicular transversely isotropic plane.

The shear moduli (G and G′) and Poisson's ratios (μ and μ′) are very small,^34,35 while the transverse elastic moduli E′ are small compared to the longitudinal elastic modulus E. Table 2 lists the elastic material data for the yarn continuum.

Table 2.

The orthotropic elastic material data for polyamide-66 filaments

E (MPa)	E′ (MPa)	G (MPa)	G′ (MPa)	μ	μ′
5980	119.6	59.8	59.8	0	0

The bursting process of specimens is mainly axial tensile fracture of the yarn. Therefore, it is only necessary to establish the yarn axial tensile failure mechanism. The ultimate strain at the material integration point is used to determine the failure of the material, that is, if ɛ₁₁ > ɛ_11max, then the unit is failed. The axial tensile ultimate strain is obtained from the yarn tensile test, ɛ_11max = 0.16. The failure criterion is achieved by the ABAQUS user subroutine “VUSDFLD.”

The property of the impactor head is defined as a Young's modulus of 2.10 × 10⁵ MPa, density of 7.8 g/cm³, and Poisson's ratio of 0.3.

The rubber matrix is assumed as an isotropic, elastic–plastic material, where the elastic–plastic parameters are a modulus of 100 MPa, yield stress of 20 MPa, peak stress of 30 MPa, and plastic strain of 100%.

Finite element model

In the finite element (FE) model, the contacts between yarns of fabric are defined as “General contact,” with a frictional coefficient of 0.05. “Surface to surface contact” is defined between the impactor and yarns of the fabric, and the impactor and the rubber, with frictional coefficients of 0.10 and 0.28, respectively. The surface of the impactor is chosen as the master surface and the surfaces of the yarns and rubber are chosen as the slave surfaces. The “TIE” constraint is defined at the interface between the yarns and the annular clamps, and the yarns and the rubber. The impactor and annular clamps are treated as rigid bodies. RP-1, RP-2, and RP-3 are correspondingly the reference points of the impactor and the annular clamps.

The annular clamps have no freedom of displacement or rotation, while the translation and rotation freedoms of the impactor are prohibited, except the translation along the direction perpendicular to the surface of the fabric, as shown in Figure 6. The impactor, annular clamps, TWF, and TWFR are meshed using C3D8R solid elements. In the FE model, there are 54,515 elements and 99,570 nodes for TWF, 50,744 elements and 118,882 nodes for PWF, 168,148 elements and 246,387 nodes for TWFR, 163,162 elements and 240,644 nodes for PWFR, and 3771 elements and 5192 nodes for the impactor head.

Figure 6.

Boundary conditions of the finite element model: (a) triaxial woven fabric; (b) reinforced triaxial woven fabric. Note: U1, U2, and U3 are the X-, Y-, and Z-directional translational degrees of freedom, and UR1, UR2, and UR3 are the X-, Y-, and Z-directional rotational degrees of freedom.

Results and discussion

Load–displacement curves of specimens

Figures 7(a) and (b) show the load–displacement curves of fabrics and fabric-reinforced rubber composites from both FEA simulations and experiments, respectively. It is obvious that the results of FEA have a larger fracture load and higher slope of the load–displacement curve, and smaller initial damage displacement. This is mainly caused by differences in the boundary condition and yarn shape of FEA and the experiment. In FEA, the boundary of the fabrics is completely fixed and yarns are considered as a continuum with identical properties, ignoring complex monofilament arrangements and twisting. In the experiment, the yarns are composed of monofilaments with curl and friction, which can result in yarn breakage at different times. Besides, a certain degree of yarn slippage can occur during the experiment. Hence, the fracture load of the experiment is less than that of FEA. For fabric-reinforced rubber composites, because the rubber matrix resists deformation better than the fabric reinforcement, the damage resistant performance of fabric-reinforced rubber composites during the bursting process mainly depends on the fabric, that is, the fabric is broken firstly followed by the matrix being destroyed by stress concentration. Accordingly, the reasons that resulted in the difference between the simulation result and the experimental result for fabric-reinforced rubber composites are similar.

Figure 7.

Load–displacement curves of specimens from the experiment and finite element analysis (FEA). Note: “N” and “E” respectively denote the results of FEA and the experiment. TWF: triaxial woven fabric; PWF: plain woven fabric; TWFR: reinforced triaxial woven fabric; PWFR: reinforced plain woven fabric.

For fabric-reinforced rubber composites, the deformation of the rubber matrix is better than that of the fabric. The damage resistant performance of fabric-reinforced rubber composites during the bursting process mainly depends on the fabric, that is, the fabric is broken firstly followed by the matrix being destroyed by stress concentration. Accordingly, the reasons that resulted in difference between the simulation result and the experimental result for fabric reinforced rubber composites is similar to fabrics.

Comparing Figures 7(a) and (b), the fabric-reinforced rubber composites have a larger failure load and steeper load–displacement curve slope than those of fabrics, but the initial damage displacement is similar to that of fabric. This is primarily due to the important role of the rubber matrix. Firstly, the rubber matrix contributes to the strength of the fabric-reinforced rubber composites. Secondly, the rubber matrix makes the fabric constitute a continuum, effectively preventing the filament yarns from slipping and transmitting load to other yarns that are not in contact with the impactor. Thirdly, the rubber matrix coheres to the monofilaments of the filament yarn as a whole, making the monofilaments simultaneously break under bursting load, as shown in Figure 8(b). In contrast, in fabrics each single filament of yarn breaks at a different time and is dispersed after fabric breakage, as shown in Figure 8(a). The loads of the fabrics drop to near zero after reaching the maximum load, while the loads of reinforced-rubber composites exhibit fluctuations and then remain near a certain value. This is mainly due to the super-elasticity of the rubber matrix. In the bursting process, for the fabrics, the fabric structure becomes loose after yarn breaking, so there is no friction between the fabric and the impactor. For the fabric-reinforced rubber composites, although the yarns contacted with the impactor come into breaks at the maximum strain, the rubber matrix prohibited them from slipping and made them still tightly grip the impactor. Because of this, the fabric-reinforced rubber composites upon breakage still bore the load until the impactor completely penetrated through. However, the load the fabric-reinforced rubber composites could bear was small. For fabrics, the results of the experiment and FEA show that TWF has steeper load–displacement curve slopes, higher maximum loads, and smaller initial damage displacements than PWF. For fabric-reinforced rubber composites, the results of the experiment show that TWFR has steeper load–displacement curve slopes and smaller maximum loads and initial damage displacements than PWFR, but the results of FEA show that load–displacement curves of TWFR and PWFR are similar.

Figure 8.

Damage morphologies of yarns: (a) fabric; (b) fabric-reinforced rubber composites (specification of the scanning electron microscope, SU1510, is 5.00 kv 7.8 mm × 65 SE).

Bursting morphologies of fabrics and their reinforced rubber composites

Figure 9 exhibits the bursting morphologies of TWF and PWF from FEA and experiments. After bursting damage, the ruptured yarn disintegrates and the fabric structure becomes loose due to pulling-out of the yarn. It is obvious that the FEA results are validated by the deformation profiles of TWF and PWF in the experiments. The damage morphology of TWF is approximately circular or hexagonal, while the damage morphology of PWF is perpendicular along the yarns. Comparing the bursting morphologies of TWF and PWF, the structure of TWF is more stable than that of PWF, and the breakage is more difficult to expand. Figure 10 shows that the bursting morphologies of TWFR are approximately circular, while those of PWFR are perpendicular along the yarns. Only the portion contacted with the impactor is subject to fracture, and the portion not contacted with the impactor is only deformed during the bursting process due to the consolidation effect of the rubber matrix. When the bursting process is completed, undamaged fabric-reinforced rubber composites return to their original state. Evidently, the rubber matrix not only significantly increases the bursting strength of the woven fabric, but also reduces the bursting damage area.

Figure 9.

The bursting morphologies of fabrics from finite element analysis (FEA) and experiments. TWF: triaxial woven fabric; PWF: plain woven fabric.

Figure 10.

The bursting morphologies of fabric-reinforced rubber composites from finite element analysis (FEA) and experiments. TWFR: reinforced triaxial woven fabric; PWFR: reinforced plain woven fabric.

This phenomenon can be explained by the self-locking feature of TWF, as shown in Figure 11, which makes the three set of yarns form a plurality of force triangles, like a knot. The resultant forces of “Fa” and “Fb” in the triangular region not only make yarns “a” and “b” gather together, but also make yarn “c” tie into a bundle. The self-locking feature of TWF prevents yarns from slipping. The number of sliding yarns and the degree of yarn slippage in TWF are less than those in PWF, as shown in Figure 10, so the maximum load of TWF is larger than that of PWF, as shown in Figure 7.

Figure 11.

Schematic diagram of the self-locking feature of triaxial woven fabric: (a) interlacing; (b) interlocking; (c) structural unit.

Bursting damage mechanism

Figure 12 shows the bursting process for fabrics and their reinforced rubber composites, respectively, which can be divided into four stages: yarn straightening, yarn slippage, yarn breakage, and breakage extension.

Figure 12.

Bursting process of fabrics by finite element analysis.

In the first stage, as shown in Figures 12(a) and (e), the impactor starts to contact the surface of the fabric, and the yarn in direct contact with the punch is gradually straightened from the flexed state. The stress is transferred to the adjacent yarn through the interleaving point, so that the fabrics are under tension.

In the second stage, as shown in Figures 12(b) and (f), the deflection of the fabric increases as the impactor moves further downward. The fabric changes from a planar-like structure to a structure consisting of a spherical crown and a truncated cone. Afterwards, the yarns start slipping, which makes the gap between the yarns increase.

In the third stage, as shown in Figures 12(c) and (g), as the impactor continues to move down, the yarns in contact with the impactor approach the fracture strain and begin to fracture, and the broken yarns are pulled out from the fabrics. The load of the load–displacement curves at this point also reaches maximum and drops rapidly.

In the final stage, as shown in Figures 12(d) and (h), as the impactor moves down further, the breakage expands in the direction of the yarn until the punch completely penetrates the fabric.

The damage mechanism of the fabric-reinforced composites is similar to that of the fabrics, as shown in Figure 13. Due to the consolidation effect of the rubber matrix, the degree of slippage of the yarns in the fabric-reinforced rubber composite is much smaller than that of the fabrics.

Figure 13.

Bursting process of fabric-reinforced rubber composites by finite element analysis.

Conclusions

The bursting performances of TWF and TWFR are investigated based on FE simulation and experiments to understand the bursting process and damage mechanism. The interlocking property between the yarns of TWF limits the lateral slip of the yarns, so TWF has a higher fracture load and smaller initial damage displacement than PWF. After breaking, the breakage of TWF is difficult to expand quickly, and TWF shows good structural stability. The rubber matrix protects fabrics from direct contact with the impactor and distributes the concentrated load of the impactor to other areas of the specimen, so that the bursting strength of the fabric-reinforced rubber composites is much greater than that of the fabrics. By comparing the bursting morphologies and load–displacement curve of specimens, the results obtained from FEA are in good agreement with those of the experiments, which proves the accuracy and feasibility of simulation with the FE method.

Footnotes

Declaration of conflicting interests

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

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of China (Grant No. 51703083), the Natural Science Foundation of Jiangsu Province (PR China) (Grant No. BK20160157), Practical training for young teachers in higher vocational colleges in Jiangsu Province (2019QYSJPX059), the Qinglan Project of the Jiangsu Higher Education Institutions of China (Grant No. 201715, 201903), and the High Education Science Foundation of Jiangsu Province (Grant No 18KJB540005).

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