In this paper, the meso-scale finite element method is used to evaluate the transverse tensile damage behaviors of three-dimensional five-directional braided composites based on the representative volume cell. Finite element models with two kinds of interior braiding angles, 30° and 45°, are established on the basis of the realistic geometry shape of each yarn. A continuum damage mechanics model, which is implemented as a user-defined material subroutines in the ABAQUS commercial finite element code, is used to capture the complete damage initiation/evolution in yarns and matrix. The local responses and the failure mechanisms are analyzed. Numerical results show that the transverse tensile strength and the failure mechanisms are significantly influenced by the braiding angle. The predicted stress–strain responses and final damage morphology agree well with the experimental data, verifying the applicability of the meso-scale finite element method.
ChenLTaoXMChoyCL. On the microstructure of three-dimensional braided preforms. Compos Sci Technol1999; 59: 391–404.
2.
MouritzAPBannisterMKFalzonPJ. Review of applications for advanced three-dimensional fibre textile composites. Compos A1999; 30: 1445–1461.
3.
BilisikKSahbazN. Structure-unit cell based approach on three-dimensional representative braided preforms from four-step braiding: experimental determination of effects of structure-process parameters on predetermined yarn path. Text Res J2012; 82: 220–241.
4.
KoFKPastoreCMStructure and properties of an integrated three dimensional fabric for structural composites. In: VinsonJRTayaM (eds). Recent advances in composites in the United States and Japan, ASTM STP 864. Philadelphia, PA: ASTM, 1985, pp. 428–439.
5.
WambuaPMAnandjiwalaR. A review of preforms for the composites industry. J Ind Text2011; 40: 310–333.
6.
KalidindiSRAbusafiehA. Longitudinal and transverse moduli and strengths of low angle 3-D braided composites. J Compos Mater1996; 30: 885–905.
7.
SunBZLiuFGuBH. Influence of the strain rate on the uniaxial tensile behavior of 4-step 3D braided composites. Compos Part A-App S**2005; 36: 1477–1485.
8.
LiJLJiaoYNSunY. Experimental investigation of cut-edge effect on mechanical properties of three-dimensional braided composites. Mater Des2007; 28: 2417–2424.
9.
LiDSLuZXFangDN. Longitudinal compressive behavior and failure mechanism of three-dimensional five-directional carbon/phenolic braided composites at high strain rates. Mat Sci Eng A Struct2009; 526: 134–139.
10.
SongLLLiJL. Effects of heat accelerated aging on tensile strength of three dimensional braided/epoxy resin composites. Polym Compos2012; 33: 1635–1643.
11.
CarvelliVPazminoJLomovSV. Quasi-static and fatigue tensile behavior of a 3D rotary braided carbon/epoxy composite. J Compos Mater2013; 47: 3195–3210.
12.
LiZMZhaoYXChenXD. Non-linear buckling and postbuckling behavior of 3D braided cylindrical panels under axial compression in thermal environments. Mech Adv Mater Struct2014; 21: 490–504.
13.
XuJLomovSVVerpoestI. A progressive damage model of textile composites on meso-scale using finite element method: static damage analysis. J Compos Mater2014; 48: 3091–3109.
14.
LeiCYun-JCKoF. Finite elment analysis of 3-D braided composites. Adv Eng Softw1992; 14: 187–194.
15.
GreenSDMatveevMYLongAC. Mechanical modelling of 3D woven composites considering realistic unit cell geometry. Compos Struct2014; 118: 284–293.
16.
BednarcykBAStierBSimonJW. Meso-and micro-scale modeling of damage in plain weave composites. Compos Struct2015; 121: 258–270.
17.
ZhangCBinienadaWK. A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite. Mech Mater2014; 76: 1–19.
18.
LiDSLuZXLuWS. Theoretical prediction of stiffness and strength of three-dimensional and four-directional braided composites. Appl Math Mech Engl2008; 29: 163–170.
19.
FangGDLiangJWangY. The effect of yarn distortion on the mechanical properties of 3D four-directional braided composites. Compos Part A App S2009; 40: 343–350.
20.
FangGDLiangJLuQ. Investigation on the compressive properties of the three dimensional four-directional braided composites. Compos Struct2011; 93: 392–405.
21.
LuZXWangCYXiaB. Effect of interfacial properties on the uniaxial tensile behavior of three-dimensional braided composites. Compos Mater Sci2013; 79: 547–557.
22.
JiangLLZengTYanS. Theoretical prediction on the mechanical properties of 3D braided composites using a helix geometry model. Compos Struct2013; 100: 511–516.
23.
LiSHLiuLFYanJH. An approach for testing and predicting longitudinal tensile modulus of 3D braided composites. J Reinf Plast Compos2014; 33: 775–784.
24.
WuLWSunBZGuBH. Numerical analyses of bending fatigue of four-step three-dimensional rectangular-braided composite materials from the unit cell approach. J Text Inst2015; 106: 67–79.
25.
XuLJinCZHaSK. Ultimate strength prediction of braided composites using a multi-scale approach. J Compos Mater2015; 49: 477–494.
26.
XuLKimSJOngCH. Prediction of material properties of biaxial and triaxial braided textile composites. J Compos Mater2012; 46: 2255–2270.
27.
ZhangYJiangLLSunBZ. Transverse impact behaviors of four-step 3-D rectangular braided composites from unit-cell approach. J Reinf Plast Compos2012; 31: 233–246.
28.
LiDSLuZXJiangN. High strain rate behavior and failure mechanism of three-dimensional five-directional carbon/phenolic braided composites under transverse compression. Compos Part B Eng2011; 42: 309–317.
29.
LiZMZhuPLinZQ. Nonlinear bending behavior of 3D braided rectangular plates subjected to transverse loads in thermal environments. Arch Appl Mech2011; 81: 585–603.
30.
ChuGPLiZM. Postbuckling behavior of 3D braided rectangular plates subjected to uniaxial compression and transverse loads in thermal environments. Sci China Technol Sci2014; 57: 1439–1453.
31.
LiJCChenLZhangYF. Microstructure and finite element analysis of 3D five-directional braided composites. J Reinf Plast Compos2012; 31: 107–115.
32.
Reifsnider K. Some fundamental aspects of the fatigue and fracture response of composite mateirals. In: GC Sih (ed.) Proceedings of the 14th annual meeting, Society of Engineering Science, USA, 1977, pp.373–384. Bethlehem, PA: Lehigh University.
BazantZPOhBH. Crack band theory for fracture of concrete. Mater Struct1983; 16: 155–177.
35.
LapczykIHurtadoJA. Progressive damage modeling in fiber-reinforced materials. Compos Part A App S2007; 38: 2333–2341.
36.
MaimiPCamanhoPPMayugoJA. A continuum damage model for composites laminates: part II – computational implementation and validation. Mech Mater2007; 38: 909–919.
37.
MurakamiS. Mechanical modeling of material damage. J Appl Mech1988; 55: 280–280.
38.
CordeboisJSidoroffF. Anisotropic damage in elasticity and plasticity. J Mec Theor Appl1982, pp. 45–60.
39.
CordeboisJSidoroffF. Damage induced elastic anisotropy. Mechanical Behavior of Anisotropic Solids1982, pp. 761–774.
40.
SeguradoJLlorcaJ. A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids2002; 50: 2107–2121.
41.
SuquetP. Elements of homogenization theory for inelastic solid mechanics. Homogenization techniques for composite media, Berlin: Springer Verlag, 1987.
42.
WhitcombJDChapmanCDTangXD. Derivation of boundary conditions for micromechanics analysis of plain and satin weave composites. J Compos Mater2000; 34: 724–747.
43.
XiaZHZhangYFEllyinF. A unified periodical boundary conditions for representative volume elements of composites and applications. Int J Solids Struct2003; 40: 1907–1921.
44.
KohlmanLWBailJLRobertsGD. A notched coupon approach for tensile testing of braided composites. Compos Part A App S2012; 43: 1680–1688.
45.
ZhangCBiniendaWKKohlman. Analytical and numerical analysis on elastic behavior of triaxial braided composites. J Aerosp Eng2014; 27: 473–483.
