Engineering application of textile composites needs simple relations for the estimation of their mechanical properties. Many homogenization and simplified models have been already proposed for the analytical characterization of the elastic moduli of this class of materials. Along this route, the current study introduces an analytical solution for the longitudinal elastic modulus of plain-woven textile composites. A hybrid beam-spring model of the representative unit cell (RUC) is postulated consisting of a horizontal beam connected to an inclined beam, two supporting springs beneath the free end of the horizontal beam and the common end of the horizontal and inclined beams, and a torsion spring at the free end of the inclined beam. The mechanical and geometrical properties of the beams and springs are calculated from the weave structure and the symmetry conditions. A reduction technique from the matrix analysis of structures is borrowed to consider the effect of internal degrees of freedom on the in-plane stiffness coefficient and a closed-form formula is extracted for the elastic modulus. The proposed analytical formula is finally verified against available experimental data and a wide range of FE predictions for the GFRP and CFRP plain-woven composites.
NaikNGaneshV. Prediction of on-axes elastic properties of plain weave fabric composites. Compos Sci Technol1992; 45: 135–152.
6.
RajuISWangJT. Classical laminate theory models for woven fabric composites. Compos Technol Res1994; 16: 289–303.
7.
TanPTongLStevenGP. Micromechanics models for mechanical and thermomechanical properties of 3D through-the-thickness angle interlock woven composites. Compos Part A Appl Sci Manuf1999; 30: 637–648.
8.
TanPTongLStevenG, et al.Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation. Compos Part A Appl Sci Manuf2000; 31: 259–271.
9.
TanPTongLStevenG. Behavior of 3D orthogonal woven CFRP composites. Part II. FEA and analytical modeling approaches. Compos Part A Appl Sci Manuf2000; 31: 273–281.
10.
HallalAYounesRFardounF, et al.Improved analytical model to predict the effective elastic properties of 2.5 D interlock woven fabrics composite. Compos Struct2012; 94: 3009–3028.
11.
HallalAYounesRNehmeS, et al.A corrective function for the estimation of the longitudinal Young’s modulus in a developed analytical model for 2.5 D woven composites. J Compos Mater2011; 45: 1793–1804.
12.
GommersBVerpoestIVan HoutteP. The Mori–Tanaka method applied to textile composite materials. Acta Mater1998; 46: 2223–2235.
13.
LuaJ. Thermal–mechanical cell model for unbalanced plain weave woven fabric composites. Compos Part A Appl Sci Manuf2007; 38: 1019–1037.
14.
ProdromouAGLomovSVVerpoestI. The method of cells and the mechanical properties of textile composites. Compos Struct2011; 93: 1290–1299.
15.
StigFHallströmS. Influence of crimp on 3D-woven fibre reinforced composites. Compos Struct2013; 95: 114–122.
16.
ChengXXiongJ. A novel analytical model for predicting the compression modulus of 2D PWF composites. Compos Struct2009; 88: 296–303.
17.
XiongJShenoiRChengX. A modified micromechanical curved beam analytical model to predict the tension modulus of 2D plain weave fabric composites. Compos B Eng2009; 40: 776–783.
18.
NaikNTiwariSKumarR. An analytical model for compressive strength of plain weave fabric composites. Compos Sci Technol2003; 63: 609–625.
19.
DerakhshanDKomeiliMMilaniA. An analytical approach to the deflection analysis of woven preforms and composites under tensile loading using the Winkler theory of curved beams. Comput Mater Sci2015; 96: 403–410.
20.
De CarvalhoNPinhoSRobinsonP. Analytical modelling of the compressive and tensile response of woven composites. Compos Struct2012; 94: 2724–2735.
21.
De CarvalhoNPinhoSRobinsonP. Numerical modelling of woven composites: Biaxial loading. Compos Part A Appl Sci Manuf2012; 43: 1326–1337.
22.
LiangBZhangWFennerJS, et al.Multi-scale modeling of mechanical behavior of cured woven textile composites accounting for the influence of yarn angle variation. Compos Part A Appl Sci Manuf2019; 124: 105460.
23.
ZhouLSunXChenM, et al.Multiscale modeling and theoretical prediction for the thermal conductivity of porous plain-woven carbonized silica/phenolic composites. Compos Struct2019; 215: 278–288.
24.
BrownDMorganMMcIlhaggerR. A system for the automatic generation of solid models of woven structures. Compos Part A Appl Sci Manuf2003; 34: 511–515.
25.
ZhouLChenMLiuC, et al.A multi-scale stochastic fracture model for characterizing the tensile behavior of 2D woven composites. Compos Struct2018; 204: 536–547.
26.
ChenYAliabadiM. Meshfree-based micromechanical modelling of twill woven composites. Compos B Eng2020; 197: 108190.
27.
BiblisEJ. Shear deflection of two species laminated wood beams. Wood Sci Technol1967; 1: 231–238.
28.
BatheKJ. Finite element procedures. 2nd ed.Watertown: Prentice Hall, 2014.
29.
ScidaDAbouraZBenzeggaghM, et al.Prediction of the elastic behaviour of hybrid and non-hybrid woven composites. Compos Sci Technol1998; 57: 1727–1740.
30.
ScidaDAbouraZBenzeggaghM, et al.A micromechanics model for 3D elasticity and failure of woven-fibre composite materials. Compos Sci Technol1999; 59: 505–517.
31.
BarberoEJDamianiTMTrovillionJ. Micromechanics of fabric reinforced composites with periodic microstructure. Int J Solids Struct2005; 42: 2489–2504.
32.
BarberoETrovillionJMayugoJ, et al.Finite element modeling of plain weave fabrics from photomicrograph measurements. Compos Struct2006; 73: 41–52.
33.
KowalczykP. Enhanced geometric model for numerical microstructure analysis of plain-weave fabric-reinforced composite. Adv Compos Mater2015; 24: 411–429.
34.
KiraneKSalviatoMBažantZP. Microplane triad model for simple and accurate prediction of orthotropic elastic constants of woven fabric composites. J Compos Mater2016; 50: 1247–1260.
35.
IshikawaTMatsushimaMHayashiY, et al.Experimental confirmation of the theory of elastic moduli of fabric composites. J Compos Mater1985; 19: 443–458.
36.
ZhangYHardingJ. A numerical micromechanics analysis of the mechanical properties of a plain weave composite. Comput Struct1990; 36: 839–844.
37.
HanXGaoJFlemingM, et al.Efficient multiscale modeling for woven composites based on self-consistent clustering analysis. Comput Methods Appl Mech Eng2020; 364: 112929.
38.
XuZChenYCantwellW, et al.Multiscale modelling of scaling effects in the impact response of plain woven composites. Compos B Eng2020; 188: 107885.
