Damaged mosaic laminate model of woven fabric composites with transverse yarn cracking and interface debonding

A variational solution based on the principle of minimum complementary energy is presented for a damaged mosaic laminate model of woven fabric composites. Two damage modes, i.e. transverse yarn cracking and interface debonding, are considered. The stress components in the debonded segments of the laminate are obtained explicitly, while those in the perfectly bonded laminate segments are presented in terms of a perturbation function, which is governed by two fourth-order inhomogeneous ordinary differential equations. All possible expressions of this perturbation function are obtained in closed forms. The effective Young modulus and Poisson ratio of the damaged laminate are calculated using the determined stress field and the associated minimum complementary energy. Being applicable to the woven laminate in either the plane strain or the plane stress state, with the yarn materials either orthotropic or transversely isotropic, the current closed-form solution is very suitable for parametric studies. To demonstrate the application of the solution, a parametric study of some 176 sample cases is conducted using two different composite systems (i.e. glass fiber/epoxy and ceramic fiber/ceramic), four transverse yarn crack densities and eleven debonded lengths. The numerical results obtained here for the cases involving only the first damage mode (i.e. transverse yarn cracking) are identical with those reported in an earlier paper by Gao and Mall [Int J Solids Struct 38 (2001) 855]. When both the first and second damage modes are present, the sample calculations of this study quantitatively illustrate the effects of the two co-existing types of damage on the reduction in Young's modulus and Poisson's ratio of the damaged woven laminate. (C) 2002 Elsevier Science Ltd. All rights reserved.