Stress and Strain Concentration Tensors for Damaged Fibrous Composites

Abstract

As composite materials undergo damage, the corresponding stress and strain concentration tensors do not remain constant even for the case of elastic deformations.These tensors are derived and presented here for fibrous composites that undergo damage in both the constituents and the interfacial surface. The damage in the matrix includes nucleation and growth of voids, etc., while in the fibers includes micro-fracture, etc. In addition, interfacial damage is described as the damage due to debonding. The damaged stress and strain concentration tensors are obtained for the elasto-plastic states of the composite material. Expressions are derived and presented here for the elasto-plastic stress and strain concentration tensors for fibrous composite materials in the damaged conigurations. The fibers are assumed to be continuous in this work. The elastic strain and stress concentration tensors using the Mori-Tanaka method for the case of undamaged fiberous composites are formulated by Chen, et al. (1992). These elastic concentration tensors are constant in the undamaged or effective configuration due to the fact that damage effects in the material are ignored. However, these damaged elasto-plastic concentration tensors are a function of the fourth order damage tensors in the damaged configuration.