Efficacy of homogenization procedure for composites under mixed mode loading conditions

The aim of this study is to investigate the accuracy of homogenization based procedures in the prediction of failure mechanisms related to interfacial crack growth for fiber-reinforced elastic periodic composites. To this end an innovative method able to predict local failure quantities (fiber/matrix interfacial stresses, energy release and mode mixity for an interface crack) in an arbitrary cell from the results of classical homogenization analysis, is proposed. These local quantities are then adopted to predict crack initiation under mixed-mode loading conditions by using a coupled stress and energy failure criterion. A new numerical strategy for automatic simulation of arbitrary crack initiation in 2D finite element models has been implemented, taking advantage of a generalized J-integral formulation. Numerical simulations have been carried out for a plane-strain model of a locally periodic fiber-reinforced composite material subjected to transverse loading and characterized by an initially undamaged interface between matrix and fibers. Predictions for the critical load factor and interface crack length at crack onset obtained by the proposed model are compared with those obtained by means of a direct analysis. Results show the dependence of the critical load, interface crack length and position of the unit cell undergoing crack initiation on the ratio of the unit cell size to the global composite dimensions and on the global boundary conditions.