Developing a stochastic model to predict the strength and crack path of random composites

Abstract

We characterize fracture and effective stress–strain graphs in 2D random composites subjected to a uniaxial in-plane uniform strain. The fibers are arranged randomly in the matrix. Both fibers and matrix are isotropic and elastic–brittle. We conduct this analysis numerically using a very fine two-dimensional triangular spring network and simulate the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. In particular, we focus on effect of geometric randomness on crack path of random composites. Based on that two stochastic micro-mechanic models are presented that can predict with confidence the failure probability of random matrix–inclusion composites.