Fracture of random matrix-inclusion composites: scale effects and statistics

We study crack patterns and effective stress-strain curves in unidirectional fiber-matrix composites subjected to a uniform out-of-plane shear. The fibers are aligned in the longitudinal direction and arranged randomly, with no overlap, in the transverse plane. Both fibers and matrix are isotropic and elastic-brittle. We conduct this analysis numerically using a very fine two-dimensional spring network and simulate the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. In particular, we focus on effects of scale and geometric randomness in these composites. We consider several 'windows of observation' (scales) and study crack patterns, types of constitutive responses, and statistics of the corresponding scale dependent effective elastic stiffness and strength of such composites. In the parametric study we cover a wide range of material combinations defined by the stiffness ratio and the strain-to-failure ratio and we employ a damage plane in terms of these two parameters to illustrate the results.