Stochastic approach to multiple cracking in composite systems based on the extreme-values theory

A stochastic model of fragmentation of brittle constituents, which has been pioneered for ceramic matrix composites, is revisited. It consists in a stochastic description of the brittle fracture of successive fragments having a decreasing size. Fracture of a fragment is caused by its most severe flaw. The approach is based on the low extremes of fragment flaw strength distributions.The paper is aimed at assessing the approach and its potential application to various composite systems containing brittle constituents, such as polymer matrix composites or multi-layers. Expressions for fragments and fibers failures involve various random variables. The influence of the random variables on tensile stress–strain behaviour predictions was investigated. Fragment strength–size relationships were established using tensile tests performed on C/SiC minicomposites in the chamber of a scanning electron microscopy (SEM). Experimental data and predictions validated the approach. Important implications for the prediction of multiple cracking and resulting stress–strain behaviour are discussed. Then simple analytical expressions were derived.