Crack path in an elastic material with a random array of small defects

This paper is devoted to the problem of interaction of a semi-infinite crack (propagating in elastic material) with a random array of small defects (e.g. inclusions, voids). This interaction manifests itself in changes of the crack orientation and, overall in randomly varying curvilinear crack trajectories. Making use of the asymptotic results proposed in (Movchan, 1991, 1995) the procedure for configurational averaging is presented which yields the mean crack path and the standard deviation from the mean. The general formulae for the mean crack path can serve as a basis for effective quantitative analysis for specific situations of practical interest. The illustrative examples elaborated in the paper show dependence of the shape of crack trajectory on the probabilistic characteristics of random locations of inclusions and on their elastic parameters. The analysis performed in the paper can be directly used in prediction of failure mechanisms of brittle materials containing small randomly distributed inclusions/voids.