Elastic interaction of a crack with a random array of microcracks

Two issues are addressed in the paper. The first deals with a new characterization of a random array of microcracks in terms of spatial distributions of the sizes, orientations and density of microcracks. The second is a formulation of crack-microcrack array interaction in terms of the distributions. The interaction problem is posed as a system of two coupled singular integral equations with respect to a vector field of an average microcrack opening and the main crack opening displacement. The approach is illustrated by a numerical solution of the interaction problem for two particular configurations of a random array of microcracks. It is shown that the morphology of the microcrack array may strongly alter elastic fields in the vicinity of the main crack. Specifically, it is found that a variation in the microcrack length distribution (for fixed distributions of microcrack orientation and density) has a profound effect on the solution. The main crack opening displacement is evaluated to compare the theory with the experimental observations.