Crack propagation in a material with random toughness

An efficient Monte Carlo procedure is presented for characterizing the propagation of a crack in a material whose fracture toughness is a random field. The simulations rely on accurate approximate solutions of the integral equations that govern the dislocation densities, stress intensity factors, and energy release rates of curvilinear cracks. For a plate containing an edge crack that propagates towards a subsurface crack representing a traction-free boundary, results for the distributions of crack trajectories, critical applied far-field stresses, and nominal fracture toughness are presented for various parameters that quantify the randomness of the material's critical energy release rate. A demonstrative probabilistic model for crack trajectories is built and size effects are discussed.