Stochastic microcrack nucleation in lamellar solids

Growth of a crack across an interface between two grains of an elastic lamellar material having different lamellar orientations is investigated for materials having a heterogeneous spectrum of individual lamellar toughnesses. Numerical analyses carried out using a cohesive zone model and the finite element method show that microcracking in the adjacent lamellae can preferentially occur at low-toughness lamellae spatially remote from the crack tip rather than at higher-toughness lamellae close to the crack tip. An analytic model based on linear elastic fracture mechanics and an initial microcrack is shown to predict the location and macroscopic toughness at which microcrack nucleation and growth occur in good agreement with the numerical analyses, using only the initial microcrack size as a single parameter. These results demonstrate that microcrack nucleation requires a sufficiently high stress over a sufficiently large region and thus that microcrack nucleation ahead of a main crack can be the dominant small-scale damage mechanism in such heterogeneous systems.