Failure probabilities and tough-brittle crossover of heterogeneous materials with continuous disorder

The failure probabilities or the strength distributions of heterogeneous on e-dimensional systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. Th e fracture behavior depends on the local bond-strength distribution, the sy stem size, and the applied stress, and crossovers occur as system size or s tress changes. In the brittle region, systems with continuous disorders hav e a failure probability of the modified Gumbel form, similar to that for sy stems with percolation disorder. The modified Gumbel form is of special sig nificance in weak stress situations. This new recursive method has also bee n generalized to calculate exactly the failure probabilities under various boundary conditions, thereby illustrating the important effect of surfaces in the fracture process.