Stastical modelling of fracture in quasi-brittle materials

The fracture behavior of heterogeneous brittle materials was studied using statistical modeling. The approach involved the homogenization of the elastic properties of the material and assumption of a local rupture stress distributed randomly inside the material. A weak link transformation rule was applied to describe the size dependence of failure probability distributions within a limited range of system sizes for a 3D array of fibers. Different mesoscale finite element models were applied to damage and fracture of brittle or quasi-brittle heterogeneous materials. It was found that, a phase of progressive diffuse damage , which contributed to the stability of the material, suddenly changed into a phase of catastrophic cracking without further load increment, the maximum stress corresponding to the transition point. The failure probability distributions obtained from simulations obeyed a weak link scaling transformation within a limited range of sample sizes.