Fracture size effects from disordered lattice models

We study size effects in the fracture strength of notched quasi-brittle materials using numerical simulations of lattice models for fracture. In particular, we consider the random fuse model, the random spring model and the random beam model, which all give similar results. These allow us to establish and understand the crossover between a regime controlled by disorder-induced statistical effects and a stress-concentration controlled regime ruled by fracture mechanics. The crossover is described by a scaling law that accounts for the presence of fracture process zone which we quantify by averaging over several disordered configurations of the model. The models can be used to study the development of the fracture process zone as the load is increased and to express this in terms of crack resistance (R-curve).