  We study size effects in the fracture strength of notched disordered samples
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 allow 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).
