Fracture toughness and maximum stress in a disordered lattice system

We model the disorder-induced increase in fracture strength by applying a two-dimensional elastic network with an initial crack. The model has all the nearest neighbors, except those on the initial crack, connected by springs, which are randomly chosen as either hard or soft. All the springs are cut at the same force threshold. Our calculations show that the maximum stress in the disordered system is increased if the initial crack length is sufficiently large, and we discuss the relationship between the crack length and the force distribution or the work done on the system. We also derive the enhancement of the stress intensity factor and fracture toughness by analyzing the generation of the fracture process zone.