The effect of quenched disorder on the fractal dimension of crack for brittle fracture in two dimensions

Two-dimensional spring square network model involving the nearest and second neighbour bonds is studied by numerical simulation with Gauss–Seidel iteration for brittle fracture Mode I. The material-dependent parameter, G0/G, is introduced in this simulation, and G and G0 are the parameters related to the elastic moduli of the nearest and second neighbour bonds, respectively. Brittle fracture of the same material with different quenched disorders is simulated. Fractal dimension of crack fluctuates with quenched disorder. It seems that it is impossible to have a universal fractal dimension of crack in brittle fracture for the same material with different quenched disorders. However, it is possible to have different so-called universal fractal dimensions in some cases.