Abstract
We perform simulations of crack growth in a brittle-elastic two-dimensional film bonded to a rigid substrate and subject to isotropic tensile stress. The motion of the film sites is dissipative and we consider both purely dissipative dynamics and dynamics with finite dissipation. In both cases, we find a threshold stress for crack growth below which the lattice is stable against further breaking. Effective fractal dimensions are computed for crack clusters nucleated by a single defect in an otherwise undamaged lattice with both finite and infinite dissipation. When the dissipation is infinite, the crack clusters have asymptotic fractal dimensions of 2-0 and exhibit a cross-over from a fractal dimension of 1 -0 to a fractal dimension of 2-0 as the stress in the lattice is increased from the threshold. When the dissipation is finite, all crack clusters grown with stress equal to or greater than the threshold stress have fractal dimensions of 2-0. These results contrast with those found in crack models which employ stochastic breaking rules. We argue that the inclusion of a realistically modelled substrate leads to the compact crack clusters that we find in our simulations.
