A simple two-dimensional model for crack propagation

Abstract

Simple models for crack growth which are closely related to the diffusion-limited aggregation (DLA) model have been explored using computer simulations. In these models the bond-breaking probabilities for bonds at the surface of a growing crack in a two-dimensional (triangular) network of bonds and nodes are proportional to ( delta _i)^eta and delta _i is the bond strain. The authors' results indicate that the cracks generated by these models have a fractal structure and that their effective dimensionalities depend on both the bond-breaking probability exponent ( eta ) and the boundary conditions (which bonds are considered to be surface bonds that can be broken) at the crack surface. Very similar results were obtained using shear and dilational strain.