Effect of disorder strength on the fracture pattern in heterogeneous networks

Abstract

We present simulation results on fracture and random damage percolation in disordered two-dimensional (2D) lattices of different sizes. We systematically study the effect of disorder strength on the stress-strain behavior and on the evolving fracture pattern. In particular, the similarity of damage-cluster statistics between fracture and random percolation is investigated. For fracture in highly disordered systems, we confirm and extend our earlier results on the existence of a percolationlike damage regime, with accurate scaling laws for the cluster statistics, but we show that this regime vanishes at intermediate disorder strength. For low disorder, a qualitatively different and anisotropic damage pattern develops from the very beginning of loading. Both for low and high disorder strengths, macroscopic localization and strong damage anisotropy set in around the maximum-stress point, leading to the final crack formation. The surface roughness of the ultimate crack shows accurate size scaling, with a universal roughness exponent independent of the disorder strength but slightly dependent on the precise definition of the crack profile. The simulated roughness exponent is in good agreement with other numerical and experimental results on 2D systems and also close to the prediction of gradient percolation.