Scaling properties of the three-dimensional fuse model as a model for brittle fracture

Abstract

Fracture morphology has for the last two decades gained much interest seen from a fundamental point of view. Experimental evidence point out a self-affine scaling of such fracture surfaces, which leads to the fact that the roughness of the fracture scales with the size of the system as w∼L^ζ. We have implemented a numerical network of random fuses in three dimensions in order to study breakdown processes of brittle materials. With this model we have been able to measure critical exponents at breakdown, and in that sense gained information of the scaling laws involved in the morphology of fracture surfaces. We have studied both the scaling of roughness and behavior of the correlation length ξ for broad distributions in order to examine the linkage between them. A newly proposed relation by Hansen and Schmittbuhl gives ζ=2ν/(1+2ν). By using the relation ξ∼|p−p_c|^−ν from percolation theory we measure the critical correlation length exponent ν=0.83±0.06. From this value we derive a value for the roughness exponent ζ=0.62±0.05 in the three-dimensional fuse model. This is consistent with previous studies on the fuse model in three dimensions.