Fracture surfaces of heterogeneous materials: a 2D solvable model

TL;DR

This paper introduces an exactly solvable 2D stochastic model for crack propagation in heterogeneous brittle materials, providing analytical insights into fracture surface roughening and offering an alternative to traditional power law analysis.

Contribution

It presents a novel, analytically solvable stochastic model for crack growth in heterogeneous materials, enhancing understanding of fracture surface roughening.

Findings

Analytic predictions for the power spectrum of crack paths.

Validation of model stability for straight cracks.

Alternative to conventional power law analysis.

Abstract

Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the non singular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.