Fracture surfaces of heterogeneous materials: A 2D solvable model

Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS UMR 8550 - 24 rue Lhomond, 75231 Paris Cedex 05, France

Corresponding author: eytan.katzav@lpt.ens.fr

Received: 24 January 2007
Accepted: 10 April 2007

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 nonsingular 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.