Fracture surfaces of heterogeneous materials: A 2D solvable modelE. Katzav, M. Adda-Bedia and B. Derrida
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS UMR 8550 - 24 rue Lhomond, 75231 Paris Cedex 05, France
received 24 January 2007; accepted in final form 10 April 2007; published May 2007
published online 8 May 2007
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.
68.35.Ct - Interface structure and roughness .
62.20.Mk - Fatigue, brittleness, fracture, and cracks .
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
© Europhysics Letters Association 2007