Summary: Europhys. Lett., 76 (3), pp. 450456 (2006)
EUROPHYSICS LETTERS 1 November 2006
Roughness of tensile crack fronts
in heterogenous materials
E. Katzav and M. Adda-Bedia
Laboratoire de Physique Statistique de l'Ecole Normale Sup´erieure
24 rue Lhomond, 75231 Paris Cedex 05, France
received 3 July 2006; accepted in final form 1 September 2006
published online 29 September 2006
PACS. 62.20.Mk Fatigue, brittleness, fracture, and cracks.
PACS. 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
PACS. 64.60.Ht Dynamic critical phenomena.
Abstract. The dynamics of planar crack fronts in heterogeneous media is studied using
a recently proposed stochastic equation of motion that takes into account nonlinear effects.
The analysis is carried for a moving front in the quasi-static regime using the Self Consistent
Expansion. A continuous dynamical phase transition between a flat phase and a dynamically
rough phase, with a roughness exponent = 1/2, is found. The rough phase becomes possible
due to the destabilization of the linear modes by the nonlinear terms. Taking into account
the irreversibility of the crack propagation, we infer that the roughness exponent found in