Roughness of tensile crack fronts in heterogenous materialsE. Katzav and M. Adda-Bedia
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05, France
received 3 July 2006; accepted in final form 1 September 2006
published online 29 September 2006
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 , 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 experiments might become history dependent, and so our result gives a lower bound for .
62.20.Mk - Fatigue, brittleness, fracture, and cracks.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
64.60.Ht - Dynamic critical phenomena.
© EDP Sciences 2006