E. Katzav and M. Adda-Bedia 2006 Europhys. Lett. 76 450 doi:10.1209/epl/i2006-10273-7
E. Katzav and M. Adda-Bedia
Show affiliationsThe 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 ζ = 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 experiments might become history dependent, and so our result gives a lower bound for ζ.
05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
Issue 3 (November 2006)
Received 3 July 2006, accepted for publication 1 September 2006, in final form 1 September 2006
Published 29 September 2006
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