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Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone

Jean Schmittbuhl·Alex Hansen·G. George Batrouni
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Abstract

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.

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Jean Schmittbuhl, Alex Hansen, G. George Batrouni. 2002-07-22. Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone. https://doi.org/10.1103/physrevlett.90.045505

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