Roughness and multiscaling of planar crack fronts

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $ξ$. The problem is shown to have two important length scales, $ξ$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $ξ$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $ζ\approx 0.39$ is recovered for scales larger than both $ξ$ and $L_c$. If $L_c > ξ$, these regimes are separated by a third regime characterized by the Larkin exponent $ζ_L \approx 0.5$. We discuss the experimental implications of our results.

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