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 Lc. 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≈0.39 is recovered for scales larger than both ξ and Lc. If Lc > ξ, these regimes are separated by a third regime characterized by the Larkin exponent ζL≈0.5. We discuss the experimental implications of our results