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 xi. The problem is shown to have two important length scales, xi and the Larkin length L(c). Multiscaling of the crack front is observed for scales below xi, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent zeta approximate to 0.39 is recovered for scales larger than both xi and L(c). If L(c) > xi, these regimes are separated by a third regime characterized by the Larkin exponent zeta(L) approximate to 0.5. We discuss the experimental implications of our results.