Roughness and multiscaling of planar crack fronts
Lasse Laurson, Stefano Zapperi
Journal of Statistical Mechanics: Theory and Experiment
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≈ 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 ≈ 0.5. We discuss the experimental implications of our results.