Universality Classes in Constrained Crack Growth
Based on an extension of the fiber bundle model we investigate numerically the motion of the crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39 +/- 0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion rather than pinning of the crack front. We find a roughness exponent consistent with 2/3, which is the gradient percolation value. The length of the crack front is fractal on these smaller scales. We determine its fractal dimension to be 1.77 +/- 0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.