Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.