Interfacial Crack Pinning: Effect of Nonlocal Interactions

We propose a perturbative approach to describe the evolution of an interfacial crack between two elastic solids with quenched disorder. The driving force is the stress intensity factor along the crack front. The latter is expressed as a function of the entire crack geometry through a linear convolution with a long-ranged kernel using a first order approximation developed by Gao and Rice [J. Appl. Mech. 56, 828 (1989)]. The resulting problem is studied numerically and is shown to give rise to self-affine geometries with a roughness exponent $\zeta =0.35\mathrm{}$ and a dynamic exponent $z=1.5\mathrm{}$, very different from the corresponding exponents obtained with a local form of the driving force.