Roughness of a mode I in-plane crack front propagating along a heterogeneous cohesive interface

The roughness of the crack front of an interfacial crack propagating along a weak plane in a heterogeneous disordered medium has been repeatedly studied both experimentally and numerically. For an interfacial toughness varying randomly on the interface, the front is self-affine. Quite often, however, the calculated roughness exponent differs from the experimental estimate. Several theoretical models have been employed up to now in the numerical simulations (elastic line depinning, random fuse and spring or beam models). In this paper we present finite element simulations (FEA) of the macroscopic mode-I static propagation of a crack front along a planar interface of an elastic or elastic-plastic coating adhered to a rigid substrate. The interfacial elements separate obeying a cohesive law, their toughness spatially fluctuating at random. The cohesive elements here employed allow for taking into account local I + II + III mixed-opening mode, i.e., allow for mode mixity at the local level. Our results indicate that for a given macroscopic toughness the crack front roughness is strongly sensitive to both the local cohesive law and the local fracture criterion.