Nucleation of interfacial shear cracks in thin films on disordered substrates

We formulate a theoretical model of the shear failure of a thin film tethered to a rigid substrate. The interface between film and substrate is modeled as a cohesive layer with randomly fluctuating shear strength/fracture energy. We demonstrate that, on scales large compared with the film thickness, the internal shear stresses acting on the interface can be approximated by a second-order gradient of the shear displacement across the interface. The model is used to study one-dimensional shear cracks, for which we evaluate the stress-dependent probability of nucleation of a critical crack. This is used to determine the interfacial shear strength as a function of film geometry and statistical properties of the interface.