  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.
