Abstract
We formulate a theoretical model of the shear failure of a thin film tethered to a rigidsubstrate. The interface between film and substrate is modeled as a cohesive layer withrandomly fluctuating shear strength/fracture energy. We demonstrate that, on scales largecompared with the film thickness, the internal shear stresses acting on the interface can beapproximated 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 thestress-dependent probability of nucleation of a critical crack. This is used to determine theinterfacial shear strength as a function of the film geometry and statistical properties of theinterface.
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