Nucleation of interfacial shear cracks in thin films on disordered substrates

TL;DR

This paper develops a theoretical model for shear failure in thin films on disordered substrates, analyzing crack nucleation and interfacial strength based on statistical properties of the interface.

Contribution

It introduces a gradient-based model for interfacial shear stresses and evaluates crack nucleation probabilities considering interface disorder.

Findings

Interfacial shear stresses can be approximated by a second-order gradient of shear displacement.

The model predicts the probability of critical crack nucleation based on stress and interface disorder.

Interfacial shear strength depends on film geometry and statistical properties of the interface.

Abstract

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.