Energy release rate for circular crack due to indentation in a brittle film on a ductile substrate

A recent method by Steffensen et al. (2013) to estimate the fracture toughness of thin, hard films uses closed-form linear elastic fracture mechanical models for an edge crack in a semi-infinite plane to calculate the energy release rate for a circumferential crack propagating from the surface of the film. Also, in the proposed model the in-plane shear stress was neglected, and it was assumed that the crack propagates perpendicular to the surface. In this paper, the accuracy of the previously proposed method for calculating the energy release rate for axisymmetric circumferential crack during indentation is investigated. Also, neglecting the in-plane shear stress and the assumed direction of crack propagation are investigated.The J-integral and the virtual crack closure technique are used to calculate the energy release rate on the basis of results from a large scale axisymmetric finite element model. Thereby, the proper geometry of the circumferential crack, plasticity in the substrate, material mismatch across the interface are included.In general, it was found that the closed-form linear elastic fracture mechanics model is sufficient for the method.