Numerical estimation of fracture toughness from indentation-induced circumferential cracking in thin films on ductile substrates

Abstract

In this paper, a method to estimate fracture toughness, Γf, from the first indenter-induced circumferential crack in a thin film is suggested. The method is based on the stresses in the film and finite element simulations are used to estimate these stresses. The film is taken to be linear elastic while plasticity is included in the substrate. Delamination is not taken into account in the method and the film is perfectly bonded to the substrate. The stress in the film is used to estimate the location where the circumferential crack will initiate from a defect in the film surface. The location is found to be at a distance away from the indenter which correlate with experiments. Also, the stress is used to calculate the stress intensity factor and the energy release rate for a plane strain crack. The energy release rate for the plane strain crack is then used to calculate the energy release for a crack channeling around the indenter forming the circumferential crack. By the energy release rate for the channeling crack fracture toughness is estimated independent of the initial defects in the film provided such defects exist. If the initial defects are smaller than a required minimum value, fracture toughness is overestimated by this method and this overestimation is calculated. Besides fracture toughness, the energy release rate for the channeling crack is used to estimate the depth of the plane strain crack which is found to be smaller than the film thickness.The method is used to estimate the fracture toughness, Γf, for an alumina (Al2O3) film using the critical indentation depth. In order to verify the result the estimated crack radius is compared to the actual radius of the circumferential crack in the alumina. The differences between the two radius is found to be within a few percent.