Crack formation beneath sliding spherical punches

Abstract

Using Hamilton's equations (1983) for computing the stress trajectories corresponding to the crack path, and the method proposed by Mouginot and Maugis (1985), based on Lawn's analysis (1967) it is possible to express the strain energy release rateG, for various crack initiation radii and various friction coefficients. The initial radius of the crack can then be determined by maximizingG, and the critical load required to initiate it can be computed by application of the Griffith criterion, as a function of the following parameters: the elastic characteristics of the materials, the punch radius, the initial flaw size and the friction coefficient. The analysis proposed by Gilroy and Hirst is shown to be the lower bound of this theory. The theoretical results are compared with published experimental results, and are discussed.