Energy Consideration on a Branched and Curved Crack Extension

Abstract

An energy method is proposed to determine noncollinear crack paths in an elastic brittle solid which exhibits quasi-static crack extension under a displacement-controlled loading condition. Defining the total potential energy as the sum of the elastic potential energy stored in the body and the surface energy, its minimization with respect to crack paths leads to an energetically favorable crack growth path. In order to calculate the energies we use a second-order perturbation solution, which has been obtained for a straight crack with slightly branched and curved extensions under general far-field boundary conditions within the framework of linear fracture mechanics. As far as homogeneous materials are concerned, the minimization of the total potential energy gives rise to the crack direction that is equivalent to the one maximizing the elastic energy release rate. Possible crack paths in materials having inhomogeneous fracture toughness are also investigated by the energy method. In this case, even in a pure Mode-I loading condition, we often observe branched and curved crack extensions, which cannot be predicted by conventional stress or strain criteria. As a practical application of the present method, a brittle crack path extending along a welded joint is predicted, where the effects of applied stresses, residual stresses, and material deterioration are taken into account.