The propagation of cracks by cavitation: A general theory

In many materials, both ductile and brittle, cracks propagate by the nucleation and growth of cavities in advance of the crack tip. During stable crack growth, a steady-state can be achieved in which the size of cavities depends only on their position ahead of the crack tip. In the present paper we have modelled this process in a general way. We assume that the stress field ahead of the crack tip can be determined independently of the cavitation process. We then use general parametric equations for the variation of local stress with position ahead of a crack tip [σ = (A/x)x], and for the growth velocity of cavities as a function of local stress (v = φσβ), to determine the average rate of crack extension. It is shown that these equations are of the right form to be used with established models of plastic relaxation ahead of a crack tip and of cavity growth. We find that the nucleation process influences the rate of crack growth only if the parameter, αβ, is less than 1. Two approaches to cavity nucleation are considered, and their affect on crack growth assessed. Finally, several examples of the use of the model are presented for both ductile and brittle materials, in which cavities grow by a variety of mechanisms involving both diffusion and plasticity. A large range of crack growth behaviour is predicted, and we find that many of the published models for creep crack growth, fit into our solution as special cases.