Nonequilibrium models for diffusive cavitation of grain interfaces

Existing models for the diffusive growth of voids on grain interfaces, at elevated temperature, are for the most part based on quasi-equilibrium assumptions: surface diffusion is assumed to be sufficiently rapid that the cavity has a rounded, equilibrium shape, and hence cavity growth is assumed to be rate-limited only by grain boundary diffusion. However, creep rupture cavities sometimes have narrow, crack like shapes and it is appropriate to investigate non-equilibrium models for diffusive rupture. This is done here by comparing the quasi-equilibrium model to another limiting case based on a narrow, crack-like cavity shape. Criteria for choosing between the models are given on the basis of representative relaxation times for the surface diffusion process, and also by examining the properties of a ''self similar'' solution for cavity shape. By a suitable choice of parameters which measure the growth rate, this solution can be made to give results corresponding to either limiting case, and aids the interpolation between them. The results suggest that if s is the ratio of the applied stress to that which just equilibrates cavities against sintering, then for circular cavities on a grain boundary with diameter equal to a quarter of their average center-to-center spacing, the quasi-equilibrium mode applies when s < 1 + 6..delta.. and the crack-like mode when s > 2 + 9..delta... Here ..delta.. is the ratio of surface to grain boundary diffusivity. Also, the stress dependence of the growth rate and rupture lifetime is established in each case, and the results are discussed in relation to the interpretation of experimental data.