Nucleation, growth and coalescence of multiple cavities at a grain-boundary

This paper presents a model for the evolution of creep damage by the nucleation, growth and coalescence of multiple cavities at a grain-boundary. Coupled grain-boundary and surface diffusion is assumed as the mechanism of cavity growth. At the core of the model is a simplified finite element formulation of cavity growth. Each cavity is modelled using a cavity element, these can be assembled together to construct a grain-boundary network with an evolving distribution of cavities. The cavity element is an extension of our previous model for the growth of a single cavity (Westwood et al., 2000). Continuous nucleation and coalescence of cavities are integrated into the model through remeshing the grain-boundary at a nucleation or coalescence event. The finite element formulation is tested using a series of cases for which the solutions are known. The finite element model is then compared with the smeared out model which was first proposed by Tvergaard (1983) and later adopted by Onck and van der Giessen (1997, 1999). It is shown that the two models only agree with each other at either a unrealistically high level of applied stress or extremely low rate of the nucleation. Under realistic values of applied stress and relative diffusivity, the smeared-out model tends to over-predict the damage growth rate. Finally the effect of relative diffusivity on creep damage is investigated. It is confirmed that materials with fast surface diffusivity possess a high resistance to diffusional damage growth, but this effect is only significant at a relatively high level of applied stress.