Abstract
A simplified model with only 2 degrees of freedom is developed for cavity growth along a grain-boundary by surface and grain-boundary diffusion following a similar model for a row of grains used by Sun et al, (1996). A variational principle for the coupled diffusion problem is used to follow the cavity growth. The approximate solution can be reduced to the well-established equilibrium cavity growth model at the fast surface diffusion extreme. By comparing the 2 degree of freedom model with the full finite element solution by Pan et al, (1997), a 'Validity Map' is constructed in terms of the relative diffusivity and applied stress relative to the capillarity stress. It is found that the simplified model accurately describes the evolution process, in terms of overall cavity profile and propagation rate for engineering alloys subject to normal levels of applied stresses. The 2 degree of freedom model for a single cavity was then extended to allow the modelling of multiple cavities. These cavities can be either pre-existing or nucleated during the lifetime of the system. The relative rotation between the grains is also considered. The initial 2 degrees of freedom were increased to six, and a cavity element has been derived. The cavity elements are assembled together using the classical finite element approach. This allows the evolution of multiple cavities and their interactions to be modelled under different applied loads and material parameters. This simplified multiple cavity finite element model was compared with a model for cavity evolution based on a 'smeared-out' approach. It was shown that the 'smeared-out' model does not accurately predict the creep damage for realistic engineering materials and conditions and results in an under prediction of creep lifetime. Using the simplified finite element model the effect of surface diffusion on the evolution of the creep damage was investigated. The evolution of a large pre-existing 'crack-like' cavity was modelled and the effects of nucleation, surface diffusion and loading were also investigated. It was shown that in the majority of cases as the surface diffusion was increased the rupture time was also increased. The results from the large 'crack-like' cavity simulations showed that there was very little crack propagation through the material and the smaller cavities tended to grow independently of the large 'crack-like' cavity.