The effects of grain size distribution on cavity nucleation and creep deformation in ceramics containing viscous grain boundary phase

The grain size distribution in a polycrystalline ceramic material is not uniform. Such microstructural inhomogeneity may give rise to nonuniform local stress distributions. Here we investigate the effect of grain size distribution on the generation of local stress concentration in ceramic materials creeping by localized flow of a viscous grain boundary phase. A simple bimodal grain size distribution is first considered. The critical stress for cavity nucleation, calculated using classical Becker-Doring nucleation theory, is compared with the local stress concentration. The results show that, because of the inhomogeneity, the local stress in the grain boundary viscous phase at the locations of large grains can exceed the critical stress for cavity nucleation. The creep rate due to localized viscous flow of the grain boundary phase and cavity growth is evaluated. Although the creep behavior owing solely to viscous flow is linear with respect to applied stress, it can be highly nonlinear when cavitation occurs. Moreover, as an example, the model has been used to study creep behavior of a whisker-reinforced Si₃N₄ matrix composite in which long whiskers are surrounded by small equiaxed ceramic grains.