Intergranular creep cavitation with time-discrete stochastic nucleation

An empirical model for the time-discrete stochastic nucleation of intergranular creep cavities is proposed. Nucleation is assumed to occur randomly in time, with the temporal behavior being governed by an inhomogeneous Poisson process. Based upon experimental evidence, the mean function of the Poisson process is taken to be a power-law function of time. The nucleation model is then implemented in conjunction with a recent analysis which treats the growth of randomly spaced populations of voids in a simplified bicrystal configuration. Numerical simulations with the resulting model indicate, among other things, that both the times-to-failure and the cavity radii are distributed according to a Weibull cumulative distribution function. Both predictions have qualitative experimental support. Moreover the presence of nucleation is found to reduce the time-to-failure by creep rupture by approximately a factor of two to eight compared to simulations without nucleation.