The lattice continuum formulation for diffusional creep is implemented into the computational framework based on the finite difference method for space and the predictor–corrector algorithm for time discretization, to solve the coupled elasticity-diffusion problem with moving boundaries. The numerical scheme is implemented and tested considering 3D periodic structures without grain boundary sliding. Of primary interest in this paper are the stress non-uniformities resulting from nonuniform composition eigenstrains.

We consider two regimes: the one where the rate limiting process is bulk diffusion of vacancies, and the one where the rate is controlled by vacancy nucleation/annihilation at grain boundaries (nucleation-controlled creep). We found that the stress concentration factor for diffusion-controlled creep is independent of the applied stress and grain size. No stress concentrations are present for the nucleation-controlled creep case.

Stress and grain size dependence of minimum strain creep rates are determined by the present model for a variety of applied stresses, grain sizes, different driving processes (diffusion and nucleation-controlled creep) and compared with the classical theory for diffusional creep. We found that steady-state creep rates varied linearly with applied stresses for both diffusion and nucleation-controlled creep. The numerical results show good correspondence to analytical predictions for idealized diffusional Nabarro-Herring creep. Significantly lower steady-state strain rates were computed for nucleation-controlled creep. These results demonstrate the ability of the present model to reproduce the stress and grain size dependence of the steady-state strain creep rates.