A coupled model of diffusional creep of polycrystalline solids based on climb of dislocations at grain boundaries

A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducing a dependence of diffusional creep on the density and mobility of boundary dislocations. Several representative examples have been solved using the finite element method and assuming representative volume elements made up of an array of regular-shaped crystals. The effect of stress, temperature, grain size, and grain boundary dislocation mobility is analyzed and compared with classical theories of diffusional creep. The simulation results demonstrate the ability of the present model to reproduce the macroscopic stress and grain size dependence observed under both diffusion and interface controlled regimes, as well as the evolution of this dependency with the temperature. In addition, the numerical implementation of the model allows to predict the evolution of microscopic fields through the microstructure.