Finite element analysis of the grain size effect on diffusion in polycrystalline materials

Polycrystalline materials with refined grain size are well known to have enhanced diffusion properties compared to coarse grain materials. Due to their high grain boundary density, the macroscopic diffusivity of such materials is increased. Indeed, grain boundaries are fast diffusion channels in the material. In this paper, a numerical method to calculate the diffusivity of polycrystalline materials as a function of their grain size is proposed. A homogenization technique is applied on polycrystalline representative volume elements on which diffusion calculations are performed with a finite element method. This technique allows to extract the effective diffusivity of the material for different grain sizes. A relationship is then built between the diffusivity and the grain size. It is shown that the extracted diffusivity follows a mixture law of both diffusivities in the grains and grain boundaries, as proposed by Hart [14], but taking into account grain boundaries randomly oriented compared to the diffusion direction.