Multi-scale approach to hydrogen diffusion in FCC polycrystalline structure with binary classification of grain boundaries in continuum model

Hydrogen mobility and distribution are key features to consider when studying material resistance to hydrogen embrittlement, especially in the case of intergranular fracture. In polycrystalline microstructure, both are mainly affected by grain structure and grain-boundary character and distribution. The homogenization approaches are an easy way to predict the effective diffusivity of complex microstructures. Classical homogenization theories have been used to predict the effective diffusivity on discrete grain boundary networks without considering the grains. Most studies show the limits of these classical homogenization techniques to predict the effective diffusivity of a continuum medium. In this paper, we propose a deductive approach using a combination of the generalized effective medium equation and the Hashin-Shtrikman formula to approximate the effective diffusivity in a polycrystal modeled by a ternary continuum composite. This approach illustrates the influence of the grain boundary topology and connectivity on hydrogen effective diffusivity. Our results will be compared to the finite element method calculation on polycrystalline aggregates with different grain sizes and grain-boundaries volume fractions. The effectiveness of this homogenization approach is accounted for the volume fraction of grain boundaries higher than 10%.