A collapsed interface approach to resolve grain boundaries in finite element simulations of polycrystalline diffusion

Abstract

Atomic diffusion affects the properties of various engineering materials, which predominantly occur in the polycrystalline state. A rigorous description of polycrystalline diffusion must therefore account for crystallographic defects, especially grain boundaries (GBs), whose structure and volume fraction - and hence the effective grain size - govern mass transport. Experiments and atomistic simulations consistently show that GBs can accelerate diffusion by up to several orders of magnitude and that fluxes along and across the interface are generally anisotropic. Conventional mesoscale models either neglect GBs or invoke idealized analytical corrections. Fully resolved finite-element meshes are accurate but computationally infeasible when nanometer-thin GB layers are involved. We introduce a collapsed-interface finite element that integrates the GB thickness analytically and embeds the result in a two-dimensional surface element. The formulation (i) treats in-plane and through-plane diffusivity independently, (ii) couples to the surrounding grain matrix without the need for mesh manipulations, and (iii) parametrizes both grain size and GB volume fraction via simple affine scalings, allowing systematic variation without remeshing. Effective diffusivity tensors are extracted by linear computational homogenization. The new finite element reproduces three-dimensional GB transport phenomena - channeled fluxes, concentration discontinuities - at a fraction of the computational cost of explicit models. Parametric studies spanning multiple orders of magnitude in GB diffusivity reveal four distinct diffusion regimes and quantify their impact on the overall response. The framework thus connects atomistic data and continuum predictions, providing an efficient tool for diffusion-driven design and optimization of polycrystalline materials.