Modeling the effect of grain boundary diffusivity and trapping on hydrogen transport using a phase-field compatible formulation

Abstract: Hydrogen grain boundary (GB) trapping is widely accepted as the main cause for hydrogen induced intergranular failure. Several studies were conducted to unveil the role of GBs on hydrogen transport; however, a clear understanding is yet to be attained. This is due to the limitations of the state-of-the-art experimental procedures for such highly kinetic processes. In this study, we aim at providing a deeper understanding of hydrogen-GB interactions using full-field representative volume element (RVE). The phase-field method is chosen for generating RVEs, since it is the an appropriate numerical tool to represent GBs. A novel fully-kinetic formulation for hydrogen diffusion and GB trapping is presented, which is compatible with the phase-field based RVEs. GB diffusivity ($D_\mathrm{gb}$) and trap-binding energy ($E_\mathrm{gb}$) were used as parameters to understand the interactions between diffusion and GB trapping. Uptake and permeation simulations were performed with constant and gradient occupancy boundary conditions respectively. In both cases, increasing $E_\mathrm{gb}$, increased the hydrogen GB occupancy. The permeation simulations showed that the hydrogen flux along the GBs increased with increasing both, $D_\mathrm{gb}$ and, surprisingly, $E_\mathrm{gb}$. Since trapping increases the hydrogen occupancy along GBs, it also increases the occupancy gradients, resulting in a higher flux. This led to the conclusion that, in the case of an external occupancy gradient, GB trapping and diffusion cooperate, rather than compete, to increase the hydrogen flux. On the other hand, the decisive factor for the retention of hydrogen at the GBs in permeation simulations was $D_\mathrm{gb}$ rather than $E_\mathrm{gb}$.