A fully kinetic model for hydrogen transport near a blunting crack tip

Abstract

The kinetics of hydrogen diffusion and trapping play a major role in hydrogen embrittlement in metals. Under mechanical loading, hydrogen is driven by hydrostatic stress and accumulates at dislocations due to their affinity for hydrogen. However, most stress-diffusion models rely on Oriani’s local equilibrium assumption, which treats hydrogen buildup at dislocations as an instantaneous process. As a result, these models inherently fail to describe the loading rate sensitivity observed in experiments. To overcome this limitation, we propose a fully kinetic formulation in which hydrogen-dislocation interactions are modeled as a diffusive flux driven by the spatial gradient of the normalized dislocation density. The Kocks–Mecking–Estrin equation is used for the evolution of dislocation density coupled with Taylor hardening model. In contrast to classical models, our formulation solves for the total hydrogen concentration as a single species, thereby removing the need to artificially partition hydrogen into lattice and trapped species. The results show that slower loading rates lead to greater hydrogen accumulation at the crack tip. Additionally, pipe diffusion is naturally incorporated by allowing the local diffusivity to vary as a function of dislocation density. We also demonstrate that correct boundary conditions require prescribing equilibrium concentration that account for both stress and dislocation effects, ensuring chemical potential continuity with the far-field lattice. This work provides a robust and extensible framework for modeling hydrogen delayed fracture.