A phase-field model for hydrogen embrittlement

This work presents a phase-field framework for hydrogen-induced failure that captures the coupled effects of mechanical deformation, crack propagation, and hydrogen diffusion. A staggered solution scheme is adopted, wherein displacement, crack phase-field, and hydrogen concentration are solved sequentially. The framework incorporates a penalty-based moving concentration boundary condition to model hydrogen ingress along propagating cracks. The model is validated through benchmark simulations of an edge-cracked square plate. Stress-assisted diffusion is examined under both tensile and mixed loading conditions. The results demonstrate hydrogen-assisted embrittlement, with increasing initial hydrogen concentration reducing fracture resistance, as reflected in the load–displacement response. The comparison of results under constant and moving concentration boundaries demonstrates their impact on diffusion and fracture behavior. The implementation is carried out in ABAQUS using a user-defined element (UEL) subroutine for solving the coupled equations, while UVARM is employed for state-variable updates and post-processing.