Hydrogen-assisted fatigue crack growth of pipeline steels under gaseous hydrogen pressure: A unified anisotropic phase-field model

Hydrogen-assisted fatigue crack growth (HA-FCG) poses a major challenge for the structural integrity of high-pressure hydrogen transmission pipelines, particularly due to the combined influences of microstructural heterogeneity, rolling-induced anisotropy, and the coupled mechanics–diffusion processes that govern crack evolution. In this work, we develop a unified anisotropic phase-field framework capable of capturing the synergistic effects of hydrogen embrittlement, fatigue damage accumulation, and direction-dependent fracture resistance. The formulation incorporates (i) an anisotropic fracture surface density via a structural tensor, (ii) stress-assisted hydrogen diffusion with enhanced transport in the fractured zone, and (iii) a fatigue-driven toughness degradation law implemented through an envelope-load cycle acceleration strategy. The model is implemented within the open-source MOOSE/ Felino environment using a staggered multi-application algorithm that couples mechanical fields, hydrogen diffusion, and cyclic damage evolution. The proposed framework reveals how preferential fracture orientations, degrees of anisotropy, hydrogen concentration, and loading frequency jointly influence crack path deviation and growth rate. Parametric studies demonstrate that increasing the anisotropy strength can either accelerate or suppress fatigue crack growth depending on the alignment between the weak fracture direction and external loading. A phenomenological hydrogen degradation law calibrated for API X52–X70 steels is introduced and integrated into the model. Validation against experimental HA-FCGR data from Sandia National Laboratories for X65 CT specimens (for rolling direction and its perpendicular direction) shows excellent agreement, capturing both orientation-dependent crack paths and the relative differences in growth rates.