Predicting high-cycle fatigue under hydrogen embrittlement with a coupled phase-field–diffusion model

We present an open-source coupled phase-field–diffusion framework for predicting hydrogen-assisted fatigue crack growth in metals, explicitly accounting for hydrogen pre-charging and multi-time-scale transport–fatigue interactions. Cyclic fatigue and hydrogen damage are linked through a physics-based degradation of the fracture toughness, G c ( c H ) , whereby the local hydrogen concentration governs the resistance to crack advance. To avoid cycle-by-cycle simulations in the high-cycle regime, fatigue is advanced in blocks of Δ N cycles using a mean-load driving measure under an envelope-loading representation, while hydrogen diffusion is progressed in physical time through an explicit cycle-to-time mapping, Δ t = Δ N / f . This separation is necessary to retain loading-frequency effects in hydrogen transport even when fatigue evolution is updated in cycle blocks. Hydrogen pre-charging is resolved through a dedicated diffusion stage, and the resulting concentration field is transferred as the initial condition for subsequent fatigue simulations. To represent rapid equilibration along newly formed crack surfaces without imposing boundary conditions on an evolving crack geometry, we introduce a damage-activated artificial diffusivity within fully cracked regions. The framework captures stress-assisted diffusion and the coupled effects of loading frequency, load ratio R , pre-charging history, and transport kinetics. Validation against experimental compact tension (CT) specimens demonstrates accurate predictions of crack paths and growth rates. Parametric studies elucidate the roles of the hydrogen damage coefficient ζ , segregation free energy Δ g b , fatigue threshold α T , and degradation exponent n , showing that lower loading frequencies and increased hydrogen exposure accelerate crack growth, while larger α T and n mitigate fatigue damage. The proposed open-source, modular, and computationally efficient implementation provides a scalable tool for assessing hydrogen-environment-assisted fatigue and for informing material selection and loading strategies aimed at reducing hydrogen-induced degradation.