Numerical Modeling of Hydrogen-Assisted Cracking With Phase Field Regularized Cohesive Zone Model and Penalty-Based Moving Hydrogen Boundary Condition

Abstract

The degradation of metallic materials due to hydrogen embrittlement (HE) poses critical challenges for structural reliability. Phase-field models offer an energy-based approach that does not require predefined crack paths and automatically determines crack initiation, growth, and coalescence. However, conventional implementations of the phase-field regularized cohesive zone model (PF-CZM) apply hydrogen boundary conditions only on the initial external surfaces, neglecting the exposure of newly formed crack surfaces. To address this limitation, this study refines the PF-CZM by incorporating a penalty approach to implicitly enforce moving hydrogen boundary conditions, ensuring realistic hydrogen exposure on evolving crack surfaces. Numerical examples demonstrate the model's effectiveness in modeling crack propagation from structural defects and highlight its capability to handle complex crack patterns. The results also show the significant influence of the moving hydrogen boundary condition in nonuniform exposure scenarios, where accelerated crack growth, elevated local hydrogen concentrations, and a transition toward brittle failure are captured.