Keywords: rail, fracture phase?field, rolling contact fatigue, subsurface crack initiation and propagation, numerical simulation, cycle-jumping algorithm.

This paper shows the development of a numerical model for fatigue crack growth in rails under rolling contact loading based on the fracture phase-field method, which accounts for fatigue damage accumulation. Within a thermodynamically consistent phase-field framework, a fatigue degradation function is introduced to describe the attenuation of material fracture energy under cyclic loading. The implicit solution of the damage field under moving Hertzian contact loads is implemented through ABAQUS user subroutines, combined with a cycle-jumping algorithm. Numerical results indicate that cracks initiate in the subsurface region at a depth of approximately 0.65 times the contact half-width, subsequently branch into disordered crack networks, and eventually exhibit a bidirectional propagation pattern extending both downward toward the rail foot and upward toward the running surface, which aligns well with the characteristics of squat-type damage in rails. The model effectively reveals the transformation mechanism from subsurface cracking to surface spalling, offering a numerical tool for understanding rolling contact fatigue damage mechanisms in rails, although it does not yet consider actual non?Hertzian contact profiles or surface material hardening. Despite these simplifications, this study successfully elucidates the evolution of subsurface?to?surface crack propagation.

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