Keywords: numerical simulations, XFEM, rail, wheel-rail contact, rail bending, frictional contact, fatigue, crack growth.

Due to the repeated passage of the wheels, rolling contact fatigue cracks can appear in the surface or subsurface of rails. These defects, such as squats and head-checks, can propagate and lead to rail fracture. If a fracture of the rails occurs, it could cause not only a heavy economic impact (delayed trains, maintenance costs), but also passenger safety (derailment). In order to avoid rail fractures, the French National Railroad Company (SNCF) performs a strict method with both corrective (consolidation or removing of damaged rails, local deep grinding, etc.) and preventive (initial and periodic grinding, periodic monitoring by ultrasound, etc.) maintenance strategy.

This paper investigates the fatigue crack growth in rails using two/three-dimensional numerical simulations with the eXtended Finite Element Method (XFEM) taking into account the frictional contact between crack faces and the rail bending. Firstly, a description is given of the models and simulation tools that were developed within the consortium IDR2 gathering SNCF, RATP the Parisian metro operator and TataSteel, one of the major rails manufacturers. Secondly, a parametric numerical study is performed using a two-dimensional model to better understand the effect on the fatigue phenomenon of various factors such as the wheel-rail contact forces, the residual stresses, the rail bending and track stiffness, the localization of the cracks (over or between sleepers), the crack path. Finally, a three-dimensional model is used to simulate the growth of different types of crack (on curves, in straight lines) subject to wheel-rail contact fatigue loading.

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