Fatigue reliability assessment of a pearlitic Grade 900A rail steel subjected to multiple cracks

•We present a new applied method for fatigue reliability assessment for rail steel.•The stress history is used to calculate SIFs and reliability assessment of rail.•Paris Equation is used as a criterion of fatigue crack growth rate.•Morgan law is used to describe the failure probability of the series system.•Fatigue reliability is evaluated for each failure mode. In this paper, a reliability analysis of fatigue crack growth for a pearlitic Grade 900A rail steel subject to the growth of multiple cracks is presented. The stress intensity factors (SIFs) at the tip of the cracks, by considering all possible combinations of all different cracks, are calculated by the boundary element method (BEM). A 3D boundary element analysis model has been applied to estimate stress intensity factors of the rail under the influence of cyclic loading conditions. For this purpose, an UIC60 rail with accurate geometry is studied. Paris Equation is used as a criterion of fatigue crack growth rate and the maximum tangential stress was considered as the crack growth direction. The geometry correction functions of the five cracks in rail steel, as a function of a crack size are determined by using nonlinear regression analysis estimating the statistical descriptors of the five geometry correction functions. Also, Morgan law is used to describe the failure probability of the series system. Fatigue reliability is evaluated for each failure mode due to multiple site fatigue cracks propagation in rail steel.