Probabilistic modeling of damage accumulation for time-dependent fatigue reliability analysis of railway axle steels

From the viewpoint of engineering applications, the prediction of the failure of railway axles plays an important role in preventing the occurrence of fatigue fractures. Combining a nonlinear damage accumulation model, a probabilistic S-N curve, and a one-to-one probability density functions transformation technique, a general probabilistic methodology for modeling damage accumulation is developed to analyze the time-dependent fatigue reliability of railway axle steels. The damage accumulation is characterized as a distribution in a general degradation path, which captures a nonlinear damage accumulation phenomenon under variable-amplitude loading conditions; its mean and variability change with time. Moreover, a framework for fatigue reliability assessments and service life prediction is presented based on the estimation of the evolution and probabilistic distribution of fatigue damage over time. The proposed methodology is then validated by experimental data obtained for a railway axle (45 steel and LZ50 steel). The time-dependent reliability is analyzed and demonstrated through probabilistic modeling of cumulative fatigue damage, and good agreement between the predicted results and the experimental measurements under different variable amplitude loadings is obtained.