Abstract

Uncertainty propagation of fatigue crack growth life commonly aims to provide the probability distribution of the lifespan needed for probabilistic damage tolerance analysis and for structural integrity assessment. This paper presents a novel methodology for efficiently estimating the parameters of the probability distribution of fatigue lifespan considering the Pearson distribution family. First, the full second-order approach for expected value and variance prediction of probabilistic fatigue crack growth life is extended to predict higher order statistical moments of the underlying distribution. That is, the expected value (first raw moment) and the variance (second central moment) equations are complemented with the probabilistic formulations for the skewness and for the kurtosis (third and fourth central standardized moments, respectively). Then, from these moments, the Pearson distribution type is automatically determined. Finally, the parameters of the particular Pearson distribution type are estimated making the statistical moments of the constructed lifespan distribution match the first four prescribed moments predicted by the probabilistic equations. The validity of the proposed method is verified by a numerical example regarding the fatigue crack growth in a railway axle under random bending loading. It is proven that the probability density function of the lifespan is properly derived by the methodology, without knowing or assuming the output probability distribution beforehand. The methodology presented enables an efficient and an accurate quantification of the lifespan uncertainties via its probabilistic distribution. This probabilistic description of fatigue crack growth life can be subsequently used in reliability studies or in damage tolerance assessment.