Full second-order approach for expected value and variance prediction of probabilistic fatigue crack growth life

Abstract

The NASGRO crack growth equation for fatigue life estimation is ordinarily used in its deterministic standard form. This paper presents a new probabilistic formulation for fatigue crack propagation based on the NASGRO equation providing a stochastic approach for predicting statistical moments of fatigue lifetime. The methodology approximates the expected value and variance, of the output random variable fatigue lifetime (N). These moments are obtained from the approximation via the Taylor series up to the quadratic terms, full second-order, of the NASGRO equation with respect to the random input variables taken into account. The validity of the proposed method is verified by two numerical examples regarding the fatigue crack growth in a railway axle under two different random loading conditions. The first one applies the probabilistic formulations under a random bending loading. The second one takes into account a service loading spectrum acting on the axle subjected to a random load. Then, the statistical moments calculated are checked by comparison with Monte Carlo simulations. The probabilistic model developed enables an efficient estimation of statistical moments, providing accurate probabilistic results that can be used in design stages, reliability studies or in damage tolerance assessment.