Uncertainty propagation method for probabilistic fatigue crack growth life prediction

Predicting the probability distribution of fatigue crack growth (FCG) life is very important for probabilistic damage tolerance analysis and structural integrity assessment. This paper proposes a novel uncertainty propagation method for probabilistic FCG life prediction, which allows efficiently estimating the probability density function (PDF), and cumulative distribution function (CDF) of the FCG life considering the randomness of the loads, material properties of crack propagation rate, and crack geometries. First, the relationship between the PDF of FCG life and the one of its logarithm is established by a logarithmic analysis. Then, the random variables are uniformly transformed into independent normal variables that obey distributions of N(0,1/2) using variable transformation technique. Thus, the bivariate dimension reduction method can be conveniently applied to calculate the first four moments of the logarithmic FCG life, and the corresponding PDF is further estimated by the maximum entropy principle. Finally, the PDF and CDF of the FCG life are analytically derived from the ones of the logarithmic FCG life. The validity of the proposed method is verified by numerical, experimental and engineering examples. It is demonstrated that the PDF and CDF of FCG life are well predicted by the proposed method, regardless of the strong nonlinearity of FCG life function and the large uncertainties of input random variables. This method outperforms the Monte Carlo simulation (MCS) in terms of computational efficiency, and in the meanwhile it has an acceptable computational accuracy.