Fatigue crack growth modeling and prediction with uncertainties via stochastic perturbation series expansion method

The fatigue crack growth process is characterized by uncertainties inherent to the variations in geometrical properties, material properties, and operating conditions. This paper proposes a novel stochastic perturbation series expansion method for predicting fatigue crack growth evolution which accounts for uncertain parameters. Unlike the deterministic method, the parameters of the crack growth model are considered to be stochastic with perturbation terms. The solution to the crack growth equation is then transformed into a perturbation series after introducing said small parameters. A series of modified differential equations for predicting the stochastic characteristics of the crack length history are derived via first-order Taylor series expansion method. The initial crack length under perturbation can be expressed via the artificial small parameter method per the measurement errors. Further, by substituting the initial conditions into the modified stochastic equations, variations in the mean value and standard deviation as well as the probabilistic region of crack length history can be successfully obtained. The performance of the proposed method is evaluated through two examples. Comparison against experimental and Monte-Carlo simulation data confirm that the proposed method is indeed feasible and effective for predicting fatigue crack growth evolution with consideration of stochastic uncertainties. (C) 2017 Elsevier Ltd. All rights reserved.