Predicting fatigue crack growth evolution via perturbation series expansion method based on the generalized multinomial theorem

In this study, a novel numerical calculation method is proposed to investigate the fatigue crack growth evolution in aluminum alloy sheets accounting for the measurement error. Unlike the deterministic numerical method, the initial crack length is considered to be a modified parameter with a small correction term due to the measurement error; the solution to the crack growth equation is expressed in the form of a perturbation series after introducing said small parameter. By combining the proposed perturbation series expansion method (PSEM) with the deterministic crack growth equation, a series of modified equations for predicting the crack length history are derived based on the generalized multinomial theorem. Further, by substituting the initial condition under perturbation into the modified equations, variations in crack length versus the cycle number can be obtained. The proposed method is verified by comparing numerical results with experimental data, and the results demonstrate that the proposed model is indeed feasible and effective for predicting fatigue crack growth evolution.