Uncertainty Analysis of MSD Crack Propagation Based on Polynomial Chaos Expansion

Widespread fatigue damage (WFD) is one of the main damages in aging aircraft structures, and the prediction of multi-site damage (MSD) crack propagation plays an important role in the safety assessment of aging aircraft. However, the existing multi-crack propagation stochastic models need to calculate multiple integrals, and the calculation efficiency is low. Based on the Polynomial Chaos Expansion (PCE) method, this paper proposes a new uncertainty analysis method to effectively solve the problem of multi-crack mutual interference. The rivet area of aircraft skin mostly appears randomly in the form of short cracks. Therefore, 30 groups of multi-crack fatigue propagation experiments are carried out to obtain the data of multi-cracks at different stages. On the basis of the existing multi-crack mutual interference model, a new semi-analytical multi-crack propagation model is designed by considering the uncertainty of multi-crack initiation and the interaction factors between cracks. The random variables are substituted into the improved multi-crack propagation model, and the Hermite polynomials are introduced and expanded into orthogonal polynomial series, and the time-varying polynomial coefficients, moments and probability densities are solved by stochastic regression method. The accuracy and effectiveness of the method are verified by comparing with the experimental and Monte Carlo methods.