Statistical Inference of Equivalent Initial Flaw Size Distribution for Fatigue Analysis of an Anisotropic Material

Abstract

A novel methodology for the fatigue life uncertainty quantification of anisotropic structures is presented in this work. The concept of the equivalent initial flaw size distribution (EIFSD) is employed to overcome the difficulties in small cracks detection and fatigue prediction. This EIFSD concept is combined with the dual boundary element method (DBEM) to provide an efficient methodology for modelling the fatigue crack growth. Bayesian inference is used to infer the EIFSD based on inspection data from the routine maintenance of the structure, simulated with the DBEM. A large amount of DBEM simulations were required for the Bayesian inference. Therefore, surrogate models are used as part of the inference to further improve computational efficiency. A numerical example featuring an anisotropic plate is investigated for demonstrating the proposed methodology. When considering a low level of uncertainty in the crack propagation parameters, an error of 0.12% was found between the estimated fatigue life obtained using the proposed method compared to actual fatigue life, and only 0.35% error when considering high level of uncertainty. The application of the estimated fatigue life can be used to determine an appropriate inspection interval for aircraft maintenance.

Evaluation method of equivalent initial flaw size and fatigue life prediction of nickel-based single crystal superalloy

“…Liang et al (2019) and Liu and Mahadevan (2009) proposed a method for determining EIFS based on the Kitagawa-Takahashi diagram to avoid the dependence of equivalent crack size on stress level. Statistical methods such as maximum likelihood estimation (MLE) (Zhuang et al, 2023;Makeev et al, 2007) or Bayesian update (Torregosa and Hu, 2013;Morse, 2020) take into account the source of uncertainty in the backward inference process, and obtain the probability description of EIFS to effectively improve the prediction accuracy.…”