Statistical inference of the Equivalent Initial Flaw Size Distribution for an anisotropic material with the Dual Boundary Element Method

A methodology to estimate the fatigue life of an anisotropic structure under uncertainty is established in this work for the first time, utilizing the statistical inference of the Equivalent Initial Flaw Size Distribution (EIFSD). The challenges of detecting small cracks and predicting their fatigue propagation are overcome by the concept of the EIFSD, combined with a highly efficient computational tool for fatigue modelling problems: The Dual Boundary Element Method (DBEM). Bayesian updating is employed to enable the estimate of EIFSD to be refined by new information in the form of inspection data simulated using the DBEM. Although the DBEM is highly efficient, a significant number of DBEM simulations are needed to create the inspection data. Therefore, the DBEM is used to create a surrogate model to further improve efficiency. To demonstrate the proposed methodology, an example of a specimen with anisotropic material properties is investigated. The fatigue life estimated from the inferred EIFSD demonstrated only 0.11% error compared to the actual fatigue life when a low-level of uncertainty was considered in the anisotropic material properties, and only 1.9% error even when a high-level of uncertainty was considered. These fatigue life estimates found using the EIFSD can be coupled with reliability analysis techniques to determine suitable intervals for routine inspections in aircraft.