Inference of equivalent initial flaw size under multiple sources of uncertainty

A probabilistic methodology is proposed in this paper to estimate the equivalent initial flaw size (EIFS) distribution accounting for various sources of variability, uncertainty and error, for mechanical components with complicated geometry and multi-axial variable amplitude loading conditions. A Bayesian approach is used to calibrate the distribution of EIFS, where the likelihood function is constructed from model-based fatigue crack growth analysis and inspection results. The variability, uncertainties and errors in the above procedures are quantified, and the distribution of EIFS is calibrated by explicitly accounting for the various sources of uncertainty. Three types of uncertainty are considered: (1) natural variability in loading and material properties; (2) data uncertainty, due to crack detection uncertainty, measurement errors, and sparse data; (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. A Monte Carlo simulation-based approach is developed for uncertainty quantification in the crack growth analysis and for constructing the likelihood function of EIFS. The proposed methodology is illustrated by a numerical example.