Identification of Equivalent Damage Growth Parameters for General Crack Geometry

Abstract

Analytical damage growth equations, such as Paris law, need the stress intensity factor for predicting damage growth. Analytical expressions for the stress intensity factor are available only for simple crack locations, geometries and loading conditions. Therefore, actual damage growth requires numerical solution, such as by finite elements. However, for estimating the uncertainty in remaining useful life (RUL), thousands of simulations of crack growth must be undertaken, which is computationally expensive. Here, an estimate of the error associated with RUL estimation based on an analytical stress intensity factor that does not consider the effects of boundary conditions, crack location or complex geometry is introduced. An effective damage parameter is identified which, although different from the true value, results in accurate damage growth prediction. Actual damage growth is simulated using the extended finite element method (XFEM) to model the effects of crack location and geometry on the relationship between crack size and stress intensity factor. The XFEM data are then perturbed with noise to simulate measurements. The damage growth parameter is then identified using least square filtered Bayesian (LSFB) method. The identified parameter can then be used with the model to estimate the RUL. Examples include center and edge cracks in a plate that experiences both horizontal and vertical finite effects and stress concentration caused by the presence of holes. For these examples, it is found that the RUL estimates are accurate even when an inaccurate stress intensity factor model is used.