Enabling high-order integration of fatigue crack growth with surrogate modeling

Abstract

Modeling fatigue crack growth is computationally challenging because the crack growth rate can only be evaluated at the current crack size. Therefore, the forward Euler method has been a common choice in integrating fatigue crack growth. However, since its accuracy can only be guaranteed with a small step size, the method cannot be applied to the investigation of systems with complex geometry (calling for expensive finite element simulations). Higher-order integration methods, such as the midpoint method, allow larger step size but require evaluation of crack growth rate at crack sizes larger than the current one. In arbitrary geometry, this is not an easy task because the direction of crack growth is unknown in advance. In this paper, surrogate models are generated for the prior crack growth direction and stress intensity factor data. These surrogates are cheap to evaluate and predict the crack growth rate without the need of additional finite element simulations. The step size for the numerical integration is chosen based on the accuracy of the extrapolated crack growth predictions for direction and stress intensity factor. Several examples were tested in which crack growth follows linear and curved paths under a range of boundary conditions leading to different relationships between stress intensity factor and crack size. Results showed that a large increase in the allowable step size may be used with increased accuracy over the Euler method with the need for fewer expensive function evaluations.