High-Order Integration of Fatigue Crack Growth Using Surrogate Model

Abstract

Modeling fatigue crack growth is a challenging computational fracture mechanics problem because the crack growth rate can only be evaluated at the current crack size. The forward Euler method has been a common choice in integrating fatigue crack growth, whose accuracy can only be guaranteed with a very small size of increment. This hinders failure investigation of systems with complex geometry, which would require expensive finite element simulations. Higher-order integration methods, such as the midpoint method, might allow larger increment size but require additional 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, and additional simulations are often prohibitive. In this paper, two surrogate models are generated for the prior crack growth direction and stress intensity factor data and are used to predict the crack growth rate at future locations without the need for additional finite element simulations. The step size for the numerical integration is chosen based on the prior accuracy of the extrapolated data for the crack growth 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 without the need for additional simulations.