Title: A Simple and Efficient X-FEM Approach for Non-planar Fatigue Crack Propagation
Abstract: A simple and efficient extended finite element method (XFEM) approach has been presented to solve the 3-D fatigue crack propagation problems. In X-FEM, the crack is approximately described by local signed distances of the nodes around the crack face which makes it possible to simulate crack propagation on a fixed mesh without remeshing. In this work, a triangulation scheme is adopted to initialize and update the crack which enables an easy level-set representation for an arbitrary shaped or non-planar crack. The level-set functions are used to search the elements that have been fully or partly cut by crack face and will be enriched with either Heaviside function or singularity function. Furthermore, the level-set functions are used to create the local coordinate systems for crack front points which serve as the basis for denoting the singular field. The 3-D interaction integral method is adopted to calculate the stress intensity factors. The maximum principle hoop stress criterion is adopted to determine the crack propagation direction. The Paris law is used to perform fatigue crack propagation simulation. Some examples of planar and non-planar 3-D crack growth are solved to demonstrate the applicability and robustness of the proposed XFEM approach.