Evaluation of Stress Intensity Factors (SIFs) Using Extended Finite Element Method (XFEM)

Abstract

Finite element method has been used for decades for calculating Stress Intensity Factors (SIFs), but it has some restrictions in crack propagation simulations mainly because the Finite Element mesh needs to be updated after each propagation step to track the crack path. Extended Finite Element Method (XFEM) suppresses the need to mesh and remesh the crack surfaces and can be used for modelling different discontinuities in 3D domains. Discontinuities can be represented independently of the FE mesh by exploiting-applying the partition of unity (PoU) method. In this method enrichment functions are added to the displacement approximation as long as the PoU condition is satisfied. Thanks to XFEM, problems involving static cracks in structures, evolving cracks, cracks emanating from voids etc., can be numerically studied and then the results can be compared against the analytical and experimental values. Cracks are propagated and after each step of the propagation the SIFs can be computed from the numerical solution at several points along the crack fronts. Interaction integrals are used to extract the mixed-mode SIFs with the help of-using the auxiliary fields. XFEM is still not fully recognized and needs to prove its practical value in order to be generally acknowledged. Results obtained by using XFEM for a complex 3D geometry are still not regarded as reliable without experimental checks. The purpose of this paper is to demonstrate that reliable values of SIFs can be obtained for three-dimensional structures with cracks. Results and conclusions given here should contribute to making a more objective judgment about XFEM usefulness in solving wide range of problems, especially those related to the fatigue design.