Xfem VS Fem: application to fretting fatigue 2D crack propagation

TLDR: In this article, a modified fretting fatigue contact model is used to compare conventional Finite Element Method (FEM) and eXtended finite element method (XFEM).

Abstract: Fretting fatigue is a combination of two complex and serious mechanical phenomena, namely fretting and fatigue. The combination of these two phenomena can cause sudden fracture of components that are subjected to the oscillatory motions (fatigue) and at the same time are in contact with each other (fretting). Fretting fatigue lifetime can be divided to two different portions, namely crack initiation and crack propagation. In this study a modified fretting fatigue contact model is used to compare conventional Finite Element Method (FEM) and eXtended Finite Element Method (XFEM) techniques for 2D fretting fatigue crack propagation model. For this purpose, Python programming language along with ABAQUS software is used to implement FEM and XFEM to fretting fatigue crack propagation. In the first step, a Double Edge Notch Tension (DENT) specimen is used to validate both FEM and XFEM results with the analytical solution. Then, the validated codes are applied to modified fretting fatigue contact model to compare the extracted Stress Intensity Factors (SIFs) at crack tips after each increments of crack propagation. Results show good correlation between FEM model using re-meshing technique and XFEM with single-mesh technique for crack propagation. Moreover, by comparing the numerical results with analytical solutions it can be concluded that the analytical results cannot predict the exact value of SIFs. However, far from the contact region the results converge to numerical ones. As a conclusion, implementing numerical methods such as FEM and XFEM to fretting fatigue crack propagation, found to be really accurate and robust.