A general interaction integral for dynamically propagating cracks in anisotropic materials

Abstract

In this paper, some relevant tools for numerical analysis of dynamically propagating cracks in anisotropic materials are discussed within the framework of the eXtended Finite Element Method (XFEM). A general interaction integral that is domain-independent is proposed to determine the Stress Intensity Factors (SIFs) for both stationary and dynamically propagating cracks in anisotropic materials. Besides, a set of functions for enriching the nodes of the tip element, which are applicable for modeling both quasi-stationary and dynamically propagating cracks in anisotropic materials, are also proposed. In addition, a modified form of the Maximum Tangential Stress (MTS) criterion is manipulated for estimating the direction of the propagating crack which takes into account the asymptotic stress field near a propagating crack tip in anisotropic materials under mixed mode plane loading. Finally, the accuracy of the suggested method is then confirmed using some numerical examples that involve both stationary and dynamically propagating cracks. Additionally, a thorough investigation is done into the impacts of material anisotropy and material orientation on the path of dynamically propagating cracks in orthotropic structures.