Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method

Abstract

A new method is presented to study the interaction of multiple cracks, especially for the areas near crack tips by using the extended finite element method. In order to track the cracks, a new geometric tracking technique is proposed to track enriched elements and nodes along the crack instead of using the narrow band level set method. This allows to accurately determine enriched elements and nodes and calculate enrichment values. A method is proposed for constructing a multicrack matrix, which involves numbering enriched nodes of multiple cracks and solving the global stiffness matrix. In this approach, the stress fields around multiple cracks can be studied. The interaction integral method is employed to study the crack propagation and its direction by calculating the stress intensify factor. The developed model has been coded in MATLAB environment and validated against analytical solutions. The application of the model in the crack interaction study is demonstrated through a number of examples. The results illustrate the influence of the interaction of multiple cracks as they approach each other.