XFEM with high-order material-dependent enrichment functions for stress intensity factors calculation of interface cracks using Irwin’s crack closure integral

Abstract

This paper presents a high-order extended finite element method (XFEM) with a novel set of material-dependent enrichment functions for the linear elastic analysis of bimaterial interface cracks. With the proposed material-dependent high-order enrichment functions, highly accurate near-tip displacement and stress fields can be obtained for arbitrary material combinations. The aim of this contribution is the direct evaluation of the complex stress intensity factors (SIFs) of interface cracks based on Irwin’s crack closure integral. To this end, a closed-form SIF formulation in terms of the enriched degrees of freedom is derived by matching the leading term in the XFEM with an analytical expression of Irwin’s integral. Hence, the SIFs of interface cracks can be directly obtained upon the solution of the XFEM discrete system without cumbersome post-processing requirements.The performance of the proposed method is validated on several benchmark examples involving straight and curved interface cracks. In particular, we examine the effect of enrichment order, mesh refinement, bimaterial mismatch, crack tip position, and integration limit of Irwin’s integral. The method is shown to work well on all examples, giving accurate SIF results. Furthermore, while the popular interaction integral method requires special auxiliary fields for curved interface cracks and also needs cracks to be sufficiently apart from each other in settings with multiple cracks, none of these limitations are required by the proposed approach.