Fracture analysis of cracked thin-walled structures using a high-order XFEM and Irwin’s integral

Abstract

Abstract We develop a novel fracture mechanics framework for cracked thin-walled structures based on the Mindlin-Reissner plate theory. The mixed interpolation of tensorial components (MITC) plate element within the extended finite element method (XFEM) is used for the discretization. High-order crack-tip enrichment functions are employed to resolve the linear elastic near field solutions and the stress intensity factors (SIFs) are extracted by using an analytical derivation of Irwin’s crack closure integral. The closed-form formulation of Irwin’s integral, given in terms of enriched degrees of freedom (DOFs), is shown to be valid for both structured and unstructured meshes. The SIFs of through-the-thickness cracks in thin-walled structures can thus be directly obtained upon the solution of the XFEM discrete system, without the need of constructing auxiliary fields for mode separation. The performance of the proposed approach is studied on several benchmark examples consisting of cracked plates and shells. We first consider plate examples with an inclined crack and two cracks approaching each other. Excellent accuracy in terms of SIFs, on structured and unstructured meshes is reported, even on rather coarse meshes. In particular, the case of two approaching cracks showcases the potential of Irwin’s integral in addressing crack coalescence problems. Finally, we demonstrate the accuracy of the proposed method on cylindrical-shell type problems with a crack subjected to either tension, torsion, or internal pressure.