Bi-material V-notched SIFs analysis by XFEM and conservative integral approach

In this paper, a new effective approach based on conservative integral approach associated with extended finite element method (XFEM) is developed for evaluating stress intensity factors (SIFs) of bi-material V-notched structures. The XFEM model for bi-material V-notches is established, which owns various features: (a) jump enrichment functions are taken for describing the intersection of notch-faces; (b) eight (real eigenvalue) or sixteen (complex eigenvalue) branch functions are employed for capturing nodes surrounding the notch-tip; and (c) interface enrichment function is used to model the material interface. These enrichments allow the representation of notch-faces and material interface independent of the finite element mesh. The conservative integral approach derived from the Betti reciprocal principle is used for the evaluation of SIFs. The conservative integral approach avoids the complicated stress fields around the notch-tip, so good accuracy of SIFs can be obtained. Also, the proposed XFEM model can easily be used to solve homogenous V-notched structures by setting the same material parameters of two materials. Numerical results of the SIFs calculated by the present method indicate the independence of integral paths. Several bi-material V-notched numerical examples for single and mixed modes fractures are analyzed to demonstrate the accuracy and effectiveness of the developed method.