Application of a hierarchical quadrature element method to interface crack analysis in bi-material systems

This paper presents an extension of the hierarchical quadrature element method (HQEM) with p-convergence to evaluating fracture mechanical parameters of bi-material interface cracks. The numerical implementation of HQEM in combination with the virtual crack closure method (VCCM) is comprehensively illustrated, and the formulas for calculating the strain energy release rate (SERR) are rederived. The relationship between components of SERR and the complex stress intensity factors (SIFs) is established. In addition, the effectiveness of an auxiliary parameter related to the dual energy release rates in measuring the accuracy of the present method is examined. The feasibility of applying HQEM to the interface crack problems is demonstrated by investigating the benchmark problem of an infinite bi-material plate with a central interface crack. Two loading cases are considered, including pure tensile loading and mixed tensile-shear loading. The influence of the crack tip element size Δa on the convergence characteristics and computational accuracy of fracture parameters is quantitatively investigated to provide guidance for choosing the most reasonable value of Δa. Numerical results show that even with very coarse meshes, together with a virtual crack extension consisting of only one element, HQEM yields highly accurate results for the total SERR and the complex SIFs, making it suitable for complex, large-scale interface crack problems in dissimilar media.