DBEM computation of T-stress and mixed-mode SIFs using interaction integral technique

Abstract

In this paper, dual boundary element method (DBEM) is combined with interaction integral (I-integral) to evaluate stress intensity factors (SIFs) and T-stress simultaneously for mixed-mode crack analyzing. DBEM is proved to be one of the most efficient boundary element methods (BEM) for solving crack problems with boundary-only discretization, however its current implementation is in lack of efficient methods to evaluate fracture parameters. The available geometrical extrapolation method and J-integral technique for calculating fracture parameters in combination with DBEM are imprecise and difficult to be implemented in mix-mode crack analysis. The presented combined DBEM and I-integral approach can be easily used to extract SIFs and T-stress for mixed-mode cracks, which does not need the decomposition of elastic field into symmetric and antisymmetric components. The fundamental basis lies in the introduction of auxiliary fields for some proper defined single mode crack, then fracture parameters are calculated by evaluating the formulated I-integral in terms of DBEM solution and auxiliary elastic fields. In this paper, the basis of DBEM is illustrated at first, then the explicit expressions for auxiliary fields of displacement gradients are derived, then an automatic scheme for generating the path of I-integral is presented. Several numerical examples are given to validate correctness of the presented method.