A combined displacement discontinuity-interaction integral method for computing stress intensity factors and T-stress

Abstract

In this paper, the displacement discontinuity method (DDM) is combined with interaction integral to simultaneously evaluate stress intensity factors and T-stress for analyzing two-dimensional mixed-mode crack problems. The displacement discontinuity method has been proved to be one of the most efficient boundary element methods for solving crack problems with boundary-only discretization character. However, there is a lack of efficient methods collaborating with the displacement discontinuity method to evaluate fracture parameters. The available geometrical extrapolation method and J-integral technique for calculating fracture parameters in combination with the displacement discontinuity method are imprecise and difficult to be implemented into mixed-mode crack analysis. The present combined displacement discontinuity method and interaction integral approach can easily extract stress intensity factors and T-stress for mixed-mode crack problems without needing any decomposition of elastic field into symmetric and antisymmetric components. The fundamental basis lies in introducing auxiliary fields for the proper defined single mode crack, then calculating fracture parameters by evaluating the formulated interaction integral in terms of displacement discontinuity solutions and auxiliary elastic fields. In this paper, the basis of the displacement discontinuity method is illustrated firstly, then the explicit expressions for auxiliary fields of displacement gradients are derived. Next, the interaction integral can be determined by being converted to an equivalent area integral. Finally, several numerical examples are examined to demonstrate the correctness of the present method.