Computing lower and upper bounds on stress intensity factors in bimaterials

This paper presents a finite element approach for finding complementary bounds of stress intensity factors (SIFs) in bimaterials. The SIF is formulated as an explicit computable linear function of displacements by means of the two-point extrapolation method. An appropriate and computable form of the SIF plays a crucial role in the dual problem involved in the computing procedure of both lower and upper bounds. In our discussions, computable forms of stress intensity factors, K0K0 and KrKr, are derived, which are related to the energy release rate, and the ratio of the open mode and shear mode SIFs, respectively. Based on a posteriori finite element error estimation, a bounding procedure is used to compute the bounds on the two stress intensity factors. Finally, bounds on the SIFs in a bimaterial interface crack problem are provided to verify the procedure.