Dual boundary element analysis of rectangular-shaped cracks in graded materials

This paper analyzes the rectangular-shaped crack in the graded materials by using the dual boundary element method. The method is based on the fundamental solutions for multilayered solids and uses a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the latter on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (i.e., displacement discontinuity) is treated as an unknown quantity on the crack surface. The layered technique is used to analyze the variation of parameters of the graded interlayer. Numerical examples of stress intensity factors (SIFs) calculation are given for the rectangular-shaped crack parallel to the graded interlayer. The results show that the SIFs obtained with the present formulation are in very good agreement with existing numerical results. The nonhomogeneous parameter and the distance of the crack from the interlayer exert an obvious influence on the SIFs of the rectangular-shaped crack in the graded material. Furthermore, it may be shown that the proposed method can be used to analyze different cracks subject to complex loads in graded materials and to model the non-homogeneous solids with multiple interacting cracks.