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

This paper analyzes the rectangular-shaped crack in the graded materials byusing the dual boundary element method. The method is based on thefundamental solutions for multilayered solids and uses a pair of boundaryintegral equations, namely, the displacement and traction boundary integralequations. The former is collocated exclusively on the uncracked boundary,and the latter on one side of the crack surface. The displacement and/ortraction are used as unknown variables on the uncracked boundary and therelative crack opening displacement (i.e., displacement discontinuity) istreated as an unknown quantity on the crack surface. The layered techniqueis used to analyze the variation of parameters of the graded interlayer.Numerical examples of stress intensity factors (SIFs) calculation are givenfor the rectangular-shaped crack parallel to the graded interlayer. Theresults show that the SIFs obtained with the present formulation are in verygood agreement with existing numerical results. The nonhomogeneous parameterand the distance of the crack from the interlayer exert an obvious influenceon the SIFs of the rectangular-shaped crack in the graded material.Furthermore, it may be shown that the proposed method can be used to analyzedifferent cracks subject to complex loads in graded materials and to modelthe non-homogeneous solids with multiple interacting cracks.