Boundary element analysis of crack problems in functionally graded materials

The present study examines the crack problems in a functionally graded material (FGM) whose upper and bottom surfaces are fully bonded with dissimilar homogeneous materials. A so-called generalized Kelvin solution based boundary element method is used in the numerical examination. The multi-region method and the eight-node traction-singular boundary elements are used for the crack evaluation. The layer discretization technique is utilized to approximate the depth material non-homogeneity of the FGM layer. The proposed method can deal with any depth variations in both the shear modulus and the Poisson ratio of the FGMs. Results of the present analysis are compared very well with the exact analytical solutions available in the literature, which demonstrates that the proposed method can accurately evaluate the stress intensity factors (SIFs) for cracks in FGMs. The paper further evaluates the effect of the functionally graded variations in the Poisson ratio on the stress intensity factors. The paper also assesses the elliptical cracks in the FGM system. The paper presents the influence of both the non-homogeneity and the thickness of the FGM layer on the three SIFs associated with the elliptical cracks.