The crack-tip higher order asymptotic fields for a mode III crack in a functionally gradient material

Crack-tip higher order stress and displacement fields for a mode III crack along the direction of property variation in a functionally gradient material (FGM), which has a power variation of shear modulus along the gradient direction, are obtained through the asymptotic analysis. I-lie asymptotic expansions of crack tip stress fields are derived to explicitly bring out the influence of non-homogeneity on the structure of the stress field. The analysis reveals that only the higher order terms in the expansion are influenced by the material non-homogeneity. Moreover, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly and theoretically account for non-homogeneity effects on crack tip stress fields.