Analytical expressions for crack-tip higher order stress functions for a plane crack in a
special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power
form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of
the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic
expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously.
Furthermore, 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 account for non-homogeneity effects on the
crack- tip stress fields. These results provide the basis for fracture analysis and engineering
applications of this FGM.