Quasi-static stress fields for a crack inclined to the property gradation in functionally graded materials

Quasi-static stress fields for a crack inclined to the direction of property gradation in functionally graded materials (FGMs) are obtained through an asymptotic analysis coupled with Westergaard's stress function approach. The elastic modulus of the FGM is assumed to vary exponentially along the gradation direction. The mode mixity due to the inclination of the property gradient is accommodated in the analysis through superposition of opening and shear modes. The first four terms in the expansion of the stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. Using these stress field contours of constant maximum shear stress, constant maximum principal stress, constant first stress invariant and constant out of plane displacement are generated, and the effect of inclination of the property gradation direction on these contours is discussed.