Asymptotic Stress Fields for Stationary Cracks Along the Gradient in Functionally Graded Materials

Abstract

Stress field for stationary cracks, aligned along the gradient, in functionally graded materials is obtained through an asymptotic analysis coupled with Westergaard’s stress function approach. The first six terms of the stress field are obtained for both opening mode and shear mode loading. It is observed that the structure of the terms other than r−1/2 and r0 are influenced by the nonhomogeneity. Using this stress field, contours of constant maximum shear stress are generated and the effect of nonhomogeneity on these contours is discussed.