Anti-plane shear of an arbitrary oriented crack in a functionally graded strip bonded with two dissimilar half-planes

An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated and its validity was verified. Finally, the effects of nonhomogeneous material parameter and crack orientation on the stress intensity factor are studied.