Analysis of Mode III Fraction in Functionally Graded Plate with Linearly Varying Properties

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. the characteristic of material behavior is assumed to change in a linear manner along the plate length. also the embedded crack is placed in the direction of the material change. the problem is solved using two separate techniques. primary, by applying laplace and fourier transformation, the governing equation for the crack problem is converted to the solution of a singular integral equation system. then, finite element technique is employed to analyze this problem by considering quadrilateral eight nodded singular element near the crack tips. the effects of material non-homogeneity and crack length on the stress intensity factor are studied and the results of two methods are judged against each other.