Mode I interaction of a periodic array of parallel cracks in a functionally graded nonhomogeneous plane

The mode I interaction of a periodic array of parallel cracks which are uniformly spaced apart in a functionally graded material is investigated. The two-dimensional theory of nonhomogeneous elasticity is employed as the basic framework for this study. The material nonhomogeneity is represented in terms of the spatial variation of the shear modulus in the exponential form along the direction of cracks, while Poisson’s ratio is assumed to be constant. Formulation of the proposed mixed boundary value problem is reduced to solving a hypersingular integral equation with the crack surface displacement as a new unknown function. As a result, the variations of stress intensity factors are illustrated as a function of possible range of periodic crack spacing in conjunction with the different values of the material nonhomogeneity parameter. Furthermore, crack opening displaccements are presented for various geometric and material combinations.