A PERIODIC ARRAY OF CRACKS IN A FUNCTIONALLY GRADED NONHOMOGENEOUS MEDIUM LOADED UNDER INPLANE NORMAL AND SHEAR

In this paper, the problem of a periodic array of parallel cracks in a functionally graded medium is investigated based on the theory of pla ne elasticity for a nonhomogeneous continuum. Both the in-plane normal (mode I) and shear (mode II) loading conditions are considered. It is assumed that the material nonhomogeneity is represented as the spatia l variation of the shear modulus in the form of an exponential functio n along the direction of cracks, and the Poisson's ratio is constant. For each of the individual loading modes, a hypersingular integral equ ation is derived, in a separate but parallel manner in which the crack surface displacements are the unknown functions. As the basic paramet ers in applying the linear elastic fracture mechanics criteria, the mo de I and mode II stress intensity factors are defined from the stress fields with the square-root singularity ahead of the crack tips. Numer ical results are obtained to illustrate the variations of the stress i ntensity factors as a function of the crack periodicity for different values of the material nonhomogeneity. The crack surface displacements are also presented for the prescribed loading, material, and geometri c combinations.