Axsiymmetric crack problem in bonded materials with a graded interfacial region

The problem of a penny-shaped crack in homogeneous dissimilar materials bonded through an interfacial region with graded mechanical properties is considered. The applied loads are assumed to be axisymmetric but otherwise arbitrary. The shear modulus of the interfacial region is assumed to be n*(z) = p, exp (MZ) and that of the adherents p, and p(l = p, exp (ah), h being the thickness of the region. A crack of radius a is located at the z = 0 plane. The axisymmetric mode III torsion problem is separated and treated elsewhere. Because of material nonhomogeneity, the deformation modes I and II considered in this study are always coupled. The related mixed boundary value problem is reduced to a system of singular integral equations. The asymptotic behavior of the stress state near the crack tip is examined, and the influence of the thickness ratio h/a and the material nonhomogeneity parameter a on the stress intensity factors and the strain energy release rate is investigated. The results show that the stress state near the crack tip would always have standard square-root singularity provided h > 0 or the material properties are continuous but not necessarily differentiable functions of z.