M. Ozturk et F. Erdogan, AXISYMMETRICAL CRACK PROBLEM IN BONDED MATERIALS WITH A GRADED INTERFACIAL REGION, International journal of solids and structures, 33(2), 1996, pp. 193-219
The problem of a penny-shaped crack in homogeneous dissimilar material
s bonded through an interfacial region with graded mechanical properti
es is considered. The applied loads are assumed to be axisymmetric but
otherwise arbitrary. The shear modulus of the interfacial region is a
ssumed to be mu(2)(z) = mu(1)exp (alpha z) and that of the adherents m
u(1) and mu(3) = mu(1)exp(alpha h), h being the thickness of the regio
n. 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 pro
blem is reduced to a system of singular integral equations. The asympt
otic behavior of the stress state near the crack tip is examined, and
the influence of the thickness ratio h/a and the material nonhomogenei
ty parameter alpha on the stress intensity factors and the strain ener
gy release rate is investigated. The results show that the stress stat
e near the crack tip would always have standard square-root singularit
y provided h > 0 or the material properties are continuous but not nec
essarily differentiable functions of z.