In this paper, the axisymmetric crack problem for a nonhomogeneous med
ium is considered. It is assumed that the shear modulus is a function
of z approximated by mu = mu0e(alphaz). This is a simple simulation of
materials and interfacial zones with intentionally or naturally grade
d properties. The problem is a mixed-mode problem and is formualated i
n terms of a pair of singular integral equations. With fracture mechan
ics applications in mind, the main results given are the stress intens
ity factors as a function of the nonhomogeneity parameter alpha for va
rious loading conditions. Also given are some sample results showing t
he crack opening displacements.