The solution of the problem of a penny-shaped crack in an inhomogeneous mat
erial with elastic coefficients which are varying continuously along the di
rection perpendicular to the crack is examined in this paper. We studied th
e problem for an inhomogeneous material which satisfies the conditions of e
ither torsional deformation and normal extension. A series form solution to
the problem is proposed and analytical expressions for the first two terms
of the series are obtained by using a Hankel transform technique. In the s
olution a homogeneous body is chosen as the reference so that inhomogeneous
quantities are treated as being perturbed from the zero's reference soluti
ons. Closed form expressions for the relevant stress intensity factors and
the crack energy are derived and specific cases of the problem are also con
sidered. (C) 1999 Elsevier Science Ltd. All rights reserved.