On the penny-shaped crack in inhomogeneous elastic materials under normal extension

The solution of the problem of a penny!shaped crack in an inhomogeneous material with elastic coe.cients which are varying continuously along the direction perpendicular to the crack is examined in this paper[ We studied the problem for an inhomogeneous material which satis_es the conditions of either torsional deformation and normal extension[ A series form solution to the problem is proposed and analytical expressions for the _rst two terms of the series are obtained by using a Hankel transform technique[ In the solution a homogeneous body is chosen as the reference so that inhomogeneous quantities are treated as being perturbed from the zero|s reference solutions[ Closed form expressions for the relevant stress intensity factors and the crack energy are derived and speci_c cases of the problem are also considered