An elastic layer with a penny-shaped crack subjected to internal pressure

Abstract

This study examines the axisymmeteric problem on an elastic layer with a penny-shaped crack situated in its middle plane. The crack surfaces are subjected to uniform pressures. The layer surfaces are free from stresses for case I while smooth-clamp conditions are prescribed on the layer surfaces for case II. By assuming series expansions for the normal displacement on the crack surfaces, both cases are reduced to analytical and exact solutions through infinite system of simultaneous equations. An expression for the stress intensity factor at the penny-shaped crack is evaluated in a simple form of a series which involves coefficients of the solutions of the simultaneous equations. Numerical results are obtained to examine the effects of the layer thickness and boundary conditions of the layer surfaces on normal stress and displacement distributions and on the stress intensity factors.