Stress distribution, crack shape and energy for a penny-shaped crack in a plate of finite thickness

Abstract

The shape of a penny-shaped crack located at the center of an elastic plate of finite thickness is related to the arbitrary axisymmetrical internal pressures applied to the crack surfaces in the form of a Fredholm integral equation, without using the methods of dual-integral equations. General expressions for the stresses in the plane containing the crack are written as the sums of the associated infinite solid stresses and the integrals accounting for the effect of plate thickness. The crack shape due to uniform crack pressures and the fracture criterion for brittle plates subjected to uniform stresses are obtained for various plate thicknesses. Using the finite stress condition, general methods for determining the radii of the plastic zone are described for ideally elastic-plastic materials. The normal stress is shown to be continuous and finite at the outer circle of the plastic zone. The crack shape and the rate of the plastic energy dissipation are calculated for various values of plate thickness and crack pressure.