Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks I. Cracks in an infinite solid and a thick plate

Abstract

Some axially symmetric stress distributions in an infinite elastic solid and in a thick plate containing penny-shaped cracks are considered. It is shown that, by use of a representation for the displacement in an infinite elastic solid containing a single crack, representations for the displacements in an infinite solid containing two or more cracks and in a thick plate containing a single crack can be constructed and used to reduce the problems of determining the stresses in these solids to the solutions of Fredholm integral equations of the second kind. Various stress distributions investigated include those due to the opening of a crack in an infinite solid by a point force acting at an interior point of the solid and the opening of cracks in an infinite solid and a thick plate under the action of constant pressures over the cracks.