A physically consistent theory of fracture in a brittle solid

Abstract

The classical problem of the equilibrium shapes of two- and three-dimensional ("penny shaped") cracks of linear elasticity is reexamined. The singularity of the stress field and the unphysical nature of the crack profile at the crack tip are removed by a consistent treatment of intermolecular or surface forces which determine the elastic behavior at the crack tip. This calculation provides a direct verification of Barenblatt's conjectures about the disposition of the crack tip. The predicted crack profile coincides with Griffith's result in the macroscopic regime but goes over to a microscopic form which does not produce any singularities in the vicinity of the crack tip. © 1987.