The fracture of brittle and ductile crystals. Force and deformation criteria

Abstract

The growth and branching of sharp cracks in ideal single crystals are investigated. Neuber-Novozhilov force and deformation criteria are proposed for the branching of sharp cracks; these criteria describe the brittle, quasibrittle, quasiductile and ductile behaviour of materials on fracture. For internal cracks, simple relations are obtained that describe the branching of cracks when the Coulomb-Mohr single-crystal theoretical strength curves are known for a generalized stress state. The possibility of multiple branching of cracks is found, which is linked to the multiplicity of the eigenvalues on loss of stability of the system. It is established that, for ideal single crystals, the principle of local symmetry is satisfied in the vicinity of the crack tip if the axis of symmetry of the crystal coincides with the axis of the crack. When there are asymmetrical disturbances of the atomic lattice in the vicinity of the crack tip, or when the axis of symmetry of the single crystal does not coincide with the crack axis, the principle of local symmetry is not satisfied.