Fracture of brittle and ductile crystals in the generalized stress state. Strength and strain fracture criteria

Abstract

The paper considers the growth and branching of sharp cracks in perfect single crystals (fracture modes I and II). Rupture of interatomic bonds in the vicinity of crack tips are described by strength fracture criteria and emission of dislocations from crack tips by strain fracture criteria. Simple relations for the branching of internal cracks are derived given Coulomb-Mohr-type theoretical strength curves of a single crystal. It is found that in perfect single crystals, the principle of local symmetry in the vicinity of the tip of an opening mode crack is met. With asymmetric disturbances of the atomic lattice in the vicinity of the crack tip or misalignment of the crystal symmetry and crack axis, the principle of local symmetry for cracks, including opening mode cracks, is violated. The paper also studies the propagation of cracks under joint actions of mode I and II fracture. Relations for the crack kink angle in an arbitrary generalized stress state are obtained given Coulomb-Mohr-type theoretical strength curves of a single crystal. The crack propagates: 1) perpendicular to the maximum tension with no shear stress in the vicinity of the crack tip where fracture is brittle (Erdogan-Sih hypothesis); 2) along the maximum shear with no normal stress in the vicinity of the crack tip where fracture is ductile (dislocation emission); and 3) in a certain direction corresponding to the generalized stress state where fracture is quasibrittle or quasiductile (interatomic bond rupture or dislocation emission in the generalized stress state).