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

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).