A dislocation theory of fracture criteria for mixed dislocation emission and cleavage in an anisotropic solid was developed. Complicated cases which involved mixed-mode loading were considered. The explicit formula for dislocation interaction with a semi-infinite crack was obtained. The governing equation was established for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions. The effects of elastic anisotropy, crack geometry and load phase angle upon the critical energy release rate and the total number of emitted dislocations at the onset of cleavage were analyzed in detail. The analyses revealed that the critical energy release rates could increase, to become one or two magnitudes larger than the surface energy, due to dislocation emission. It was also found that elastic anisotropy and crystal orientation had significant effects upon the critical energy release rate. The anisotropic values could be several times higher than the isotropic value in one crack orientation. The values could be as much as 40% less than the isotropic value for another crack orientation and another anisotropy parameter. The theory was applied to a face-centered cubic single crystal. An edge dislocation could be emitted, from the crack tip, along the most highly shear-stressed slip plane. Crack cleavage could occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation was carried out step-by-step. At each step, it was decided which slip system was the most highly shear-stressed one, and which slip system had the largest energy release rate. The calculation clearly showed that the crack orientation and load phase angle had significant effects upon crystalline brittle-ductile behaviours.

Dislocation Theory of the Fracture Criterion for Anisotropic Solids. T.C.Wang: Philosophical Magazine A, 1998, 77[1], 31-53