The Sih, Paris and Irwin analytical solution for cracks in anisotropic elastic media has been developed for an hcp Ti single crystal and shown to lead to crack tip normal stresses which are independent of crystal orientation but other stress components which are dependent. Detailed finite element studies confirm that the stress intensity remains independent of crystal orientation but ceases to do so in an edge-cracked bi-crystal.

The incorporation of crystallographic slip demonstrates that single-crystal crack tip stresses largely remain independent of crystal orientation but that the plastic zone size and shape depends greatly upon it. Significant differences result in both the magnitude and extent of the plasticity at the crack tip with crystallographic orientation which can be quite different to that predicted using Mises plasticity. For an edge crack terminating in a bi-crystal, the slip fields which result depend upon both crystal mis-orientation and morphology.