Why does an anisotropic shaft split axially under excessive torque?

Answer 1

For in anisotropic material, it could be that the plane of lowest tensile strength is close to axial. Torsion stress (from the applied torque) will then cause it to fail along that plane.

In general, where it fails will depend upon the failure mechanism. Brittle materials (like a stick of chalk) will fail along a 45 degree plane inclined to the axis