What are the Principle directions? Are they unit normals of three planes perpendicular to each of the principle stresses?
I think that "Principle directions" can be used both in terms of stress (the direction of principal stresses) and in terms of inertia (the 3 direction where the inertia matrix is diagonal).
I mainly use "principal direction" in terms of inertia.
I think that you can ganeralize: principal directions are the unit vector where something 3D distribution (inertia, stresses...maybe other things) can be represented as a diagonal matrix.