In the theory of stress at a point, an octahedral plane is a plane equally inclined to all three principal stress axes (direction cosines equal in magnitude, 1/√3); the normal and shear stresses acting on such a plane — the octahedral normal stress and octahedral shear stress — depend only on the principal stresses σ1, σ2, σ3 and can be expressed compactly in terms of the first and second stress invariants. This extends the general stress-transformation and Mohr's-circle framework for evaluating stress on an arbitrary plane to a special, invariant-based measure of the overall stress state at a point, independent of the choice of coordinate axes.
In the theory of stress at a point, an octahedral plane is a plane equally inclined to all three principal stress axes (direction cosines equal in magnitude, 1/√3); the normal and shear stresses acti…