We think of stresses acting on faces, so we often associate the state of stress with a coordinate system. However, the selection of a coordinate system is arbitrary (materials don't know about coordinates - it's a mathematical construct!) and we could choose to express the stress state acting on any set of faces aligned with any coordinate system axes. Furthermore, we can relate the states of stress in each coordinate system to one another through stress transformation equations.
Heads up!
Cauchys stress theorem builds on this content in later solid mechanics courses.
For any surface that divides the body ( imaginary or real surface), the action of one part of the body on the other is equivalent to the system of distributed internal forces and moments and it is represented by the stress vector
The state of stress at a point in the body is defined by all the stress vectors
Angle:
Because of symmetry, the stress tensor (