Von Mises stress is also referred to as the stress intensity, and is equal to: SI=max(|S1-S2|,|S1-S3|,|S2-S3|)
where Si are the principal stresses.
It also equals two times the maximum shear stress and it is used in the von Mises failure criterion for checking the acceptability of stress states.
You should consult a basic theory book on failure criteria to know more: it's a quite complex subject. prex
motori@xcalcsREMOVE.com
Principal stresses are stresses on planes with zero shear.
The von Mises yield criterion uses stresses on octahedral planes.
This subject is complex, but well described in a variety of textbooks such as Mechanical Engineering Design by Shigley and Mischke or Mechanical Behavior of Materials by Dowling. Try the following website for an intro:
prex and I posted nearly simultaneously, so I read his response after mine. prex is in error - the information he provides is for the Tresca yield criterion (also known as the maximum shear stress yield criterion). The von Mises criterion uses a more complex formula involving the root of the sum of the squares of the differences of the principal stresses.
Oops! Thanks to CoryPad for pointing out my mistake.
The formula for the von Mises stress should be: SvM=sqrt(S12+S22+S32-S1S2-S2S3-S3S1) prex
motori@xcalcsREMOVE.com
As CoryPad pointed out, the principle stresses are the three mutually orthogonal stresses acting on planes which bear no shear stresses. For every possible state of stress, the principle stresses and planes are unique. They are directional with magnitude. If a crack is present, the max principle stress will be in the driver's seat.
Von Mises stress is a function of the stress state. Each state has only one value of the Von Mises stress. In continuum mechanics, you learn that any stress state can be broken down into the hydrostatic and deviatoric stress tensors. The hydrostatic stress is the stress which is trying to change the volume of an element of material. The deviatoric stress is trying to change the shape. The Von Mises is related to the deviatoric stress. The Von Mises theory of failure claims that failure of ductile materials is due to the change in shape (twist, pull, bending.)
Von Mises can not be used for predicting fatigue. (See Socie, Multiaxial Fatigue, page 418)
