Use of Von Mises stress
Von mises stress is considered to be a
safe haven for design engineers.Using this information an engineer can
say his design will fail if maximum value of Von Mises stress induced in
the material is more than maximum strength of the material. It works
well for most of the cases especially when material is ductile in
nature.
Distortion energy theory
Concept of Von mises
stress arises from distortion energy failure theory. According to
distortion energy theory failure occurs when distortion energy in actual
case is more than distortion energy in simple tension case.
Distortion energy
It
is the energy required for shape deformation of a material, during a
pure distortion shape of the material changes but volume does not
change. This is shown in figure 1.
 |
| Fig.1 Representation of a pure distortion case |
Distortion energy required per unit volume,
ud for a general 3 dimensional case is given interms of
principal stresses by
For simple tension case it is given as
Expression for Von Mises stress
Above 2 quantities can be connected using distortion energy, so the condition of failure will be as follows.
Left hand side of above equation is denoted as Von Mises stress.
So
as a failure criterion engineer can check whether Von mises stress
induced in the material exceeds maximum strength of the material.So the
failure condition can be simplified as
Industrial Applications of Von Mises Stress
Distortion
energy theory is the most preferred failure theory used in industry. It
is clear from above discussions that whenever an engineer resorts to
distortion energy theory he can use Von Mises stress as failure
criterion. So an engineer's duty is to keep maximum value of Von Mises
stress induced in the material less than its maximum strength.
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