What is Von Mises Stress ?

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Von Mises stress is widely used by designers to check whether their design will withstand a given load condition. In this lecture we will understand Von Mises stress in a logical way.

Detailed webpage version of the video lecture along with the industrial applications of Von Mises stress is listed below.

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 the maximum value of Von Mises stress induced in the material is more than strength of the material. It works well for most of the cases, especially when the 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 at the time of failure.

Distortion energy

It is the energy required for shape deformation of a material. During 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 stress values as
Distortion energy for simple tension case at the time of failure 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 yield strength (for ductile) of the material.So the failure condition can be simplified as

Industrial Application 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.Let's see one example.

Suppose an engineer has to design a cantilever beam using mild steel as material, with a load capacity of 10000 N. Materials properties of mild steel are also shown in figure. Yield stress value of mild steel is 2.5x108 Pa. He wants to check, whether his design will withstand the design load.

Fig.2 A design problem, the cantilever should be able to withstand design load
Following figure shows Von Mises stress distribution obtained by FEA analysis of the beam.
Fig.3 Distribution of Von Mises stress in the beam obtained from FEA analysis
One can note that Von Mises stress is maximum towards the fixed end of the beam, and the value is 1.32x108 Pa. This is less than yield point value of mild steel. So design is safe. In short an engineer's duty is to keep maximum value of Von Mises stress induced in the material less than its strength.

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