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.
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 cases, especially when the material is ductile in nature. In the folowing sections we will have a logical understanding of Von Mises stress and why it is used.
When does a material fail?
One of the most easy way to check when a material fails is a simple tension test. Here the material is pulled from both ends. When the material reaches the yield point (for ductile material) the material can be considered as failed. The simple tension test is a unidirectional test, this is shown in the first part of Fig.1.
Distortion energy theory
The concept of Von mises stress arises from the distortion energy failure theory. Distortion energy failure theory is comparison between 2 kinds of energies, 1) Distortion energy in the actual case 2) Distortion energy in a simple tension case at the time of failure. According to this theory, failure occurs when the distortion energy in actual case is more than the distortion energy in a simple tension case at the time of failure.
It is the energy required for shape deformation of a material. During pure distortion, the shape of the material changes, but volume does not change. This is illustrated in Fig.2.
|Fig.2 Representation of a pure distortion case|
Expression for Von Mises stress
The above 2 quantities can be connected using distortion energy failure theory, so the condition of failure will be as follows.
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 a failure criterion.Let's see one example:
Suppose an engineer has to design a cantilever beam using mild steel as the material, with a load capacity of 10000 N. The materials properties of mild steel are also shown in the figure. The yield stress value of mild steel is 2.5x108 Pa. He wants to check whether his design will withstand the design load.
|Fig.3 A design problem, the cantilever should be able to withstand design load|
|Fig.4 Distribution of Von Mises stress in the beam obtained from FEA analysis|