# Understanding von Mises stress

• DTM
In summary: This is a great question and one that is often left unanswered or glossed over in traditional physics curricula. The explanation for this comes down to the fact that shear stress is a measure of the difference in stresses on a specimen and is what leads to failure in ductile materials. In contrast, hydrostatic pressure is a static pressure that remains unchanged regardless of the motion of the parts within it. This difference in behavior is what leads to the different failure modes that can occur under different conditions.
DTM
TL;DR Summary
Following the formula for von Mises stress, can you give an intuitive explanation of why the von Mises stress may go down when the minor principal stress goes up.
The formula for von Mises stress for a plane stress (2d) condition with no shear stress is:

So if S1 = 1000, S2 = 0 , then Svm = 1000.

If the S2 is now increased from 0 to 500. The von Mises stress will go from 1000 to 866

I understand this is how the equation works, but can someone give me an intuitive understanding of why, when you increase a minor principal stress, the von Mises stress (and the likelihood of failure) should go down?

VM stress is a measure of shear which is a function of the DIFFERENCES of the principal stresses. Don’t forget that the third principal stress is zero.

Last edited:
cherish, Chestermiller and DTM
Frabjous said:
VM stress is a measure of shear which is a function of the DIFFERENCES of the principal stresses. Don’t forget that the third principal stress is zero.
So differences in principal stresses is what makes ductile metals fail. That does make some sense and is somewhat intuitive. Thank you.

Here is a nice video about failure theories which includes Von Mises.

I recommend checking out almost all vídeos from that channel. It's fantastic.

This actually raises the question of why is it that shear stress is responsible for failure in ductile materials while hydrostatic pressure does not contribute. Often textbooks present this kind of information as FACTS because it is not really necessary to know the underlying reasons to be able to squeeze every drop of utility out of a structure by using math.
Since the amount of material to be covered during courses is huge, more often than not these kinds of details are left for the student to research on their own if interested or in separate courses. In my opinion, knowing the experimental and historical context within which such formulas are derived usually helps significantly in their understanding.

Here is some additional info about that hydrostatic pressure scenario and failure modes.

https://physics.stackexchange.com/q...l through shear,move dislocations in this way

DrClaude and DTM

## 1. What is von Mises stress?

Von Mises stress is a measure of the maximum equivalent stress experienced by a material under a combination of different types of stress, such as tension, compression, and shear. It is used to predict the potential failure of a material under complex loading conditions.

## 2. How is von Mises stress calculated?

Von Mises stress is calculated using the von Mises yield criterion, which takes into account the principal stresses and their orientations. The formula for von Mises stress is σv = √(σ1² + σ2² + σ3² - σ1σ2 - σ1σ3 - σ2σ3), where σ1, σ2, and σ3 are the principal stresses.

## 3. What is the significance of von Mises stress in material testing?

Von Mises stress is a useful tool in material testing as it allows for the evaluation of a material's strength and ductility under various loading conditions. This information is crucial in determining the suitability of a material for a specific application and can aid in the design and optimization of structures.

## 4. How does von Mises stress differ from other stress measures?

Von Mises stress differs from other stress measures, such as maximum principal stress or shear stress, in that it takes into account the combined effect of multiple stress components. This makes it a more accurate representation of the stress state of a material under complex loading conditions.

## 5. What are the limitations of using von Mises stress?

One limitation of using von Mises stress is that it assumes that the material being tested is isotropic, meaning it has the same properties in all directions. This may not always be the case in real-world applications. Additionally, von Mises stress does not take into account the effects of temperature, strain rate, or material microstructure on the material's behavior.

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