Why Does Increasing Minor Principal Stress Decrease von Mises Stress?

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.
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DTM
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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:
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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?
 
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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.
 
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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.
 
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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
 
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FAQ: Why Does Increasing Minor Principal Stress Decrease von Mises Stress?

What is von Mises stress?

Von Mises stress is a scalar stress value derived from the stress tensor that is used in engineering and materials science to predict yielding of materials under complex loading conditions. It is particularly useful because it allows for the comparison of different states of stress to the material's yield stress, providing a criterion for failure.

Why is von Mises stress important in engineering?

Von Mises stress is important because it provides a way to predict the onset of yielding in ductile materials under multiaxial loading conditions. This helps engineers design safer and more reliable structures by ensuring that the stress in any part of the structure does not exceed the material's yield strength, thus preventing plastic deformation and potential failure.

How is von Mises stress calculated?

Von Mises stress is calculated using the principal stresses of a material. The formula is given by:

\(\sigma_{VM} = \sqrt{\frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2}}\)

where \(\sigma_1\), \(\sigma_2\), and \(\sigma_3\) are the principal stresses. This formula combines the effects of the different stress components into a single equivalent stress value.

What is the difference between von Mises stress and Tresca stress?

Both von Mises and Tresca criteria are used to predict yielding of materials, but they differ in their approach. The von Mises criterion is based on the distortion energy theory and provides a more accurate prediction for ductile materials under complex loading. The Tresca criterion, on the other hand, is based on the maximum shear stress theory and is simpler but more conservative. Von Mises stress generally provides a less conservative estimate of the yield point compared to Tresca stress.

Can von Mises stress be used for brittle materials?

Von Mises stress is primarily used for ductile materials because it is based on the assumption that yielding occurs due to distortion energy. Brittle materials, which fail by fracture rather than yielding, are better analyzed using criteria that consider maximum normal stresses, such as the maximum principal stress criterion or the Mohr-Coulomb criterion. Therefore, von Mises stress is not typically used for brittle materials.

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