Tresca stress

w1961

I don't if anyone has mentioned this before.
When the option for Tresca stress is set, the stress value displayed is about twice as high aa the difference between the 1st and 3rd principal stresses.
By definition the Tresca stress is the max shear stress = (S1 - S3)/2.

Please check if this is the case in your result.

Victor

Mecway calculates Tresca stress as the maximum difference between principal stresses without dividing by 2. If you're seeing results that are not that, it could be due to node averaging and lack of mesh refinement.

As for whether it should divide by 2 or not, that's a tricky one. From what I understand, there isn't a standard definition of the term "Tresca stress". Do you have any references that would help confirm that? Some other FEA software (Strand7 and Abaqus) doesn't divide by 2 while Autodesk Simulation sort of does, calling the same quantity "Tresca*2".

w1961

Hi Victor,

My understanding is that Tresca stress is by definition the max shear stress. Thus, it is one half of the difference between the 1st and 3rd principal stresses. This should be mentioned in any advanced strength materials where the criterion for brittle fracture is involved.

Yes, other FEA packages may also not divide the difference by two. Some people just take the "Tresca stress" as the max shear stress but it is actually twice of that. This may cause confusion that leads to claims that the stress is too high for some design after it is involved in an bad accident. The fact is that the max shear stress calculated is half of the Tresca stress.

It may be possible that the stress in the Tresca criterion is half of the Tresca stress. However, Tresca stress is usually taught the same time as von Mises stress. Their definition can be found, for example, in https://www.failurecriteria.com/misescriteriontr.html

Victor

I can't find any evidence that the term "Tresca stress" means maximum shear stress. I think it's just a sloppy ambiguous shorthand. Neither the page you linked to nor a textbook I have which covers the topic use that term at all. My textbook does define what it calls "effective stress for the maximum shear stress criterion" which is the same as Mecway's Tresca stress. It also has a "maximum shear stress" which is half that. It doesn't call either of them Tresca stress.

I could clear up the ambiguity by deprecating Tresca stress and replacing it with "maximum shear stress" that's half the value but I suspect that quantity isn't so useful because you'd normally compare it to the uniaxial tensile strength, not the shear yield stress, wouldn't you?

w1961

Here is textbook that refers to Tresca stress as the max shear stress (see attached for a copy of the text):

Richard G. Budynas, "Advanced Strength and Applied Stress Analysis", 2nd edition, MicGraw-Hill, 1999, ISBN 0-07-008985-X, p. 509

From test results Tresca stress is not as useful as von Mises stress for yielding but is a good indicator for brittle fracture e.g. shear under compression.

The issue arises when the torsion or other shear related loading conditions are involved. The design specification always requires a comparison of the max shear stress and one half of the allowed tensile stress. If some one evaluates a part designed by someone else and assumes that the Tresca stress is the max shear stress, he will find the part is under-designed because the shear stress is too high from a FEA. The worst scenario happens when it is used as an evidence in a lawsuit ...

Victor

Thanks. I'll do a rough survey of literature and see if there's any consistency to this. Do you have a suggestion for an alternative name for this quantity? Perhaps "Tresca stress × 2".

w1961

Since Tesca stress is the stress used in the Tesca yield criterion, it is often taken as the synonym of the max shear stress. I think "Tresca stress × 2" is exactly the name that represents the stress calculated currently under the name of "Tesca stress".

Victor

This is pretty unscientific but I found 21 sources (journal articles, books, FEA software manuals) that describe the Tresca criterion:

3/21: Tresca stress refers to maximum shear stress
1/21: Tresca stress refers to 2*maximum shear stress
2/21: Tresca equivalent stress refers to 2*maximum shear stress
2/21: stress intensity refers to 2*maximum shear stress
17/21: No use of the term Tresca stress that I could find.

My conclusion is that Tresca stress mostly means maximum shear stress but it's also a very uncommon term that's hard to find the definition of so it should probably not be used anywhere. In contrast, maximum shear stress was used almost universally.

So my intention now is to rename Mecway's Tresca stress to maximum shear stress × 2.

Thanks for bringing this up. I hadn't realized how misleading it was.

MartinB

Stress intensity is a widely known and understood term, eg as used in ASME codes.
my 2c worth

Victor

Thanks for adding that but I'm going to have to get a bit ranty - Stress intensity is awful. It's apparently the same thing as stress intensity range, so good luck describing a range of stress intensities! Does intensity here have any common meaning with any other use of that word? Google's first result is about stress intensity factor which is nothing to do with it. Wikipedia too needs a disambiguation page because of the two meanings and identifies it as Tresca effective stress which is not the same as Tresca stress. So just a massive pit of confusion there for anyone who doesn't work with pressure vessel codes. I appreciate w1961's prompting me to correct and clean up this mess.