Von Mises beyond Yield, is it valid for Ultimate loading - Part 3

[aaronsmith0402]

thread727-349560
I didn't like how this question/thread ended and I'm sure there are some engineers out there who are in the same boat.

The question seems to be: Can I use Von-mises failure criteria against and ultimate strength requirement. (von-mises is less than a factor of safety and ultimate tensile strength of a material)

The answer is: Depends on the material that you have? I assume we are taking metals here. (Aluminum, steel, etc...)

You need to determine is the material is brittle or ductile. If it's brittle, the material usually doesn't have a yield strength so von-mises would not be appropriate. You would use a Modified Mohr failure criterion (or others). If it's ductile, the material does have a yield strength and von-mises can be used. Usually if the elongation of a material is less than 5%, then it is brittle. (Shigley)

There are exceptions such as components, COTS parts such as lugs or rivets, that have working limits (ultimate loads) from manufacturer data. Even if these components are ductile, you would just use loading criteria.

Anyway, back to the question.

If you have a ductile material, can we compare von-mises to ultimate criteria? Yes.

Maximum principal stress theory is usually used for brittle materials. However, I'd recommend Modified Mohr.

The ultimate criteria, is the tensile strength of the material. (the point before necking occurs and strength decreases) - Refer to ductile stress strain curve. The region between yield and ultimate is called work hardening. The strength of the material increases with increase in plastic working. Usually, we assume isotropic work hardening which strength increases uniformly in all directions. Referring back to von-mises, the yield locus gets stretched out uniformly all around and is a function of plastic strain and the tangent modulus. The increase in yield locus equates to the ultimate strength. Therefore, the von-mises criteria should still be used.

Note: Honestly, Hill's criterion (which stems from von-mises) should be used if you are designing in the ultimate region, it pretty pointless for ductile materials since we usually design to yield. Here is a link to a good paper on the history of each failure criteria and type of hardening.

https://www.researchgate.net/public...inearity_during_deformation_using_FEM_sofware

Note: If you are conducting non-linear analysis with ANSYS. You should take a close look if you want to consider isotropic hardening (Bilinear Isotropic Hardening) or kinematic hardening (Multi-linear isotropic hardening). Then please watch this video and read this thread for how ANSYS calculates von-mises stress (yield surface) in the plastic region.

https://www.youtube.com/watch?v=rCFmcNWRds4

https://lsdyna.ansys.com/the-equations-for-isotropic-von-mises-plasticity/

 

[rb1957]

fundamentally von mises is a limit criteria, not an ultimate criteria. It does not account for plastic strain. I'd say it's more applicable to brittle materials but that'll start a huge bun fight !

but do "we" use it as an ultimate criteria ? many do ... MS = ultimate allowable/von mises -1 ... as this is very conservative.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[centondollar]

No, and it's stated in the name: yield criterion. Hardening changes the stress-strain relation after yielding, but this stress is not the material's yield stress, nor its ultimate stress.

Furthermore, some codes applying von Mises equivalent stress and ultimate tensile strength in capacity checks for ductile welds is related to empirical evidence suggesting significant work-hardening and non-linear ultimate capacity of such connections, but it does not imply that a yield criterion (von Mises) can be used for loading causing ultimate tensile stress.

 

[rb1957]

I'll use von mises in places where I have a true 3D stress field, as it combines the three principal stresses. On flat sheet I'll use principal stress.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[human909]

Thanks for this. I haven't yet properly digested your post or you links. But I appreciate it as I routinely use FEA for a whole bunch of complex structural scenarios. (Which are probably not that complex in the context of mechanical or aerospace!)

I would considered myself reasonably adept at suitable FEA modelling and interpretation, but there is always more to learn.

(I use NASTRAN. And where necessary I will normally investigate non-linear plastic modelling. But in general that is excess to my requirements, but it helps check that my interpretation of the linear elastic modelling results are applicable.)

 

[centondollar]

For steel, the von Mises criterion predicts yielding with remarkable accuracy and therefore also onset of plasticity, necking and failure - principal stresses do not.

 

[aaronsmith0402]

Great discussion people. The goal of this thread is to get good consensus, so that younger/unexperienced engineers who are reading these posts/threads can accurately analyze their designs.

The Von-Mises we all know and love from our textbooks is an equivalent stress to predict yielding of ductile materials. 100% agree with everyone on here that it should be used for yield criterion only. (Please read on)

In most engineering requirements, we usually have a factor of safety (FS) for both yield and ultimate strengths. Most of the materials (talking metals here) are ductile; Von-mises failure criteria is used against our yield FS.

In the case where we have both yield and ultimate requirements, the ultimate FS is just an extra provision to limit our applied stress. Understand, in order to meet yield requirements, the material is not in the plastic range; therefore, you don’t need to worry about how the stress in calculated in plastic range. (I have seen the ultimate FS requirement drive design (needed to lower von-mises stress). This depends on the difference between the yield and ultimate factors of safety and the difference between yield and ultimate strengths of the material.

So don’t assume since yield requirements have been met, ultimate requirements have also been met. You should check both against von-mises stress.

In the rare case (maybe not rare for the aerospace peers) where you are designing in the plastic range of a ductile material, therefore ultimate tensile strength is your criteria. Then what I’m getting at is that Von-mises, in its stress matrix form, can be re-written to include the effects of plastic strain and be used to accurately predict stress in both the elastic and plastic range.

This is done by using flow theory of plasticity which describes the yielding of the material by work hardening. (This is what ANSYS does as well as other FEA programs).

The ultimate tensile strength is at the very end of the work hardening range (before necking and strength decreases, refer to a ductile stress strain curve). Therefore, Von Mises (maybe a better term is equivalent stress or yield surface) can accurately predict stress in this range.

As for principal stress, this theory simply asserts that the breakdown of material depends only on the numerical magnitude of the maximum principal stress. Stresses in the other directions are disregarded. While the maximum stress theory is sometimes accurate for brittle materials (only in tension or compression, refer to Shigley), it is not always accurate for ductile materials. Ductile materials often fail along lines 45° to the applied force by shearing, long before the tensile or compressive stresses are maximum.

Principal stresses are accurate for brittle and ductile materials for uniaxial stress or when one of the principal stresses is large in comparison to the others. There’s usually a discrepancy between principal and von-mises when more than one principal stress is numerically equal.

My recommendation for failure criteria for brittle and ductile metals:

Brittle: Use Coulomb Mohr or Modified Mohr for the ultimate failure criteria.
(Unless you have one principal stress higher than the others, then Maximum Principal Stress theory can be used.)

Ductile: Use Von-Mises for both yield and ultimate failure criteria.
(Unless you have one principal stress higher than the others, then Maximum Principal Stress Theory can be used, ex would be biaxial stress, where the principal stress normal to the surface of the plate is small in comparison to the other principal stresses.)

 

[rb1957]

in the words of a past mentor of mine ... sure, fill your boots !

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.