When should I use principal stresses instead of von Mises stresses and vice versa? 2

[EdwardNigma]

Hello guys. I know this has been asked many times but I’m interested in knowing the main differences between von Mises, Tresca, and Principal Stress theory and when to apply them.

The reason why I ask is because I've mostly worked in aerospace and I first started my career out of college as a stress engineer at a small company. I used extensive FEA to perform static and dynamic analysis and applied von Mises stress criterion to calculate MS against Ftu material allowables (metallic structures steel, aluminum and Inconel). Then I worked performing stress analysis of airframe fuselage metallic (aluminum) repairs for an OEM and used max principal stresses to compare against Ftu in MMPDS to calculate margins of safety. General guidelines suggest using von Mises for ductile materials, not max principal stresses, but I used principal stresses in this case.

After some time, I spent the majority of my career as a designer and leading up to this I didn't question the senior stress engineers in my short stint as a stress engineer. When I returned to stress analysis, I worked on nacelle repairs and, in one occasion, I had to calculate the margin of a blended metallic fitting, which was certified using FEM in the SCN using von Mises stress criterion. Due to limited data, my approver said it would be sufficient to compare the change in area and apply a knockdown factor to the FEM data and refer to Fty (yield), not Ftu (ultimate), due to the use von Mises stress during certification. That made me become curious about different failure modes but whenever I questioned things with other engineers I only seem to get in trouble as I discredited them from doing things the right way.

The question I have is, what’s the difference between von Mises, Tresca, and Principal Stress theory, and similar theories for that matter in the general sense (FEA or hand analysis)? Are there different names for these (ie max distortion energy = von Mises, max shear stress = Tresca)? Is there a way to down select which failure criteria one should use to calculate the margin of safety? Also, when can one use Ftu vs Fty for these failure modes in aerospace stress analysis? Aerospace typically calculates margins against Ftu (ultimate loads ~ 1.5 limit loads). Do you guys recommend any sources that go over this which would clarify why I was applying max principal stresses for a ductile material?

Even though I’m not an expert in composites, failure modes make more sense when dealing with composites in aerospace. For example, maximum strain criteria use over max stress criteria because the homogenized ply strains have determinate correlation to fiber/matrix phase in the fiber direction. The use of Tsai-Wu criteria over Tsai-Hill also makes sense as Tsai-Wu considers both tension and compression stresses. However, the use of linear criteria (max strain criteria specifically), is simpler to use, more closely related to the physics, and accurate enough.

I'd really appreciate any information. Thanks in advance!

 

[rb1957]

To me, outside the technical definition of von Mises, which I know, ... von Mises is good for 3D fittings with 3 principal stresses as it combines them together.

Principal stress is good for 2D sheet panels, but you need to think about shear and compression stresses (buckling the panel).

Of course one way is to use the maximum (max peincipal, von Mises).

And thank you for principAL (not LE) !

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

 

[LiftDivergence]

This question has been discussed ad nauseam on these forums. I would start by searching "von Mises". Here are a few threads that I have personally participated in:

thread16-512694

thread507-480814

thread2-413046

Here's a handy picture:

There is an element of this where it can depend on if you're trying to assess ductile or brittle failure. Or there may be situations where you might not be simply trying to assess failure on a peak point stress basis, you could be interested in the actual element state of stress.

But in general for peak point stress MoS the relative conservatism of the failure envelope can be visualized in the attached picture and some of the others I put in the other threads.

Keep em' Flying
//Fight Corrosion!

 

[SWComposites]

for metals,
vonMises is a yield criterion, so strictly not valid beyond the onset of yielding, but is often used (conservatively I think) at ultimate because it is easy.
principal stress is a criterion for brittle materials and often appropriate for predicting onset of fatigue cracking that is due to tensile principal stress.
there's probably better discussions in the threads linked above.
and if you have not had a good strength of materials class, then get ahold of a good strength of materials textbook

for composites,
for carbon fiber polymer composites,
failure should be driven by the fibers, not the matrix,
so I strongly recommend max strain criteria as it best correlates to actual laminate multi-axial loading test data
max stress does not correlate as well as max strain
tsai-wu is rubbish and does not correlate to anything
tsai-hill is also rubbish in that it also interacts completely different failure modes, but in the right hands can be set up conservatively to be ok(ish)
I've posted on previous threads about composite failure criteria

 

[LiftDivergence]

vonMises is a yield criterion, so strictly not valid beyond the onset of yielding, but is often used (conservatively I think) at ultimate because it is easy.

It is true that von Mises effective stress is a Hookean model (

https://www.continuummechanics.org/vonmisesstress.html)

It cannot account for level of ductility, Ramberg-Osgood shape factors, or hardening parameters.

Analysis generally works by defining a limit load and then checking stresses at limit load with a yield factor against yield, and checking limit load with an ultimate factor against ultimate. Obviously by definition the ultimate strength is beyond yield and for a material to actually reach ultimate it will have to permanently deform. But it is common practice to use linear-elastic analysis to check peak point stress against ultimate, despite this. Theoretically this should be conservative for stress MoS because the stress will rise much faster if you adhere to the Hookean model instead of Ramberg-Osgood.

However, a major caveat to this is that if your limit load * ultimate factor actually predicts a stress over the yield strength you MUST write a strain margin to check rupture, and that strain MUST be predicted using some kind of pseudo-nonlinear method (there are many models for predicting local strain), and triaxiality must be accounted for where relevant (a reduction in ductility often occurs just prior to fracture).

The question still remains relevant, which stress to use for the ultimate check. In my experience von Mises equivalent stress is generally fine and conservative, if you compare local notch stress & strain corrections computed with von Mises stress & strain as a reference to local stress & strain calculated via Hencky total deformation theory. Situations where this might not be true are those in which the hydrostatic component of the stress is significant.

Keep em' Flying
//Fight Corrosion!

 

[EdwardNigma]

Thanks guys! A lot of useful information referenced here.

 

[LiftDivergence]

I worked on nacelle repairs and, in one occasion, I had to calculate the margin of a blended metallic fitting, which was certified using FEM in the SCN using von Mises stress criterion. Due to limited data, my approver said it would be sufficient to compare the change in area and apply a knockdown factor to the FEM data and refer to Fty (yield),

By the way, I don't know what your situation was with this approver, but I completely disagree with whoever that was. Generally, it is not a good idea to simply compare net area to apply a factor to an existing margin. So many reasons why this could be completely inaccurate. I guess I'd need more details on what exactly the situation was, but my first impression when I read that was... yikes

I didn't question the senior stress engineers in my short stint as a stress engineer

Just note, you should always be able to question a stress lead or an approver on their recommended methods. Just because they are in that position doesn't mean they know everything (or are even competent to be honest).

First rule of being an analyst... your analysis needs to convince YOU just as much as it convinces a reviewer / approver. If you are doing the report, YOU are the one who knows the most details.

Keep em' Flying
//Fight Corrosion!

 

[SWComposites]

LD, re:
Generally, it is not a good idea to simply compare net area to apply a factor to an existing margin.
Yeah, I agree, but in the aftermarket wild west world where repairs are approved, you might be appalled at a lot of the assumptions and very simplified analyses that are done, particularly when the OEM info is not available. And then there is the wild wild west world of MRB Stress where if you really don't have a strong stomach you really don't want to know what they do. I'm not condoning any of it, and have fought it all too many times, but it happens.

 

[tim1958]

Something else to consider: you might have encountered differences in approach when doing classical hand analysis vs. using detailed FEM stresses. Classical hand analysis usually uses average stresses. For example, Bruhn section D1.10 for fitting analysis shows simple checks for net section (using Ftu), bearing (using Fbru), and shear out (using Fsu). The stresses you by hand compute to compare to those allowables are total load divided by relevant total area.

When using a detailed FEM on the other hand, you are getting local stresses at points all over the volume of the part. If you made a 3D solid FEM of Bruhn's example joint, and you ran a linear elastic analysis, you would see lots of variation in the local stresses, and in some places exceeding Ftu, Fbru, and/or Fsu even though the hand analysis said the part was good. So, if you limited the maximum von Mises stress in your FEM to Ftu, you would most likely be conservative, but perhaps super conservative, which is one reason the classical methods still have much value.

Getting back to the failure theories, they relate to material strength, but parts fail for other reasons. Aerospace structures especially tend to be thin and slender, and failure modes like buckling are often the driver. In these cases, calling the part good because the FEM von Mises stresses are low can be a serious mistake.

Regarding von Mises vs. Tresca, I think that von Mises is generally preferred theoretically to predict yielding in ductile materials, but in the old days, Tresca was somewhat easier to compute (not as many squares involved), and the difference between the two is not that great when you consider the uncertainties in all the other factors. FYI I have attached a page from a book that shows comparisons of test data to von Mises and Tresca (Plasticity: Theory and Applications, Alexander Mendelson, Macmillan Company, 1968).

 

[rb1957]

"When I returned to stress analysis, I worked on nacelle repairs and, in one occasion, I had to calculate the margin of a blended metallic fitting, which was certified using FEM in the SCN using von Mises stress criterion. Due to limited data, my approver said it would be sufficient to compare the change in area and apply a knockdown factor to the FEM data and refer to Fty (yield), not Ftu (ultimate), due to the use von Mises stress during certification."

with all due respect (not sarcastic) to LD, I think you've missed the point. How can you do a quantitative analysis of a repair, or any other change, without the OEM data, without the full detail of the "daytime" job this fttg is doing ? "All" we're doing is creating a story to show the change has minimal effect on the part. Maybe the repair is in a lightly loaded area of the fttg. But rather than worrying about principal or von Mises stress, I'd suggest doing a comparative analysis ... the original fttg vs the repaired fttg under some set of loads and show that the fttg is not much affected by the repair.

I think these types of analyses are not well suited for juniors, because so much depends on "feeling", on experience. If they're just following along with what a senior says, they aren't learning where the senior think that way. An antenna installation is a much better learning tool ... you can explain the direction of the analysis, and let they run with it. Later you can explain some shortcuts, and let them figure out why the shortcuts are legitimate (and maybe when not) and how significant (conservative) the short cut is. Some many repairs are "PBI" but a junior engineer doesn't have the experience to have acquired a proper level of "Inspection", so they're left following someone else's led.

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

 

[EdwardNigma]

Once again guys, thanks for the additional input. Just some clarification, I worked fleet support stress analysis, often designed and performed analysis, when I worked fuselage and nacelle repairs. So, with the nacelle repair job, information was limited and this was a one-off repair to get an aircraft on the ground. We relied on certification analysis and did not have the FEM model under time constraints. So, in this world which is similar to MRB stress, you buy it off with some sort of substantiation but in an ideal world it's often incorrect. So, I understand why it makes some of you guys shake your head.

 

[LiftDivergence]

Yeah, I agree, but in the aftermarket wild west world where repairs are approved, you might be appalled at a lot of the assumptions and very simplified analyses that are done, particularly when the OEM info is not available. And then there is the wild wild west world of MRB Stress where if you really don't have a strong stomach you really don't want to know what they do. I'm not condoning any of it, and have fought it all too many times, but it happens.

I worked for a 3rd party engineering company with two staff DERs doing post-production support for commercial aircraft (Part 25) for quite a long time and I have worked in a similar capacity for Part 23 aircraft. We were kind of the engineering support for several small airlines who didn't want to pay the OEM for repair support. I have for sure seen substantiations for repairs which were pretty appalling. I know it can be pretty fast and loose. I had an internship with a multi-decade ex-Boeing stress liaison and I've heard some "interesting" stories from MRB world. Admittedly this type of thing is a bit of a pet peeve. I'm sure you've seen/heard a lot too, I'd be very curious to hear you're "war stories"

with all due respect (not sarcastic) to LD, I think you've missed the point. How can you do a quantitative analysis of a repair, or any other change, without the OEM data, without the full detail of the "daytime" job this fttg is doing ? "All" we're doing is creating a story to show the change has minimal effect on the part. Maybe the repair is in a lightly loaded area of the fttg. But rather than worrying about principal or von Mises stress, I'd suggest doing a comparative analysis ...

Sarcasm? I'd never think it! You are right though, without internal loads data a comparative analysis is the way to go, once the load paths are understood. Maybe I was taking things a bit too literally with the area comparison comment, but my point is... that is far too simplistic, even for a repair analysis without OEM data. A relative analysis can be pretty detailed. The problem is if you simply compare area, you are inherently assuming that the stresses are proportional to area. But (and I know you guys already know this, but to illustrate my point):

[ul]What if the part supports bending moments? Bending stress is not proportional to area, it's dependent on the section modulus[/ul]
[ul]Similarly, transverse shear is relative to the first moment of area[/ul]
[ul]Stability is dependent on the effective column length and radius of gyration [/ul]
[ul]If you're concerned with peak point stresses, local stress due to Kts is generally not proportional to area reduction or addition[/ul]
[ul]If you're creating new joints, sometimes the thickness of the replacement parts is not dictated by net area loss, it might be dictated by a stackup needed for joint strength and load transfer

In short, strength assessment is not just a matter of area or amount of material. It's also about how the area and mass is distributed, and what stress risers are being created.

Even a comparative analysis needs to account for all this. If it's a nacelle, maybe you could get away with something simplistic. But I feel like reasonable approver would look for more. But I have been sometimes been overly technical in my approach.

Keep em' Flying
//Fight Corrosion!

 

[rb1957]

my 2c ... your supervisor had already decided this was PBI, and used it as an "excuse" to get you doing some calcs ... any ol' calc that'll show it good. I'm not advocating this approach, much less in a teaching situation, but I understand it happening in the real world ... I'm sure I've done it some time myself. For what it's worth, his "story" is pretty much just that ... very little hard substance, but a story he'd sign up to (that last bit is critical !)

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