Max Principal Stress vs Von Mises failure Criteria 2

[flyforever85]

Hi all,
I am an aerospace engineer and recently I analyzed a complex structure and submit the report to the FAA for evaluation.
Some premises:
- the structure was in aluminum;
- I applied ultimate loads since it was a crash conditions;
- All the Von Mises results came back well below yield;
- I calculated all the UMS as stress(Von Mises from FEM)/Stress(Ultimate)-1

The FAA came back saying they will accept the report as it is with no concern although I will have to use the max principle stress criteria from now on instead of Von Mises. I think Von Mises is more conservative than the max principle stress, at least at lower sigma2 values. What am I missing?

 

[rb1957]

1) it's principAL (like in your title) not LE (as in your text).

2) von mises is better IMHO for membranes as it combines together the two principal stresses.

3) principal is better for more linear things.

4) the FAA is always right.

5) when you submit a report with principal stresses, they'll comment about von mises (as most likely it'll be another guy reading it (or even the same guy on a different day).

6) I don't believe von mises is always greater than max principal. If the 2nd (lower) principal has the same sign as max principal then von mises is less than max principal. It is possibly this awareness that they are looking for ... what is the most conservative stress ?

another day in paradise, or is paradise one day closer ?

 

[rb1957]

there are also other "quibbles" with von Mises. It is a linear stress theory, so it's "correct" allowable is fty (but everyone uses it like you have so ... NP).

another day in paradise, or is paradise one day closer ?

 

[dik]

Ya... like the Boeing Max...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[flyforever85]

QUOTE
6) I don't believe von mises is always greater than max principal. If the 2nd (lower) principal has the same sign as max principal then von mises is less than max principal. It is possibly this awareness that they are looking for ... what is the most conservative stress ?


It's not. In case sigma1 is high and sigma 2 negative, it can be above Von Mises. I was just discussing with my manager if there are real life cases where that actually happens (also considering that usually buckling becomes the primary problem at high compression)

It's also true though that in the first quarter of sigma1-sigma2 plot, Max Principal Stress criteria is more conservative than Von Mises.

 

[LiftDivergence]

(Copied from another thread I posted this in). The Von Mises technique is just a different, slightly less conservative failure criterion.

To be more correct, "Maxwell–Huber–Hencky–von Mises" theory.

Basically, using a stress vs strain curve with some yield stress from uniaxial test data is very conservative because the area below said curve represents the total strain energy per unit volume stored in the material. Basing the notion of failure on this is not entirely accurate (although as mentioned it is conservative) because there are two components to this total strain energy. That is, the hydrostatic, and distortion components. The distortion component comes from the intergranular shear and is what is key to failure.

The Von Mises effective stress is the equivalent uniaxial tensile stress on a member which would create the same distortion energy as created by the actual applied stresses. It is just a way to take a complex stress state, and distill it down so it can be used with a typical stress-strain curve, which are generally made from uniaxial tests.

Von Mises stress formulation, like many things, is easy to abuse. In my opinion you have to be very aware of what is happening to use it. You'd be surprised how many people using FEM to pull stress results don't fully understand the difference between the options and how they relate to the stress tensor.

My general approach is to start by checking the max and min principal stresses, as well as the max shear. One reason I don't like Von Mises as much is that, since it is a derived stress (based on principal stresses) and is an equivalent uniaxial stress, you loose a sense of direction. Unless you use signed Von Mises which is another layer entirely. It is also not really useful if you also want to check compressive instability.

Keep em' Flying
//Fight Corrosion!

 

[flyforever85]

THank you LiftDivergence.

I'm just trying to understand why the FAA would prefer one over the other.

 

[LiftDivergence]

Probably because people abuse it often without really knowing what it means.

The most complete approach to stress analysis would be at every point in the continuum, or at every element, find each component of the stress tensor (nine for 3 dimensions) and compare each to the appropriate allowable in each direct L-T, T-L, S-T etc. Obviously this is way too cumbersome for anyone to actually do.

The next best thing is to compute the max principal, min principal, and max shear at each element. You retain your sense of tension & compression for each element.

Von Mises effective stress adds yet another level of derived stress to the result because you work with the principal stresses themselves as an input. And generally speaking, it produces a less conservative result (although to be fair, as I mentioned, it is somewhat more appropriate if your allowable data is based on uniaxial curves).

Additionally, there is some amount of legacy performance. It varies a bit in aerospace... you will find companies that always use one thing or the other. This is just the way the FAA has done it for a long time.

Keep em' Flying
//Fight Corrosion!

 

[JoshPlumSE]

I'm more of a structural guy and don't know as much about mechanical uses of the two failure criteria. But, here are my thoughts:

1) If you're concerned about material yield, then Von Mises is probably the best criteria to use. I probably overuse it because I understand it better.

2) Principal stress is important when you're looking at something else. If you are concerned about buckling (i.e. compression only stresses), fracture (i.e. tensile stresses) or such where directionality is important then principal stresses probably become more important.

 

[HS_PA_EIT]

Could the reviewer have meant "max shear stress theory" (Tresca stress)? Tresca is always more conservative than Von Mises. Here's a rough diagram showing the different theories.

 

[SWComposites]

And VM stress is only applicable for ductile metals. Not applicable for any other materials.

 

[flyforever85]

HS_PA_EIT, that what I would have thought. But I know Tresca is used conventionally more fore concretes and less ductile materials.

Thank you all for your answers, this is my final interpretation: The Max principal stress gives you the actual max stress in the structure when an appropriate coordinate system is used. VM is an number useful to the engineer to know if the structure yields or not, nut that value of the stress is not present in the structure. Also, in the first quadrant of a sigma1-sigma2 plot, Max princ stress is more conservative than VM.

Again, just my interpretation to the comment.

 

[ATSE]

Fly: I do not believe the 2nd sentence in your summary is quite correct.
It is probably better to think of VM criteria as deviatoric stress (yield criteria). VM is indeed a real stress.
Also, sometimes, VM > principal, and sometimes VM < principal.
As noted above, principal stresses are most useful for fracture and brittle material response. [And when the regulator requires it.]

 

[rb1957]

max principal stress does have a direction, yes. von mises is an artifical stress relying on a failure theory but if it indicates failure then it's not really right to say "not present in the structure". If the failure theory is valid, then vM reasonably predicts the failure of the part (so it is present in the structure).



another day in paradise, or is paradise one day closer ?