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Trying to understand Von Mises a bit better

Trying to understand Von Mises a bit better

Trying to understand Von Mises a bit better

(OP)
A little while ago, we contracted a small local FEA company to give some assistance with a solid FEA analysis we were carrying out.  The contractor had made the statement that the material will begin yielding upon reaching sqrt(3)*Fy or 1.73 * yield strength of the material under a generalized stress condition.  He stated that this is the allowable von mises stress and he mentioned that it was analogous to the Pythagorean theorem in 3 dimensions comparing it to the von mises ellipse for planar stress expanded to 3d...

I know that whenever I've done FEA modeling, that I usually first look to the max von mises stress state as a measure of 'closeness' to the yield strength of the material as a first assessment of the stress state.  I then usually carry on with hand calculations of allowable stresses for plate buckling given the geometry etc...

I have not been able to find the (3)^.5 * Fy anywhere... what is up?  Does this have something to do with solids versus shell elements?  

thanks for any insight

DRW
 

RE: Trying to understand Von Mises a bit better

From Wikipedia:

the magnitude of the shear yield stress in pure shear is times lower than the tensile yield stress in the case of simple tension. Thus, we have Pure hear Ys = Ys/sqrt(3), or the Ys in tension is sqrt(3) x Yield stress in shear.

 

corus

RE: Trying to understand Von Mises a bit better

Can your contractor provide a sample verification of an actual stress condition?
It might be time to look for another contractor.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Trying to understand Von Mises a bit better

is the thing being modelled a lump with tri-axial stresses, or a plate with bi-axial stresses, or a rod with uni-axial stresses ?

this affects how to apply von mises ... clearly if it a uni-axial stress state then the yield criteria is fty (and not 1.73*fty).  because this is what von mises is doing ... correcting/applying uni-axial strength data in a multi-axial application.

RE: Trying to understand Von Mises a bit better

(OP)
The analysis was completed in SolidWorks (COSMOS) using all solid elements (28 noded elements I believe) which would be subject to full triaxial stresses.  

I've attached (I think) the excerpt from their report explaining von mises stresses... it just seems off to me.  I am going to send it along to our FEA division for comment, but I wanted to get a feel if I was out in left field or not.

 

RE: Trying to understand Von Mises a bit better

DRW75,

SigmaY in the equation is incorrectly called yield stress, when it is in fact the Von Mises stress.

Think about it, how on earth could yield stress be at all related to principal stresses?????  In a linear analysis principal stresses like all stress results are a function of the applied load and the geometry of the structure and have nothing to do with the yield strength of the material (only in a non-linear analysis where secondary effects like plasticity come into play does yield strength matter).

Finally never trust anyone who cannot spell Von Mises correctly!!

 

RE: Trying to understand Von Mises a bit better

It is time to look for another contractor.
First problems that come to mind with that report:
-the figure is taken from Wikipedia
-what the figure shows is certainly not that the maximum vM is √2σy, instead that, (as an example), when σ12=σ, the vM stress is √2σ, or that, when σ2(and σ3)=0, then the vM stress is σ1
-nothing tells us that the vM stress in a triaxial state of stress should be (at yield?) √3σy, the state of stress is some 70% beyond yield there
-as exposed in the report and as also Wikipedia teaches ponder, the vM stress is simply σv=√(((σ12)2+(σ23)2+(σ13)2)/2) and of course when this value reaches σy then the material is starting to yield
-and what about the allowable stress? Of course the vonMises stress should be compared to an allowable, that is not stated in the report and is likely to be far less than 780 MPa (?!)
-the last statement in the report is very poor: the remark that the high stresses are peak stresses may be to the point, but of course the volume or the extension (2-3 mm?) of the overstressed zones is unrelevant, as is the statement that the peaks are only due to the (poor) meshing

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Trying to understand Von Mises a bit better

i'm not at all sure about this ...

he's got the von Mises failure criteria ok ... ie if sqrt((s1-s2)^2 + ...)/2) = fy then the component has yielded.  the FEA is quite happy to calculate "von mises stress" (i put it in quotes 'cause someone's bound to post ... "there's no such thing as a von mises stress").  if this equals fy, not sqrt(3)*fy, then the part has yielded.

now in the 2nd para he makes a comment about square corners.  i'd say his observation is valid, regading singularities, but it also shows bad modelling practice.

RE: Trying to understand Von Mises a bit better

drw75:

Maybe this will clarify a bit...The generalized second invarient of stress is:

j2'=sqrt(1/6[(sigx-sigy)^2+(sigy-sigz)^2+(sigz-sigx)^2]+tauxy^2+tauyz^2+tauzx^2)

(note..if the principal stresses are used then the tau's become zero and the sigma's become the principal values in the above eqn.)

and

sig-von-mises = sqrt(3) j2'
tau-octrahedral = [sqrt(2)/sqrt(3)] j2'

where yielding may be defined by any and all of the above depending on the code used.

You can use the above equations to compute the values of yielding based on the particular stress state you have the information for....i.e. for a uniaxial stress state j2' becomes j2'=sigx/sqrt(3) and sigvm=sigx and tau-oct=(sqrt(2)/3) sigx

Hope this helps.....

Ed.R.
 

RE: Trying to understand Von Mises a bit better

sig-von-mises = sqrt(3)*j2'

j2'=sqrt(1/6[(sigx-sigy)^2+(sigy-sigz)^2+(sigz-sigx)^2]+tauxy^2+tauyz^2+tauzx^2)

so sig-von-mises = sqrt(3)/sqrt(6)*[...] = [...]/sqrt(2)

RE: Trying to understand Von Mises a bit better

Perhaps we need to see more of the report.  I just took a quick glance, but it looks to me like he is trying to define ultimate strength of the material as 1.73*yield. His statement should have to do with fracture rather than yield, but all the math above is starting to hurt my head neutral, so I will leave it up to you smarter guys smarty to decipher the rest  

Garland E. Borowski, PE
Engineering Manager
Star Aviation

RE: Trying to understand Von Mises a bit better

RB1957:

I think your algebra is messed up a bit....the 1/6 only multiplies the terms in the [...] (not the shear terms)...If you factor the sqrt(1/6) out then you need a different multiplier on the shear terms.....(it is a 3.0 for sig-von-mises)

Ed.R.

RE: Trying to understand Von Mises a bit better

i agree Ed ... the math is wrong as i've shown it, however i was trying to show the expression for von Mises you give is the same as the one given in the post ... in principal stresses.

RE: Trying to understand Von Mises a bit better

rb1957:

Got it and agree with the 1/sqrt(2) [...] ....By the way if you keep the equation in the original form the multiplier is 6.0 on the shear terms...I got the 3.0 because I also expanded the normal terms.....

Ed.R.
 

RE: Trying to understand Von Mises a bit better

In the UK we'd say the guy was waffling, or wonder what he was rabbiting on about.  

corus

RE: Trying to understand Von Mises a bit better

Then he IS waffling and rabbiting on!

RE: Trying to understand Von Mises a bit better

BS baffles brains ...

"we'll have to clean up the BS baffles"

RE: Trying to understand Von Mises a bit better

Is his "logic":

one dimension - maximum von Mises stress = yield stress x 1^0.5
two dimensions - maximum von Mises stress = yield stress x 2^0.5

so extrapolate:

three dimensions - maximum von Mises stress = yield stress x 3^0.5

Just confirmed my view...never trust anyone using Solidworks (Cosmos) for FEA.

RE: Trying to understand Von Mises a bit better

Wow. No wonder I seem to earn earn about half my money fixing broken designs. It's been a little quiet on that front recently, looks like the work is building up again.



 

RE: Trying to understand Von Mises a bit better

(OP)
Thanks for the replies.  some were halirious.  I am glad that others can appreciate my frustration and surprise to finding out these new laws of engineering.  

I've also discussed with our FEA experts and they basically said all the same things.

On related news, it turns out that i am not losing me mind (completely). :)


 

RE: Trying to understand Von Mises a bit better

Out of pure curiousity, why did you not go to your FEA division/experts in the first place?

RE: Trying to understand Von Mises a bit better

(OP)
Fair comment - and funny story to boot.  We put in a proposal for our guys to do the work, however the client decided to save 20% and go with the other guys...

 

RE: Trying to understand Von Mises a bit better

arh, so now you're in for a huge bun-fight ... you don't like the client's FEA, the client won't pay for more analysis (without suing someone's a$$), the client's FEA people are happy with their model and think you're overly conservative.

good luck

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