Trying to understand Von Mises a bit better

[DRW75]

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

 

[corus]

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

 

[prex]

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

prex

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[rb1957]

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.

 

[DRW75]

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.

 

[johnhors]

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!!

 

[prex]

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 [√]2[σ]_y, instead that, (as an example), when [σ]₁=[σ]₂=[σ], the vM stress is [√]2[σ], or that, when [σ]₂(and [σ]₃)=0, then the vM stress is [σ]₁
-nothing tells us that the vM stress in a triaxial state of stress should be (at yield?) [√]3[σ]_y, the state of stress is some 70% beyond yield there
-as exposed in the report and as also Wikipedia teaches , the vM stress is simply [σ]_v=[√]((([σ]₁-[σ]₂)²+([σ]₂-[σ]₃)²+([σ]₁-[σ]₃)²)/2) and of course when this value reaches [σ]_y 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

 

[rb1957]

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.

 

[EdR]

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.

 

[rb1957]

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)

 

[GBor]

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 , so I will leave it up to you smarter guys to decipher the rest

Garland E. Borowski, PE
Engineering Manager
Star Aviation

 

[EdR]

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.

 

[rb1957]

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.

 

[EdR]

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.

 

[corus]

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

corus

 

[johnhors]

Then he IS waffling and rabbiting on!

 

[rb1957]

BS baffles brains ...

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

 

[crisb]

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.

 

[gwolf2]

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.

 

[DRW75]

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).