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
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
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
It might be time to look for another contractor.
prex
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RE: Trying to understand Von Mises a bit better
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
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
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
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 σ1=σ2=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
-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
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
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
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
Garland E. Borowski, PE
Engineering Manager
Star Aviation
RE: Trying to understand Von Mises a bit better
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
RE: Trying to understand Von Mises a bit better
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
corus
RE: Trying to understand Von Mises a bit better
RE: Trying to understand Von Mises a bit better
"we'll have to clean up the BS baffles"
RE: Trying to understand Von Mises a bit better
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
RE: Trying to understand Von Mises a bit better
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
RE: Trying to understand Von Mises a bit better
RE: Trying to understand Von Mises a bit better
good luck