Von Mises Vs Max Principle 4

[KnacKeN]

thread727-148480

Can someone explain the logic of using Von Mises for static failure (i.e. ultimate)? I thought it was only really useful for determining if yielding has occured. Once you get close to failure you're in the non-linear portion of the stress/strain curve, so is Von Mises still relevant?

Isn't Von Mises derived assuming you are more or less witin the limit of proportionality (ie 1/2 stress x strain = area of triangle = area under curve)? The would have thought the equation for distortion strain energy at ultimate failure would look different...?

 

[kellnerp]

The derivation of stresses is independent of material properties. Stress quantities like principal stress and vonMises are calculated on a differential element and are based on a geometrical construction and force balance.




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[rb1957]

it's principAL ... geez.

von Mises is a failure criteria, a yield criteria as you point out. both vM and principal stresses are ways to combine complicated stress states to a simple uni-axial stress to compare with uni-axial strengths. either approach should produce similar results, i prefer max principal myself.

 

[KnacKeN]

Hmm...Im still not seeing the applicability to ultimate failure. What does vMises physically mean when you are near fracture (to me failure = fracture, perhaops im not being clearer).

Regardles, I found interesting discusion here.

http://www.eng-tips.com/viewthread.cfm?qid=171174

 

[kellnerp]

vonMises is a measure of the stresses causing distortion of a material without regard to hydrostatic pressure. In plasticity you are concerned with distortion, not hydrostatic volume change. In other words plasticity is the distortion of the material as the internal structures slide past each other.

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[rb1957]

von mises isn't "correctly" applicable for fracture, but consider it's application to limit loads ... thus it's reasonable to use in practice. what you're really saying is that the limit RF = yield stress/(limit von mises) and this isn't too different to ult. stress/(ult. von mises).

 

[johnhors]

Hmm...Im still not seeing the applicability to ultimate failure. What does vMises physically mean when you are near fracture (to me failure = fracture, perhaops im not being clearer).

Von Mises is a Yield criterion only, and to answer your original question, no, it is not relevant beyond yield.

http://www.Roshaz.com

 

[kellnerp]

John,

You have to get your terminology right.

vonMises stress is the square root of half the sum of the square of the differences of the three principal stresses. It is related to I2 or J2.

vonMises yield criterion is a surface depicting the stress state at yield based on the vonMises stress calculation.

vonMises stress can be calculated whether the material is in the elastic or plastic range. You can even calculate vonMises stress in liquid water. It would be zero unless the water is moving in some way. In water s11=s22=s33 and sij (i<>j)=0 so sVM=0.

He asked about using vonMises stress past yield as determined by the vonMises yield criterion.

When in the plastic range the triaxiality factor comes into play as well.

vonMises stress is not a material property. It is calculated from the stress tensor. vonMises stress should correlate to a simple tensile test even at failure (ultimate) stress.

vonMises yield criterion is a material property that correlates yield in a 3D stress field to a simple 1D stress test.

In a simple physical way to understand vonMises stress is that is causes shearing or distortion in plastic materials rather than volumetric (hydrostatic) changes.

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[40818]

Airbus commonly use VM stresses against Ftu for ultimate failure calculations.
Testing of the ductile aluminiums used in aero give better correlation to a von mises stress at (static) failure than against principal stresses.

 

[KnacKeN]

kellnerp thanks for answer but what about the fact that derivation of vM assumes that the total strain energy is area under stress/strain curve that is proportional? the derivation following (Total Strain Energy - Hydrostatic Strain Energy) = Distortion Strain Energy. Thats is the only issue I have here.

Does the strain energy per unit volume for vMises stress at the failure of point under consideration = strain energy per unit volume of a uniaxial tensile test at ultimate stress? Or do you use a different ultimate allowable other than ftu.

 

[kellnerp]

The derivation of vM stress has nothing to do with strain and is not a measure of energy. I think that is where the misunderstanding lies. s11, s22, s33 are stress measures (force /area ). There is no assumption regarding strain or any area under a stress/strain curve. The fact that stress is one of the quantities (independent) used in the stress/strain curve should tell you that.

When you look at your FEA program you will find that it groups stress related quantities apart from strain related quantities until you come to strain energy density (SED).

When you look at this, epsilon = E sigma, for uniaxial stress the sigma is independent of epsilon (strain). A material property (E) ties the two together. There is no measure of distortion, only of the stress components causing distortion in vM stress.

In any textbook treatment of FEA methods you will see that equations for determining stress are first derived, then separately equations for strain are derived and THEN the C tensor is derived which ties the two together. The C tensor is reduced to a pair of numbers for isotropic materials, E and Poisson's ratio.

Consider a tension test of three identical dogbones, steel, aluminum and titanium. If you place a 1kip force on them the state of stress will be the same in the center section. But the strain in the center section will be quite different. So will the strain energy. So for the same stress (vM or sx) you can have quite different SEDs.

Don't confuse vM stress with the vM yield criteria. The later is depicted as a surface determined by material properties in terms of the vM stress. The vM yield surface says nothing about strains or energy either. After yield it is still perfectly acceptable to measure stress using vM just as it was before yield.

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[MechEng2005]

I think another issue has arisen, which is when you need to account for deformation. In kellnerp's example of 3 identical dog bones: steel, Al, Ti the initial stress on the center section would be the same. However, the materials will deform differently. Necking will cause the Al sample to elongate more and reduce the cross-section at the center. Therefore, the max stress will be higher on the Al sample. Since stress = force/area, accounting for the decreased area while the force stays the same...

My opinion is that vM would be accurate for the stress up to failure, if you apply it dynamically and note that the stresses calculated from F/A after a certain point should not use the original, unloaded/undeformed area.

-- MechEng2005

 

[seymours2571]

Kellnerp,

Just to clarify a statement made: My understanding of the derived stress quantity vM stress was that it was to be used in conjunction with the vM failure theory for ductile materials. While it may be possible to determine/derive a vM stress value at a stress state beyond yield, is it really meaningful? While it may be useful in representing a complex triaxial state of stress as a single value, outside the realm of the vM failure criterion I don't know if it has any physical meaning. However, there may be a plastic or ultimate failure criterion based on vM stress that I am not aware of.

Am I out in left field on this one?

Thanks,

Steve

 

[kellnerp]

vM is just a number. It has found application to materials that deform plastically such as steels, aluminum and titanium. It has application beyond specifying the yield surface for these materials. The triaxiality factor is essentially the hydrostatic pressure/stress divided by vM and this is used for rupture. vM is also an easier to understand indicator of hot spots in a model when designing regardless of how close to yield the model it.

vM is not much use on brittle materials like cast irons and glass for establishing a failure theory.

In this thread I have noticed some referring to yield as failure. This is not necessarily true. Local yielding is sometimes permitted. In a building or a roll cage, behavior after yield is important in protecting the occupants of these structures and must be calculated. In a beam, yielding can happen in the outer fibers and the beam will still carry a significant load.

The load I chose for the dogbone was supposed to be in the elastic range so no necking would happen and Cauchy stress would be OK. In a non-linear FEA true stress is used (Piola) and this accounts for the necking. My point was that at some load in the elastic range the aluminum strain will be 3 times that of the steel at the same stress and will therefore have 3 times the strain energy. Of course the aluminum will yield much sooner.

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[rb1957]

boy we're touching alot of topics ...

necking ... yes the dog-bone specimens behave differently but we engineers have already thought about that and collectively said "geez, that's alot of bother, let's base our stresses on the original area and call that "engineering stress" and "engineering strain" (as opposed to "true stress" and "true strain" which would account for the change of area as the element yields).

"vM is just a number" ... sorry kellnerp but that's about the silliest thing i've read about vM. vM is a means to combine complex stresses into an equivalent uni-axial stress to compare with standard tests. it is an elastic theory.

 

[kellnerp]

"vM is just a number" ... sorry kellnerp but that's about the silliest thing i've read about vM. vM is a means to combine complex stresses into an equivalent uni-axial stress to compare with standard tests. it is an elastic theory.

I stand by this statement. vM is a number used for many things, some of which you have mentioned and which I fully acknowledge. It is calculated from the stress tensor which has nothing in it in any way requiring knowledge of stress/strain behavior. vM can be calculated for water, materials in the plastic or elastic regime with equal ease. I am trying to unconfuse the use of the number with the number itself and that is the context in which I made that statement. My point is that stress is not a material property, nor is strain. But the two are related to each other through a modulus of elasticity prior to yield and by a flow rule after yield.

Von-Mises is typically used for metal plasticity.


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[BlasMolero]

Hello!,
I think the target of the question posed here is to find a criteria to assess the safety of the design. Well, in mechanical engineering we have many failure criterion, one is the maximum vonMises or also known as the Shear-energy theory or the Maximum distortion energy theory, that is based on the von Mises-Hencky theory. This theory states that a ductile material starts to yield at a location when the von Mises stress becomes equal to the stress limit.

In most cases, the yield strength is used as the stress limit. For me the important is that Maximun vM Stress is the best criteria to asses the safety of design with linear static behaviour & ductil material.

For ductile material you have also the maximum shear stress criterion (also knowed as Treska Yield criterion), but is more conservative than the von Mises stress criterion since the hexagon representing the shear stress criterion is enclosed within the ellipse representing the von Mises stress criterion. For a condition of pure shear, von Mises stress criterion predicts failure at (0.577*yield strength) whereas the shear stress criterion predicts failure at 0.5 yield strength.

Best regards,
Blas.