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Limitation on Use of von Mises

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Lcubed

Structural
Aug 19, 2002
124
Hi All,
I understand the principles behind the von Mises Yield Criterion, and I think I know when it should and should not be used, but I have seen it mis-used on several occasions, and I'm doing further research.

Most references state that it is used to find Yield and, as Corypad pointed out in a related thread, it is the von Mises YIELD Criterion, but what I am seeking is an authoritative reference which clearly limits the conditions under which the criterion may be applied.

Specifically, I'd like a reference which states flatly that the criterion does not generally apply to the ultimate strength of ductile materials. Alternatively, if it CAN be used to predict the rupture strength of ductile materials, I'd like a reference for that.
Regards
Lcubed
 
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i don't have a reference for you, but in my mind von mises is just a formulae to combine together stresses to give you a scalar quantity to determine a failure index. To this end it is no different than principal stresses. IMHO either one (or any other failure index) should be acceptable, mostly i see the choice as being personal preference rather than a technical matter; tho' i can accept that there may be cases where you may get significantly different conclusion depending on the different combinations ... in these cases i'd be careful and (without specific test data) conservative.

i'd apply von mises as an ultimate failure index. since you're asking the question, what is the alternative ? why do you want a formal reference ? it implies someone is arguing the point, which implies they're proposing an alternative.
 
Von Mises YIELD stress criterion definitely is not recommended for use as an ultimate failure index in most ductile materials. It is basically a truncated version of distortion energy theory, which generally applies to ductile materials (strain over 5%) and materials that have an Syt = Syc (isotropic yield strength properties).

For brittle materials (strain < 5%), Mod. II-Mohr and Maximum-normal-stress criteria can be used and taken to ultimate (they are compared with Sut and Suc).

The problem with ductile materials taken to ultimate is that they are far more dependent on geometry than anything else. Also, it's not just the geometry the part started with, it's the geometry it ends with after yielding and beginning its venture into plastic territory.

An advanced course in plasticity would help you immensely.

For a reference, I checked back in a Shigley and Mischke "Mechanical Engineering Design" book and it supports most of what I gave above. I can't put my hands on a book right now that exactly defines what you're asking, but I'll do some more hunting when I get home.
 
Hi rb1957,
IMHO, Von Mises is not exactly a "just a formulae to combine together stresses to give you a scalar quantity to determine a failure index". As far as I know, the Von Mises value is calculated in order to determine wether a multiaxially loaded material has yielded or not. How?: Von Mises citeria establishes that it happens when the strain energy per unit volume in the considered point under multi-axial stress equals the strain energy per unit volume when the material reaches the YIELD stress in the pure tension test.
Now, I understand that some people generalize the mathematical expression of the von Mises tension and use it as combination of stresses, even beyond the yield point, where its physical concept is not applicable any more. The question is then: under which conditions the mathematical expression of Von Mises compared with the ultimate allowable is giving a realistic/conservative reserve factor?
Regards
 
that' a good point Trajano, and the yield notation is because strain energy is being calculated from the linear portion of the stress/strain curve.

but then isn't it conservative to extrapolate this into the plastic portion of the stress/strain curve (the plastic strain energy per unit volume is much higher than the elastic strain energy).
 
Your strain energy is there, but the strength (stress resistance) is not. If you linearly extrapolate the stress-strain curve above yield, for a given strain you quickly get strengths above the ultimate strength of the material. In this case, it is not conservative.

Trajano is correct in stating that using von Mises past yield is beyond the physical concept of application. To answer his/her question, I don't know of a case where the mathematical expression of von Mises can be compared to ultimate tensile strengths of ductile materials. Ultimate ALLOWABLES, on the other hand, can be set at yield arbitrarily, and in that case it would apply.
 
i'd reckon that the area under the stress/strain curve extrapolated beyond yield is less (much less) than the area under the elastic/plastic stress/strain curve. therefore i'd expect von Mises to be conservative beyond yield.

swearingen is right if you have a plastic strain and extraploate that. but if your results are coming from a linear FEM, then i think it's conservative (if without rigour, ie without theoretical basis).
 
Below yield, the stress-strain curve is usually taken as a straight line with a positive slope. As you pass yield, it levels off in ductile materials. If you extrapolate that positive slope straight line on past yield, the area under it will certainly be much greater than the area under the actual stress-strain graph of the material, considering it levels off instead of continuing up.
 
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