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Von Mises Vs Max Principle
2

Von Mises Vs Max Principle

Von Mises Vs Max Principle

(OP)
Given the legal design requiremnt: The Stress level, under load condition, at any point in the structure shall be limited to a level that provides a safety factor of 3 against permanent deformation.

Whould you use Von Mises or Max Principle in your FEA modle?

RE: Von Mises Vs Max Principle

TrapperJohn

First point, there is no such thing as "Principle Stress".

Von Mises is a theoretical measure of stress used to estimate yield failure criteria in ductile materials and is also popular in fatigue strength calculations (where it is signed positive or negative according to the dominant Principal stress), whilst Principal stress is a more "real" and directly measurable stress.

Since you have a legal design requirement, then you would be best advised to cover yourself using either stress values.

RE: Von Mises Vs Max Principle

I'm assuming you are using isotropic materials (metal).  If so, I usually try to use Von Mises because of the stress combination nature that is considered with this criterion.  The metallurgists of the world usually try to drive back to a Max Principle stress because it fits their crack propogation analysis methods.  It may help to know what you are designing (more specifically).

RE: Von Mises Vs Max Principle

There is no such thing as "Max Principle". For a static loadcase I would always consider yield against Von Mises stress. Principal stresses are *generally* used in the evaluation of fatigue or fracture based loading (against some value based on a portion of the static yield or the UTS -  Goodman approach. Many others are used.).

Where does this requirement come from (ASME or similar)? What are the loads? What is the structure? Which industry (Civil, Nuclear, Marine...) is the structure designed for? Etc.


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RE: Von Mises Vs Max Principle

(OP)
All

   Thanks for the replies and sorry for the spelling.  This is a general question for our engineers in the design of aircraft support equipment.  Currently some our engineers use Von Mises while other’s use the max/min principal stress.  Clearly we all should be designing the same way.  Since the requirement to design to is as stated in my 1st post, my question is based on the interpretation of the stated requirement.  Could you interpret “The Stress level, under load condition, at any point in the structure shall be limited to a level that provides a safety factor of 3 against permanent deformation” to mean Yield Stress of the material must be greater then 3 times the calculated Von Mises Stress?    Or do I need to use the max/min principal stress?  Follow up question: how would you define ductile material? Is there a maximum % elongation or some other material property which could define weather a material would be ductile enough to use Von Mises?

RE: Von Mises Vs Max Principle

i'd interpret the requirement as the maximum value for stress (von mises or principal depending on your preference) to be less than 1/3 of yield, at limit load (which i'd interpret as the loads they've specified).  there shouldn't be that much difference between vM or principal, but if there is either use the more conservative one, or the more convenient one (!!) and state which one you've used.  i'd doubt that, if you met one of these criteria, that the structure is dangerous; and it'd only be "legal bitching" to say you were diliquent on the requirements 'cause a different interpretation of stress missed the mark by a small margin (in this case you could say that we stated how we met the critieria and it's up to the customer to know the difference, if it matters that much to him).

hope this helps,

RE: Von Mises Vs Max Principle


Given possible legal implications I would use the safest criteria and clearly state it

RE: Von Mises Vs Max Principle

That would be Max Shear criteria then, wouldn't it?

RE: Von Mises Vs Max Principle

Pardon my ignorance, but why can't you define maximum
 principal stress? If there are 3 principal stresses, and one is larger than the other 2, doesn't that make it the maximum principal stress? (I assume the dispute wasn't over the spelling of 'principal' but over the concept of max. principal stress.)

 Yield criteria are a completely different discussion. The main reason in my experience for engineers using different yield criteria (of which there are many: max. principal stress, von Mises yield, max. shear stress, etc.) to define failure is that one criterion seems to have worked better in the past than others. Assuming that this experience is based on reliable test data, it is hard to argue against a particular choice of yield criteria. The selection of Yield Criterion seems to be mainly experience based.

Since the criterion given "The Stress level, under load condition, at any point in the structure shall be limited to a level that provides a safety factor of 3 against permanent deformation" seems to be a purely static strength criterion, I agree with rb1957 that this means limit load is 1/3rd of the yield stress for the material.

If the object being designed undergoes fatigue loading, then a completely different method must be used to ensure design safety (for instance, crack initiation or crack propagation).

I am interested in finding out TrapperJohn would propose to 'unify' the selection of Yield criterion (after having made statement "Clearly we should all be designing the same way") given the huge amount institutional bias (prior experience, design tool documentation, informal "best practices" that are defined in most organizations, etc.) in the selection of Yield criterion for design optimization. Define a test or a series of tests that could be used to test criteria?

RE: Von Mises Vs Max Principle

Isn't the von Mises criterion a way to predict failure in a 3D stress state by using the uniaxial stress strain curves? Stress strain curves are almost always derived from simple, uniaxial stress (or strain) tests. From this test, you get such key material parameters as (among others) Young's modulus (stiffness), 0.2% yield stress, ultimate stress, ultimate strain, and maximum elongation. Since your material data is for a uniaxial stress condition, but your object's stress condition is most likely three dimensional, then von Mises stress (which gives you a measure of the three dimensional stress state) is the stress you use to compare to the yield stress (if this is your design limit) derived from the uniaxial stress curves and then to decide how close to the design limit you are.

RE: Von Mises Vs Max Principle

von Mises and max principal are both contenders for failure criteria ... really they both describe any critieria (failure or yield).  i'd only apply them to plates.  In aircraft design with stiffened, thin gauge sheet panels we have other strength criteria (crippling and diagonal tension).

RE: Von Mises Vs Max Principle

sychronised posting ? ...

prost you're perfectly correct ... max principal and vn Mises are both accepted ways of describing the complex stress state of a structure in terms that are comparable to uni-axial test (strength) data.

RE: Von Mises Vs Max Principle

Would it be worthwhile for everyone to describe what static strength failure criterion they use and for what situations? I know I'd be interested in such a list. If you also described the rationale for your choice, that would also be useful to the Forum!

(myself, I rarely do static strength analysis, being more often concerned with fatigue, fracture and damage tolerance).

RE: Von Mises Vs Max Principle

(OP)
Would it be worthwhile for everyone to describe what static strength failure criterion they use and for what situations?

Sounds like a good idea!

RE: Von Mises Vs Max Principle

i apologise in advance for this post, but i just can't resist (i did try) ...

i think everyone listing their static strength criteria and how they apply them would be next to pointless.

first, we represent many different industries which naturally focus on different things.

second, if you're working in an industry, you should know common practice

third, if you don't know, then these forums (sorry, i refuse to say fora) really aren't the place to educate your self (on such a general topic).

i'll go now.

RE: Von Mises Vs Max Principle

Well said rb. However: to get the ball rolling, I ignore stresses completely when using FEA, for most jobs that I do.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Von Mises Vs Max Principle

From memory, I believe that in the NASTRAN theory manual there is a discussion of failure criteria (or margin of safety) that illustrates the different criteria on a stress plot.  I'm too lazy to walk upstairs to check the manuals right now.

Similar informat can be found with a google search, such as "von mises stress shear failure criteria"

http://www.efunda.com/formulae/solid_mechanics/failure_criteria/failure_criteria_ductile.cfm

http://courses.washington.edu/me354a/strength_theories.pdf

http://www.mech.uwa.edu.au/DANotes/SSS/failure/theories.html

In the past, for metals, I have generally used Von Mises to identify the highly stressed areas, and then looked at normal and shear in that area.

Also need to check buckling, cripling, etc.

Also, I've experienced more difficulties in getting agreement on the which failure criteria to use with composites.

I would like to see a list of failure criteria also.  Everytime I write a stress report, it is a topic of discussion.

RE: Von Mises Vs Max Principle

For composites, there isn't one "all encompassing" stress criteria unless you have performed a lot of material characterization testing and are very comfortable with your test results.  After that, I usually use max strain and check each of the directional strains.

RE: Von Mises Vs Max Principle

From memory, I believe Tsi-Wu indicates failure prior to max strain, see NASTRAN theory regarding margin of safety.  So that is part of the issue.  And, of course, we are talking about limina strains, not laminate strains.  The main problem I have is lack of coupon data for the allowable off axis strains and also allowable.  When asked/requested/directed, I've tried to estimate reasonable values for these allowables (from coupon / theory) and I tend to find that designed structures don't satisfy reasonable values for off-axis or shear allowables.  Just indicates that criteria wasn't used during the design.  Anyway, I haven't done a composite analysis for a couple of years, and don't have any planned in the foresable future.  Previously, I have obtined I did get good correlation with coupon values for strain distribution around a hole.

RE: Von Mises Vs Max Principle

Hi,
there is not a "better" or "worse" criteria to combine stresses. There are plenty, which apply for ductile materials, or for fragile materials, or for laminar composites, and so on.
Of course, if you trace the sigma-tau plot of all these criteria, you may find that some are more "conservative" than others, BUT the real point is that you may have to choose the most appropriate for YOUR kind of material (see Drej's questions...).
Another point to pay attention to is: do you have to respect a NORM? If so, you don't have any choice: you MUST use the specified criteria. For example, if you decide that you will design a pressure vessel according to ASME, because you think ASME is recognized "de facto" worldwide, you will have to use Trescà-Guest. In the same scenario, if you decide to use European "PED" with the appropriate EN norm, you will have to use Von Mises.

Regards

RE: Von Mises Vs Max Principle

If you have a near triaxial state of stresses s1~s2~s3, it is not safe to use the Von Mises stress.

RE: Von Mises Vs Max Principle

Hi, All,

My question may be a little away from the original discussion and I appologize. I also appreciate if you experts can cast some lights on my question.

I am working on Aluminum casting process of automotive suspension parts such as control arms and knuckes.  It seems to me that the part design is mainly focusing on stress requirement (von mises)instead of cyclic fatique.

My question is:
If the casting alloy's fatique strength is increased while the other properties (tensile, elongation, etc) remain the same, will it be helpful to reduce the part weight in the part design?


Thanks again.

YY

RE: Von Mises Vs Max Principle

Probbly not. Suspension arms and spindles are designed to meet stiffness criteria first and foremost, then you use static strength for things like kerb strike and other maximum load cases, then you migh have to add a little metal in some places for fatigue life.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Von Mises Vs Max Principle

In general i use vonmises for 3d modelling and for 2d max/min 2D principal stress...even if performing plastic analysis it is required to read in vonmises stress i prefer the second one also in linear analyses because of is more conservative for 2D fem.In compression what to read?vonmises is +?

RE: Von Mises Vs Max Principle

In general I use what ever the design standard tells me to use.

corus

RE: Von Mises Vs Max Principle

The statement “against permanent deformation” implies plastic deformation, i.e., yielding. Yielding, in ductile materials, results from shear stresses. Only von Mises criterion (shear deformation energy) and Max Shear criterion (maximum difference between principal stresses) are useful to evaluate the tendency to yielding. Principal stresses are not useful to predict permanent deformation. Consider a “hydrostatic stress state” (S1=S2=S3). No matter the value of the stresses, the material never yields. I think you have to use von Mises (or Max Shear) criterion.

RE: Von Mises Vs Max Principle

i would have thought that a principal stress exceeding yield was an indication of plasticity

RE: Von Mises Vs Max Principle

rb1957

In a uniaxial stress state (where P1 = Von Mises and P2 = 0) , yes.

In a fully biaxial stress condition where P1 = -P2, the Von Mises stress value is higher than P1, and is thus a safer value to use. After all Von Mises is an energy based yield criterion. What does puzzle me though is why some people (are they really people?) insist on using a "signed" Von Mises in fatigue analysis!!

RE: Von Mises Vs Max Principle

i knew i'd get a multiple axis stress response ! in the case of bi-axial tension/compression the vM stress is higher indicating that failure will happen at a lower applied stress.  my only comment would be the change "safer" to "more appropriate".

as for signed vM stresses ... actually that makes sense to me, to distinguish between tenisle conditions and compressive conditions for fatigue analysis (but then i'd use principal stress anyways).

RE: Von Mises Vs Max Principle

"Consider a 'hydrostatic stress state' (S1=S2=S3). No matter the value of the stresses, the material never yields. I think you have to use von Mises (or Max Shear) criterion."

If S1=S2=S3 then the von Mises stress is zero. I don't think you can say that it would not yield is not quite right. If you could produce a stress state where Si are all equal, and tensile, the material would yield. I'm not sure what a real material would do if you applied Si compressive to extremes. You could try this by dropping a bowling ball sized sphere of chewing gum into the Mariannas Trench (35,000 ft deep water) and observe what happens.

A general state of stress can be divded into the hydrostatic and deviatoric stresses. Hydrostatic stresses change the volume of the solid element while deviatoric stresses are changing its shape. Von Mises theory assumes that damage is caused by this deviatoric stress. In the case of a uniaxial tension test, the von Mises stress and the maximum principal stress are equal and both can be used to predict the onset of yield in a ductile metal.

Doug

RE: Von Mises Vs Max Principle

It is generally assumed that if a high tensile hydrostatic stress state is applied to a metallic material (steel), it will not yield but it will undergo a brittle failure. This is the reason to avoid “triaxial tensile stress states” in steel structures (joints, notches).
A steel ball submerged in oceanic trench is the same example cited on Kachanov’s “Plasticity” text. According him, it will not yield, it just will be elastically compressed.
Yielding (change of shape) is produced just by the deviatoric component of the stress tensor. Von Mises stress is a measure of its magnitude; it coincides with the second invariant of the deviatoric component of the stress tensor.
Regards.

RE: Von Mises Vs Max Principle

"Principle Stress" is stress along the "priciple axis".  By definition, the principle axes is the orientation along which the transverse stress goes to zero.  When an isotropic material is so orientated, you will find a maximum value in one direction and a minimum value normal to it.

This can be visualized via Mohr's Circle.

--
Great Spirits have always encountered violent opposition from mediocre minds
                                          -- Albert Einstein

RE: Von Mises Vs Max Principle

Joekm,

To re-iterate my previous response:-

there is no such thing as "Principle Stress".

In the English language Principle and Principal have very different meanings and cannot be interchanged. Sorry if I appear over bearing on this point, but I believe this to be very important. There has already been more than enough deterioration in the quality of work produced by engineers during my career.

RE: Von Mises Vs Max Principle

In addition, the meaning of the phrase "transverse stress" is ambiguous. Transverse usually means 'perpendicular' to a main direction  (normally I would say 'principal direction' but since we normally use principal direction to indicate the direction in which the shear stress goes to zero, I will use 'main' instead).  For instance, in a rolled material such as aluminum, the 'longitudinal' direction (L in some parlance) is the direction the material has been rolled, and would be considered the main direction. The longitudinal-transverse direction (LT) is perpendicular to the L direction, and the short-transverse (ST) is perpendicular to both L and LT. Perhaps "joekm" you meant "shear stress" and not "transverse stress"?

RE: Von Mises Vs Max Principle

Hi,
Johnhors, you're right, but English is not the only language in the universe, and I know some extremely good engineers who know it only approximately, so please let's concentrate on the concept and not so much on terminology when all the context is clear... This said, of course this forum is anglo-saxon so everybody should make an effort to "speak" correctly...

The given definition is 100% correct, though perhaps it doesn't add so much to the topic. I feel this thread is now beginning to turn round and round in circles when, historically, different failure theories have been formulated for the simple reason that some are more appropriated for some materials, some for others.
And, from the given definition of "principal stress", IMHO it is obvious that "transverse stress" was written for "shear stress"...

RE: Von Mises Vs Max Principle

cbrn, if you think the thread is going round and round in circles, then by all means, you are free to stop reading and adding to it. It appears to carry some interest with others.

My intention was not to criticize anyone's English, I know how I struggle with comprehension of the two other languages I sometimes use as well as English; nevertheless, there are many ways to use 'transverse stress' and just because it's obvious some doesn't mean it's obvious to all. I sometimes find it very difficult to establish up front what particular terms mean, depending on the client; sometimes defining 'obvious' terms is one of the most important steps you can take on a project.

RE: Von Mises Vs Max Principle

Hi,
prost,
<if you think...stop [adding to it]> : yes, I agree. This is, by all means, the last post of mine in this thread unless it takes a well-defined direction.

<there are many ways... doesn't mean it's obvious to all> : once again, I agree: my previous was not a critic to what you wrote. Saying "transverse" is vague almost every time. Nevertheless, in THIS case, the poster gave a definition which didn't leave any space open to interpretation... Simply my opinion, of course.

Regards

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