Von Mises beyond Yield, is it valid for Ultimate loading - Part 2

[AeroStructAnalyst]

thread727-253537

thread727-253537


I know in this forum the issue of Von Mises stress has been discussed time and time again,(e.g

http://www.eng-tips.com/viewthread.cfm?qid=253537)

however having gone through most of the threads, I am still left wondering about the validity of Von Mises stress beyond yield for the following reasons;

1. The derivation of Von Mises stress has its origin from Distortion energy which is Total strain (Ut) - Hydrostatic strain (Uh), therefore,
Ud_3D = 1+v/3E[(s1-s2)^2+(s2-s3)^2+(s3-s1)^2/2] where s1, s2, s3 are principal stresses.

The above equation holds true for a 3D stress state, and can be shown that for a 1D case, as in the case of uni-axial tensile testing,
Ud_1D = 1+v/3E*Sy, (where Sy = yield stress). This was first postulated by Maxwell years ago, verified by Hencky and subsequently dozens of testing has demonstrated this to be some what true with a limited scatter.

Hence by distortion energy per unit volume equivalence, Von Mises postulated that Yielding will occur when [(s1-s2)^2+(s2-s3)^2+(s3-s1)^2/2] is equal to or greater than the material Yield stress, Sy. Hence generally, failure of a material is assumed when the Yield strength is exceed.

However, beyond Yielding, does Von Mises stress actually tell you anything about Rupture of the material which is what those of us that do assess structures against ultimate strength really do worry about. As far as the postulate of Huber, Hencky and Von Mises are concerned, I struggle to understand the validity of using Von Mises beyond Yielding.

I would appreciate if someone can provide a valid explanation of why Von Mises is valid in predicting Rupture of material as is the case with Ultimate strength - Also, I know Von Mises is a computed number, which is suppose to be compared against material Yield strength to failure, and not rupture.

 

[ESPcomposites]

Von Mises is a yield criterion only.

Use of Von Mises beyond yield may work to some degree, but you are outside of the validated domain at that point. Other approaches, such either using principal stresses or "R ratios" are often employed to deal with ultimate capability (rupture).

Brian

http://www.espcomposites.com

 

[AeroStructAnalyst]

@ ESPcomposite,
Thank is also my understanding. Pertaining to max or min Principal stresses, aren't they suppose to be less than Von Mises? Again is there any validity in their use against rupture?

 

[inline6]

Principal stresses can be higher than vonmises. i would look at plastics strain when past yield stress. To design something that sees moderate plastic strains you would want a fair amount of testing to make sure the material models used in FEA are a valid tool for predictions.

 

[rb1957]

"Pertaining to max or min Principal stresses, aren't they suppose to be less than Von Mises?" ... look at the formulation for von Mises ... it is based on the differences between the principal stresses.

i'd use principal stresses when designing a 1D part, I'd prefer to use von Mises on a 2D or 3D part as i think it accounts for the interaction between the principal stresses. consider your allowable is something like ftu, a uniaxial value. principal stresses are uniaxial and so comparable to your allowable. but if you believe your stresses are 2D (or truly 3D) then i think you should account for the other principal stresses.

Quando Omni Flunkus Moritati

 

[AeroStructAnalyst]

@rb1957,
Why would you use Von Mises beyond yield when clearly the mathematical formulation and physical justification is only valid as an indicator of the 'on-set' of yielding and as such beyond that, its actual meaning seriously I do not know.

@inline,
What component of plastic strain are you going to use? Codes like Abaqus gives your principal options including strain intensity and equivalent strain. However, I am not sure how much they tell you about material rupture physically.

 

[rb1957]

i use von mises as a conservative failure model

Quando Omni Flunkus Moritati

 

[AeroStructAnalyst]

@rb1957,
"i use von mises as a conservative failure model"... If one may ask, ( not an academic question but one of practical interest), Von Mises beyond yield is conservative to what? If the Von Mises derived stress beyond yield tells you nothing about rupture, how then can one say it is conservative?

 

[rb1957]

von mises is based on elastic strain energy. the material absorbs lots more strain energy when it goes plastic (look at the area under the stress/strain curve). so i think von mises is conservative in the plastic range.

the problem is how to extract a single stress to compare to ftu from a complex stress state. vM is IMHO somewhere between reasonable (in the elastic range, allowable = fty) and conservative (in the plastic range, allow = ftu).

Quando Omni Flunkus Moritati

 

[MechEng2005]

I believe von mises assumes a linear stress/strain curve

 

[rb1957]

"I believe von mises assumes a linear stress/strain curve" ... that's what i meant with "von mises is based on elastic strain energy"

Quando Omni Flunkus Moritati

 

[missil3]

We use equivalent plastic strains for rupture in our dynamic analysis, this is backed up by our experimental results database. In high speed impact models we have seen that strain rate effects affect the point at which rupture occurs so its best to use plastic strain as the failure criteria. Not sure if this would change for stat ic analysis.

 

[AeroStructAnalyst]

@rb1957
"I believe von mises assumes a linear stress/strain curve" ... that's what i meant with "von mises is based on elastic strain energy"... Don't you think this statement is highly misleading? Is Yielding not a purely non-linear phenomenon in most metals commonly used in designs i.e., Yielding commences after the non-proportional part of your stress-strain curve?

In any case, I am still not clear as to why using Von Mises for assessment against rupture is deemed conservative.

 

[AeroStructAnalyst]

@missil3
You stated: "We use equivalent plastic strains for rupture in our dynamic analysis, this is backed up by our experimental results database"

My question for you is: Does your allowable strain not derived from a uni-axial stress strain testing, hence how sure are you that such a strain magnitude represent the true allowable strain behaviour at fracture in 3D which your dynamic analysis is likely to represent for real?

 

[EngAddict]

Yielding does not always mean failure as the theory suggests. In the pressure equipment industry von Mises stress can be compared to twice yield to check for ratcheting / shake down. Provided the stress is self-limiting by nature this allowable limit works well where localised yielding is permitted.

von Mises is also used above yield in fatigue analysis when comparing with S-N curves. The curves have typically been developed based on measured plastic strains that are converted to pseudo-elastic stresses with the elastic modulus for which the curves are valid. Therefore the hotspot stress exceeding yield in a linear elastic analysis is commonly used.