Neuber Method Applicability and Questions

[jdps]

I've been looking into the applicability of the Neuber Method/Correction for reducing elastic stress values in static analysis. I believe I have a pretty good grasp of the concept but have some question,

- Many of the online resources seem to apply this method when dealing with cyclic/fatigue loading. Is there a reason this method would not apply to static analysis?
- Most online resources apply this method to areas with peak stresses created by stress raising features such as holes or fillets. Some sources even state that this method should only be utilized at such features. Why would this be the case? My understanding is that, assuming an appropriate material, peak stresses above yield will be reduced by plastic redistribution and this is the basis behind the Neuber Method. So why should the method be reliant upon being at a stress raising feature?
- Another assumption of the method is that the inelastic region is local and constrained from redistribution by the surrounding elastic material. This seems to go against the basis of the method mentioned above in terms of plastic redistribution. Also, how do I bound the size of the area that can plasticly redistributed?

Thank you in advance

 

[rb1957]

good questions …
- Many of the online resources seem to apply this method when dealing with cyclic/fatigue loading. Is there a reason this method would not apply to static analysis?
I would bother with localised plasticity in static analysis. Static analysis (for me) is about gross section stress.

- Most online resources apply this method to areas with peak stresses created by stress raising features such as holes or fillets. Some sources even state that this method should only be utilized at such features. Why would this be the case? My understanding is that, assuming an appropriate material, peak stresses above yield will be reduced by plastic redistribution and this is the basis behind the Neuber Method. So why should the method be reliant upon being at a stress raising feature?
I think they're saying that to extrapolate the method to "any" stress concentration would require more validation, but I get where you're coming from and pretty much agree.

- Another assumption of the method is that the inelastic region is local and constrained from redistribution by the surrounding elastic material. This seems to go against the basis of the method mentioned above in terms of plastic redistribution.
Ok, imagine you run an FEM with linear stress and see a very high stress at a concentration. Now run the same model with NL stress (material non-linearity since someone corrected me for being too general). The stress peak will smooth out (to something practical) and the yield boundary (the line around the concentration where the stress is equal to yield) will have moved away from the concentration.

Also, how do I bound the size of the area that can plasticly redistributed?
imagine you're moving stress from the fictitious area near the concentration away from it and adding this stress to areas further from the concentration. What is the boundary unaffected (like where does the linear FEM agree with the (material) NL FEM) … probably quite some distance.

another day in paradise, or is paradise one day closer ?

 

[jdps]

Thank you for the quick response.

When answering my first question, you stated the following,
"I would bother with localised plasticity in static analysis. Static analysis (for me) is about gross section stress."
I am guessing you meant wouldn't "I wouldn't bother...". I agree with static analysis being about gross section stresses. Regardless, many sources seem to imply that this method only applies to cyclic loading and I do not see why this would be the case.
Currently I have a hinge FEM that is showing high stresses in certain regions. I do not know of a way to obtain gross section stresses with the complex loading and complex geometry. I have tried to factor out stress concentration factors (Kt) but that is not possible due to the complex loading and geometry in the region. I would not be able to approximate a valid Kt and even if I were able to, I would have to refine the mesh in those areas significantly.

With regards to my third question, sources state that the inelastic region must be local and constrained from redistribution by the surrounding elastic material. When it says constrained from redistribution, my understanding is that the local region can not shed load to neighboring regions. I agree with your logic were the stress speak will smooth out. I am not sure if im misinterpreting the wording but constrained from redistributing load seems to imply that the peak cannot smooth out.

Following this comment,
"imagine you're moving stress from the fictitious area near the concentration away from it and adding this stress to areas further from the concentration. What is the boundary unaffected (like where does the linear FEM agree with the (material) NL FEM) … probably quite some distance."
That's a good way to visualize what is happening but is there a general rule of how much material in the elastic region must surround the stress peak region?

Would you happen to know of any documentation that supports what weve discussed? The idea that this method can be applied to areas without geometric discontinuities or stress raisers? I've searched the forum and others seem to agree with these points but don't cite sources. This forum post cites some sources but I have not had any luck with them,

https://www.eng-tips.com/viewthread.cfm?qid=456136

 

[rb1957]

"would" in this case means "wouldn't" ! … yes !!??

I think people are saying that it's useful in fatigue analysis and not so useful in static analysis (as static analysis is less interested in localised yielding); I don't think they're saying neuber is incompatible with static stress analysis ?

Now you have a complex fttg, with complex results. Ok, the easiest way is probably testing the fttg. Next easiest would be (material) NL FEA. Next easiest may be increasing loads by 10% (15%, 25%, x%) and seeing if neuber shows it good. I suspect that applying neuber to a complex fttg is "difficult".

sorry, no references.

another day in paradise, or is paradise one day closer ?

 

[SWComposites]

If you have a complex part/loading, then you need to run a nonlinear FEM, not attempt some hand calc.

And re the 3rd question, you don't want the entire part yielding at fatigue or even limit loads. So the yielded areas need to be kept small. If you dont like that, then test the part in all its loading conditions.

 

[Ng2020]

Neuber isn't the right tool for gross plasticity. It's only an approximate method.

Before diving into NL FEMs, I'd recommend further hand calcs to validate and understand what's going on in your Fe model. If the loading is complex, break it down. Apply orthogonal unit load cases to your FEM. Progressively implify the model one step at a time until you can correlate to hand calcs. Compute compounded kts from peterson. Etc.
Once you understand the linear elastic FEM, you will have several paths available to complete strength checks.

Complex FEM results will usually yield the truth when subjected to this method of investigation.

 

[cyt4]

Without seeing the model, it is quite hard to say since it really is dependent on loading(bending,shear vs axial). Neuber effectively blunts the stress concentration but you have to be carefeul about assuming that stress concentrations just plasticizes and plastic region does not grow or it is ok to argue the stress concentration away.Neuber assumes a small region as others point out.

The bending for instance can be quickly checked by cozzone plastic bending.Instead, I would try to simplify the features to ensure that the stresses are below yield or ensure that petersons type of stress analysis can be performed and section cuts would be easier. We as stress engineers sometimes forget that sometimes we should improve a bad design.

Moving on to the drawbaks: fatigue and fracture. For certain materials Bauschinger type of effects prevail and cause earlier lower compression or tension for certain materials.If the part goes under cyclic loading these effects have to be considered and some sort of plastic strain cyclic analysis(Smith?) should be done and this is not an easy task. Unfortunately fracture after gross plasticity is not too well understood and mostly based on extensive material testing.