Linear Finite Element Analysis & NeuberÆs Rule 3

feajob,

I have had some extensive use with Neuber and linear-elastic FEA results. The concept can be applied to any region of "local" stress which would result in plastic deformation which is limited to a small region compared to the overall section.

Bear in mind that Neuber is not a "free" method for reducing peak stresses around geometric discontinuities. In reducing the peak stress, the overall net section stress increases due to the load redistribution of the "local" stress concentration. Therefore, the net section stress should not be near Ftu (or Fty if concerned abount a plastic hinge developing). Secondly, the area it is applied to must be "local" with enough bulk material around the area to ensure that there is sufficient material to fully develop plastic stresses within the net section. Next, Neuber is only applicable to ductile materials with significant elongation prior to failure, otherwise it does not hold valid. Thought there was another rule, but don't remember it at this time.

I have used Neuber as an alternate arguement to stress signularities where questioned on the validity of the signularity. If I could still show it good with Neuber, the issue of it being a singularity or not went away.

One failing of the Neuber method that non-linear material analysis addresses is the redistribution of load and overall deflection of the structure. In some structure, the local stress is significant enough to set the entire section into the plastic region, and thus results in a change in loadpath for the applied loads. This in turn can overload another area.

jetmaker

Thank you jetmaker. Your explanation is quite helpful. I use Neuber's Rule to reduce peak stresses around geometric discontinuities. However, in our group, there are some concerns about the validity of this approach versus performing Non-linear (material) FEA. Good advantage of this approach is saving time, but if I understand correctly then there is a disadvantage for Neuber's rule as you mentioned:

"One failing of the Neuber method that non-linear material analysis addresses is the redistribution of load and overall deflection of the structure. In some structure, the local stress is significant enough to set the entire section into the plastic region, and thus results in a change in load path for the applied loads. This in turn can overload another area."

Now, if we neglect the increase of computation time for Nonlinear FEA then can we conclude that to be conservative, we should do Nonlinear FEA instead of doing Linear FEA + Neuber Rule?


Thanks,
A.A.Y.

no, it's like jetmaker says ... if your structure goes plastic enough, then the loadpaths within the structure will change, and you're not sure what's going to happen.

i think you're ok to apply neuber on a localised stress peak (such that there are elastically stressed elements on the cross-section).

If computation time (including setup) is not an issue, then I would suggest using non-linear always over Neuber. However, as there is usually a difference in computation time, I would verify that my net section stresses were sufficiently low as to provide an adequate margin of safety, then apply Neuber. If the margin of safety is low (5-10%), then I would run a non-linear FEA. Exceptions would be if the influence of the peak stress was very localized on the net section, then you could get away with a lower MS before doing an FEA.

jetmaker

Regarding applicability of Neuber's rule

jetmaker, you said that this rule can be applied to any region of "local" stress which would result in plastic deformation.

It's my understanding that Neuber's rule could be applied only on geometrical discontinuities, ie notches or open holes.

In case of fasteners, problem is much more complicated due to to complex nature of load transfer, so Neuber's rule is not applicable.

Am I wrong?
Is that corect?

39minuteman,

You raise a good point. My experience has been that regardless of what is going on geometrically, you can apply Neuber. The concept as I understand it is based on the strain limitations arising from constrain fo adjacent material. If you have a stress concentration, say a round hole in an infinite plate, the stress at the hole edge is 3x the nominal stress. Consequently, the strain must also be 3x nominal. As strain relates to displacement, the hole can not physically strain that amount when the bulk of the material is still elastic. Thus it sheds some of the load to the bulk as the strain rate changes within the plastic region of the stress/strain curve.

It is this concept that allows it to be applied to stress signularities in the FEA as they are often limited to a single node which is surrounded by a bulk of elastic material.

Now the complication for fastener locations arises in that the deformation of the hole, secondary bending stresses, frictional load transfer, etc... require additional consideration to make sure the region has been modelled properly to obtain representative stresses. If your model is sufficiently complicated that you have the fastener details modeled in such detail, then Neuber would not be appropriate as a non-linear analysis would be typically required to obtain proper load distribution on the fasteners anyways. However, if you are just representing the fasteners as springs or RBEs then Neuber would likely be applicable.

jetmaker

One of the areas that has not been addressed in this thread so far is the issue of material properties/model. Some of the participants in this disucussion appear to have good expereince. Could you please briefly describe what kind of material properties would be required to carry out a non-linear fatigue analysis? Would one need to work with cyclic
plastic properties of the material? Normally these are different from the monotonic properties. There are kinematic and combined kinematic+isotropic models.

I have a rather unusual bolt/stud application. The mean stress in the threads is above yield. However the application is still infinite life and not low cycle fatigue. The reason is that the threads are inside a stiff bolted joint and the resulting dynamic stress is very low. One difficulty in using the Neuber's method is trying to define Kt from FEA results. The failure occurs in the nut threads and not the studs. It is hard to define a nominal stress in the nut.

Thanks,

Gurmeet

Hi,
Gurmeet,
"The mean stress in the threads is above yield. However the application is still infinite life and not low cycle fatigue. The reason is that the threads are inside a stiff bolted joint and the resulting dynamic stress is very low. One difficulty in using the Neuber's method is trying to define Kt from FEA results. The failure occurs in the nut threads and not the studs. It is hard to define a nominal stress in the nut".
It's not entirely true. From VDI-2230, it results that a bolted joint has 3 main mechanisms of failure, depending on the geometric ratios of the elements and on the relative compliances. Whether it's true that a high-prestress, heavy-duty bolt never sees significative alternating stresses (unless it is poorly designed), you however do can make it fail in the shank; you can also make it fail in the threads, and you can also make it fail in the nut. It is very uncommon to preload above yielding, but I know it's a technique which is sometimes used in particular applications and with very strict control of the elongations.
However, this may lead us a bit off topic. A high-prestress bolted joint is non-linear by nature, so it's better to leave Neuber off anyway: either go with normated analytical calculations, or build up a non-linear FE model with pretension elements.

Regards