Margin of Safety for Ultimate Loads with FEM 1

[feajob]

Hello,

I would like to know what is the best approach for calculating the Ultimate Margin of Safety with FEM? I know that the nonlinear FEA is a better
approach, but it is not a cost-effective approach for 3D complex geometry models.

Consequently, I would like to employ the linear FEM with Neuber elastic stress correction. I have the following approaches in my mind:

1) Using Max. Principal Stress and calculating M.S. with Ftu.

2) Using Von Principal Stress and calculating M.S. with Ftu.

3) Using the real stain obtained with Neuber correction and calculating M.S. with Percent Elongation at Ultimate Load (shown in MMPDS).

I know that there are many alternatives and I appreciate to know your feedback.

Thank you,

A.A.Y.

 

[SWComposites]

What particular structure are you analyzing?

What is the material?

What is Von Principal Stress? Von Mises Stress?

How would you calculate the margin if you were to analyze the part by hand, using a classical stress analysis?

Note: non-linear FEM is NOT "better". It is appropriate in some cases, in others it is not. And it is easier to get a wrong with a nonlinear analysis.

 

[ESPcomposites]

SW is correct. If you provide additional information, it will be easier to help.

Based on your questions, there may be some basic problems with the way are approaching the problem.

Brian

http://www.espcomposites.com

 

[feajob]

Hi SWComposites,

Thank you for your reply.

What particular structure are you analyzing? Landing Gear Parts.

What is the material? Aluminum Alloys (usually)

What is Von Principal Stress? Yes, I meant Von Mises Stress.

How would you calculate the margin if you were to analyze the part by hand, using a classical stress analysis? By using conventional stress methods, we have to calculate a section under combined loads (bending, axial, shear, torsion and some times inside pressure, ...).

Note: non-linear FEM is NOT "better". It is appropriate in some cases, in others it is not. And it is easier to get a wrong with a nonlinear analysis.

Yes, you are right. Non-linear FEM is not always better. It is not cost-effective and you may get a wrong solution too.

 

[corus]

Generally you'd apply various factors to the applied loads for such things as impact etc., which by themselves provide a margin of safety. The stresses you'd get from the analysis would be assessed using the appropriate design standard.

Tata

 

[SWComposites]

"By using conventional stress methods, we have to calculate a section under combined loads (bending, axial, shear, torsion and some times inside pressure, ...). "

And what stress would you use to calculate a margin?

The answer to that is (generally) what you should do if you calculate stresses using a FEM.

Are you really letting landing gear parts yield before DUL? Aren't they sized by fatigue loads, and the ultimate stresses fairly low?

 

[feajob]

It depends on the size of aircraft. For VLJs, fatigue is not a FAR requirement. But, we do it to be more comfortable.

As you know, in a conventional analysis we take advantage of plastic bending (by using Fbu instead of Ftu). I believe that you have a good suggestion (doing similar approach). I will think about it to find a practical and reliable way of M.S. calculation for Ultimate loads.

Thanks,
A.A.Y.

 

[ESPcomposites]

Why are you using Neuber's rule? That has been developed for fatigue analysis. I suppose I could see some correlation to a static analysis, but I have never seen that used.

- If it is "brittle", then you might directly use the Kt. Do you have a reference to using Neuber's rule for a static analysis? I suppose it could be done, but it seems like you are mixing concepts?

- If it is ductile, how large of a region is in the high Kt area? If it is relatively small, you might generally neglect the Kt completely. For example, the ultimate tension strength of plate with a hole is close to that of Ftu*(net section).

- If it is ductile, but the elongation limit will be reached within then ultimate load, then you could apply something like a plastic factor (i.e. plastic bending).

What SW mentions about landing gear is true as well, at least for typical aerostructure landing gear that we are used to. But those are generally high strength steels, which have very different static and fatigue behavior than would a "typical" aluminum.

Could you better define the material, failure model, fatigue approach? By asking whether or not use max principal or von mises, indicates to me that you are not sure about which failure model to use (and how to apply it properly). Before you start your FEM or get anything useful out of it, I would think you should better understand that.

Brian

http://www.espcomposites.com

 

[rb1957]

a problem with FEA is that it gives you much more detail than classical hand calcs, like plasticity at the edge of a hole. the classical static world ignores these and MSs are derived on a stress more typical of the whole section; classical analysis says these features are highly localised (as borne out by FEA) and don't affect the overal load carrying capacity of the part.

you mention classical analysis like plastic bending. i use an FE result as a linear elastic bending stress, and use Form factors to adjust the FTU.

i guess the problem is that fatigue designs large plane gears, and VLJ folks have been relieved of that requirement ... funny when you think these are thought of as flying taxis, but ... maybe there isn't a FAA requirement, but maybe there'll still be a product warrantee committment ??

 

[feajob]

Hi ESPcomposites,

Following are responses to your questions:

Why are you using Neuber's rule? That has been developed for fatigue analysis. I suppose I could see some correlation to a static analysis, but I have never seen that used.

---> I apply this rule to a static analysis to avoid nonlinear analysis. Please check the attached picture. For the same mesh and load, Linear Solver found the peak Von Mises Stress a 119 ksi and Nonlinear solver results to 70 ksi. By using Neuber's elastic stress correction, I found 73.9 ksi. I prefer the Linear FEA + Neuber's rule versus Nonlinear FEA, because linear model with 848,664 DOFs runs in 29 minutes, but the same model with nonlinear material runs in 1444 minutes. So, nonlinear analysis is computationally 50 times more expensive.

---> I know that four other companies are using Neuber's rule to correct the linear FEA stresses. But, you are right this rule is coming from fatigue analysis. Specially, strain-life method (low cycle & high magnitude of stress).

- If it is "brittle", then you might directly use the Kt. Do you have a reference to using Neuber's rule for a static analysis? I suppose it could be done, but it seems like you are mixing concepts?

---> I think that there is a misunderstanding, when we use FEA the stress concentration is implicitly included (if we mesh all tiny features).

- If it is ductile, how large of a region is in the high Kt area? If it is relatively small, you might generally neglect the Kt completely. For example, the ultimate tension strength of plate with a hole is close to that of Ftu*(net section).

- If it is ductile, but the elongation limit will be reached within then ultimate load, then you could apply something like a plastic factor (i.e. plastic bending).

What SW mentions about landing gear is true as well, at least for typical aerostructure landing gear that we are used to. But those are generally high strength steels, which have very different static and fatigue behavior than would a "typical" aluminum.

---> We are dealing with landing gears for VLJs, so we manufacture some parts from steel and some others from aluminum.

Could you better define the material, failure model, fatigue approach? By asking whether or not use max principal or von mises, indicates to me that you are not sure about which failure model to use (and how to apply it properly).

---> For Static purpose, we know that for brittle material, failure occurs in a multiaxial system when either a principal tensile stress reaches the uniaxial tensile strength or a principal compressive reaches the uniaxial compressive strength. On the other hand, yield test of ductile materials have shown that the Von Mises criterion interprets well the results of a variety of biaxial conditions.

---> For Fatigue purpose (Ref. MSC.Fatigue Manual), the results of fatigue tests conducted under proportional loading at various biaxiality ratios suggest that the best parameter to use for loadings with 0>ae>-1 (i.e., between uniaxial and pure shear) is the absolute maximum principal strain. For 0<ae<1 (i.e., between uniaxial and equibiaxial) it is better, and more conservative, to use the signed Tresca parameter.

Before you start your FEM or get anything useful out of it, I would think you should better understand that.

---> Your last paragraph is not appropriate, I am always open to learn from more experienced engineers like SWComposites & rb1957.

For aluminum alloy, since it is a ductile material Von Mises stress is better. This is not the case for a brittle material. Based on my personal experiences, I did not see more than 2-3 percent difference between peak of Von Mises stress versus Max. Principal stress.

I believe that there is a mis-understanding, maybe you are not aware of the benefit of using Neuber's rule + Linear FEA versus Nonlinear FEA.


Thank you for your reply,
A.A.Y.

 

[ESPcomposites]

A.A.Y.,

Isn't this just a lug? If so, why not do a lug analysis. Bruhn has some curves for this.

If you are do treat this problem as a lug, there is an "effective Kt" that is used. For the classical solution, the "effective Kt" will be a function of the material, due to % elongation.

Brian

http://www.espcomposites.com

 

[feajob]

ESPcomposites,

The idea behind these models is to demonstrate the benefit of Linear FEA + Neuber's rule versus Nonlinear FEA. There are many references to do conventional stress analysis for lugs. For example, you can find conventional stress methods to perform stress analysis in "BRUHN Method §D1.11".

 

[ESPcomposites]

A.A.Y.,

I have been trying to recollect and do now remember seeing Neuber's rule mentioned before, in the same context. But as a blanket approach, it will not work as demonstrated by the difference between a problem like that of a lug and that of a plate with a hole. The Kt effect for a lug is real to the stress analysis, whereas it would not be for the plate with a hole (assuming a "ductile" material in each case).

So in that sense, wouldn't you need to identify if the Neuber approach might be applicable for your particular problem? If your problem is a lug, then can't you just directly compare the results from the classical solution to that of your proposed approach? If you find them acceptable, then you could say that it would be applicable.

Going back to your original question, it is a bit hard to determine what your goal might be. As demonstrated, you cannot in general use Nueber's rule since the applicability would be a function of type of problem.

Or perhaps we are just on different pages on this one. I will have a deeper look into Neuber's approach as well, out of curiosity.

Brian

http://www.espcomposites.com

 

[ESPcomposites]

A.A.Y,

I saw this thread as well:

http://www.eng-tips.com/viewthread.cfm?qid=210076

What Jetmaker says is same point I have been making. I suspect you are looking at specific problem (i.e. lugs), where there may be applicability. But since you did not quantify the problem in that sense (until the picture), it becomes impossible to determine if usage is applicable. This is very important and without defining that, it could imply other things (i.e. that you may think it is a general purpose model).

Using the Neuber's rule is simply a "model". Whether or not that model works well will depend on many variables and an understanding of the problem. The applicability of this model is certainly not general.

If your company (or others) have extensive history and good correlation using this "model" for specific parts, then that is fine. But the source of that is probably based on test data and classical methods that demonstrate effectiveness over a certain range of problems.

As Jetmaker said and you implied in your other thread, it will break down in some cases. That is simply due to the physics of the problem and the fact that Neuber's rule is just a failure model and nothing more.


Brian

http://www.espcomposites.com

 

[ESPcomposites]

A.A.Y,

Let me ask a straight forward question. Are you treating Neuber's rule as a general purpose approach? Based on this
thread and the other one, it might appear so?

As you can see from the curves in Bruhn, the W/D parameter will be a function of the "effective Kt". In other words,
if the ligament is small (as in the case of a lug) the Kt effect is realized. But in the case of a "large" plate with a hole, the Kt effect really is not (or minor). I don't believe Neuber's rule can differentiate these scenarios.

Based on this, what you are doing is applying a "rule", applicable to only to some types of problems. Looking back
on your original question, you are asking how to best apply Neuber's rule. But I believe you have already answered that once you decided to use the rule in the first place. It is effective for whatever failure criteria it has been validated to and developed for. You cannot try to then apply physics to it anymore, since the physics have been lost at this point. You can only use it within the domain that it has been substantiated, if that makes sense.

I am very familiar with the material failure criteria you mention, (i.e. the dilatational and deviatoric tensor are separated in the Von Mises and validated via hydrostatic testing) but you see, that is not what this is. You are using a failure "rule" or "model" to account for the plasticity of the material, which Max Principal, Von Mises, etc. do not account for. There are many "models" like this in engineering, but the the approach is inherent to them. You are outside of the domain where those failure criteria have been accepted. This is not to say one does not fit better than the other, but you cannot make that decision of which would be after the fact. If you have test data to support that one fits better than another, that is another thing.

Make sense? If not, please let me know and I will try to better answer your question. I was only indicating that I think this is less of a "FEM" problem and more of a mechanics problem that would warrant further discussion before the FEM aspect was introduced. Sorry if I may have offended you or if that was taken the wrong way. Sometimes things can get lost in translation on internet forums.

Brian

http://www.espcomposites.com

 

[feajob]

ESPcomposites,

I don't have enough evidence and references to consider Neuber's rule as a general purpose approach for static stress analysis. I am still looking for more reference documents and papers. I already read some of them, but I am not convinced yet. But, I believe that this rule has been accepted as a valid approach for strain-life fatigue analysis.

As you mentioned, I have previously started another similar Thread and Jetmaker replied to it with good comments.

I am not trying to analyze a specific structure (lug or ...). There are few questions in my mind, I already used different approaches. But, I keep working to improve our methodology. Following is my principal question:

Q1) What is the best approach to perform FEA for 3D Structures under Ultimate Loads? Please think in general. 3D parts can be any Automotive or Aeronautics parts. It can be manufactured from Aluminum Alloy, Steel Alloy or ...

From my understanding, non-linear material FEM can be helpful. If nonlinear model is properly done then FEM results should be reliable. But, based on my personal experience and apparently others, it is not a cost efficient approach.

Now, the idea is to find an alternative (efficient) approach. Calculating M.S. is a secondary issue.

I have to mention that whatever we do for conventional stress analyzes or FEM for static strength analysis will be validated by test. All conventional analysis and FEAs help us to have a good level of confident to pass successfully tests.

By the way, I am not offended by your comments and I appreciate your replies.

Thanks,
A.A.Y.

 

[ESPcomposites]

A.A.Y,

Well, I don't know that I have either a simple or direct answer for you. But I am very familiar with how to deal with stress concentrations for brittle, ductile, and composite materials as they relate to aircraft structure. I have sized many composite parts and dozens of metallic lugs at Lockheed and Boeing and an intimately familiar with the standard methods and why they work...as well as why some of what you are proposing may not.

I can only guess at the area you want to further discuss based upon your comments, but I will take a stab at it:

- First thing is to understand the material system, as has been discussed to some degree. Brittle materials will fail directly due to Kt effects. But for that reason, brittle materials are not commonly used (ironically with the possible exception of high strength steel landing gear which leans towards that). Composite materials fail in a "pseudo-plastic" mode. They are neither brittle or ductile. When dealing with ductile materials (as the current problem is), you should start to look at elongation (more on this next).

- The type of problem will dictate your solution. Let us again look at the lug versus the plate with a hole. The Kt effect in a lug is "real" to a static analysis, because the entire ligament is under the highly stressed region. However, for the plate with the hole, the stress concentration is very localized. For the lug, the elongation limit will be reached before significant redistribution can occur. The opposite can be said about the plate with the hole. Hence, you completely (or almost completely) neglect the effect of the Kt.

- You should start to see that any model such as applying Neuber's rule is only going to be effective for a certain type of material, geometry, etc. (see previous paragraph).

- So part of my question to you is, why is a FEM required to approach a problem like a lug? I understand you may have a desire to do so, but let us also consider that all of these types of problems can be solved via classical solutions. I have never done a FEM to solve a lug problem. FEM is somewhat uncommon for large aircraft analysis and almost never used when a classical solution exists. The exception is a loads model and some fine-grid detail models for special problems not covered by classical solutions. I also sometimes use FEM to assist in the understand of the problem or to add confidence to my classical solution approach where there is a grey area. I have used FEM more often in space applications or in scenarios where a classical solution is not available. Military aircraft tend to use more FEM than commercial though, probably due to FAA requirements and the FAA's seemingly preference for classical solutions (with good reason in my opinion).

- I am still confused as to what you are trying to attempt to do with Neuber's rule as applied to static analysis. Hopefully I have demonstrated that you will have difficulty with this as a general approach. A non-linear FEM would in fact reproduce the two scenarios I mention and you should be able to see the discrepancy. One caveat is that non-linear FEM is generally not used for composites, but rather a criterion (i.e. point stress) is more common to account for the "pseudo-plastic" effect. Though there are also many approaches to solve this effect via nonlinear FEM.

- As I said, I doubt I have directly answered your questions, but perhaps there is some information in there that will help you to decide how approach your problem better. But I pose this question to you. Do you feel you already understand the failure mechanisms at a high enough level to then develop a simplified approach (i.e. generalized linearization of a nonlinear effect). If the answer is no, then you may want to focus your efforts on this part first. Part of the issue is that each type of problem may require a different approach and a "one size fits all" linearization solution probably does not exist. You would either need to run a nonlinear FEM (of course with caution, or rely upon the physical understanding of the problem). Looking at the two basic examples, you could solve the lug via nonlinear FEM and the plate with the hole simply by engineering knowledge and a linear solution.

- You can also contact me directly if you would like and perhaps you can share some additional information about what you are proposing.



Brian

http://www.espcomposites.com

 

[feajob]

Hi Brian,

Thank you again for your reply. I would like to clarify that we perform all conventional stress analysis for our parts. In fact, FEM is mostly used calculating fatigue stresses (or strain, depending on the strain-life or stress-life approach). All classical parts like lugs, sockets, single shear pins, double shear pins, threads, springs, arbitrary sections under combined loads are subjected to all ultimate load conditions and M.S. are calculated for all of them in a very conventional way (as many other companies). The lug example shown before, is just an example.

Since, I already have to prepare the FEMs for the 3D major parts, consequently is it a good parallel check without much effort. Once, I have correct mesh then using Patran PCL language, I can apply easily Ultimate interface loads as well as fatigue interface loads. I usually did this kind of check for previous projects in our company and I found good agreement between the classical methods & linear FEA + Neuber's rule.

One easier approach is to check Limit static load conditions instead of Ultimate static load conditions. In this way, I can avoid Neuber's rule too.

Yes, I am agreeing about your arguments with regard to the failure modes for different materials.

Finally, I found this paper published in Machine Design. I liked it and thought to share it with you:

http://machinedesign.com/print/74495

Thank you,
A.A.Y.

 

[ESPcomposites]

A.A.Y.,

Sounds like you are on the right path. But as you have noticed, and what that paper does not demonstrate, is that "rules" are only applicable to some problems.

The lug is a special problem where the Kt effect is real to a ductile material under static loading, which is not mentioned in that paper. This could then confuse some people as it might appear that the rules don't work or that nonlinear FEM is always required.

Rather than looking at "rules of thumb", you can also look at the physics of the problem, which will give you the correct solution for any of the discussed scenarios. When I say "you", I am generalizing this to anyone and not specifically you. This will also help to determine if the rule makes sense in your particular scenario (which is where the engineer must step in and the FEM cannot easily or directly interpret).

For fatigue analysis, the approach is completely "different", as you understand. But again, by looking at the physics of the problem, it is quite easily demonstrated why the Kt is important (i.e. crack initiation is a local phenomenon as a opposed to a static failure which is considered at the part level). FEM can be useful in determining Kt's and stress intensity factors, but I have never done a fatigue or crack growth analysis within FEM. Once we have found the Kt, the classical methods are powerful and time tested.

Brian

http://www.espcomposites.com