FEA static stress for fatigue calc VS. hand calc

[peyto]

All, I am trying to determine the fatigue life of a shaft (with splines machined into it) in combined rotating and bending. Assuming high cycle fatigue.

According to FEA, the max von mises stress is 55 ksi at the fillet between the splines. This agrees fairly well with hand calculations multiplied by a static stress concentration factor from a good source.

Question: Since the material has relatively good notch sensitivity, the calculated Kf is much lower than Kt, like about half as much. Is it OK to use this lower K to calculate the max stress for the fatigue life calc?

This makes a huge difference in the estimated # of cycles. In the past I have used the signed von mises stress (when alpha is < 0, >-1) straight from static FEA for fatigue calcs. Is this overly conservative since it doesn't take into account reduction of Kt to Kf?

 

[johnhors]

"Question: Since the material has relatively good notch sensitivity, the calculated Kf is much lower than Kt, like about half as much. Is it OK to use this lower K to calculate the max stress for the fatigue life calc?"

No.

Also consider using Principal Stresses not Von Mises (which is supposed to be used as a yield criterion - not for fatigue)

 

[rb1957]

not to be (simply) argumentative, but a quick google "notch sensitivity" found ...

http://www.utm.edu/departments/engin/lemaster/Machine Design/Lecture 04.pdf

... which suggests that Kf is ok.

principal or von Mises i don't think it should make much difference ... though i prefer principal (conservative?).

question ... how sure are you that you're looking at the peak surface stress ?

personally i think it sounds like the design is marginal ... would you consider shot peening the spline roots to improve their fatigue performance ?

 

[corus]

For rotating shafts I also use factors for the size of the shaft and the surface finish, both of which can adversely affect the fatigue life. Look at this site for factors

http://www.roymech.co.uk/Useful_Tables/Fatigue/FAT_Mod_factors.html

corus

 

[peyto]

Thanks for the responses so far.
RB - I am fairly confident that the FEA has converged, and that the peak 55 ksi is real. The material is 303 stainless and it can be hardened to 60 rockwell .06" deep. I am currently looking into whether this will help or hurt the fatigue properties. (any help here would be appreciated as well)

Johnhors - I have read from a few sources that von mises is conservative provided the alpha is < 0 (and it is)

corus - thanks for the link. I added Csurf and Csize to the calc.

But, the question remains: Is linear static FEA peak stress conservative for fatigue calcs because it doesn't take into account the reduction of Kt to Kf due to notch sensitivity.
Thanks!

 

[peyto]

Ok, replying to myself now. I realized that I used a generic formula for austenitic SS to calculate the notch resistance. From some further reading, it might not apply to 303 due to its sulfide content to improve machinability. Now its looking like the design is on the hairy edge. So, to be safe, it might be best to use Kt, not Kf since I can't find specific data for 303.
The hand calculated max von mises in the shaft is 14ksi, but if I use Kt = 3.8 for the fillet at the end of the spline, we are up to 53ksi for the peak. This agrees well with the static FEA.

 

[johnhors]

Peyto,

In a uniaxial stress field Von Mises and Principal Stress are the same, as at the peak stress caused by a hole in a plate. However in general on 3D structures, say on a fillet around the intersection of two tubes, the stress field on the surface is biaxial with both the max. and min. principal stresses being usually of the same sign at the peak stress location. In this situation the Von Mises stress is substantially lower in magnitude than the principal stress and it would be unsafe to use Von Mises in a fatigue calculation. The only time I have found Von Mises to be greater is at the run-off area of splines on a shaft in torsion (just as you have!), but not for bending and tension.

 

[gurmeet2003]

Peyto,

I have done a number of analysis for crankshafts. I have tried to understand the theory behind the concept of notch-snsitivity, but so far I am not very clear.

The idea behind notch sensitivity is that the full effect of the notch need not be considered, if the material is ductile. If the material is brittle, full effect needs to be considered.

One reason that is given for above is the effect of yielding at a sharp notch. Suposedly in a ductile material the yielding at the notch would redistribute the stresses. But what if the stress at the notch is below the yield stress. Then there would be no redistribution, why does one distinguish between a ductile or brittle material in such a case.

For the same reason I do not use the size factor. When one has a notch in the part, the high stress region is confined to a very small volume at the notch. In such a case should one not consider this volume? How does the size of the part matter. Also what about number of notches?

Therefore I do not use either notch sensitivity or size effect for fatigue calculation with FEA. I do include the effect of surface finish.

Gurmeet

 

[VoyageofDiscovery]

This may be a little beyond me, but I design steel bridges.

Why do you discuss yield stresses at all when the applied stresses create failure well below yield in ductile materials. The idea is that you keep the tensile stress range below a tensile threshold. This threshold will be a function of the specific material behavior with respect to strain.

 

[peyto]

Gurmeet, that is a logical way to look at it, and it makes sense. Thanks for your input.

Voyage, if I understand your question, I think that the answer lies in that fatigue occurs due to tiny areas that are in fact above yield stress. Even if the whole part in theory is below Sy, there are tiny imperfections or inclusions where "micro" yielding occurs, so fatigue failure from cycling is possible as the area grows into a crack. - actually, i just realized that maybe this is why the notch sensitivity correction might be valid...

The interesting part is that this shaft is actually designed and supplied by a vendor of ours, and they are well aware of the loads it should see (its a motor shaft, and they build the motors). We decided it would be wise to analyze the part just in case.
Thanks to everyone that contributed.

 

[truckcab]

Gourmet2003,
just one comment considering your discussion about the size factor. The size factor is meant to deal with the probability that there is a defect in the material such as e.g. surface flaw etc. The probability of a defect will of course increase with the size of your part. I think that your local interpretation of the size factor is not correct. I'll try to illustrate with an example:

Lets say we have 1dm3 of melted steel which is polluted with some material causing defects when the steel is solidified. Let's say that there are 100 such "pollution parts" in the 1dm3 melted steel. If you cast one piece using 0.9dm3 of the melted steel and one part using the 0.1dm3 then of course the number of defects (sensitive to fatigue loading) will be greater in the 0.9dm3 piece. This is the way to interpret the size factor i.e. it shall be interpreted "globally". I.e. he probability that you have a material defect in your sensitive notch increases with the size of your shaft.



Live Long and Prosper !

 

[FeX32]

Some decent comments.
Use kf as the (empirical) theory suggest that you should.
You may also want to look into performing a fatigue analysis in you FE software. Many packages include this. This is more likely to give you a value to compare with your hand calcs as opposed to the static FE analysis.



Fe

 

[gurmeet2003]

truckcab,

You have raised a good point. This is another reason given for using notch sensitivity. Suposedly a material that already has internal flaws, should not be as sensitive to new flaws (such as a notch). For this reason no correction is applied to grey cast iron for size or surface finish.

I understand the qualitative nature of this arguement. However I am curious to know how these size factors are determined. My guess is that they come from tests on unnotched specimens.

Your arguement about effect of size factor is valid up to a point. When a part has notches (holes, fillets etc,: most real parts have these), the high stress zone is confined to a very small volume at the notch. The stress concentration due to the notch can be up to 3. If the internal material flaws can give a stress concentration at the same level, then total size would matter. But I think that most generally used engineering materials (such as steels), do not carry internal flaws with stress concentration factors of 3.

My feeling is that the size factor is a carry over from the past without adequate theoratical and experimental backup for notched parts. The concept is valid for unnotched parts.

Thanks,

Gurmeet

 

[FeX32]

Yes, those internal flaws are dislocations. Any dislocation motion (small permanent deformation) causes some strain hardening. Which in turn strengthens the material. This is a way of interpreting 'kf'.



Fe