Fatigue Calculation - equivalent stress

[user71]

I need to estimate the mean life of a cross section that has a very significant stress concentration (approx 10X average stress) The loading in the section cycles from 25 to 100% and I expect it to fail around 100,000 cycles so infinite life does not apply.

What is the correct approach to calculate the equivalent fully reversing stress for the load? Do I just use the average stress in the cross section to get mean and amplitude values for Goodman? But the stress concentration messes up the endurance limit in Goodmans equation since it needs to be reduced for short life (which is unknown). Or do you need to iterate the life until an answer is found?

I've looked through several textbooks but havent found one that clearly estimates finite life with variable loading, only fully reversed loading. If you can recommend a good book for explaining this, or can it explain this it would be appreciated.
Thanks

 

[desertfox]

Hi user71

Have a look at this link:-

http://www.fgg.uni-lj.si/kmk/ESDEP/master/wg12/l0100.htm

it might help.

desertfox

 

[PriamEngineering]

if you average the stress across the section you’ll be seriously over estimating the life of the component. That 10x stress concentration will be your likely crack initiation point…. Don’t ignore it.

“But the stress concentration messes up the endurance limit in Goodmans equation since it needs to be reduced for short life (which is unknown). Or do you need to iterate the life until an answer is found?”

I don’t really understand what you are on about here… can you expand please


you need to perform a rainflow analysis and sum the damage using miners rule
Regards

http://www.priamengineering.co.uk

 

[user71]

Thanks for the link desertfox - I will have a read.

Sounds like the rainflow method is what I need to do.

I was using the Marin equation from Mark's to determine the endurance limit. It states the following about stress concentration reductions - this really confuses me for finite life prediction:

Note that the miscellaneous effects factor (ke) for stress concentration applies to the endurance limit (Se) at (N =10^6) and greater. However, below (N =10^3) cycles it has no effect, meaning (Kf = 1) or (ke = 1). Similar to the process for finite life, between(N =10^3) and (N =106) cycles define a modified stress concentration factor (Kf ) where K f = aN^b and the coefficients (a) and (b), both dimensionless, are given in Eq. (7.18) as
a = 1/Kf and b = ?1/3log(1/Kf)
where the reduced stress concentration factor (Kf ) is found from Eq. (6.23).

Thanks

 

[PriamEngineering]

I had a look at my copy of Marks with little success. However I did find an expanded explanation in the excellent Mechanical engineering Design by Shigley.
I could however find no reference to the application of the strength reduction being different in the finite and infinite stress ranges.
As you have performed a finite element simulation with the geometry of the concentration accurately captured (I assume) and your increased stress in this area can be used instead of modifying your endurance strength. I am of course assuming that the stress concentration is NOT due to a weld (which is a totally different kettle of fish).
If you nee more help can you point me to the chapter in marks that you took the marin formula from?

Regards

http://www.priamengineering.co.uk

 

[rb1957]

rainflow ? ... how complicated is the spectrum ? if it's just 25% to 100% then you don't need rainflow (which connects the turning points on different cycles in a complex spectrum).

i think you've got other complex matters to ponder ... presumably at 100% load there is plasticity around the stress concentration. what's the material ? (ductile ??)

it's pretty common (in my world) to work with spectra that aren't fully reversed, usually with Smin = 0. look into "stress ratio". what fatigue data are you using ??

 

[user71]

This is a forging. The peak stress does go over ultimate so plasiticity would happen - does that rule out any typical SN type calculations to predict life like I was looking at?

We are going to cycle test a bunch of these and would like to have a calculated life going in. We have some initial results on life of the part, but not enough of a sample size to be sure.

I was using Mark's Calculations for Machine Design chapter 7.3 - Marin Equation to determine the endurance limit. I am going to get my hands on Shigley as it appears to be a more commonly used reference, hopefully more info there.

Any recommendations on the approach? Or is this something that is difficult to calculate with really poor correlation anyway? Any other recommend books would be appreciated.

Thanks for the inputs.

 

[PriamEngineering]

If your speak stress goes over UTS then I don't think that a fatigue analysis is going to help you any. what kind of load case is this? crash? if you test these in real life you should consider the loading sequence, ie. if your largest loading comes first and the forging breaks then the rest is academic.

http://www.priamengineering.co.uk

 

[user71]

Yes - we are only testing the worst case loading as that is what we are interested in. What is bad about the part is the geometry/loading is a smaller surface is highly stressed (10 times the average), yet the rest of the large cross section is low stress. Perhaps that area just yields then the rest takes over, without immediate crack initiation?

 

[rb1957]

i think you need to be very careful. your loading produces plasticity so there'll be bulk yielding around the stress concentration and most typical fatigue calcs assume small scale yielding. forget about load sequence (unless your spectrum has many levels) ... if it has only two load levels it doesn't matter much which comes first (the chicken or the egg).

ok, it's a forging, but what material .. steel ? high ductility ?? (or high strength ?)

if you're doing FEA (like the forum name suggests) then do a NL run to investigate the scope of plasticity.

i think your problem is more an ultimate strength issue than a fatigue issue ... if you've got that much yielding, you probably don't have much life.

 

[aeroflynn]

I know you want a number, but classical fatigue analysis is flawed -- or rather not flawed depending on how you look at it.

All "fatigue" fractures in the real world do not emmanate from notches. In classical fatigue analysis, if a number is desired instead of the infinity symbol, you pick the life you want to arrive at, then back-track to the notch or stress concentration factor that will give you that number. Sounds bad, and it is.

In either classical fatigue analysis or fracture mechanics, if you test a "dogbone" coupon started with the largest crack (crack not notch) that can be missed in inspection, you can obtain empirical data that can be used to emmulate crack growth or fatigue analytically.

In other words, Goodman, Oswald, S-n chart types of analysis are for college courses, not professional engineering. It took me three years to begin to understand my specialty of fracture/fatigue.

If you really want to look at fast numbers, just look up "fracture toughness (KIc)," and at least you'll be able to easily estimate what the critical crack size (crack length at failure) for your highest stress location. You don't really want to see what a professional has to do to estimate the inspection interval should be for a part unless that will be your only job.

 

[user71]

We broke 12 of these and the cracks did start at that high concentration. Juvinalls book suggested adjusting the mean stress down to account for the material over yield and that brought it just under the life range that was observed, of course it too warns against using this as anything more than a rough estimate, which is all I am really after here.

For the question I had with Marks adjusting the stress concentration - it should not be done as others stated here, because the equation takes it's effect to zero for you at the low/high cycle limit. I think Marks just put it in there to explain the approach they are taking, not as an adjustment you need to make...a little confusing I must say...Shigleys and Juvinall were much more clear.

Thanks!