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(OP)
I need to calculate Fatigue life for a fully threaded screw loaded purely in cyclic tension (preload + additional cyclic load). The screw is 300 series CRES, .164-32 UNC-2A. This is already designed, so I cannot change anything; I just have to report fatigue life. I would like to get some input on accounting for uneven thread loading and thread stress concentration factors in a fatigue calculation.

As I understand it stresses in the thread root include axial stress (P/A) as well as bending stress (6P/(pi*n*d_r*p)) (and torsional shear primarily during torquing). I understand the first thread takes 30-38% of the total load, and I've found reference suggesting that the bending stress should be calculated using a fraction of the total load (load on first thread = .38*P) rather than being distributed among the engaged threads (load on each thread = P/n). Combining the axial stress and bending stress gives me von Mises stress in the thread root. I've calculated thread root stress this way for both the preloaded and design load conditions (using a joint stiffness calculation to get the max bolt load). I think I also need to apply a fatigue stress concentration factor to this von Mises stress.

Shigley and other references report fatigue thread stress concentration factors of Kf=2-5+. For now, I'm using kf=3. I'm unclear as to whether kf applies to the von Mises stress or if it applies only to the axial stress (P/A).

Using kf with the von Mises stresses and using the 38% first thread load assumption is resulting in essentially zero fatigue life (I also have to apply temperature and surface finish knockdown factors for material strength). I'm pretty sure I'm well below the endurance limit as alternating axial stresses are ~16 ksi, but I don't know if my method is too conservative and how the fatigue stress concentration factor should be applied. I've got R=-1 fatigue data, so I've also converted my mean and alternating stress to an equivalent alternating stress at R=-1 in order to predict life.

I want to be conservative, but I don't want to be double counting if the thread stress concentration factor is meant to account for the true von Mises stress state or for the uneven thread loading. Any input would be appreciated.

-Paul

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

For small stainless screws like that, a calculated fatigue life of approximately zero pretty much matches my experience.

I.e., it shouldn't take long for a realistic test on a modest sample to validate your calculations.

I would start the redesign and the validation program at the same time, e.g. now, but that's just me.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

bending stress from P (endload) ?

a bolt under preload usually has a very low cyclic stress, depending on the bolt stiffness, and a high R (min/max) for the cycle. Not sure how you adjust R=-1 s/n for your case

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Paul P... not enough info here...

WHAT Aerospace screw PN are You referring to [spec]? IF NOT, then what alloy/temper, head style [flush or protruding, recess style], length and are the threads rolled or cut?

Is this for a mechanical or an electrical installation? Lubricated [oil or cadmium plating + Lube] or un-lubricated [bare and NO lube] on installation. Is a washer under the head and/or under the nut?

WHAT installation torque value(s) [min-max]?

Single screw install: or multiple screw [pattern] install?

Is the screw threaded into a nut or nutplate or blind-nut; or into a tapped aluminum or steel or [???] hole... and without or with a helical coil thread insert?
operational environment?

NOTES.

Mike Halloran is exactly correct: In general 3xx [series] CRES, .164-32 UNC-2A screws are considered non-structural.

IF screw is an aerospace PN, there is likely to be a static strength table, for each Dia at a specified torque. IF the PN refers to a procurement spec this info is likely in that spec. ALSO, the exact strength of 3xx CRES is hard to nail down: especially when strain hardening is involved [very unpredictable]. IF the part were made from LA steel or A286 CRES HT 160-KSI, then tensile and shear strength would be fairly predictable... and these alloys would NOT tend to yield with reasonable install torque-tension. See NAS1219 or NAS8100--8106 for these quality flush and protruding heads screws.

In general, if the torque-tension preload is well-below the yield strength, but is above any cyclic loading, then this Install may last indefinitely. However, IF torque-tension preload is close to yield and/or the cyclic load approaches yield, then fatigue life will be extremely low due to a bunch of factors including yield creep which will result in a loose joint very rapidly... screw elastic or plastic stretching loosens the joint and bad things happen fast.

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

(OP)
Thanks for the replies. Just to be clear, I'm not necessarily looking for an answer from this forum as to how long the screw will last. I'm more interested in nailing down the methodology in terms of relating calculated stresses in the threads to an S/N curve.

I realize the limitations of the screw/material selection in terms of strength and prediction. This is a MS24693 screw (100 deg countersunk head) and there are four in the pattern. In this case, I am only an analyst and I need to provide a life cycle estimate regardless. Zero life is an acceptable answer if it is the best estimate. The spec does provide minimum tensile force and a material procurement spec (which is not very useful). This is a screw used in a fuel valve, so I don't think any high temperature creep effects will come into play.

I've already calculated the preload from the torque (taking into account the lubrication and head friction), and calculated the additional cyclic load based on the joint stiffness. For context, the preload estimate is ~300 lbf, and additional cyclic load is ~200 lbf (per screw). The spec lists a minimum tensile load of 1120 lbf. Again, I have to apply surface finish and temperature degradation factors that will approximately double stresses (or loads). Based on this, I believe I am below infinite life without a doubt, and realistically the life may be fairly short. I've read some rules of thumb which suggest cyclic loads should only be 5-6% of UTS to ensure infinite life.

I guess what I am really trying to nail down is whether I should be reading the S/N curve based on:
1) Net Section Stress (P/A)
2) Net Section Stress x Kf (P/A x Kf)
3) Von Mises Stress at the Thread Root (P/A + Tooth Bending Stress)
4) Von Mises Stress at Thread Root x Kf

If the answer is Von Mises at thread root, do I include the additional effect of uneven thread loading? Any input on these two questions would be most useful. I have a bunch of fatigue life estimates I need to provide on other bolts as well, so I'm also interested in nailing this down for future use.

Thanks,
Paul

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

ok, you've done your work and have a cycle 100-500 lbs (or 300-500 ?).

as you say the next question is an s/n curve. Whatever s/n curve you can find will have an associated stress model, be it minor area or tooth bending or etc. Maybe you find an s/n curve for specific Kt ... then you need to understand Kt with it's associated stress model. Have you tried Petersen ?

You mentioned you have s/n data for reversed loading (R = -1) ... how did you apply this to your problem ?

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

(OP)
rb1957- I used the SWT method as described in equation 7 of
http://www.ewp.rpi.edu/hartford/~ernesto/F2011/EP/...
The idea is to calculate an equivalent alternating stress cycle at R=-1.

Again, my questions are actually the following:
1) Which calculated stress to use?
2) How to apply Kf?

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

aul P

WHAT TORQUE-TENSION are the screws 'set' to?

CAUTION: under or [mostly] over-torqueing small screws is usually the primary mode of failure.

Typical torque-values [dry] for electrical threaded installations, this small in dia...

0.164-32 UNC >> 11-to-17-in# [SAE ARP1928, AIR6151]

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

STF

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Paul P.,

I am not reading carefully here and probably you have noticed this. The MS27039 pan head structural screws in corrosion resistant steel have a minimum ultimate strength of 130ksi. The MS24694 flat head screws have an ultimate strength of 85ksi, i.e., they are annealed 18-8 stainless. Both types of screw have an ultimate strength of 125ksi in carbon steel.

--
JHG

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

drawoh...

Paul P. 28 Feb 17 19:04

... This is a MS24693 screw ...

/14/ BASED ON 60 KSI MINIMUM ULTIMATE TENSILE STRENGTH FOR CARBON STEEL, 55 KSI FOR BRASS, 62
KSI FOR ALUMINUM ALLOY, 60 KSI FOR COPPER-SILICON ALLOY, 80 KSI FOR NICKEL-COPPER ALLOY AND
80 KSI FOR CORROSION RESISTANT STEEL. LOAD POUNDS ARE CALCULATED BY THE STRESS AREAS
INDICATED IN SCREW THREAD STANDARDS FOR FED-STD-H28.

TABLE III – MINIMUM TENSILE STRENGTH – LBF /14/

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

(OP)
Yup, I saw the 80 ksi value as well. But this is a static strength value, and I need to calculate fatigue life. Also, I can't make the 80 ksi value jive with the hand calc'd stresses in the thread root at the listed 1120 lbf load.

In my case, I've calculated preload section stresses(P/A) at 22 ksi for 300 lbf load, and design load section stresses at 36 ksi for 500 lbf load (mean 29 ksi, alternating 7 ksi). Stresses in the thread root are much higher due to tooth bending, assuming 38% load on the first tooth(Principal Stress = 57 ksi preload, 94 ksi design load or 76 ksi mean, 18.5 ksi alternating).

I made a quick FEA model which showed S1 = 198 ksi in the thread root for a 500 lbf load which comes out to a Kt ~2.1 as compared to the hand calc.

Still, the spec lists 80 ksi as min UTS and I'm calculating stresses well beyond that at less than half of that listed max load (1120 lbf). What am I missing here? If I run the hand calc on the 1120 lbf load, with even thread loading, I get S1 = 90 ksi in the thread root but that completely omits stress concentration which I know is at least 2X.

Maybe the spec listing of 80 ksi is referring to section stresses? I just have a hard time ignoring the much higher thread root stresses.

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Paul P.

Suggest re-looking at torque-tension relationship thru following documents...

SAE J1710 Torque-Tension Tightening for Inch Series Fasteners

SAE AIR1471 Torque Tightening Threaded Fasteners

MIL-HDBK-60 Threaded Fasteners - Tightening to Proper Tension http://quicksearch.dla.mil/

NASA RP-1228 Fastener Design Manual

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Maybe the spec listing of 80 ksi is referring to section stresses? that's how I read it.

and you're showing a much higher local stress at the thread root, Kt = 2 sounds low to me.

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

(OP)
After more research, I'm pretty sure fatigue thread stress concentration factors (Kf) are typically calculated and applied based on the average section stress (P/A). This just isn't made clear in Shigley and other sources. While stresses in the thread root are much higher, they apparently do not lead to fatigue failure as quickly as their magnitude would suggest. Without it being clearly stated, it just seemed more logical to apply Kf to the theoretical localized stress state in the thread root (P/A + thread bending stress) as a way of accounting for the thread root fillet geometry.

Disregarding actual thread root stresses also solves my other question of uneven thread loading as thread bending is not included. In the end, it's a simple answer to a complicated question, but most sources don't really discuss the full picture in terms of how fatigue failure works in threads. Hopefully, this will help some poor sot in the future.

The clearest discussion of this I could find comes from a 1934 thread fatigue experiment.
https://www.ideals.illinois.edu/bitstream/handle/2...

In the end, with all of my required conservative factors, I calculated a life well below 5K which confirms that this screw is not really suited for the design loading.

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Tmoose,
That article is interesting to read. The author's point of view is clear and dominates the text.
I can see how someone would be inspired to draw after reading it.
The drawing is printed in Bruhn's Analysis of Flight Vehicle Structures, and credited to SPS Technologies, Aerospace Fasteners Group there.

STF

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

Paul P.
From my own experience, I would not recommend using generic material sn curves with a kt factor. Fastener fatigue life is very dependent on the bolt threads, the nut/collar or retaining device, and the amount of pre-load or torque. Obviously designing bolts to be fatigued in tension is not an ideal approach however it has widespread historical precedence. The normal practice for analysis is to use fastener or bolt sn curves. These are available. I have used the ESDU 80028 as well as several other methods which employ sn curves specifically developed from fastener fatigue tests. Older references exist as well such as "Fatigue Analysis of Aircraft Bolts" by Brilmyer which was performed by the Huck company. Normally a good tension nut is used with a bolt designed to be in tension and has an appropriate torque applied to limit the cycling of the bolt under fatigue loading. The ESDU approach works well for this and includes curves for various threads: cut, ground or rolled and also for medium and high strength steels.
Anyways, best of luck.

### RE: Calculating Fatigue Life of Threads & Thread Stress Concentration Factor

The issue with this particular screw is not just the generic quality cres material permitted, which allows use of a crappy 303 alloy, but also the class 2A UNC thread form specified. The 303 cres material and UNC 2A thread form would never be acceptable for a fatigue-sensitive aircraft fastener application. A fatigue-sensitive .164-32 aircraft screw would typically be made from something like A286 cres and use a UNJC-3A thread form.

If you're stuck using the MS screw described for your analysis case, then you need to apply very conservative factors to be safe.

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