Residual Strength - FTy or FTu for Net Section Calcs? 5

[FastMouse]

When performing a residual strength assessment of cracked structure of Part 23 & 25 aircraft, net section yielding is usually assessed. Should this be done using the material's yield stress, ultimate tensile stress, or something else?

DISCUSSION

I have encountered three approaches:
(1) use ultimate tensile stress,
(2) use yield stress, and
(3) use an allowable stress between yield and ultimate tensile stress.

An argument for using ultimate tensile stress is that while a static strength substantiation of undamaged structure should show that there is no detrimental deformation at limit load, when performing a residual strength assessment of cracked structure, we are beyond the conditions of no detrimental deformation since we might be dealing with a quite large critical crack (possibly up to circa two bays in the fuselage). The critical crack size calculated based on crack instability, perhaps using an R-curve approach, will return a crack size that is just at the point of instability and potentially catastrophic failure at limit load. To be consistent with this, the critical crack size calculated using net section strength criteria should use ultimate tensile stress, again to calculate a crack size that is at the point of potentially catastrophic failure at limit load.

A side issue is that this might indicate an inconsistency in the FARs/CSs. (That’s not a criticism of the regulations; it’s simply the result of a framework that has evolved over many decades, guided by many, many individuals with inputs from about a billion different sources.) A static strength analysis could be done and the net-section margin at limit load calculated using yield stress. Then, a residual strength analysis could be done and if the critical crack is small due to, say, thick material having low fracture toughness, G/N is not significantly affected, and higher net-section strength margins would be calculated at limit load using ultimate tensile stress. So you end up with two margins: one from the static strength assessment of undamaged structure at limit load, and a higher margin for damaged structure at limit load. It's a bit of a stretch, but it could happen.

Arguments for using yield stress include (1) strength at limit load is being considered, so ultimate tensile stress does not apply, (2) it is not unconservative, and (3) it avoids having to debate the conservatism with whomever has to concur with the findings.

The arguments for using an allowable stress between yield and ultimate tensile stress are not clear, at least not to me. This method accepts potentially catastrophic failure via crack instability, accepts potentially-large scale yielding via net section strength, but having done so, does not take full benefit of using ultimate tensile strength to demonstrate a critical crack size that is as large as possible.

That’s a lot of text. If you’ve stuck it out to the end, thank you! Any comments?

 

[rb1957]

net section yielding is just that (and nothing to do with Ftu). The "ultimate" issue is that you don't apply ultimate load, just limit load. You can apply ultimate load to the cracked structure, if you want to fly with known cracking (but that is a whole different topic).

"The critical crack size calculated based on crack instability, perhaps using an R-curve approach, will return a crack size that is just at the point of instability and potentially catastrophic failure at limit load." ... correct.

"To be consistent with this, the critical crack size calculated using net section strength criteria should use ultimate tensile stress, again to calculate a crack size that is at the point of potentially catastrophic failure at limit load." ... incorrect. There are onetwothree net section yield situations ...
1) in small parts with a limited area you can calc a clear cross section area, and you can determine a crack length/area (including yield zone, the yielded material ahead of the cracktip) that will create yield stress over the entire remaining area at limit load.
2) in skin panels there are net section cut-offs for the fracture curve, refer Feddersen.
3) in skin/stringer panels you need to account for yielding of the stringers as a failure mode.

"... and higher net-section strength margins would be calculated at limit load using ultimate tensile stress." and so you reveal the fallacy for using Ftu. You'd sensibly expect that the cracked structure will be critical for net section yielding, with limit load and Fty.

The issue is some materials (like 2024T3) are very tough and so have long critical crack length, but low Fty so they could easily yield before fracture.


another day in paradise, or is paradise one day closer ?

 

[Sparweb]

AC 25.571 helps clear this up for me:

6.d.Extent of damage. Each particular design should be assessed to
establish appropriate damage criteria in relation to inspectability and
damage extension characteristics. In any damage determination, including those
involving multiple cracks, it is possible to establish the extent of damage in
terms of detectability with the inspection techniques to be used, the associated
initially detectable crack size, the residual strength capabilities of the
structure, and the likely damage-extension rate, considering the expected stress
redistribution under the repeated loads expected in service and with the
expected inspection frequency. Thus, an obvious partial failure could be
considered to be the extent of the damage for residual strength assessment,
provided a positive determination is made that the fatigue cracks will be
detectable by the available inspection techniques at a sufficiently early stage
of the crack development.

Further on in section 6, there are examples of partial failures that could come about in cracked structure. I think that's where you should be going - not your "side note".

The arguments for using an allowable stress between yield and ultimate tensile stress are not clear, at least not to me.

No such thing.

STF

 

[FastMouse]

Hi rb1957,

Apologies for the slow response.

Thank you very much for the detailed reply. I did not say it in my original post, but the question was biased toward single load path analyses. However, the point about stringer yielding is important. If using a SIF solution that takes into account the benefit of the stringers, when the stringers start to yield, the SIF solution obviously becomes invalid.

fastmouse

 

[FastMouse]

Hi SparWeb,

As I said to rb1957, apologies for the tardy response.

AC 25.571-1D is in my desk file. Your response prompted me to refer to it again and for me a key line for this question is in 6.a. "...the remaining structure can withstand reasonable loads without failure or excessive structural deformation until the damage is detected."

The way I interpret this is that if Ftu is used in the residual strength assessment, perhaps it can be argued that catastrophic failure will not occur prior to damage detection (remembering rb1957's stringer yield point above) but it is certainly not possible to state that excessive structural deformation will not occur. This indicates to me that the intent of the AC is that residual strength assessment is to be performed using Fty, and certainly it is aligned with my past practice.

Concerning use of an allowable stress somewhere between yield and ultimate: yeah, it's puzzling. I've nothing more to add to that one!

Best wishes,

fastmouse

 

[LiftDivergence]

Just throwing this in here since NASGRO / NASFLA is a common tool in this industry - when using NASFLA it will by default check net section yield of the module you are using as a failure criteria, along with stress intensity exceeding the fracture toughness.

NASFLA checks NSY using what SWRI refer to as the "flow stress" which is simply the average of yield and ultimate for the material, as stated in the user manual.

NASFLA computes the imput stress on the remaining area as the crack progresses and takes the maximum of any input stress S0, S1, S2 etc, as well as the user defined limit stresses, and checks them against the flow stress. Often the failure mode is net stress exceeding flow stress.

Just something to keep in mind if you are relying on NASGRO in your analyses. It may be prudent to perform other residual strength checks.

Keep em' Flying
//Fight Corrosion!

 

[rb1957]

ok, but I won't use Ftu for a residual strength analysis of a cracked structure.

25.571 gives you a reduced set of residual strength cases, so setting residual strength analysis apart from static strength. Static strength analysis assumes intact (uncrakced, unflawed) structure to the full ultimate load with the full ultimate allowable ... all straight forward and proper.
damage tolerance (and residual strength) assumes flawed structure and applies less load (more like limit conditions). To go beyond yield strength would require plastic fracture mechanics which whilst not incomprehensible is at least more difficult and has less data available (for probably minimal return).

fail-safe residual strength is, of course, a completely different analysis; much closer to static strength in that it doesn't assume flawed structure. Here I think you could apply Ftu in the surviving loadpaths.

another day in paradise, or is paradise one day closer ?

 

[LiftDivergence]

RB,

Agree 100%. Generally use the residual strength stress computed from 25.571(b) can be used as a limit say in NASFLA, which could be below yield. Of course, there is highly localized yielding at a crack tip but we are talking about net section strength retention here, so the yielding criteria arises due to net area in the presence of the crack. As you state if the net section goes beyond this you are looking at EPFM, not LFEM, which is a different story altogether. So agreed, it does not makes sense from that perspective to use Ftu that way.

This is why I mention it is good to make other checks on NSY depending on how you model your LEFM.

Keep em' Flying
//Fight Corrosion!

 

[rb1957]

yes, LD, some materials (2024) are very tough for their strength (how is it that we manage to get some materials just right ? like 2024 or ductile low carbon steel), and so panels have nsy (Feddersen) cut-offs. I wonder if the R-curve approach solves this, I suspect it would.

another day in paradise, or is paradise one day closer ?

 

[crackman]

Fastmouse
To just add some information, try looking at Tom Swifts stiffened panel residual strenght paper on the DC10. Also, his FAADER training class. They are truly the best with regards to your questions. They explains it far better than any AC and the crack growth softwares do not cover it. You will see that Ftu is used for the stiffener strength in the "restraint" of the panel.
Good luck

 

[FastMouse]

Thanks, crackman. I have Swift's paper that you mentioned. It's a good read. I did not know that he offered DER training, though. Will look into it.

 

[rb1957]

I don't think Tom's still active ... a shame if he isn't, a most amusing/engaging presenter.

another day in paradise, or is paradise one day closer ?

 

[FastMouse]

I did some digging, and drew a blank. As you say, no longer active. Too bad!

 

[crackman]

I took Tom Swifts class back in the mid 90s when he was the FAA NRS for DTA. His FAA course was offered to DERs and it was a 2 week, 80 hour intensive class. The course notes are about 3 to 4 inches thick. Very thorough course. You might try locating the course notes from the FAA.
Good luck.

 

[Sparweb]

I believe you can get the same "bang for your buck" from Safarian's class, which is still on offer, and (so I'm told) just as hard.

https://fdtcourse.com/

...and you missed it by 2 weeks.

STF

 

[FastMouse]

@crackman: Thank you crackman! I am not in touch with the FAA so often since I am currently living in EASAland, but looking for Swift’s notes via the FAA is a good prompt. If the chance arises, I will not neglect to follow it up.

@SparWeb: Thank you SparWeb! I was in touch with Mr Safarian a long time ago. I have experience with F&DT and the course would probably be a nice "reheat". I think that the real benefit would come from the side-discussions about interpretation and the like, like earlier in this thread. What would we do without Eng-Tips?

 

[WKTaylor]

Following may be useful for Your analysis...

The Stress Analysis of Cracks Handbook, Third Edition
Author(s)/Editor(s): Hiroshi Tada, Paul C. Paris and George R. Irwin


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]

 

[FastMouse]

Thanks! Already got it, and yes, it is definitely a useful reference. "Canned" SIF solutions packaged in crack growth software are great, but sometimes they do not adequately match non-standard geometries. It is easy to conservatively idealize a geometry to fit a canned solution, but there is still a place for Tada et al, Rooke & Cartwright, and the others, when you're trying to justify taking benefit of some structural material that does not exist in a pre-prepared SIF solution.

 

[Sparweb]

You're welcome FastMouse.
This may sound self-serving... please give Crackman and Wil a star if you believe their contributions have been helpful to you. All members should be able to judge the credibility and quality of the answers they get, and the stars system is one way that people posting questions can judge the expertise of those who answer.

STF

 

[FastMouse]

Oops, yes! Done!