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# Fatigue life calculation - aircraft components - scatter factor and S-N curves

## Fatigue life calculation - aircraft components - scatter factor and S-N curves

(OP)
Hi,
I am started to work in the area of aircraft fatigue life estimation and please help me with the following:
I have few questions regarding fatigue life estimation of metallic aircraft components. Let say, The life can be computed using S-N curves (from MMPDS) and Miners damage under given loading conditions. The final life of a component is the estimated life/Scatter factor. My Question is
1. For the S-N curve, Does the aircraft industry use the mean/best fit S-N curve or some type of x% probability S-N Curve.
2. If we use the mean curve, it means a 50% chance of component failure. How it is accounted for?
3. what variability in the component is accounted for using the scatter factor?
4. Is there any practical reference with practical examples to estimate such aircraft component life estimation?
5. If we want to estimate the scatter factor (not just get it from AC 25.571), what parameters to consider and how to estimate the same. Is there any references available?

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

1. yes, mostly mean life curves.
2. see 3
3. there is a safe life factor applied the the raw result. From the S/N curve you read a life, N, then safe life = N/K. Safe life factor is typically 5, or 3 for landing gear.
4. Yes lots, google "fatigue life calculation".
5. There are all sorts of variables. 5 is the industry standard, it's quite the argument to use less.

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

This is a pretty big topic and in order to fully understand it requires digging in to things like probabilities and Weibull distribution. However, I can try to answer based on the methodologies that I am familiar with.

1. Generally, when using test data, the mean or average curve is used; however, it is recognized that there is scatter in the data which is accounted for with the scatter factor you are referring to.

2. A scatter factor is applied to the life to adjust it to a level of statistical confidence and reliability we want. Usually the goal is to obtain equivalent 95-95 or 95-99 life.

3. The scatter factor does not just account for component variability, it accounts for variability in the test data which includes many things associated with the data and testing itself. However, it is also useful to think of the scatter factor like it is presented in a machine design course, where fatigue life is often adjusted by various factors accounting for the surface finish, etc. In general, sources of scatter include different material batches being using in the testing, surface quality, lab vs service environment and more. Basically, anything that can cause the service data to differ from the test data.

Patrick Safarian has presented a methodology for this which breaks down the total scatter factor into four parts: a testing factor, a confidence factor and a reliability factor (which effectively reduce the life to 95-95 or 95-99), and a scale factor. After all is said and done, it is not uncommon to reduce the average life by a factor of 12 or more. [Ex: 1 / (0.7*0.7*0.32*0.5) = 12.76]

4. Yes, there are many. Probably the simplest, as it is intended for direct use in industry, is given in a course presented by Patrick Safarian who I reference above. If you search I am sure you can find a copy of those course notes somewhere, although I would also recommend taking the whole thing yourself.

5. I'm sure there are examples in many textbooks and also the course above. It is broken down so you basically just have a few tables to select your factors from. These are derived using statistical analysis assuming a Weibull distribution. So unless you want to do that yourself with the fatigue data, a reference is your best option.

A couple things to be aware of:

First off, as astutely pointed out by crackman in the following threads (thread2-457747: Kt values for CSK Fasteners, thread2-83550: Fatigue of Riveted Connections) - depending on the detail you have, S-N data from MMPDS (the most common source) could actually be a poor representative for your structure. Specifically, things like riveted joints and connections are not very well represented by that data.

Second, you have to be careful with the type of loading you are dealing with. The test data will be made using specimens in either constant amplitude or variable amplitude loading. This can be a source of scatter, and I would say it is partially accounted for by the "testing factor" mentioned above. However, you should be aware that many aircraft details may have residual stresses or pre-stresses which affect the mean stress of the detail. Regarding Mean and Alternating stresses - the mean stress has a far greater effect for notched components. This is another factor you need to be aware of when using S-N which may not represent your detail. In some cases you might want to start with the smooth specimen data and then go into Haigh diagrams or the modified Goodman approach.

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

a safe life factor of 12 ! ... wowww

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

I've always wondered how aircraft can fly... specially with a factor of 12.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

RB,

I wouldn't really call it a safe life factor since we (meaning the FAA, and industry in general) have gone away from a safe-life approach for almost everything. But your point is taken.

For a long time the general approach was to follow the guidance of SACO's publication "Guidelines for Developing Damage Tolerance Based Inspection Programs". In which, it is stated, [Section X, Establish Inspection Threshold], "[In addition to rogue-flaw methods], it is intended that the threshold of inspection will not be greater than one fourth of the unfactored fatigue life of the detail being addressed". However, I would caution anyone from using a factor of 4 or 5 since this guidance is somewhat outdated (it was published in 1999).

The scatter factor methodology I describe above is the contemporary guidance. Whether it is seen as overly conservative is another discussion. But it is rooted in statistical uncertainty of the data most often relied on.

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

Dik,

The factors I am referencing are generally for post-production support. That is modifications, repairs, etc.

OEMs can usually rely on full-scale testing. So for example, the testing factor is non-existent and the scale factor would be 1.0.

Rather than statistical fatigue data of this nature, OEM inspection threshold are often driven by LEFM. So SSID, AWLs etc. are not necessarily established this way.

What I'm referencing is specific to post-production data, especially if you are not an OEM.

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

yes, safe life is a substitute for threshold.

yes, fatigue is somewhat outdated, but is still a valid approach, particularly for structures that are not historically damage tolerant, like LG.

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

ok, as repairs/mods (without full OEM support and data) then sure, use a high safe life, it's impact to the airplane is limited, and conservatism off-sets (lack of) data.

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

OK, we are really getting off topic here, but I'm not sure what you mean by "safe life is a substitute for threshold"? Can you elaborate?

Safe life approach is almost wholly outdated and has it's origins in CAR 4b.316 prior to 1956. Basically the idea is to retire the airframe before the fatigue life limit. "Safe-life" approach is the era of regulations where there was no real requirement for an ongoing inspection program. You just show the desired life is below the effective "endurance" limit, and usually includes a factor which is essentially a safety factor.

I didn't say fatigue is an invalid approach. When you say "fatigue" I think you are referring to S-N approach rather than LEFM, which is a frustrating industry misnomer (yes, macroscopic crack growth / LEFM is fatigue. Fatigue is simply the accumulation of damage due to cyclic loading).

As a matter of fact, the FAA has a two-pronged approach required.
1. Check total life from pristine to fracture based on test data (typically S-N) with appropriate scatter factor applied.
2. Assume a rogue flaw and analyze using LEFM to fracture

Threshold is established as the lesser of item 1, or half of the life from initial rogue flaw to critical flaw size (either by NSY or critical stress intensity) from Item 2.

Repeat interval is established as time taken from detectable crack size to critical crack size with appropriate factor applied.

Therefore, to set an inspection regimen, it is required to approach the problem in multiple ways. This is the crux of the damage tolerant design approach. And per the Aging Aircraft Safety Rule, this is required to be performed even for structure which was not originally type-certified as damage tolerant.

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

"what you mean by "safe life is a substitute for threshold" ...
exactly what you wrote ... "it is intended that the threshold of inspection will not be greater than one fourth of the unfactored fatigue life"

"When you say "fatigue" I think you are referring to S-N approach rather than LEFM, which is a frustrating industry misnomer (yes, macroscopic crack growth / LEFM is fatigue. Fatigue is simply the accumulation of damage due to cyclic loading)." ... no, "fatigue" to me is Miner's rule fatigue damage accumulation. I've never heard of an "S-N approach rather than LEFM" ... since the two analyses (fatigue and crack growth) are fundamentally different ... one assuming an uncracked structure (and not caring too much about the crack growth phase) and the other wholly with cracked structures. {I think we both know what we mean ! and the differences.)

In my experience, fatigue is used early in the design process to get a quick handle on how the structure will perform. And DTA is used to establish threshold and repeats, analysis supported by test. Inspection methods are the last thing to be solved, usually design intends the structure to be inspectable, sometimes it calls on "extreme measures".

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

"exactly what you wrote ... "it is intended that the threshold of inspection will not be greater than one fourth of the unfactored fatigue life""

But that is not a safe-life approach...

I'm not disagreeing, those are how the terms are generally used in this industry. But to me it is frustrating because it has a slant which I blame on the historical development of the CFRs. I mentioned this more in this thread: thread2-460174: Fatigue Doubt

Any textbook will define fatigue as, the accumulation of damage due to cyclic or repeated loading - something to that effect. I don't think anyone will argue the term fatigue only applies to analysis where the Palmgren-Miner rule is used.

A DTA is not a methodology. It is just an assessment to be performed. And per 25.571, it must include assessments of accidental damage, corrosion, and fatigue.

#### Quote (rb1957)

the two analyses (fatigue and crack growth) are fundamentally different ... one assuming an uncracked structure (and not caring too much about the crack growth phase) and the other wholly with cracked structures.

I know what you mean... but this is my point - you are saying "fatigue" is assuming a pristine specimen test data (ie stress life or strain life curves). And you are saying "crack growth" is basically synonymous with rogue flaw analysis.

I think this is a confusing definition. Even for a test specimen starting pristine, we have voids, inclusions, etc which lead to crack initiation. It doesn't matter if the crack is microscopic or macroscopic, it is still a crack and it is still growing. So why do we refer to only macroscopic flaws treated with LEFM as "crack growth"? If we have a macroscopic flaw propagating due to cyclic load, you would agree that is a form of fatigue, right? Hence the term fatigue crack growth. So why are we only referring to analysis that includes pre-macroscopic cracks as "fatigue"?

The bottom line to me is that the FAA requires a threshold and repeat to be established. The guidance is to use multiple approaches. One is to factor statistical test data which is made for pristine specimens with no artificially induced or assumed flaws. The other is to assume a macroscopic flaw and treat using LEFM. The threshold is taken from the lesser of either.

These approaches really are both fatigue and they are both crack growth. And both must be included in a DTA. We are just treating the same phenomenon with different methodologies or data. Although obviously this is not how people in aircraft structures talk about the matter and I've had to put up with it for a long time.

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

"But that is not a safe-life approach" ... sure it is ! with a safe life factor of 4 ... what else is "one quarter of the unfactored fatigue life" ?

fatigue does not assume a preexisting flaw, or rogue manufacturing damage, or corrosion rack starter. Fatigue starts with a nominal specimen, sometimes a polished specimen. Fatigue analysis makes no mention of flaws (or flaw size). Damage tolerance assumes an initial flaw. The two key elements of DTA (as opposed to fatigue) are
1) the inspectability of the structure, and
2) the residual strength of the largest crack expected in service.
Fatigue analysis doesn't talk to these, it assumes the structure is intact one cycle and broken the next. And the safe life factor protects us from the sudden failure. The problem with fatigue is throwing away structure without cause "just" because it's fatigue (safe) life has expired.

Saying that DTA is not a methodology is just being pedantic.

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

The factor of 4 you are working with is used to set an inspection threshold. The point of a safe life approach is to show you do not need any inspections. Safe-life approach says we have shown the structure will not develop detrimental flaws throughout the intended service life, so we are good. Or the inspection is so impractical, we can barely do it, we'll support the analysis with fail-safe approach.

I am well aware of the industry definitions of "fatigue" and "DTA". Essentially everything you wrote, I had already stated above. That is, the idea of "fatigue" based on cyclic data for pristine specimen and "DTA" or "crack growth" including assumed macroscopic flaws.

The whole point I'm trying to make is that I think these are bad names. They are confusing.

25.571(b) itself says:
Damage-tolerance evaluation. The evaluation must include a determination of the probable locations and modes of damage due to fatigue, corrosion, or accidental damage. Repeated load and static analyses supported by test evidence and (if available) service experience must also be incorporated in the evaluation.

The fatigue analysis is not distinct from the DTA. It is one element of it. I would argue we need to stop referring to macroscopic rogue flaw analysis as simply "DTA".

Keep em' Flying
//Fight Corrosion!

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

words have meanings, and our meanings are different.

To say that an unfactored life divided by a factor is not a factored (or safe) life is pendantic.

I agree damage tolerance analysis (since you dislike the term "DTA") encompasses more than "rogue flaw analysis. I never said it didn't. It includes fatigue damage but doe not include fatigue analysis. Yes, you can set a threshold using fatigue analysis, but most use the rogue flaw since if you're doing crack growth from detectable, you may as well start at a small size. And most certifying authorities don't really like the fatigue analysis based threshold.

Let's call it quits. Maybe some readers will get something out of this ?

### RE: Fatigue life calculation - aircraft components - scatter factor and S-N curves

Hi Jnnal,
Welcome to Eng-Tips.
A lot of your questions (maybe all of them) are answered (in considerable detail) by Jaap Schijve's book Fatigue of Structures and Materials.

I'm not trying to win the argument between the rest of you, but scatter factor is also a subject of MANY chapters. Of course, as we always say, "it depends". How the S-N data was created is just one factor of many.

Please remember: we're not all rednecks!
www.sparweb.ca

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