Stress Intensity Factor Compounding

[FastMouse]

A couple of questions have been on my mind for a while. They’re a bit wordy, so apologies in advance!

(1) STRESS INTENSITY FACTOR COMPOUNDING METHODS

When I do SIF compounding, I use the equivalent stress method given in “An Improved Compounding Method for Calculating Stress-Intensity Factors”, Rooke.

I have worked for other companies where they used the equivalent crack length compounding method given in “Approximate Stress Intensity Factors Compounded from Known Solutions”, Cartwright & Rooke. This is also given in ESDU 78036.

Equivalent crack length compounding takes more effort to perform than equivalent stress compounding. Is there a reason why it should be used in preference to equivalent stress compounding? I discussed this with my colleagues at the time, but we never really found a reason why equivalent crack length compounding should be preferred.

(2) CONTRIBUTION OF BOUNDARY INTERACTIONS

Compounding methods usually take the form of a sum of geometry factor terms for the ancillary configurations, plus a “boundary interaction term” that is really just an error correction term and often denoted Ye. Something like...

Yr = Y0 + Y0 • Σ( Yn - 1 ) + Ye

Yr = geometry factor of complex geometry
Y0 = geometry factor of reference geometry
Yn = geometry factors of ancillary geometries
Ye = boundary interaction term

I’ve seen calcs where Ye was quantified, and others where it was neglected. I did some quick work with a specific geometry and I found that Ye was ~7% of the Y0 + Y0 • Σ( Yn - 1 ) term for shorter cracks, and about 3% for larger cracks. In another case, Ye was negligible.

How much effort do others put into assessing the value of Ye? Is it ever just assumed to be a percentage of everything else on the right hand side of the of the equation?

Thanks in advance for any info that you can supply!

FastMouse

 

[rb1957]

(1) not familiar with this method, do you have a reference ? i use the equivalent crack length approach ... for a crack at a hole appraoching another hole, i'd first model the crack at a hole (bowie) then to model the effect of the 2nd hole replace the original cracked hole with a simple crack 2aeq long (aeq = beta^2*a) with the crack tip the same physical distance from the 2nd hole as the real crack tip. not so difficult.

(2) never delt with Ye ... i guess if you know Yr then why bother ? i guess you're making use of test results and trying to extraploate to un-tested configurations.

 

[FastMouse]

Thanks for the response!

> (1) not familiar with this method, do you have a reference ?

An Improved Compounding Method for Calculating Stress-Intensity Factors
Rooke, D. P., Royal Aircraft Establishment
Engineering Fracture Mechanics
Volume 23, Issue 5, 1986, Pages 783–792

Available online for a fee:
[URL unfurl="true"]http://www.sciencedirect.com/science/article/pii/0013794486900901[/url]

Rooke wrote a book, and although I have never seen a copy, I *think* that it also documents the method.

Compounding Stress Intensity Factors: Applications to Engineering Structures
(Research Reports in Materials Science, Series 1, Vol 1)
Rooke, D. P.
Parthenon Pub Group, 1986
ISBN-10: 1850701105
ISBN-13: 978-1850701101

With equivalent stress compounding, you don’t need to determine aeq and then get the new geometry. It saves a couple of Excel columns for each ancillary solution. That’s not going to change anyone’s life, but it’s a small plus IMHO.

> (2) never dealt with Ye ... I guess if you know Yr then why bother ?

My problem is that 99% of the time, I do not know Yr, so I need to calculate it. I do the usual compounding calc to find Y0 + Y0 • Σ( Yn - 1 ), and then have to make an informed judgement about the relative importance of Ye. Does Ye equal 0%, 5% or 10% of Y0 + Y0 • Σ( Yn - 1 )?

I recognise that determining Ye is borderline inconsequential. Determining its actual value rather than making a judgement is not going to significantly affect inspection intervals. Rooke’s paper provides guidance concerning how Ye can be calced, but even if the information is available to allow it to be assessed, the time is usually not and a faster, but slightly more conservative judgement must be made.

 

[rb1957]

my 2c ... if you feel uncomfortable about your superposition, add 10% (or 20%, or 50%); or as my guru would do, factor the resulting life (a 10% factor on beta doesn't look like as "impressive" as a 33% (reduction) factor on life, even though they amount to roughly the same thing).

 

[FastMouse]

I don’t feel uncomfortable estimating Ye. The issue is that being able to demonstrate an additional 100 flights on the inspection interval sometimes prevents having to pull a plane for inspection a month early or whatever. (Plus my boss starts to recognise that I do a great job for him.) Showing that Ye is, say, 0.07 rather than conservatively estimating that it is 0.10 can give you that, and I was wondering if anyone does the calc to get the “real” value of Ye rather than conservatively estimating a value. I currently do not! A rigorous Ye calc would take me far too long.

Your point about quoting an impressive conservatism factor on CPL rather than a less-impressive conservatism factor on ∆K is noted, and you are right, they result in the same thing, but the CPL reduction sounds grander!

 

[FennLane]

'How much effort do others put into assessing the value of Ye? Is it ever just assumed to be a percentage of everything else on the right hand side of the of the equation'

I guess it depends on how much risk you are prepared to accept.

With values as high as 7% I think it should be considered so unless you can develop a model that tells you when its value is negligible I would think you are stuck witth doing the calcs.