On the Relationship Between the Cubic Rule and the USAF ... · On the Relationship Between the Cubic Rule and the ... 0 is the initial crack-like flaw size ... • DST Group 7075-T6

CRC for Aircraft Airworthiness and SustainmentCoE-Structural Mechanics

On the Relationship Between the Cubic Rule and the USAF Approach to Assessing the Risk Of Failure

Professor Rhys JonesCentre of Expertise in Structural Mechanics,

Department of Mechanical and Aerospace Engineering, P.O. Box 31, Monash University,

Victoria, 3800, Australia.

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Contact: [email protected]

CoE Structural Mechanics


• The US Joint Services Structural Guidelines JSSG2006 requires anassessment of the risk of failure.

• In this context it has long been known that the growth of lead cracks, i.e. the fastest growing cracks as defined in [1, 2], in operational aircraft is generally exponential [1-4].

1. Berens AP., Hovey PW., Skinn DA., Risk analysis for aging aircraft fleets - Volume 1: Analysis, WL-TR-91-3066, Flight Dynamics Directorate, Wright Laboratory, Air ForceSystems Command, Wright-Patterson Air Force Base, October 1991.

2. Molent L., Barter S.A., Wanhill R.J.H., (2011) The lead crack fatigue lifing framework, International Journal of Fatigue, 33. 323–331.

3. Barter S., Molent L., Goldsmith N. and Jones R. (2005) An experimental evaluation of fatigue crack growth. Engng Fail Anal, 12/1. 99-128.

4. Shanley FR. A theory of fatigue based on unbonding during reversed slip. Rand Corp Report No. P350, Nov 1952.

2CoE Structural Mechanics


Exponential Crack Growth in Operational Aircraft

In the USAF report by Berens et. al., “Risk analysis for aging aircraft fleets”, and the Lincoln Lecture at ASIP 2013 by Brussat it is noted that crack growth in operational aircraft can often be expressed as:

a = ao e( T) (1)

where T is the number of “flight hours”, load blocks, or cycles.

is a parameter that is geometry and load dependent,

a is the crack depth/length

a0 is the initial crack-like flaw size (depth of the crack at the start of loading) which is commonly referred to as the Equivalent Pre-crack Size (EPS).

Brussat T., When "What we always do" won't solve the problem, Lincoln Presentation, ASIP 2013, Bonita Springs, Florida, December 3rd-5th, available on line at; www.meetingdata.utcdayton.com/agenda/asip/2013/agenda.htm



• So how do real cracks behave ?

4

0.001

0.01

0.1

1

10

100

0 10000 20000 30000 40000 50000 60000

Crac

k de

pth

(mm

)

Simulated Flight Hours

P3C Wing DSTO Mirage Wing Swiss F&W Mirage Wing BH#2 A7 length, 200 hrs

T37B Wing Steel Strap F-16 12L/Spar 6 Zone III F-16 RP-10 Zone III F4 C/D Wing Skin

FA-18 FT46 Y598 Stub F/A-18 FT55 Y453 Web Taper F/A-18 ST16 Y453 Web Taper PC9 Wing BH#133

F111 A4 Splice AL2024 F111 A4 Splice D6ac F111 A4 FFH58 F111 FAS281 FTG

Isreal Mantra Jet Access Panel Mustang Wing N40 Skin F111 FFH13 In-service crack F111 SRO2 A8-109 in-service

Macchi A7-076 Mirage A3-094

From: Molent L., Barter SA. A comparison of crack growth behaviour in several full-scale airframe fatigue tests, International Journal of Fatigue, 9. pp.1090-1099. 2007.


• The Royal Australian Air Force (RAAF) independently developed a similar approach (to the USAF exponential equation) for managing for the F/A-18 Classic Hornet, AP3C (Orion) and PC9 fleets [5- 7].

• The difference is that the RAAF approach assumes that as a first approximation the parameter is proportional to the cube of a reference stress in the spectra ref in the spectrum, see [5-7] for more details.

• This formulation is an extension of the Frost-Dugdale crack growth equation [8] which was originally developed for the growth of long cracks under constant amplitude loading.

[5] B. Main, Structural Analysis Methodology – F/A-18, Issue 2 AI2, RAAF, Directorate General technical Airworthiness, Dec 2007.

[6] J. Duthie and E. Matricciani, DSTO P-3 Repair Assessment Methodology (RAM) coupon testing to validate the cubic rule, DSTO-CR-2010-0367, July 2011.

[7] Molent L. and Jones R., A stress versus crack growth rate investigation (aka stress - cubed rule), International Journal of Fatigue, 87, pp, 435-443. 2016.

[8] Frost NE and Dugdale DS. The propagation of fatigue cracks in test specimens. Journal Mechanics and Physics of Solids 1958; 6: 92-110. 5


• As such the exponent can be expressed as

= REF3 (2)

• Here REF is a reference stress in the spectrum, usually either the max stress in the spectrum (max) or ∆ rms; and

is both a spectrum and a geometry dependent constant.



• Thus if we have two tests under the same spectrum

• One with a max stress 1 in the spectrum and a corresponding 1 and

• Another with a different peak stress in the spectrum 2

• Then the value of 2 can be obtained using the Cubic Rule:

2 = 1 (2/ 1)3 (3)



The physical basis and the associated mathematics underpinning this formulation is given in:

Mandelbrot BB, Passoja DE, Paullay AJ. Fractal character of fracture surfaces of metals, Nature, 1984; 308:721–2.Bouchaud E., Scaling properties of cracks, J. Phys.: Condens. Matter, 1997; 9: 4319–4344.Carpinteri An and Spagnoli A. A fractal analysis of size effect on fatigue crack growth, International Journal of Fatigue 2004;26:125–33.Jones R, Chen F, Pitt S, Paggi M and Carpinteri Al. From NASGRO to fractals: Representing crack growth in metals, International Journal of Fatigue 2016; 82: 540-549.Molent L., Spagnoli A., Carpinteri An and Jones R., Fractals and the Lead Crack Airframe Lifing Framework, Proceedings 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy, Procedia Structural Integrity, 2016, 2, pp. 66-71.

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Example

• The experimental data presented in [9] included surface-etched and as-machined AA7050-T7451 coupons with a high Kt configuration and were fatigue tested under the fighter aircraft WRBM spectrum.

• The net-section stress range tested was 155 to 250 MPa. • The KT of the hole was 3.32.

[9] Huynh J, Molent L and Barter S. Experimentally derived crack growth models for different stress concentration factors; Int. J. Fatigue 2008; 30/10-11:1766-1786. 9


• For example in the 155 MPa test we see that the fastest growing crack, i.e. specimen KK1H343, could be expressed as per equation (1) with a value of = 0.1302.

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y = 0.0173e0.1113x

R² = 0.9949

y = 0.0097e0.1059x

R² = 0.9907

y = 0.0226e0.1302x

R² = 0.9977

0.001

0.01

0.1

1

10

0 20 40 60 80 100

Cra

ck d

epth

(mm

)

Load Blocks

155_Etched_KK1H353

155_Etched_KK1H348

155_Etched_KK1H193

155_Etched_KK1H339

155_Etched_KK1H343

Fastest growing crack at 155 MPa



• This enables the crack growth histories to be predicted, using eqn (3) at other stress levels, viz: Value of at 225 MPa = 0.1302*(225/155)3.

Good agreementeven though at225 MPa there is extensive yieldingat the hole


0.001

0.01

0.1

1

10

100

0 5 10 15 20 25 30

Cra

ck le

ngth

(mm

)

Load block

225_Etched_KK1H322225_Etched_KK1H325225_Etched_KK1H337225_Etched_KK1H370225_Etched_KK1H377225_Machined_KK1F78225_Machined_ KK1F85225_Machined_KK1H314225_Machined_KK1H344225_Machined_KK1H372Prediction


• The AP3C Orion RAM:

• The AP3C (Orion) RAM has an extension to this “Cubic Rule” that enables crack growth data at one stress concentrator (Kt1), with an associated remote reference stress σ1, to be used to assess crack growth at a different stress concentrator (Kt1) with a different remote reference stress (σ2).

• This was proposed by Louli and Moews at QinetiQ so as to enable the effect of a structural mod on crack growth to be assessed.

1/ 2 = (Kt1 σ1) 3 / (Kt2 σ2)3 (4)

Louli Z. and Moews J., Stress Cubed Rule Investigation, Qinetiq, Ref 4-4-12-91.3S5979, 22 June, 2010.



• Application to F/A-18: DST Group surface crack specimen tests under RAAF operational flight load spectrum. Max stress was 396 MPa.

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Huynh J, Molent L and Barter S. Experimentally derived crack growth models for different stress concentration factors; Int. J. Fatigue 2008; 30/10-11:1766-1786.


AA7050-T7451


• For the lead crack = 0.1476

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y = 0.0698e0.1476x

R² = 0.9897

y = 0.0133e0.1445x

R² = 0.9941.0E-02

1.0E-01

1.0E+00

1.0E+01

0 10 20 30 40

a (m

m)

Load Blocks

KD 13KD1R23KD1R10KD1R12KD1P14KD1P24KD1P29



The slopes for the DST Group open hole tests can now be calculated using equation (4) and are thus:

(250) = 0.1476* (3.32*180.4/(1.04*395.6))3 = 0.455(155) = 0.1476* (3.32*124.3/(1.04*395.6))3 = 0.149

Measured and predicted crack growth histories for the open hole tests at 155 and 225 MPa respectively- correspond to remote stresses of 180.4 and 124.3 MPa.

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0.001

0.01

0.1

1

10

0 20 40 60 80 100

Cra

ck le

ngth

(mm

)

Load Blocks

155_Etched_KK1H353155_Etched_KK1H348155_Etched_KK1H193155_Etched_KK1H339155_Etched_KK1H343Prediction



Potential to scale from one fatigue critical area (FCA) to a second FCA with a different spectrum and a different peak stress.Crack growth in P3C dome nut hole (DNHS) specimens under two different RAAF P3C load spectra, viz: FCA352 and FCA361.

Location FCA352-PDN-1 correspond to “the fairing dome nut holes in the lower surface panels at the inboard nacelle”; location FCA361-PDN-3 correspond to “the outer wing lower panels 1 to panel 3 – inboard nacelle – outboard fillet fairing dome nut holes”.



• DST Group 7075-T6 test specimen geometry representative of a DNH: Specimen has InterGranular Cracking (IGC) at the central hole

Loader, C., Goudie, D., Salagaras, M., Underwood, J. and Walliker, A., RAAF AP-3C Interaction between Intergranular Corrosion and Fatigue, DSTG-TR-3048, DSTG, December 2014.



• Typical IGC at the central hole

From: Loader, C., Goudie, D., Salagaras, M., Underwood, J. and Walliker, A., RAAF AP-3C Interaction between Intergranular Corrosion and Fatigue, DSTG-TR-3048, DSTG, December 2014.

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Crack growth in DNH specimens with IGC under the FCA352 (clipped) spectrum is essentially exponential with a slope ψ = 4.78 x 10-4.


Stress = 133 MPa


• Since for FCA352 and FCA361 the ratio ∆σrms/σmax in the spectra are essentially the same

• We can use the cubic rule together with the value of ψ for the FCA352 tests to estimate the crack growth history in the FCA361 tests. Stress was 124 MPa.

• This yields a predicted slope of

• Ψ(for FCA361) = (4.78 x 10-4 ) x (124/133)3 = 3.87 x 10-4.

Ratio of the remote stresses in the two tests



The resultant predicted crack growth history in DNH specimens with IGC (for the FCA361 spectrum) is in good agreement with the experimental data.

This illustrates the potential for the RAAF-DST Group approach to use data at one location to predict crack growth at a different location providing that the differences the ratio ∆σrms/σmax in the spectra are essentially the same. 21



• The RAAF-DST Group extension to the USAF approach to assessing the Risk of Failure has several advantages:

• However, additional work is needed to fully validate the modification contained in the AP3C RAM.

• Additional work is also needed to validate the potential for using this approach to use crack growth data at one location to assess cracking at a different location with a different flight load spectrum.

• The implication of this study is that the approach should be applicable to other RAAF aircraft types, e.g. C-130J (Hercules).

2222

CONCLUSION



AcknowledgementThis work was funded by DASA and DST Group.

With the (greatly appreciated) help and assistance of:

L. Molent, S. Barter, A. Walliker (DST Group); Wing Commander Ben Main, SqdnLdr Matthew Gordon, SqdnLdr Rupert Walker (DASA-ADF); Sqdn Ldr Michael Dorman (MPSPO); SqdnLdr Adam Bowler (P-8A Joint Program Office, Naval Air Systems Command, Pax River, USA); Dustin Edwards and James Ayling (AGAP).Juergen Meows (Qinetiq)



Slides in Reserve

USAF Repair to simulated C-141 weep hole specimens

Butkus LM., Gaskin JA., Greer JM., Jr., Guijt CM., Jacobs NJ., Kelly DF., Mazza JJ., Bonded Boron Patch Repair Evaluation: Final Report, USAFA-TR-2007-06, October 2007.

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The problem & the USAF repair

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• Two different integrally stiffened test panel geometries were considered.

• A narrow panel with one central stiffener. These specimens were given the prefix N.

• A wide panel with three stiffeners.These specimens were given the prefix W.

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Wide panel geometry from: C. B. Guijt, "The Effect of In-Service Conditions and Aging on the Fatigue Performance of Bonded Composite Repairs," Center for Aircraft Structural Life Extension, United States Air Force Academy, Technical Report USAFA-TR-2007-07, May 2007.

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• USAF Repair to simulated C-141 weep hole specimens

• For each of the C-141 weep hole repairs, three patches were applied to the stiffened panel.

• A double sided repair was applied to the cracked stiffener.

• A single sided repair was applied to the flat skin side of the panel.

• Both boron and glare patches were evaluated.

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• The boron-epoxy skin patches consisted of 13 plies of Textron Specialty Materials 5521/4, with a thickness of 0.13 mm per ply,resulting in a total patch thickness of 1.69 mm.

• The stiffener patches had 8 plies with a total thickness of 1.04 mm. These lay-ups were chosen to keep the extensional stiffness (the Young’s modulus multiplied by the thickness) as close as possible to the extensional stiffness of the Glare patches.

• The stiffness ratio of the repairs, this is the extensional stiffness of the repairs divided by the extensional stiffness of the structure, was 1.2.

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• Glare patches

The Glare patches were made out of two different custom made Glare2 lay-ups:

• Glare2 8/7 0.3 with a thickness of 4.15 mm for the skin patches

• Glare2 6/5 0.3 with a thickness of 3.05 mm for the stiffener patches.

The stiffness ratio for these repairs were 1.2, as for the stiffness ratios for the boron-epoxy repairs.

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• The patched and unpatched specimens were subjected to:

• The full C-141 load spectra &

• A modified C-141 spectra where the compressive loads were suppressed.

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Measured and predicted crack growth histories under full C-141 spectra.

y = 2.68E+01e3.51E-03x

R2 = 0.996

y = 12.084e0.0058x

R² = 0.9626

y = 5.15E+00e5.69E-02x

R² = 9.83E-01

y = 3.64E+01e4.69E-02x

R² = 9.83E-01

1

10

100

0 10 20 30 40 50 60 70

a m

m

Load blocks

Wide Panel Glare Patch W6Predicted Glare Patch W6Wide Panel Boron Patch W4Predicted Boron Patch W4Narrow Panel Boron Patch N6Predicted Boron Patch N6Narrow panel No patchWide Panel No Patch


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Measured and predicted crack growth histories under modified C-141 spectra, i.e. no compressive loads.

y = 2.20E+01e3.07E-03x

R² = 9.91E-01y = 10.906e0.0039x

R² = 0.9554

y = 12.084e0.0058x

R² = 0.9626

y = 7.60E+00e4.16E-02x

R² = 9.89E-01

y = 5.18E+00e4.17E-02x

R² = 9.85E-01

1

10

100

0 20 40 60 80

a m

m

Load blocks

Wide Panel Glare Patch W7Predicted Glare Patch W7Wide Panel Boron Patch W5Predicted Glare Patch W5Narrow Panel Boron Patch N5Predicted Boron Patch N5Narrow panel No patchWide Panel No Patch


• This example illustrates how the RAAF-DST Group extension to the USAF Risk of Failure methodology is applicable to Military Transport Spectra.

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On the Relationship Between the Cubic Rule and the USAF ... · On the Relationship Between the Cubic Rule and the ... 0 is the initial crack-like flaw size ... • DST Group 7075-T6

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