Development of Advanced Risk Assessment Methodologies for Aircraft Structures Containing MSD/MED

M. Liao, Y. Bombardier, G. Renaud, N. Bellinger, T. Cheung (DTAES/DND)

Structures and Materials Performance LaboratoryInstitute for Aerospace Research

2

Acknowledgements

This work was performed with financial support from the DRDC-NRC collaborative project “Quantitative Risk Assessment of CF Aircraft Structures”

Project members:

Dr. G. Renaud, Mr. Y. Bombardier, Dr. M. Khan, Dr. G. Li, Dr. M. Liao

Dr. A. Fahr, Mr. N. Bellinger

DND support:Mr. K. McRae of DRDC

Mr. T. Cheung, Mr. Y. Caron, Mr. J. Gaerke of DTAES

Capt. T.J. Cadeau, Sgt. M. Bunn of ATESS/DND

3

Contents

• Risk Management for CF Air Fleets• NRC Risk Analysis Methods/Tools• MSD Damage Tolerance Analysis

– MSD/MED crack growth analysis– MSD/MED residual strength analysis

• Risk Analysis for MSD/MED Structures– ICSD/EIFSD– Monte Carlo MSD crack growth analyses– Maximum Stress Distribution

• Probability of Failure (PoF) Results• Concluding Remarks• Future work

4

Risk Management for CF Air Fleets

RARM (Record of Airworthiness Risk Management)• Hazard Id.� Risk Ass.� Risk Ctrl. �RARM Approval� Risk Tracking• Affecting all CF fleets (DND-AD-2007-01)

When “sufficient” data is available, Quantitative risk assessment (QRA) substantiates the assignment of a risk number in Qualitative risk assessment

TAM, C-05-005-001/AG-001,

DTAES/DND, 2001

TAM, C-05-005-001/AG-001,

DTAES/DND, 2001

TAM, C-05-005-001/AG-001,

DTAES/DND, 2001

5

• NRC developed methods and tools to calculate the single flight hour probability of failure (PoF, ~hazard rate) based on extensive durability and damage tolerance analysis (DaDTA)and stress-strength interference model

NRC Risk Analysis Methods

hourflight per on distributi stress maximum theis ][ where

)]([1)( :criterionstrength residualFor

)]),([1)(()(:criterion For

)()()]or ,([)(

0

0

σ

σ

σ

σσσ

σ

σ

σ

H

aHaPOF

dKKaHKfaPOFKc

daaPOFafKaPtPoF

RS

CCCCK

RSCCriticalMax

C

−=

−=

=≥=

�

�∞

∞

• Crack size distribution update based on NDI and repair

),( )](1[ ),(),()(),( ,

0 ,, tafaPODtafdatafaPODtaf beforeaRCSDbeforeaaftera −+⋅= �∞

6

NRC Risk Analysis Tools ProDTA

• ProDTA calculates the PoF using probability integration method or Monte Carlo technique

• ProDTA is under development, aiming to become a tool for CF fleets

Maximum stress(Gumbel / others)

Initial crack size distribution

(ICSD/EIFS)

Crack growth curve and β-solution

NDI POD(Log-logistic / others)

Failure criteria(KC, ac, σRS)

ProDTA

Maximum pit depth(Gumbel)

Corrosion growth rate(Weibull / database)

Corrosion protection breakdown time

(Normal)

Corrosion POD/NDI error

(Normal)

PoF

Fatigue inputs Corrosion inputs

Re. ICAF 2005 paper

7

Case Study: CC-130 Centre Wing MSD/MED Issue

The crisis

C-130A catastrophic failure in Walker, CA. 2002

The causes

“fatigue cracks in the lower wing skin” and “multiple site fatigue damage/ MSD” (NTSB)

The method neededAdvanced DaDTA and Risk Assessment Methodologies for Aircraft Structures Containing MSD/MED

8

CC-130 Center Wing Lower Surface Panel

CC-130 Center Wing, Lower Surface Panel, Location CFCW-1

Standard Crack (SC) scenario: single dominant crack, phase-by-

phase (PBP) approach (OEM DTA)

∅ 0.339” (BBR=1.587)

∅ 0.267”

7075-T7351 0.22” thick

VIII VII VI V IV III I II

Phases I & II

Phases III & IV

Phases V & VI

Phases VII & VIII

Multi-phase single crack growth analysis:

SC-PBP (OEM analysis, duplication)

9

Crack Growth AnalysisScenarios

MSD scenario: MSD approach

Standard Crack (SC) scenario:MSD approach

Primary crack(0.050”)

Secondary cracks(0.005”)

SC-MSD MSD

Primary crack(0.050”)

Secondary cracks(0.005”)

10Good agreement between NRC closed-form

equations, OEM, and FEA (StressCheck)

ββββ-Library

• Currently available & validated �-functions:

c

a

φ

Thickness (T)

B

σbearing

σtotal

W

c

σbypass

BBR=σbearing/σbypass

D B

σtotal

W

c

σtotal

B

D=2R2c

Corner crack

Radially crack at hole with bearing load

σtotal

Load path

Plate

Crack

Stiffener

c

Ligament failure

Stringer/Cap effect

Edge crack through hole

Crack approaching a

hole

11

ββββ-Library

• Additional available & validated �-functions:

2a1 2a2

A B C D

b

Gap

B

σbearing

σtotal

W

c1

σbypass

c2

BBR=σbearing/σbypass

B1

σtotal

W

c1 c2

σtotal

B2

D2D1

W

ci c2

σtotal * W/(W-Σci)

σtotal * W/(W-Σci)

Diametrically cracks at hole with bearing load

Crack interactioneffect

Linked-up crack Net section effect(under investigation)

Good agreement between NRC closed-form equations, OEM, and FEA (StressCheck)

12

Verification of MSDββββ-Solutions

MSD ����-solution from a benchmark MSD problem was verified with FEA (StressCheck) results (ICF12 paper, Ottawa, 2009)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

0 10 20 30 40 50

a0 (mm)

ββ ββ-so

lutio

n

CGCC130MSD (A11)CGCC130MSD (A12)STRESSCHECK (A11)STRESSCHECK (A12)

a12 and a21 merged

a22 and a31 merged

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

50 100 150 200 250 300

a0 (mm)

ββ ββ-so

lutio

n

CGCC130MSD (A11)

CGCC130MSD (A12)

STRESSCHECK (A11)

STRESSCHECK (A12)

a11 merged with left edge

a32 merged with a41 and a41 merged with a51

�-solutions for the lead crack a0 (< 50mm)

�-solutions for the lead crack a0(50mm<a0<300mm)

13

CC-130 Global and Local FE Modeling

Full aircraftCenter wing

Lower panel (βas2)

Local model (βas1)

ββββ-solution for adjacent

structural effect and MED

ββββas= ββββas1 * ββββas2

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Effect of Load Re-distribution (ββββas2)

• Methodology:– Detach elements in global FEM

• Crack faces• Stringers when failed

– Sum of loads across WS61• skin, cap, stringer

Detailed FEM is needed to refine the results

a = 20 in, no stringer failure

ββββas2

15

Effect of Cap/Stringer and Load Re-distribution

Assumption: Stringer #24 fails when the lead crack reach 12-inch; stringer #23 fails at 17-inch

9) .( 2

1

21

FigreductionLoadas�

uKsK

�aTu�

�aTs�as�

as�as�as�

=

==

∗=

16

Crack Growth Analysis Tool

• CGA Software: NRC Crack Growth Software, CGCC130MSD– β-library (or user defined β)– Standard crack problem (single dominant crack, phase-by-phase )– MSD problem– Forman Equation and Retardation (Hsu model)– Monte Carlo simulation– In-service finding regression

• Spectrum: Medium usage spectrum developed by L3-Spar and used by QETE for coupon testing of CFCW-1

17

SC vs. MSD:ββββ-Solutions

18

SC-PBP

SC

MSD

SC vs. MSD:Life Prediction

~25%

Using NRC Crack Growth Software, CGCC130MSD

OEM DTA Duplicating

19

MSD/MED Residual Strength Analysis

• RS failure criteria used:– Ultimate or yield strength (σult, σys)– Fracture toughness – Abrupt Fracture (Kcr)

Stringer #24 failedStringer #23 failed

Residual strength (normalized to �ys) curves for SC and MSD/MED scenarios

��

�

�

��

�

�=

�a�(a)

K,�(a)RS� C

ysmin

20

ICSD/EIFSD Methodologies

• Approach 1 (ICSD/EIFSD): with a small sample size (n < 40) of crack data from service, full scale test, and/or teardown

• Approach 2 (ICSD/EIFSD): with an extremely small sample size (n<5) of crack data from service or full scale tests

• Approach 3 (IDS/HOLSIP): with no crack data available from service, material and/or coupon test data can be used to determine an ICSD

Affecting Factors

• DaDTA vs DTA curve

• Lognormal vs. Weibull

• Uncensored vs. censored sample

• Confidence bands

• Effect of NDI uncertainty

Ref: RTO-MP-AVT-157 (Montréal, 2008)

21

ICSD/EIFSD Approach 1

• Direct regression in-service findings to EIFS, and then find a best-fit statistical distribution

0.00001

0.0001

0.001

0.01

0.1

1

0 10,000 20,000 30,000 40,000Flight hour

Cra

ck L

engt

h (in

) In-service finding

xxxx

EIFS

For small sample (n<40) crack data from service/full scale test/teardown

Regression (back calculation) methods:

a) Using DaDTA/DTA curve (Master curve) b) Using the calibrated crack growth program

Similar results are obtained using both methods

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MSD/MED Monte Carlo Simulation

Monte Carlo Random EIFS generator

Crack growth from EIFS

Crack size (a) vs. time (t)

Crack size distribution at time ti ,F(a)

Probability of Failure (PoF)

x N

t

a

t1 t2 t3 t4

START

23

EIFSD for MSD and Monte Carlo F(a)

EIFSD and MSD/MED Monte Carlo crack size distribution F(a) matched in-service findings

24

MSD/MED Monte Carlo Simulation

• Challenge: TIME!– 3.5 min./trial x 1,000,000 trials (Laptop) > 6 years!!!

• Strategy– Reduce number of trials to 100,000: 8 months– 10% tails results (10,000 trials only): 24 days– Parallel computing (NRC’s Linux cluster):

• 24 days / 84 CPU = 7 hours• 24 days / 25 CPU = 23 hours

Still has room to improve!

25N=10,000 of 100,000 runs

Matched

Matched

Crack Size Distribution F(a) Tail Sampling

10% tail sampling

100% sampling

N=10,000 runs

26

Max. Stress Distribution (per flight hour)

Example stress exceedance curves

• Table look-up format was used as they fit the data better than a Gumbel distribution

1E-111E-101E-091E-081E-071E-061E-051E-041E-031E-021E-011E+00

0 0.2 0.4 0.6 0.8 1Maximum stress as a ratio of limit stress

Pro

babi

lity

of e

xcee

danc

es p

er H

our

(1-C

DF

)

Gumbel fit

Table look-updata (CF2004)

Max. stress distribution

MaxMin

27

PoF Results for SC and MSD/MED

• PoF(MSD) is significantly HIGHER than PoF(SC), especially after a certain point in the end of service life

• Maintenance actions should be adjusted according to MSD/MED based crack growth, residual strength, and risk analyses

1E-121E-111E-101E-091E-081E-071E-061E-051E-041E-031E-021E-011E+00

0 10000 20000 30000 40000 50000 60000 70000 80000

EBH

Sin

gle

hour

PoF

, PoF

(t)

Standard crack scenario(Monte Carlo, ProDTA)

MSD scenario (MonteCarlo, ProDTA) ~24%

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Discussion: Master Curve vs. Monte Carlo

• The master curve and Monte Carlo approaches gave similar PoF. Since the master curve approach is significantly faster than the Monte Carlo approach, further investigation is worthwhile for MSD/MED risk analysis

1E-121E-111E-101E-091E-081E-071E-061E-051E-041E-031E-021E-011E+00

0 10000 20000 30000 40000 50000 60000 70000 80000

EBH

Sin

gle

hour

PoF

, PoF

(t)

ProDTA: SC (Monte Carlo,same EIFSD)

ProDTA: SC (Master curveapproach)

ProDTA: MSD (Mastercurve approach)

ProDTA: MSD (MonteCarlo, same EIFSD)

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• Developed advanced MSD/MED analysis methodologies and tools, including beta library, crack growth analysis, residual strengthanalysis, and Monte Carlo simulation to support DaDTA of build-up structures of aircraft like CC-130, CP140

• Developed ICSD/EIFSD using CF in-service damage data

• Improved NRC-ProDTA software to calculate the PoF for MSD/MED scenario, using Monte Carlo based MSD crack size distributions

• Results showed that the PoF of MSD is significantly higher than the PoF of SC (standard crack), especially after a certain point in the end of service life. The maintenance actions can be adjusted according to the MSD/MED risk analysis, crack growth, and residual strength analysis results.

Concluding Remarks

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Future Work: Quantitative Risk Assessment

(Project funded in 2008-2011)• Objectives:

– Continue DaDTA and PoF studies for other locations in CC-130 and CP-140 aircraft

– Support the CF life cycle management • Partners:

– Structures, NDE, DTAES/DND, IMP Aerospace …