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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 Laboratory Institute for Aerospace Research

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 2

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 3

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 4 TAM, C-05-005-001/AG-001, TAM, C-05-005-001/AG-001, TAM, C-05-005-001/AG-001, DTAES/DND, 2001 DTAES/DND, 2001 DTAES/DND, 2001

NRC Risk Analysis Methods • 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 � ∞ = σ ≥ σ σ = PoF ( t ) P [ ( a , K or )] f ( a ) POF ( a ) da Max Critical C RS 0 ∞ � = − σ For Kc criterion : POF ( a ) f ( K )( 1 H [ ( a , K )]) dK σ K C C C C C 0 For residual strength criterion : ( ) = 1 − [ σ ( )] POF a H a σ RS σ where H [ ] is the maximum stress distributi on per flight hour σ • Crack size distribution update based on NDI and repair = � ∞ ⋅ + − f ( a , t ) POD ( a ) f ( a , t ) da f ( a , t ) [ 1 POD ( a )] f ( a , t ) a , after a , before RCSD a , before 0 5

NRC Risk Analysis Tools ProDTA Initial crack size Maximum pit depth distribution (Gumbel) (ICSD/EIFS) Crack growth curve Corrosion growth rate and β -solution (Weibull / database) Maximum stress ProDTA (Gumbel / others) Corrosion protection breakdown time NDI POD (Normal) (Log-logistic / others) PoF Corrosion POD/NDI Re. ICAF Failure criteria error (K C , a c , σ RS ) 2005 paper (Normal) Fatigue inputs Corrosion inputs • ProDTA calculates the PoF using probability integration method or Monte Carlo technique • ProDTA is under development, aiming to become a tool for CF fleets 6

Case Study: CC-130 Centre Wing MSD/MED Issue The causes The crisis “fatigue cracks in C-130A the lower wing catastrophic skin” and failure in “multiple site Walker, CA. fatigue damage/ 2002 MSD” (NTSB) The method needed Advanced DaDTA and Risk Assessment Methodologies for Aircraft Structures Containing MSD/MED 7

CC-130 Center Wing Lower Surface Panel Standard Crack (SC) scenario: single dominant crack, phase-by- phase (PBP) approach (OEM DTA) Multi-phase single crack growth analysis: Phases I & II ∅ 0.339” Phases III & IV (BBR=1.587) ∅ 0.267” Phases V & VI Phases VII & VIII 7075-T7351 0.22” thick I II IV III VII VI V VIII SC-PBP CC-130 Center Wing, Lower Surface 8 (OEM analysis, duplication) Panel, Location CFCW-1

Crack Growth Analysis Scenarios Standard Crack (SC) scenario: MSD scenario: MSD approach MSD approach Primary crack Primary crack (0.050”) (0.050”) Secondary cracks Secondary cracks (0.005”) (0.005”) SC-MSD MSD 9

β -Library β β β Currently available & validated � -functions: • σ total σ bypass Thickness (T) a BBR= σ bearing / σ bypass φ c B σ bearing Corner crack c c 2c D=2R D B B σ total Plate W W Crack Crack approaching a c σ total σ total hole Ligament Radially crack at hole Edge crack failure Load path with bearing load through hole Stiffener Stringer/Cap effect Good agreement between NRC closed-form 10 equations, OEM, and FEA (StressCheck)

β β -Library β β Additional available & validated � -functions: • σ total * W/(W- Σ c i ) σ total σ bypass BBR= σ bearing / σ bypass b D 1 D 2 σ bearing A B C D c i c 2 c 1 c 2 c 1 c 2 2a 1 Gap 2a 2 B 1 B 2 B W W W Crack interaction effect σ total * W/(W- Σ c i ) σ total σ total Diametrically cracks at Linked-up crack Net section effect hole with bearing load (under investigation) Good agreement between NRC closed-form 11 equations, OEM, and FEA (StressCheck)

Verification of MSD β -Solutions β β β 2.2 2.2 a32 merged with a41 and a41 merged with a51 CGCC130MSD (A11) CGCC130MSD (A12) 2.1 2.1 STRESSCHECK (A11) 2 2 STRESSCHECK (A12) a22 and a31 merged 1.9 1.9 1.8 1.8 a11 merged with left edge 1.7 1.7 β -solution β -solution 1.6 1.6 β β β β β β 1.5 1.5 1.4 1.4 1.3 1.3 CGCC130MSD (A11) 1.2 1.2 CGCC130MSD (A12) 1.1 1.1 STRESSCHECK (A11) STRESSCHECK (A12) a12 and a21 merged 1 1 50 100 150 200 250 300 0 10 20 30 40 50 a 0 (mm) a0 (mm) � -solutions for the lead crack a 0 � -solutions for the lead (50mm<a 0 <300mm) crack a 0 (< 50mm) MSD � � -solution from a benchmark MSD problem was verified with � � FEA (StressCheck) results (ICF12 paper, Ottawa, 2009) 12

CC-130 Global and Local FE Modeling Center wing Full aircraft Lower panel ( β as2) β -solution for β β β adjacent structural effect and MED β β β β as= β β as1 * β β β β β as2 β 13 Local model ( β as1)

Effect of Load Re-distribution ( β β β β as2) • Methodology: – Detach elements in global FEM • Crack faces • Stringers when failed – Sum of loads across WS61 a = 20 in, no stringer failure • skin, cap, stringer β β β as2 β Detailed FEM is needed to refine the results 14

Effect of Cap/Stringer and Load Re-distribution � � � = ∗ as as 1 as 2 � � a K Ts s � = = as 1 � � a K u Tu � = Load reduction ( Fig . 9) as 2 Assumption: Stringer #24 fails when the lead crack reach 12-inch; 15 stringer #23 fails at 17-inch

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 16

SC vs. MSD: β -Solutions β β β 17

SC vs. MSD: Life Prediction OEM DTA Duplicating SC ~25% SC-PBP MSD Using NRC Crack Growth Software, CGCC130MSD 18

MSD/MED Residual Strength Analysis • RS failure criteria used: � � K � � – Ultimate or yield strength ( σ ult , σ ys ) � � C = (a) min , � � RS ys � (a) � a � � – Fracture toughness – Abrupt Fracture (K cr ) Stringer #24 failed Stringer #23 failed Residual strength (normalized to � ys ) curves for 19 SC and MSD/MED scenarios

ICSD/EIFSD Methodologies Affecting Factors • Approach 1 (ICSD/EIFSD): with a small sample size (n < 40) of crack data from service, full scale • DaDTA vs DTA test, and/or teardown curve • Lognormal vs. • Approach 2 (ICSD/EIFSD): with an extremely Weibull small sample size (n<5) of crack data from service • Uncensored vs. or full scale tests censored sample • Approach 3 (IDS/HOLSIP) : with no crack data • Confidence bands available from service, material and/or coupon • Effect of NDI test data can be used to determine an ICSD uncertainty Ref: RTO-MP-AVT-157 (Montréal, 2008) 20

ICSD/EIFSD Approach 1 For small sample (n<40) crack data from service/full scale test/teardown • Direct regression in-service findings to EIFS, and then find a best-fit statistical distribution 1 Crack Length (in) In-service finding 0.1 Regression (back calculation) methods: 0.01 a) Using DaDTA/DTA curve 0.001 (Master curve) EIFS 0.0001 x b) Using the calibrated crack x x growth program x 0.00001 0 10,000 20,000 30,000 40,000 Flight hour 21 Similar results are obtained using both methods

MSD/MED Monte Carlo Simulation START Monte Carlo Random EIFS generator a Crack growth from EIFS t 1 t 2 t 3 t 4 x N Crack size ( a ) vs. time ( t ) t Crack size distribution at time t i ,F(a) Probability of Failure (PoF) 22

EIFSD for MSD and Monte Carlo F(a) EIFSD and MSD/MED Monte Carlo crack size distribution F( a ) matched in-service findings 23