Development of Reliability-Based Damage Tolerant Structural Design Methodology

Transcription

1 Development of Reliability-Based Damage Tolerant Structural Design Methodology Dr. Kuen Y. Lin and Dr. Andrey Styuart Department of Aeronautics and Astronautics University of Washington

2 Outline Background and Objective Probabilistic Structural Design Approach Formulations Program Capabilities Monte Carlo Simulation Software Architecture SDR Data Mining Damage Maps PDF of Detected Damage Results Sample Problems Parametric Studies Summary 2

3 Development of Reliability-Based Damage Tolerant Structural Design Methodology Motivation and Key Issues: Composite materials are being used in aircraft primary structures such as 787 wings and fuselage. In these applications, stringent requirements on weight, damage tolerance, reliability and cost must be satisfied. Although currently there are MSG-3 guidelines for general aircraft maintenance, an urgent need exists to develop a standardized methodology specifically for composite structures to establish an optimal inspection schedule that provides minimum maintenance cost and maximum structural reliability. Objective: Develop a probabilistic method for estimating structural component reliabilities suitable for aircraft design, inspection, and regulatory compliance. 3

4 Contributors Principal Investigator: Dr. Kuen Y. Lin, Aeronautics and Astronautics, UW Research Scientist: Dr. Andrey Styuart, UW Research Assistants: Chi Ho Eric Cheung, UW FAA Technical Monitor: Peter Shyprykevich Other FAA Personnel: Dr. Larry Ilcewicz, Curtis Davies Industry Participants: Dr. Cliff Chen, Dr. Hamid Razi, Mr. Gerald Mabson, Dr. Alan Miller (All from Boeing) 4

5 Example of Impact: Hail Damage 5

6 Fatigue Damage vs. Impact Damage Type of uncertainty Location of uncertainty Size of uncertainty Fatigue damage, metals Quite certain: fatigue crack Quite certain: high stress concentration locations For good designs, grows slowly from initial crack size. Can be stopped. Impact damage, composites 3-5 damage types should be considered for any particular structure type All surface: relative damage frequency is known Created instantly, then usually doesn t grow. Predictive methods Well developed. Good prediction of fatigue life Poor prediction due to lack of appropriate statistical data 6

7 Present Approach The present study is based on a probabilistic failure analysis with the consideration of parameters such as inspection intervals, statistical data on damages, loads, temperatures, damage detection capability, residual strength of the new, damaged and repaired structures. The inspection intervals are formulated based on the probability of failure of a structure containing damage and the quality of a repair. The approach combines the Level of Safety method proposed by Lin, et al. and Probabilistic Design of Composite Structures method by Styuart, at al. No damage growth is assumed in the present model. 7

8 Probabilistic Approach Various Failure Modes Strength/Stiffness vs. Temperature Moisture Content vs. Time Residual Strength/Stiffness vs. Damage Size & Damage Type Probability of Detection vs. Damage Size & Damage Type R W,% R Failure Load T Lifetime 2L Strength/Stiffness Degradation due to Environmental Exposure R Life time Probability of Failure Maximum Load vs. Time of Damage Existence Damage Size & Damage Type Spectra Structural Temperature Spectra Damage Detection Maximum Load Damage Size Temperature Inspection Intervals, Repair Repair Criteria, Structural Risk Risk 8

9 Probability of Failure Formulation Deterministic Input Parameters: Type of damage T D Failure mode/ load case FM Inspection intervals T 1, T 2, r r r r r P = f( N, D, R, t, td, L, T T, FM, T, T, T...) dv f Ω r r r r dv = dn dd dr dt d( td) dl dt ; Ω= failure domain D Probabilistic Input Parameters: Failure load (initial strength) R J 0 Number of damages per life N J Damage size D J J Time of damage initiation t ii J Time of damage detection td ii Residual strength R J ii J External load L ii J Structural temperature T ii Effects of environmental aging and chemical corrosion Piecewise random history method: Relations for one type of damage and failure mode/ load case NJ N j j j j j 1 P = 1 [1 P ( R,( td t )]; P ; ( ); i i i i f = Pj N = f Δ N i= 1 ( td t ) j j j Life P = 1 { F [ R ( D ) μ, σ ]} ; F = CPF of maxload per life i L i L L L j j j td = f [ P ( D ), t ] i Detect i i i j i j i j= 1 9

10 Finding Inspection Intervals Specified inspection intervals T 1,T 2 Deterministic Data Input Probabilistic Data Input Reduce T1,T2 NO POF<10-8? Probability of Failure Calculation YES Satisfactory design with T1,T2 10

11 Probabilistic Model Probabilistic Input Parameters: Type of damage T Number of damages per life Initial failure load (initial strength) Damage size Time of damage initiation Time to detect Damage External load Structural Temperature T Effects of environmental aging and chemical corrosion ith interval of constant damage size: Width (time) t i [T 1,T 2,D], Damage type TD i, Residual strength S i (D,TD i ), First, First, we we simulate simulate random random time time histories histories of of residual residual strength strength as asa a sequence sequence of of intervals intervals between between damage damage initiation initiation and and detection/repair. The The probability probabilityof of failure failure (POF) (POF) can can then then be be evaluated evaluated as as the the sum sum of of POF POF for for all all intervals. intervals. 11

12 Probabilistic Model Load R 0 R 1 Life 2 Strength R 2 L 1max t i t Di Damage type 1 Life 1 Strength L 2max L 3 max Load T Temperature Time Time 12

13 Software Architecture MS Excel: database management MS VBA macro: input data check, MS Excel: post processing; POF, sensitivities Automation DLL (Fortran 95) 13

14 Program Capabilities Static failure: load exceeds the strength of damaged structure Excessive deformations Flutter: airspeed exceeds the flutter speed of damaged structure* High amplitude limit cycle oscillations: the acceptable level of vibrations is exceeded* *See the FAA Grant Combined Local ->Global Variability and Uncertainty in the Aeroservoelasticity of Composite Aircraft 14

15 Example of POF Calculation for One Structure Number of Exceedances per Life Ht(Load) Number of Exceedances per Life Ht(Load) Load Exceedance Curve Load Exceedance Curve 1.00E E E E E E E E E E E E E E E E E E E E E E E E-05 Load Load = 3 = N f f i i i= 1 P 1 [1 P ( R, t )] P ( R, t) = 1 exp{ H ( R) t} f t Interval # Probability of Failure 1 (new structure); R= E-06 2 (damaged structure); R= E-02 3 (repaired structure) ); R= E-06 Total POF = 4.26E-02 15

16 Damage Size History Simulation Damage Size Life History, Inspection interval = 10% of Life, Assume one damage per life Damage Size, X10 in Time 16

17 Residual Strength History Simulation 1.1 Res. Strength degradation vs. Damage Size Dam age Size Delaminat ion Hole Res.Strength Delamination Hole Time Damage Size Res. Strength degradation due to aging Combined Damage+Aging R es.streng th Delaminat ion Hole 1.2 R e s. S t r e n g t h Delaminat ion Hole Time Time 17

18 Residual Strength Analysis of a Simple Wing Box Max Stress in the Undamaged area σ = 18,490 psi Max Stress in the Damaged Panel σ = 22,858 psi 18

19 Input Data Management 19

20 Results on POF 20

21 Service Difficulty Report (SDR) The Service Difficulty Report (SDR) is a database that contains damage reports almost exclusively from line and base maintenance in the U.S. A typical SDR is like a mechanics report on an inspection/ maintenance task, details including aircraft type and registration, damage type, damage location, sometimes a brief description of the damage itself SDRs containing external skin damage may be used to help determining the frequency and severity of impact damage occurrence in different part of the aircraft The SDRs for Boeing 767 from year 01/2002 to 03/2006 have been compiled as examples shown in the next couple pages 21

22 SDR: External Damage Map 22

23 SDR: External Damage Map 23

24 SDR Summary Aluminum-Honeycomb sandwich delamination is a reoccurring problem slats, flaps and stabilizers on 767s shows large number of delamination occurrences Nearly all dents, holes and gouges are on the lower fuselage and are caused by ground activities, e.g. trucks and operation staff Majority of the damages on the upper fuselage are caused by lightning strikes Large number of cracks and fatigue damages occurred near the horizontal stabilizer cutout region Although the wings have very large areas, relatively few major damages are recorded 24

25 SDR Data Source Limitations Scarce description of the source of damage, thus hard to evaluate the effect of the same impact event to a composite structure, i.e. what kind of damage will result in cracks, delamination or even no damage at all? Composite vs. metal a drunk catering truck driver causing a dent in the metal fuselage, may now causes a crack (or other forms of damage) Since reports are generated during line and base maintenances, the time of event is mostly lost, thus it is hard to know if damage occurred in-flight or on ground, and under what kind of loads No information about repair quality, which could greatly affects the residual strength and modulus of the composite structures 25

26 PDF of Detected Damages LogNormal Probability Density Fuctions for Baseline Fleet Damage Data, Ref. AR-95/17 Detected Damage Density po(a) p o ( a ) Holes Delams Cracks 1 1 = ln 2 exp ( a / θ 2 ) aσ 2π 2σ Damage Size a (in) 26

27 Probability of Detection Log-Odds Detection Probability Functions 1.2 Detection Probability P D (a) Holes Delams Cracks Damage Size a (in) 27

28 Sample Problem 1: Input Data Load Exceedance Data Exceedances per life 1.0E E E E E E E x H t ( x) = H0 exp( ); b H = 4.268e 9; b = E-04 Load Damage Size Exceedance Data D Et ( D) = E0 exp( ); B E = 0.4; B= Exceedances per life 1.0E E E E E E E E-02 Damage Size, in 28

29 Sample Problem 1: Input Data Damage Detection Characterization Damage detection probability Damage Size, in 6.50 α D PD ( D) = 1 exp ; β β= 2.0; α= 1.4 Residial Strength Characterization D Y( D) = A+ (1 A)exp( ); G A= 0.55; G = 2.0 Residial Strength Damage Size, in 29

30 Sample Problem 1: Output on POF Damage Rate = 0.1, Mean =-10.53, StD= Damage Rate = 10, Mean =-5.32, StD= Cumulative Frequency LOG10(POF) Cum Freq Normal Cumulative Frequency LOG10(POF) Cum Freq Normal Histogram Histogram Frequency Log10(POF) % % 80.00% 60.00% 40.00% 20.00%.00% Frequency C umulative % Frequency Log10(POF) % % 80.00% 60.00% 40.00% 20.00%.00% Frequency Cumulative % 30

31 Probabilistic Sensitivities: Classical S-R model Sensitivity Coefficients: POF = P( s > r) = 1 P( s < r) P f ( ) ( ) 1 ( ) ( ) 0 f s xf r xdx = = 0 f r xf s xdx Cμ = ( Pf / μ) ( σ / P) Cσ = ( Pf / σ) ( σ / P) Probability of Failure: Classical S-R model: Stress: Normal; Resistance: Weibull μ = 1; σ = 0.08; μ = 1.5; σ = 0.12; s s R R C = 1.134; C = 1.206; C = 1.628; C = μs σs μr σr Stress: Extreme Value I; Resistance: Weibull μ = 1; σ = 0.08; μ = 1.5; σ = 0.12; s s R R C = 1.025; C = 1.617; C = 1.509; C = μs σs μr σr 31

32 Sample Problem 1: Probabilistic Sensitivities Sensitivity coefficients for load i i C ( P / μ ( σ / P) / μ) μ j= 1 i= 1 i i C ( P / σ ( σ / P) / σ) σ j= 1 i= 1 ( td t ) i i 1 Life N N j j j 1 ( td t ) = f ) ( FL ; N Life N N j j j 1 ( td t ) = f ) ( F N Life L j j ( td t ) i i 1 Life j j Probabilistic Sensitivities (Standard Regression Coefficients) Sample Problem: Sensitivity coefficients (disturbance method) Probability of Detection Damage Size Damage Rate Initial Strength SRCs 32

33 Sample Problem 1: Comparison With NESSUS NESSUS Model feature: Exactly one damage per life Random variables: 1. Load Lmax, LmaxD, LmaxR for undamaged, damaged and repaired item; Gumbel distribution 2. Initial Strength Rini; Normal distribution 3. Damage size D; Exponential distribution; 4. Random inspection Interval Cv=10% Comparison with NESSUS FORM 7.00E-04 Satisfactory comparison with NESSUS POF 6.00E E E E-04 FORM ProDeCompos 2.00E E E Inspection Interval, Flights 33

34 Sample Problem 1: Parametric Study Inspection Interval determined corresponds to Probability of Failure = 1e-4 per life Effect of Average Detected Damage Inspection interval, Flights Beta parameter, in Variable Strength Recovery Percent Inspection Interval. Flights D P D ( D) = 1 exp ; β α = 1.4; β = Variable Effect of Strength Repair Quality α % 70% 80% 90% 100% 110% % of Strength Restoration after Repair 34

35 Sample Problem 2: Lear Fan 2100 Composite Wing Panels Structural Component: Lear Fan 2100 composite wing panels Source of Data: Report DOT/FAA/AR-01/55, Washington DC, January 2002 Output: Inspection schedule over the life-cycle of a structure for maximum safety Features: Two Damage Types: Delamination and Hole/Crack Two Inspection Types: Post Flight and Regular Maintenance Two Repair Types (Field and Depot) Relatively Low Damage Sensitivity Temperature Effects Included Relatively Low Output Reliability 35

36 Sample Problem 3: TU-204 Composite Aileron Structural Component: TU-204 commercial aircraft composite aileron Source of Data: Report DOT/FAA/AR-01/55, Washington DC, January 2002 Output: Inspection schedule over the life-cycle of a structure for maximum safety and optimum cost Features: Comparison of Integration and Full Monte-Carlo Two Damage Types: Delamination and Hole/Crack Two Inspection Types: Post Flight and Regular Maintenance Two Repair Types (Field and Depot) Relatively Low Damage Sensitivity Temperature Effects Included Relatively Low Output Reliability POF 1.00E E E E E Interval for 1st Inspection, Flights Integration Full M-C 36

37 A Look Forward Benefit to Aviation The present method allows engineers to design damage tolerant composite structures for a predetermined level of reliability, as required by FAR 25. The present study makes it possible to determine the relationship among the reliability level, inspection interval, inspection method, and repair quality to minimize the maintenance cost and risk of structural failure. Future needs A standardized methodology for establishing an optimal inspection schedule for aircraft manufacturers and operators. Enhanced damage data reporting requirements regulated by the FAA. 37