development of reliability-based damage tolerant ... · development of reliability-based damage...

The Joint Advanced Materials and Structures Center of Excellence

Development of ReliabilityDevelopment of Reliability--Based Damage Based Damage Tolerant Structural Design MethodologyTolerant Structural Design Methodology

Presented by Dr. Kuen Y. LinPresented by Dr. Kuen Y. LinDepartment of Aeronautics and AstronauticsDepartment of Aeronautics and Astronautics

University of WashingtonUniversity of Washington

2The Joint Advanced Materials and Structures Center of Excellence

Research Team

Principal Investigator:Dr. Kuen Y. Lin, Aeronautics and AstronauticsResearch Scientist: Dr. Andrey StyuartResearch Assistants: Cary Huang, John Moore

FAA Technical Monitor: Peter Shyprykevich

Other FAA Personnel: Dr. Larry Ilcewicz, Curtis Davies

Industry Participants: Dr. Cliff Chen (Boeing Phantom Works), Dr. Hamid Razi, Dr. Alan Miller (Boeing 787)


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. Presently there is no industry-wide standard to establish appropriate inspection intervals for a damage-tolerant structure based on the consideration of structural reliability, inspection methods, and quality of repair. An urgent need exists to develop a standardized methodology for establishing anoptimal inspection schedule that provides minimum maintenance cost and maximum structural reliability.

Objective: Develop a probabilistic method to estimate structural component reliabilities suitable for aircraft design, inspection, and regulatory compliance.


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 damages 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 Model.


Phase I Research Tasks

Develop a Probabilistic Method to Determine Inspection Intervals for Composite Aircraft Structures

Develop Computing Tools and Algorithms for the Probabilistic Analysis

Establish In-service Damage Database from FAA SDR and Other Sources

Demonstrate the Developed Method on an Existing Structural Component


Typical In-service Damage– Hail Damage


Typical In-service Damage- Lightning Strike

• Engine Cowl


PDF of Detected Damages

LogNormal Probability Density Fuctions for Baseline Fleet Damage Data, Ref. AR-95/17

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

Damage Size a (in)

Det

ecte

d D

amag

e D

ensi

ty p

o(a

) HolesDelamsCracks

⎥⎦⎤

⎢⎣⎡−= )/(ln

21exp

21)( 2

2 θσπσ

aa

ap o


Typical Damage Mapsfor a Wing


Damage Mapping

Wing Tip

FlapAileron

Leading Edge

Main Wing Body


PDF of Detected Damages


Visual Inspection PODfor Shiny Surface at 20 ft Distance

Damage Diameter (inches)

Pro

babi

lity

of D

etec

tion


Identification of Critical Parameters

Various Failure ModesVarious Failure Modes

Strength vs. TemperatureStrength vs. Temperature

Moisture Content vs. TimeMoisture Content vs. Time

Maximum Load vs. Time of Damage Existence

Maximum Load vs. Time of Damage Existence

Damage Size & Damage Type Spectra

Damage Size & Damage Type Spectra

Structural Temperature Spectra

Structural Temperature Spectra

Probability of Detection vs. Damage Size & Damage TypeProbability of Detection vs.

Damage Size & Damage Type

Lifetime

W,%

Damage Size

Failure Load

Maximum Load

Damage Size

T°

R

2L

R

Strength Degradation due to Environmental Exposure

Strength Degradation due to Environmental Exposure

Life time

R

Inspection Intervals, Repair Criteria, Structural Risk

Inspection Intervals, Repair Criteria, Structural Risk

Probability of FailureProbability of Failure

Residual Strength vs. Damage Size & Damage Type

Residual Strength vs. Damage Size & Damage Type

Temperature


The Probabilistic Model

Res

idua

l Str

engt

h

Time

12

3

45

67

8

ith interval of constant strength:Width (time) ti[T1,T2…,D],Damage type TDi,Residual strength Si(D,TDi),

Probabilistic Input Parameters:

• Type of damage TD

• Number of damages per life ND

• Initial failure load (initial strength) S

• Damage size D

• Time of damage initiation

• Time to detect Damage t=t(D,T1 ,T2…)

• External load Lmax(t)

• Structural Temperature T°

Probabilistic Input Parameters:

• Type of damage TD

• Number of damages per life ND

• Initial failure load (initial strength) S

• Damage size D

• Time of damage initiation

• Time to detect Damage t=t(D,T1 ,T2…)

• External load Lmax(t)

• Structural Temperature T°

First, we simulate random time histories of residual strength as a sequence of intervals between damage initiation and detection/repair. The probability of failure (POF) can then be evaluated from the POF for all intervals.

First, we simulate random time histories of residual strength as a sequence of intervals between damage initiation and detection/repair. The probability of failure (POF) can then be evaluated from the POF for all intervals.


The Integration Model

∏∏==

−−=−=N

iiit

N

iiiLfixed tSHtSFPOF

11max ])(exp[1),(1

°=

°°= ∫Ω

dTdTDdTDdtdtdSdSdNvd

vdTTDTDttSSNfTTDTDttSSNPOFTTPOF

I

IIfixed

.........

),...,,...,,...,,,(),...,,...,,...,,,(,...),(

212121

21212121212121

r

r

The Integration Technique:

• Monte-Carlo Integration + Importance Sampling + Latin Hypercube

The Integration Technique:

• Monte-Carlo Integration + Importance Sampling + Latin Hypercube

Res

i dua

l Str

engt

h

Time

12

3

45

67

8


Simulation Algorithm

Sample 1 Strength

Load

Load

Snew

L1max tex

Sdamaged

L2max

Srep

Time

L3max

Damage type 1

T° Temperature

Time

Sample 2 Strength

ti


The Integration andFull Monte-Carlo Models

Integration -> Features Covered:

Random External Load ___Random Damage Sizes & NumberRandom Failure Load ____Random Damage Detection Time vs. Damage Size ___Random Temperature & Properties Degradation ___

Multiple Load Cases _____Multiple Damage Types __Multiple Inspection Types __

Various Repair Types & Repair Logic Multiple Damage Interaction _____

?

Full M-C -> Features Covered:

Random External Load ___Random Damage Sizes & NumberRandom Failure Load ____Random Damage Detection Time vs. Damage Size ___Random Temperature & Properties Degradation ___

Multiple Load Cases _____Multiple Damage Types __Multiple Inspection Types __

Various Repair Types & Repair Logic Multiple Damage Interaction _____? ?

Integration -> Advantages:High SpeedHigh Accuracy

Full M-C -> Advantages:Consistent Temperature Presentation Detailed Failure Data Output


Algorithm Implementation

Cv Strength PF Load Exceedance Matrix1.00E-01 WBL

N Design Load Cases2

N Rows in Exceedance Data9

Load Freq Load Freq0.00 153901.00 0.00 4.50E+023.70 153900.00 2.00 4.50E+025.50 35340.00 3.50 4.35E+027.00 15675.00 5.00 3.90E+028.50 4845.00 6.50 3.00E+01

10.20 1197.00 7.00 1.50E+0112.00 162.45 8.50 7.50E+0013.70 57.00 0.00 0.00E+0015.40 11.40 0.00 0.00E+00

Load Exceedance

1.00

10.00

100.00

1000.00

10000.00

100000.00

1000000.00

0.00 5.00 10.00 15.00 20.00

Load

Load

Exc

eeda

nce

Series1

1.00

10.00

100.00

1000.00

0.00 2.00 4.00 6.00 8.00 10.00

Series1

Directory to Run Simulation

Full M-C P.O.F. = 3.1794095E-04Integration P.O.F. = 1.0158544E-04

Interval Integration Full M-C1 7.82E-07 8.62E-07

10 7.58E-06 7.97E-0650 4.04E-05 3.80E-05

100 7.27E-05 7.63E-05200 1.50E-04 1.48E-04500 3.20E-04 3.18E-04

1000 5.74E-04 5.70E-04

Run Simulation

Check Data Consistency

C:\projects\ProDam Find Directory with Monte-Carlo.exe and IProDam.exe

Generic Demonstration Example

Run IntegrationPOF vs. Interval Comparison

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+001 10 100 1000

Inspection interval, Flights

POF Intergal

Full M-CMake7Points

N Damage Types Expected Max damages Defect & Damage Size Data1 20 Expected in 6.4889E+18 lives

N Rows in Defect Matrix N Rows in Damage Matrix3 4

Characteristic Size Exceedances per life0.0 1.0E-031.0 1.0E-042.0 1.0E-050.0 1.0E+00 E0 = 1.00001.0 5.1E-01 B = 1.50002.0 2.6E-013.0 1.4E-014.0 6.9E-02

Delaminations

1.0E-02

1.0E-01

1.0E+000.0 1.0 2.0 3.0 4.0 5.0

Damage Size, in

Exce

edan

ces

per l

ife

Here the damage size exceedance curve follows the function:

Ed(D)=E0 exp(-D/B),

where E0 = 1; B = 1.5

This column represents nodal values of defect/damage size in ascending order.

This column represents a number of defects/damages exceeding one given in the left column per life.

MS Excel (Data) +

Excel Macro (VBA) +

Automation DLL (C++)+

EXE Module (Fortran 95) = P.O.F.

MS Excel (Data) +

Excel Macro (VBA) +

Automation DLL (C++)+

EXE Module (Fortran 95) = P.O.F.


Sample Problem 1: Input Data

1127.0;9268.4

);exp()(

0

0

==

−=

beHbxHxHt

0

0

( ) exp( );

0.4; 1.5

tDE D EB

E B

= −

= =

Damage Size Exceedance Data

4.0E-01

2.1E-01

1.1E-01

5.4E-02

2.8E-02

1.0E-02

1.0E-01

1.0E+000.0 1.0 2.0 3.0 4.0 5.0

Damage Size, in

Exce

edan

ces

per l

ife

Load Exceedance Data

1.0E-04

1.0E-02

1.0E+00

1.0E+02

1.0E+04

1.0E+06

1.0E+08

1.0E+10

0.0 1.0 2.0 3.0 4.0

Load

Exce

edan

ces

per l

ife


Sample Problem 1: Input Data

Damage Detection Characterization

0.00000.20000.40000.60000.80001.00001.2000

0.0 2.0 4.0 6.0 8.0 10.0

Damage Size, in

Dam

age

dete

ctio

n pr

obab

ility

( ) 1 exp ;

2.0; 1.4

DDP D

α

ββ α

⎛ ⎞= − −⎜ ⎟

⎝ ⎠= =

0.2;55.0

);exp()1()(

==

−−+=

GAGDAADY

Residial Strength Characterization

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Damage Size, in

Res

idia

l Str

engt

h


Results of Parametric Study

Variable

DDPD

==

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

βαβ

α

;4.1

;exp1)(

Inspection Interval determined corresponds to Probability of Failure = 1e-4 per life

PercentRecovery Strength Variable

Effect of Average Detected Damage

50.0000

150.0000250.0000

350.0000

450.0000

550.0000650.0000

750.0000

850.0000

0.0 2.0 4.0 6.0 8.0 10.0

Beta parameter, in

Insp

ectio

n in

terv

al, F

light

s

Effect of Strength Repair Quality

259

553

695746 748 748

0100200300400500600700800

60% 70% 80% 90% 100% 110%

% of Strength Restoration after Repair

Insp

ectio

n In

terv

al. F

light

s


Further Results of Parametric Study

VariableAinGGDAADY

==

⎟⎠⎞

⎜⎝⎛−−+=

;0.2

;exp)1()(

( ) (1 )exp ;

0.55;

DY D A AG

A G Variable

⎛ ⎞= + − −⎜ ⎟⎝ ⎠

= =

Effect of Residual Strength Asymptote

1.0000

10.0000

100.0000

1000.0000

10000.0000

48% 50% 52% 54% 56% 58% 60% 62%

Residual Strength Asymptote, % of Initial

Insp

ectio

n in

terv

al,

Flig

hts

Effect of Res. Strength Slope

0.0

500.0

1000.0

1500.0

2000.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Characteristic exponent, in

Insp

ectio

n In

terv

al. F

light

s





VariableBEBDEDE

==

⎟⎠⎞

⎜⎝⎛−=

;0.1

;exp)(

0

0

VariableEBBDEDE

==

⎟⎠⎞

⎜⎝⎛−=

0

0

;5.1

;exp)(

Effect of Damage Exceedance Intercept

1

10

100

1000

10000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Damage Exceedance Intercept

Insp

ectio

n In

terv

al.

Flig

hts

Effect of Damage Exceedance Slope

2561

737

342189 950

500

1000

1500

2000

2500

3000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Characteristic exponent, in

insp

ectio

n In

terv

al. F

light

s



Various Extensions of Load Exceedance Curve

1.000E-201.000E-161.000E-121.000E-081.000E-041.000E+001.000E+041.000E+081.000E+12

0.00 1.00 2.00 3.00 4.00

Load Factor

Exce

edan

ces

per k

ifw

1

2

3 Effect of Various Extensions of Load Exceedance Curve

771

1365

1765

0200400600800

100012001400160018002000

1 2 3

Insp

ectio

n In

terv

al. F

light

s

Variable Exceedance Curve

Extension



Sample Problem 2Lear Fan 2100 Composite Wing Panels

Structural Component: Lear Fan 2100 composite wing panelsSource of Data: Report DOT/FAA/AR-01/55, Washington DC, January 2002Output: Inspection schedule over the life-cycle of a structure for maximum safety

Features:

Two Damage Types: Delamination and Hole/CrackTwo Inspection Types: Post Flight and Regular MaintenanceTwo Repair Types (Field and Depot)

Relatively Low Damage Sensitivity

Temperature Effects Included

Relatively Low Output Reliability


Sample Problem 3TU-204 Composite Aileron

Structural Component: TU-204 commercial aircraft composite aileronSource of Data: Report DOT/FAA/AR-01/55, Washington DC, January 2002Output: Inspection schedule over the life-cycle of a structure for maximum safety and optimum cost

Features:

Two Damage Types: Delamination and Hole/CrackTwo Inspection Types: Post Flight and Regular MaintenanceTwo Repair Types (Field and Depot)

Relatively Low Damage Sensitivity

Temperature Effects Included

Relatively Low Output Reliability

Comparison of Integration and Full Monte-Carlo

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-011 10 100 1000

Interval for 1st Inspection, Flights

PO

F IntegrationFull M-C


Work Accomplished

Two methods, the Integration and Full Monte-Carlo Simulation, have been developed for determining the inspection intervals

Computer software (Version 1.0) for calculating the inspection intervals has been completed

Database for Reliability-Based Damage Tolerance Analysis has been established

Three sample problems have been demonstrated on existing structural components

Two parametric studies for Inspection Intervals have been completed


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.

development of reliability-based damage tolerant ... · development of reliability-based damage...

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