development of reliability-based damage tolerant structural...

The Joint Advanced Materials and Structures Center of Excellence

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

Progress ReportProgress Report

Dr. Kuen Y. Lin and Dr. Andrey Styuart Dr. Kuen Y. Lin and Dr. Andrey Styuart Department of Aeronautics and AstronauticsDepartment of Aeronautics and Astronautics

University of WashingtonUniversity of WashingtonOctober 13, 2005October 13, 2005

2The Joint Advanced Materials and Structures Center of Excellence

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.


Research Team

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

FAA Technical Monitor: Peter Shyprykevich

Other FAA Personnel: Dr. Larry Ilcewicz, Curtis Davies

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


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.


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


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)( 22 θσπσ

aa

ap o


PDF of Detected Damages


Visual Inspection PODfor Shiny Surface at 20 ft Distance

Pro

babi

lity

of D

etec

tion

Damage Diameter (inches)


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


Work Accomplished

Two methods, based on Importance Sampling and Monte-Carlo Simulation, have been developed for determining the inspection intervals.

Computer software (Version 1.2) for calculating the inspection intervals has been completed.

Database for Reliability-Based Damage Tolerance Analysis has been established.

Three sample problems with parametric studies have been demonstrated on existing structural components.

Results from the present study have been compared with those obtained by other methods and software (NESSUS).

Effect of environmental aging and chemical corrosion added


Reliability Formulation 1

Load Exceedance Curve

1.00E-051.00E-04

1.00E-031.00E-021.00E-011.00E+00

1.00E+011.00E+021.00E+031.00E+04

1.00E+051.00E+06

0 0.5 1 1.5 2

Load

Num

ber o

f Exc

eeda

nces

per

Life

Load Exceedance Curve

1.00E-051.00E-04

1.00E-031.00E-021.00E-011.00E+00

1.00E+011.00E+021.00E+031.00E+04

1.00E+051.00E+06

0 0.5 1 1.5 2

Load

Num

ber o

f Exc

eeda

nces

per

Life

3

1

1 [1 ( , )]N

f f i ii

P P R t=

=

= − −∏Interval # Probability of Failure

1 (new structure) 6.12E-06

2 (damaged structure) 4.26E-02

3 (repaired structure) 6.12E-06

Total POF = 4.26E-02



1 5 8

ith interval of constant damage size: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

• 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

Probabilistic Input Parameters:

• Type of damage TD

• 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

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 as the sum of 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 as the sum of POF for all intervals.



Combined Damage+Aging

0

0.2

0.40.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

T ime

Res.S

treng

thDelamination

Hole

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ti me

Dam

age

Size

Delaminat ion

Hole

Res. Strength degradation due to aging

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.2 0.4 0.6 0.8 1 1.2

Ti me

Res

.Str

engt

h

Delaminat ion

Hole

Res. Strength degradation vs. Damage Size

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Damage Size

Res

.Str

engt

h

Delamination

Hole


The Integration Model

Res

idua

l Str

engt

h

Time

12

3

45

67

8

∏∏==

−−=−=N

iiit

N

iiiLfixed tSHtSFPOF

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

°=

°°= ∫Ω

dTdTDdTDdtdtdSdSdNvd

vdTTDTDttSSNfTTDTDttSSNPOFTTPOF

I

IIfixed

.........

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

212121

21212121212121

ρ

ρ

The Integration Technique:

• Monte-Carlo Integration + Importance Sampling

The Integration Technique:

• Monte-Carlo Integration + Importance Sampling


Simulation Algorithm

Life 1 Strength

Load

Load

Snew

L1max tex

Sdamaged

L2max

Srep

Time

L3max

Damage type 1

Life 2 Strength

ti

TemperatureT°

Time


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 Properties Degradation due to Temperature ___Multiple Load Cases _____Multiple Damage Types __Multiple Inspection Types __Various Repair Types & Repair Logic Multiple Damage Interaction _____ Effects of environmental aging

?

Full M-C -> Features Covered:

Random External Load ___Random Damage Sizes & NumberRandom Failure Load ____Random Damage Detection Time vs. Damage Size ___Random Properties Degradation due to Temperature ___Multiple Load Cases _____Multiple Damage Types __Multiple Inspection Types __Various Repair Types & Repair Logic Multiple Damage Interaction _____Effects of environmental aging

? ??

Integration -> Advantages:High SpeedHigh Accuracy

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


Algorithm Implementation

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

MS Excel (Data) +

Excel Macro (VBA) +

Automation DLL (Fortran 95)

MS Excel (Data) +

Excel Macro (VBA) +

Automation DLL (Fortran 95)


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


Sample Problem 1:Comparison With NESSUS

NESSUS Model feature: Exactly one damage per lifeRandom variables:1. Load Lmax, LmaxD, LmaxR for undamaged, damaged and repaired item; Gumbel

distribution2. Initial Strength Rini; Normal distribution3. Damage size D; Exponential distribution; 4. Random inspection Interval Cv=10%

Comparison with NESSUS FORM

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

0 500 1000 1500 2000 2500

Inspection Interval, Flights

POF FORM

ProDeCompos

Satisfactory comparison with NESSUS


Sample Problem 1:Sensitivity Study from NESSUS


Sample Problem 1: Probabilistic Sensitivity Factors from

NESSUS


Summary

What we have:

The preliminary method for determining POF and the inspection intervals for no growth concept.

Basic computer software for calculating POF and and the inspection intervals.

Some restricted database for Reliability-Based Damage Tolerance Analyses.

What we will have:

The established method for determining POF and the inspection intervals including material degradation.

User friendly computer software for commercial use in probabilistic design.

Acceptable database for Reliability-Based Damage Tolerance Analyses.


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.


Phase 2: Analysis Refinement and Methodology Implementation

(September 1, 2005 – August 31, 2007)

The primary objective of Phase 2 is to apply the developed methodology to the maintenance of current fleet and design of future aircraft.

Major tasks to be accomplished in Phase 2:

Analysis Method Enhancement

Analysis Method Implementation


Task 2.1:Analysis Method Enhancement

The analysis method developed in Phase I will be enhanced to include:

1. Effects of environmental aging and chemical corrosion. The mathematical model of aging will be represented by an Arrenius type equation to include the empirical UV and fuel degradation. The aging effects will be incorporated into computer software and algorithm that help designers to compare various aging environments and impact of aging/corrosion on the structural reliability.



2. Development of optimum inspection schedule to minimize maintenance cost and risk. Typical algorithms for minimum LCC design will bestudied and incorporated into the software. The developed computer program will take into account the factors such as inspection cost and associated repair and downtime costs, cost of consequence of failure and possibly acquisition and operating costs.



3.3. Development of database and tools to automate the entire evaluatDevelopment of database and tools to automate the entire evaluation process. ion process. Such tools may be used as production tools for maintenance plannSuch tools may be used as production tools for maintenance planning.ing.

Database on impact damage condition: The goal is to establish a set of standard design damage types along with their frequencies. Each of them has distinct characteristics such as geometry, energy (or any invariant metric), and density. The specific work items for this task may include:

(1) Data mining and grouping, (2) Reverse engineering to estimate impact energy with known or best assumed

geometry and density, (3) Establishment of frequencies or exceedances.

These tasks need to be performed for each primary structural locations. Engineering judgment and assumptions will play a big role here; nevertheless, it should be acceptable as long as we take every measure conservatively. To do reverse engineering, we may try to simplify the process by making some parametric analyses for both metal and composite structures based on a conservative representative configuration for each structural area (e.g., fuselage skin-stringer panels). As such, for a given damage record, we may do interpolation to get an energy estimate based on the descriptions of the reported damage.



3.3. Development of database and tools to automate the entire evaluatDevelopment of database and tools to automate the entire evaluation process. ion process. Such tools may be used as production tools for maintenance plannSuch tools may be used as production tools for maintenance planning.ing.

Tools: In order to conveniently apply the developed reliability method to industry, we need to develop "self-explanatory" software with built-in initial data sets, "transparent" simplified solutions, expert help system and clear sample results. Ideally, the tool should be applicable not only to maintenance but also to design as well.

With full characterization of damage, loads, environments, materials and costs available, the developed code can be used as a single design tool for a unified design (i.e., combining static strength, damage tolerance, inspections and fail-safety). The developed reliability code can be integrated into standard structural analysis and design optimization programs.


Task 2.2:Methodology Implementation and

Regulatory Compliance

This task will focus on the application of the developed methodology. Key to the implementation of the reliability methods is the development of an accidental damage rating system (ADR) that is compatible with the methodology and complies with MSG-3 guidelines.

The developed reliability method may help the industry in two ways:Finding rational inspection intervals. Establishing more reasonable design requirements compared to the present requirements derived from AC-107 and so on. In fact, AC-107 regulates the residual strength curve depending on the probability of damage detection only. It seems that Boeing’s approach is also based on the assumption that composite design is primarily driven by damage detectability. There is no connection with real impact conditions. Using results of this research, we can demonstrate to the FAA that in some cases the AC-107 requirements are too conservative, but in other cases they may be inadequate.


Phase 2 Milestones (September 1, 2005 – August 31, 2007)

9/1/05-11/30/0512/1/05-2/28/06 3/1/06-5/31/06 6/1/06-8/31/06

Task 2.1

Subtask 1 Subtask 2

Subtask 3

Task 2.2

Development of Reliability-Based Damage Tolerant Structural Design Methodology:Progress ReportDevelopment of Reliability-Based Damage Tolerant Structural Design MethodologyResearch TeamApproachPhase I Research TasksTypical In-service Damage– Hail DamagePDF of Detected DamagesPDF of Detected DamagesVisual Inspection PODfor Shiny Surface at 20 ft DistanceIdentification of Critical ParametersWork AccomplishedReliability Formulation 1Reliability Formulation 2Reliability Formulation 3The Integration ModelSimulation AlgorithmThe Integration andFull Monte-Carlo ModelsAlgorithm ImplementationResults of Parametric StudySample Problem 1:Comparison With NESSUSSample Problem 1:Sensitivity Study from NESSUSSample Problem 1: Probabilistic Sensitivity Factors from NESSUSSummaryA Look ForwardPhase 2: Analysis Refinement and Methodology ImplementationTask 2.1:Analysis Method EnhancementTask 2.1:Analysis Method EnhancementTask 2.1:Analysis Method EnhancementTask 2.1:Analysis Method EnhancementTask 2.2: Methodology Implementation and Regulatory CompliancePhase 2 Milestones (September 1, 2005 – August 31, 2007)

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