Upload
tranhanh
View
270
Download
7
Embed Size (px)
Citation preview
NASGRO®
Fatigue Crack Growth Analysis SoftwarePresented at
UTMIS Spring MeetingFinspang, Sweden
May 31, 2006
Joseph W. CardinalSouthwest Research Institute®
San Antonio, [email protected]
(210) 522-3323
Outline of NASGRO Presentations
8:30 – 9:00 Introduction» SwRI Overview» NASGRO History & Background
9:00 – 9:30 NASGRO Overview9:30 – 10:00 Modeling Fatigue Crack Growth with NASGRO10:00 – 10:30 Key NASGRO Features
» K Solutions» Spectrum Input» Results
2:45 – 3:15 NASGRO Demonstration Examples3:15 – 4:15 NASMAT Materials Database4:15 – 4:45 DARWIN Overview & FEM Interface Demonstration
SOUTHWEST RESEARCH SOUTHWEST RESEARCH INSTITUTEINSTITUTE
SwRI in
1947
SwRI in
2006
3000 employees; 1200 acres
2 million sq ft of facilities
MISSION STATEMENT
Develop Technology
Package Technology
Transfer Technology
Independent
Nonprofit
Stable and Conservative
Broad Technological & Scientific Breadth
Project Management Approach
ORGANIZATIONAL CHARACTERISTICS
Revenue Provided By R & D Contracts
Internal Research Encouraged
Confidentiality Emphasized
Unique Patent Rights Policy
A Good Teaming Partner
OPERATIONAL CHARACTERISTICS
20052005
505000 100100 150150 200200 250250 300300 350350Millions ($)Millions ($)
$435M
450450400400
19601960 $5M
19701970 $18M
19801980 $82M
19901990 $199M
20002000 $315M
2005 figure asof Sept. 30, 2005
GROSS REVENUES
Southwest ResearchInstitute
Industry
Industrial ResearchLabs
Federal Agencies
Federal Labs
Universities
R & DInstitution
Technology Spectrum
ResearchBasic Applied
Development Production
R & D INSTITUTIONSIN THE TECHNOLOGY SPECTRUM
SwRI® ORGANIZATION
CommunicationsContracts
Accounting
Business DevelopmentLegal
Quality Assurance
Chemistry &Chemical Engineering
(Div 1)
Fuels and Lubricants Research(Div 8)
Training, Simulation, &Performance Improvement
(Div 7)
Engine, Emissions and VehicleResearch (Div 3)
Aerospace Electronics &Information Technology
(Div 9)
Automation &Data Systems
(Div 10)
Applied Physics(Div 14)
Space Science andEngineering
(Div 15)
Signal Exploitation& Geolocation
(Div 16)
Mechanical &Materials Engineering
(Div 18)
Center for NuclearWaste Regulatory Analyses
(CNWRA)(Div 20)
PresidentExecutive Vice-President
Chief Financial Officer and Vice-President of Finance
Board of Directors
9
Mechanical & Materials EngineeringOur mission is to improve the safety, reliability, efficiency and life of new or existing mechanical components, structures and systemsfor the economic benefit of our clients.
Mechanical & Fluids Engineering
Materials Engineering
Engineering Dynamics
Structural Engineering
10
Structural EngineeringStructural systems design and analysis Component to full-scale static and fatigue testingStructural life management including inspections, repair/replace decisions, modernization, and life extensionStructural evaluation – prototype, qualification and forensic analysis
Fatigue & fatigue crack growth analyses (DTA)Smart or adaptive structures advanced concept development and testingEvaluation of structures in high-temperature, high-pressure marine environments
Structural usage monitoring and loads predictionsStructural integrity assessment Composite repair for metallic and composite aircraft structurePrototype marine systems design/development
Structural Integrity Testing
Subsea System Optimization
11
Materials EngineeringFailure analysis and preventionSpecialized mechanical and micromechanics testingMaterial property optimization
Fatigue and fracture mechanics analysisStructural life prediction and managementCorrosion science and engineeringBiomechanics and bone micromechanics
Biocompatible materials developmentApplied polymers developmentFuel cell design and testingIon beam surface engineering and coating technology development
MaterialsCharacterization
Materials Testing
Reliability and Materials Integrity
Gas & steam turbine materials and coatings life assessmentPressure vessel and pipeline integrity prediction and evaluationReliability methodology and software development
Life, damage, integrity and material failure monitoring and modelingLong-term materials compatibilityHigh temperature, high pressure, hazardous environment exposure testingElectrochemistry
Corrosion and Environmental Degradation
MaterialsDevelopment
12
Engineering Dynamics
Computational solid mechanics & wave propagationComputational fluid mechanicsComputational fracture mechanicsChemical mechanical polishing
Impact physics & penetration mechanicsBody armor & vehicle armorHypervelocity impactProjectile package design & evaluation
Foreign object damageExplosion and fragment hazards analysis & evaluationBlast resistant analysis & designWeapons of mass destruction
CeramicAluminum
Computational Mechanics
Survivability & Hazards Mechanics
Penetration & Armor Mechanics
13
Mechanical & Fluids Engineering
Structural dynamics researchAcoustics systems researchEnvironmental testingMechanical systems development
Flow measurement researchGas meter calibrationMultiphase flow assuranceSafety and pollution prevention equipment testing
Space propellant dynamics researchFluid machinery pulsation control designPlant and field engineering servicesGas machinery research
Space Flight Experimentation
Field Services
Qualification Testing
14
Extensive Laboratory FacilitiesFluidsStructural
Metering Research Facility
Ballistics Test Facility
Materials Test Facility
Ballistics Materials
DeepWater Simulation Facility
15
www.integrityandreliability.swri.orgwww.integrityandreliability.swri.org
NASGRONASGRO®®
Fatigue Crack Growth Fatigue Crack Growth and Fracture Analysisand Fracture Analysis
DARWINDARWIN®®
Probabilistic Fracture Probabilistic Fracture Analysis of Turbine Analysis of Turbine Engine RotorsEngine Rotors
NESSUSNESSUS®®
Probabilistic Probabilistic Structural AnalysisStructural Analysis
NASGRO®
History and Background
Joe CardinalSouthwest Research Institute®
San Antonio, [email protected]
(210) 522-3323www.nasgro.swri.org
2
NASGRO® Modules
NASGRO is a suite of analysis software having four distinct modules:• Fracture mechanics and fatigue crack growth
analysis (NASFLA)• Material property database for fracture and fatigue
crack growth and fitting of experimental data (NASMAT)
• 2D boundary element stress analysis and stress intensity factor computation (NASBEM)
• Fatigue crack formation (initiation) analysis (NASFORM)
3
NASGRO® Features
• K Solutions• Material Property Database• Crack Growth Algorithms• Spectrum Input• Output Features• Other Special Features
4
NASGRO® History
• NASA/FLAGRO development to provide fracture control analysis for manned space programs (early 1980s)
• NASA Fracture Control Methodology Panel formed to standardize methods and monitor NASA/FLAGRO development (1985)
• NASA Interagency Working Group (NASA, DoD, FAA, ESA, industry) formed to provide guidance for NASA/FLAGRO development (1993)
• NASA/FLAGRO 2.0 released (1994)
• Additional NASA, FAA, USAF support for aging aircraft (1990s)
• Significantly improved NASGRO 3.0 released as “publicly available” from JSC web site via NASA Form 1676 (1999)
5
NASGRO® History
• Southwest Research Institute® (SwRI®) takes a leading role in the ongoing development and support of NASGRO (2000)
• NASA and SwRI sign Space Act Agreement for joint NASGRO development (2000)
• First NASGRO Industrial Consortium formed by SwRI (2001)
• Significantly improved NASGRO 4.0 released by SwRI (2002)
• NASGRO 4.1 released by SwRI (2003)
• NASGRO 4.2 released by SwRI (2004)
• NASGRO 5.0 planned for release in late June 2006
6
NASGRO®
Supporting Community
• NASA (all centers)• NASGRO Industrial Consortium• Federal Aviation Administration• NASGRO Commercial Licensees• European Space Agency• NASA Fracture Control Methodology Panel• NASGRO Interagency Working Group• NASGRO University Partners• Southwest Research Institute®
7
NASGRO® Use at NASA
SSME
Payloads
ISS
NSTS Ground Test Facilities
8
NASGRO® Use in Industry
Large AircraftLarge Aircraft
Small AircraftSmall Aircraft
RotorcraftRotorcraft
Gas Turbine EnginesGas Turbine Engines
PetrochemicalPetrochemical
Railroad Tank CarsRailroad Tank Cars
BridgesBridges
Ship SystemsShip Systems PipelinesPipelines
9
Initial Consortium Members (2001-2004 Cycle)
• Agusta• Airbus France• Airbus Germany• Bell Helicopter Textron• Boeing• EMBRAER• Israel Aircraft
Industries
• Korea Aerospace Industries• Mitsubishi Heavy Industries• Northrop Grumman• Volvo Aero• Siemens Westinghouse• United Technologies Corp:
– Sikorsky– Hamilton Sundstrand
The NASGRO Consortium was renewed fora second three-year period, beginning June 2004.
10
Current Consortium Members (2004-2007 Cycle)
• Airbus• Boeing• Bombardier• Embraer• Honeywell• Israel Aircraft
Industries
• Lockheed Martin• Mitsubishi Heavy Industries• Northrop Grumman• Volvo Aero• Siemens Power Generation• Sikorsky• Hamilton Sundstrand
Bold = multiple sites, Underline = new or expanded member
Renewal of the NASGRO Consortium for a third three-year period is planned, beginning June 2007.
11
Commercial Licenses
NASGRO single seat licenses:
CommercialNASGRO VersionRelease Release Number of LicensesVersion Date US Europe Asia Other Total
4.0 Aug-02 19 4 1 0 244.1 Feb-04 19 6 0 1 264.2 Jan-05 27 4 4 1 36
65 14 5 2 86
12
NASGRO Availability
• Consortium membership– Single site membership: $20,000/year for 3 years– Corporate-wide membership: $50,000/yr for 3 years– Members receive many benefits, including
• Site license for code (unlimited copies)• User support• Automatic distribution of all new versions and upgrades• Direct influence over future development plans
• Individual copies of code– Perpetual license for current version: $3,000 (one user)– Perpetual site license for current version: $20,000– Includes one year of technical support
• Runs on all Windows platforms, some Unix platforms
13
NASGRO® Development and Support Team
SwRI Team
NASA-JSC Team
Royce FormanShiva ShivakumarJoachim BeekLen WilliamsRandy ChristianFeng Yeh
Craig McClungJoe CardinalGraham ChellYi-Der LeeBrian GardnerMichael Enright
14
NASGRO Awards
“One of the 100 Most Technologically Significant New Products of 2003” (R&D Magazine)
NASA Software of the Year Award (2003)
15
NASGRO® Web Site
www.nasgro.swri.org• Code distribution
(password protected)• Demo version 4.0
(public)• Bug reporting• General information• Code licensing• Information for
Consortium members
16
Summary
• NASGRO is a state-of-the-art computer code for fracture mechanics and fatigue crack growth analysis that is used extensively around the world.
• NASGRO continues to be aggressively enhanced, and broad support ensures stability and substantial additional development in the future.
NASGRO® Overview
Joe CardinalSouthwest Research Institute®
San Antonio, [email protected]
(210) 522-3323www.nasgro.swri.org
2
Overview Outline
• NASGRO Scope• How NASGRO Can be Used• NASGRO Features
– K Solutions– Material Property Database– Crack Growth Algorithms– Spectrum Input– Output Features– Other Special Features
• Development Chronology (v4.0, 4.1, 4.2)• v5.0 and Development Plans for v5.1
3
NASGRO Scope
Crack Formation
Small-Crack Growth
Large-Crack Growth
Failure by Fracture
Strain-life and stress-life analysis
Conventional damage tolerance analysis
Scope of NASGRO crack growth analysis
Material, manufacturing, or service damage
4
How NASGRO Can Be Used
• Calculate K for specified load and geometry
• Examine the fatigue crack growth properties of various materials
• Calculate fatigue crack growth properties from test data
• Calculate cycles required to grow a crack from an initial size to a final critical size
• Calculate the critical crack size at failure
5
NASGRO® K Solutions
• NASGRO Library has more than 50 stress intensity factor solutions:– Many developed specifically for
NASGRO– Much more accurate modeling of
component-crack geometry, stress field, and fatigue life
– Other codes typically have 25-35, mostly old NASA/FLAGRO solutions
• Only code with 3D weight function Ksolutions for bivariant stress fields
• Only code with an integrated boundary element module to calculate accurate new K solutions for user-defined 2D geometry and loads
6
NASGRO® K Solutions
• Through cracks (13)• Corner cracks (9)• Surface cracks (17)• Embedded cracks (2)• Tabular data (4)• Standard test specimens (12)• Polynomial series (1)• Boundary element solutions (2)• Compounding available for
some solutions
7
NASGRO® GUI for Selection of K Solutions
8
NASGRO®
Material Property Database
• Massive material property database– 476 different metallic materials– 3000 sets of fatigue crack growth data– 6000 fracture toughness data points– Statistically-derived crack growth
equations for all materials• Other codes have zero to 80
materials, except for some copies of older (smaller, less accurate) FLAGRO databases
• Contains all original test data and reference citations so users can evaluate equation fits, and generate new fits as needed
• NASGRO can fit crack growth equations to user-supplied test data
1e-009
1e-008
1e-007
1e-006
1e-005
0.0001
0.001
0.01
1 10 100
da/d
N [i
n/cy
cle]
Delta K [ksi*sqrt(in)]
M2GC11AB01N1 R = 0.1 thk = 0.5 ref: 1M2GC11AB01N2 R = 0.7 thk = 0.5 ref: 1M2GC11AB01N3 R = 0.4 thk = 0.5 ref: 1Fit for R = 0.1Fit for R = 0.7Fit for R = 0.4
Al 2124-T851Lab AirC(T) specimenL-T orientation
ΔK (ksi√in.)
da/d
N(in
./cyc
le)
9
NASMAT GUI(Material Selection)
10
NASGRO®
Crack Growth Algorithms
• Unique NASGRO crack growth equation:
• Provides a proper physical basis for the effects of mean load level on crack growth rate
• Contains a physically-based crack closure model providing significantly improved accuracy for load interaction effects
• Includes proper corrections for small-crack and stress-ratio effects on crack growth threshold
dadN
CfR
K
KK
KK
nth
p
c
q=−−
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢
⎤
⎦⎥
−⎛⎝⎜
⎞⎠⎟
−⎛⎝⎜
⎞⎠⎟
11
1
1Δ
ΔΔ
max
11
NASGRO Database Contains NASGRO Equation Material Constants
12
C, n, m, p = constants derived from curve fits to empirical data and contained in NASGRO material database
Kc = fracture toughness, also in NASGRO material database
Kmax = ΔK / (1-R)
f = Kop / Kmax= crack opening function (Newman) that accounts for plasticity induced crack closure and models load interaction effects = f(α, R, Smax/σo)
α = plane stress/strain constraint factorSmax/σo = ratio of max applied stress to flow stress
dadN
CfR
K
KK
KK
nth
p
c
q=−−
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢
⎤
⎦⎥
−⎛⎝⎜
⎞⎠⎟
−⎛⎝⎜
⎞⎠⎟
11
1
1Δ
ΔΔ
max
Parameters in the NASGRO crack growth equation:
13
ΔKth = threshold stress intensity factor = f( f, R, ΔK1, ao, Cth)
ΔK1 = threshold stress intensity factor range as R ⇒ 1
ao = small crack parameter or an “intrinsic” crack size
Cth = empirical fit constant with different values for +R and –R
ΔK1, ao, and Cth are contained in the NASGRO material database.
dadN
CfR
K
KK
KK
nth
p
c
q=−−
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢
⎤
⎦⎥
−⎛⎝⎜
⎞⎠⎟
−⎛⎝⎜
⎞⎠⎟
11
1
1Δ
ΔΔ
max
Parameters in the NASGRO crack growth equation:
14
NASGRO®
Crack Growth Algorithms
• Additional crack growth models:• Walker: da/dN = C [ ΔK /(1-R)(1-m) ] n
• Tabular input of da/dN vs ΔK
• Other available interaction models:• Generalized Willenborg• Modified Generalized Willenborg• Walker-Chang Willenborg• Strip Yield Model
• Constant constraint-loss• Variable constraint-loss
• Constant Closure
15
Spectrum Input
A variety of flexible options are available:• Traditional NASGRO steps & blocked format:
• N, S01, S02, S11, S12, S21, S22, S31, S32• N, S01, S02, S11, S12, S21, S22, S31, S32
• Long block file formats:• NASGRO format• Peak-valley• Max, Min, N or Min, Max, N• Multi-block
• Manual (keyboard) input• Cycle Counting (range-pair & rain-flow)• Options for spectrum editing• Spectrum generation from time series data• Cycles, flight hours, flights
16
Output Features
View, Print, Save & PlotResults
Many options!
Spreadsheet Word processor
17
Other Special Features
• Failure criteria:– LEFM fracture instability– Net section yielding
• Stress intensity factor solution (NASSIF) module• Critical crack size (NASCCS) module• Elastic-plastic fracture mechanics (EPFM) module:
– J-integral calculation (EPRI & reference stress methods)– Five models available– Crack growth computed using ΔJeff
– Brittle and ductile (tearing instability) failure criteria
• NASMAT curve fitting module
18
NASMAT Curve Fitting
19
NASGRO 4.0
• NASFLA enhancements– Total redesign of GUI– Extensive new printing/plotting output options– 9 new or improved K solutions– 3 and 4 DOF growth for multiple site damage– Rainflow and range-pair cycle counting algorithms– Improved threshold formulation - stress ratio, load interaction effects– User-supplied values of small crack parameter, a0– Elastic-plastic fatigue crack growth– Batch processing
• NASMAT enhancements– New materials added– New and improved fits for all materials– Improved visualization of original data and curve fits– Improved treatment of threshold data
• NASBEM enhancements– Total redesign of GUI for easier model building– Stress calculations for zones without cracks
20
NASGRO 4.0K Solution Enhancements
• Revised TC03 – crack at offset hole in plate • Revised TC05 – crack at row of holes in plate • New BE02 – two thru cracks from offset hole in plate• New BE03 – thru and part-thru cracks from offset hole in plate• New bivariant K solutions based on 3D weight functions
– SC15 – surface crack in plate (symmetric stresses)– CC05 – corner crack in plate
• New EC02 – off-center embedded crack in plate• Revised CC01 – corner crack in a plate – faster• Revised SC02 – surface crack in a plate – wider a/c ratio
21
NASGRO Version 4.1
• NASFLA Enhancements– Substantial speed improvements for many analyses– 8 new or improved K solutions– Specify spectrum blocks/output in terms of flights or flight
hours– Load spectrum visualization– Many convenience features added
• NASMAT Enhancements– Walker and spline fits added– GUI completely rewritten– Improved curve fits for numerous materials
• NASFORM module added– Stress-life– Strain-life
22
• New weight function solutions– TC13 (through crack at hole)– CC08 (corner crack at hole)– SC17 (surface crack in plate)– Two loading modes
• Arbitrary crack plane stress gradient• Remote tension
• Improved solutions– CC07 (one or two corner cracks at hole, uniform tension or bend)– TC03 (through crack at hole, added in-plane bending)– CC02 (compounding tables added)– SC13 and SC14 (bending added)
NASGRO 4.1K Solution Enhancements
23
NASGRO Version 4.2
• NASFLA Enhancements– 5 New or improved K solutions– “Shakedown” analysis for local yielding (WF K
solutions)– Temperature dependence for crack growth
• Different material properties at different temperatures• Different temperatures at different load steps
– Residual strength diagrams• Based on fracture and net section yield
– Exceedance diagrams and load spectrum statistics– Additional cycle-counting options– Additional batch mode capabilities
24
• New weight function solutions– TC11 (off-center through crack in plate)– TC12 (edge through crack in plate)– EC02 (offset embedded crack in plate)– CC09 (bivariant corner crack in plate)
• Improved solutions– SC08 (bolt preload added)
NASGRO 4.2K Solution Enhancements
25
What’s New in Version 5.0?(currently in beta testing)
• New CC10, corner crack at offset hole in plate, bivariant weight function solution
• New SC18, surface (bore) crack at hole in plate, univariant weight function solution
• New SS12, standard specimen: eccentrically-loaded single edge crack tension ESE(T)
• New piecewise linear and Hermite polynomial interpolations for the 1-D data table crack case, DT01
• Spectrum generation, editing & visualization options
26
Development Plans for v5.1(a partial list)
• New K Solutions and Related Technology– Improved speed for WF solutions – for CC/plate, CC/hole, SC/plate, EC/plate, SC/hole– Improved/new WF solutions for SC/plate, CC/SC/TC/edge notch,
TC/variable thickness plate– Flexible, adaptive point spacing for 1D and 2D stress gradients– Additional crack transitioning capabilities
• Residual Stress Effects– Tabular entry and superposition of static RS fields for WF K– Library of typical RS profiles– Redistribution of tensile RS due to crack extension– Redistribution of RS due to plasticity from applied loads– Bivariant shakedown module
• Improved Documentation
Modeling Fatigue Crack Growthwith NASGRO®
Joe CardinalSouthwest Research Institute®
San Antonio, [email protected]
(210) 522-3323www.nasgro.swri.org
2
Modeling Fatigue Crack Growthwith NASGRO®
• Understanding the NASGRO Equation• NASFLA Material Selection Process • Display of NASGRO Equation Fits• User Defined Tabular Data Input• Additional Options
3
Understanding the NASGRO® FCG Equation
The NASGRO equation was originally formulated in 1994 for implementation into NASA/FLAGRO 2.0 where different elements of the equation were developed by:
R. Forman & J. Newman, Jr at NASAA. deKoning at NLRT. Henriksen at ESAV. Shivakumar at Lockheed Martin
4
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1 10 100
ΔK
da/d
N
ΔKth
Kc
II
III
I
Typical FCG Behavior in Metals
• FCG data are commonly represented on a log-log graph of ΔK vs. da/dN
• Three typical regions:– Region I (near-threshold)
• Very slow growth• No growth below ΔKth
– Region II (steady-state)• ΔK vs. da/dN is linear
– Region III (near instability)
• Rapid, unstable growth
• Fracture at Kmax = Kc
5
Effect of Mean Stress
• FCG rates generally increase with increasing mean stress (increasing R)
0
0.2
0.4
0.6
0.8
1
1.2
Time
Norm
aliz
ed S
tres
s
R = 0.8R = 0.5R = 0.1
max
min
max
min
KKorR
σσ
=
6
Understanding the NASGRO® FCG Equation
• NASGRO 4.0 Equation:
• f = stress ratio correction (based on crack closure theory)
• p, q are empirical constants describing curvature near threshold and instability
dadN
CfR
K
KK
KK
nth
p
c
q=−−
⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢
⎤
⎦⎥
−⎛⎝⎜
⎞⎠⎟
−⎛⎝⎜
⎞⎠⎟
11
1
1Δ
ΔΔ
max
Near-threshold factor
Stress ratio factor
Near-instability factor
7
Understanding the NASGRO® FCG Equation
log da/dN
log ΔK
da/dN = C ΔKeffn G / H
da/dN = C ΔKeffn
H = [1 – Kmax/Kc]q
G = [1 – ΔKth/ΔK]p
8
NASGRO Threshold Equations
• NASGRO determines the threshold as a function of R and crack size:p
th
pth
CRRC
th ARf
RKK )1(0
)1(*1 )1/(
][11 −
+
−⎥⎦
⎤⎢⎣
⎡−−
Δ=Δ
)(0
)1(*1 )1/(
][11 m
thp
th
mth
RCCRC
th ARf
RKK −+
−⎥⎦
⎤⎢⎣
⎡−−
Δ=Δ
0≥R
0<R
2/1
01
*1 ⎥
⎦
⎤⎢⎣
⎡+
Δ=Δaa
aKK (Small crack correction)
ΔK1 is the threshold stress intensity factor range as R → 1Cth is a factor that models threshold “fanning” for variations in R
Cth = 0 implies that near-threshold curves are parallelCth > 0 implies that near-threshold curves fan out
f is the Newman closure function and A0 is a closure constant Both are based on constant values of α = 2 and Smax/σ0 = 0.3
9
– Based on curve-fits to constant amplitude strip-yield model analysis
– α = constraint factor– σ0 = avg of yield and ultimate stresses
Newman’s Opening Function
10
Threshold as a Function of R
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-2 -1.5 -1 -0.5 0 0.5 1
Thr
esho
ld S
tress
Inte
nsity
Fac
tor,
DK
th
Stress Ratio, R
DK1 = 0.98 Smax/Sflow = 0.30 Alfa = 2.00 Cth+ = 1.6 Cth- = 0.20
DataCurve
11
NASGRO Model for Thickness Effect on Fracture Toughness
( )K K B ec Ic kAk
tt/ = + −1 0
2 ( )t KIc ys0
22 5= . / σ
0
10
20
30
40
50
60
0 2 4 6 8 10
Kc,
[MP
a*sq
rt(m
)]
Thickness, [mm]
t0 = 1.62
t0 = 1.62 Ak = 0.35 Bk = 0.5
Kc = 40.32
C(T) - KIcM(T) - KcPS(T) - KIeKIc = 28Kc
Beryllium-Copper Alloy
12
0
50
100
150
200
0 50 100 150 200
KIe
, [M
Pa*
sqrt(
m)]
KIc(1+Ck*KIc/Sy), [MPa*sqrt(m)]
SteelAluminumTitaniumInconelMagnesiumBe-CuEquation
KIc(1+Ck KIc/σys)
( )K K C KIe Ic k Ic ys= +1 / σ
NASGRO Model for Surface Crack Fracture Toughness
13
The Distinction Between NASFLA and NASMAT
• NASFLA– NASFLA is the main crack growth analysis module. – Use NASFLA to specify material properties for use in a
fatigue crack growth analysis.– NASFLA provides access to the library of NASGRO equation
curve fits.
• NASMAT– NASMAT contains the database of “raw” material property
data (da/dN vs ΔK, Kc).– Allows user to fit NASGRO or Walker equation to data.
14
Material Model Selection Options in NASFLA
• Data sources:– NASGRO Material File– User Material File– New Data– NASGRO and User Temperature Dependant Data
• Data formats:– NASGRO Equation Constants– Walker Equation Constants– 1D and 2D Tabular Data
15
NASFLA Material Selection Process
NASGRO equation
is the default
Then, click on “Show materials list” button to display materials selection tool.
In NASFLA, click on “Material” tab:
NASGRO equation
is the default
Then, click on “Show materials list” button to display materials selection tool.
NASGRO equation
is the default
16
NASFLA Material Selection Process
• Select material category, alloy group, alloy and heat treatment, and product form/orientation/environment from each successive window:
Note: Letters and numbers in square brackets define the material ID code. M7GE31AD1 in this example.
17
NASGRO Equation Fits
Once a material has been defined, the NASGRO 4.0 equation fit parameters are displayed.
You can also display the data and the curve fit by clicking on the “View curve fit” button.
18
NASGRO Equation Fits
The “View curve fit” button first displays a plot options utility:
Default “show plot”
19
NASGRO Equation Fits
• The “plot destination”pull-down menu permits:– Sending plot to printer– Saving “raw” da/dN-ΔK data
and fit curve data to text file– Saving plot in a number of
picture file formats
• Closing the plot options tool provides access to the references for the original da/dN-ΔK data.
20
NASGRO Equation Fits
• Example exercise:– Display NASGRO
equation fit for 7075-T73511 Ext (L-T)
– Plot curve fit– Save data to text file– Examine references
21
User Defined Data Input(1-D and 2-D Data Tables)
• 1-D data table:– Data for a single stress ratio
• Three different 2-D data table options:– Same da/dN data set for each R value
• Cubic spline interpolation– Different da/dN data set for each R value
• Cubic spline interpolation– Same da/dN data set for each R value
• Walker interpolation
22
Tabular da/dN vs. ΔK Data
• Enter data directly as tables of da/dN vs. ΔK
• Flexible number of points per curve
• Enter data at different R values– da/dN values for different R values
do not have to be common
• Alternatively, enter single set of ΔKeff values for closure model
• Piecewise Hermite polynomial interpolation in log-log space between adjacent points at the same R
• Two options for interpolation between different R values
log dadN
p
1
p-1
. . .
65
4
3
2
. . .
logΔK
23
Interpolation Methods for R
• Option 1:– Cubic spline fits of
log(ΔK) vs. R at common da/dN
• Option 2: “Walker Interpolation”– Calculate effective
Walker exponents for two adjacent stress ratios at individual da/dN values
– Use effective Walker exponents to interpolate between these two stress ratios
log dadN
logΔK
m11
m13
m16m25
m38
m37
R4 R3 R2 R1
da/dN1
da/dN2
da/dN3
da/dN4
da/dN5
da/dN6
da/dN7
da/dN8
da/dN9
24
User Defined Data Input(1-D Data Table Input)
Two column grid for entering da/dN-ΔK data for a single R value.
Enter data from keyboard or right-click on cell for more convenient options.
25
User Defined Data Input(2-D Data Table, Single da/dN)
Multiple column grid for entering ΔK data for multiple R values at a single da/dN value.
Enter data from keyboard or right-click on cell for more convenient options.
26
User Defined Data Input(2-D Data Table, Multiple da/dN)
Multiple column grid for entering different da/dN-ΔK data sets at multiple R values.
Enter data from keyboard or right-click on cell for more convenient options.
27
Additional Options
• Walker Equation Fits
• User supplied fit parameters– Can be obtained using NASMAT from user data– NASGRO Equation – Walker Equation
• Ability to create a database of user defined data for easy recall (user material file)
• Temperature dependant data capability
n
mRKC
dNda
⎥⎦
⎤⎢⎣
⎡−Δ
= −1)1(
Key NASGRO® Features
Joe CardinalSouthwest Research Institute®
San Antonio, [email protected]
(210) 522-3323www.nasgro.swri.org
2
Outline
• NASGRO K Solutions• NASGRO Spectrum Input• NASGRO Results• Advanced Analysis Capabilities
3
NASGRO K Solutions
• Overview• GUI for Selection of K Solutions• Tabular Solution Input• Weight Function Models
4
NASGRO® K Solutions
• Through cracks (13)• Corner cracks (9)• Surface cracks (17)• Embedded cracks (2)• Tabular data (4)• Standard test specimens (12)• Polynomial series (1)• Boundary element solutions (2)• Compounding available for
some solutions
5
NASGRO® GUI for Selection of K Solutions
Selection of model for a corner crack at an offset hole in a plate (CC02)
6
NASGRO® GUI for Selection of K Solutions
Input screen for corner crack at an offset hole in a plate (CC02)
7
Tabular Solution Input
• User defined K-solutions may be input in the form of data tables.
• Permits the use of existing solutions• 1D & 2D tables for through cracks• 2D & 3D tables for part-through cracks• Interpolation options (linear, hermite,
spline)
8
Tabular Solution Input
1D table of user-supplied geometry factors plotted and fit using linear interpolation option
9
Weight Function Models
• Most standard K solutions accept only “uniform” remote loading (tension, bend, pin, pressure, etc.).
• These solutions cannot be applied when:– Applied loads (stress gradients) are arbitrary– Non-uniform residual stresses are
superimposed on uniform remote loading• Weight function K solutions accept arbitrary
stress distributions on the crack plane.
10
Univariant vs. BivariantK Solutions
• Most weight function K solutions address nonlinear stress gradients in only one direction (univariant).
• Solution assumes this gradient is uniform in the orthogonal direction.
• Assumption may be overconservative for “hot spot” stresses (stresses may drop off away from univariant gradient line).
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-1.0-0.5
0.00.5
1.0
0.0
0.5
1.0
1.5
z
X
y
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-1.0-0.5
0.00.5
1.0
0.0
0.5
1.0
1.5
z
X
y
11
New Weight Function KSolutions in NASGRO 4.0
• First-generation bivariant weight function Ksolutions– SC15 – surface crack in plate (symmetric stresses)– CC05 – corner crack in plate
12
• Univariant weight function K solutions– TC13 (through crack at hole)– CC08 (corner crack at hole)– SC17 (surface crack in plate)
New Weight Function KSolutions in NASGRO 4.1
13
• New univariant weight function solutions– TC11 (off-center through crack in plate)– TC12 (edge through crack in plate)– EC02 (offset embedded crack in plate)
• New bivariant weight function solution– CC09 (bivariant corner crack in plate)
New Weight Function KSolutions in NASGRO 4.2
14
Univariant Weight Function Method for Cracks at Holes
• Determine K at a-tip and c-tip by direct integration:
• Weight function at the a-tip is
• M-factors are given by
• Q is the shape factor:
( )∫=c
caca dxxWK0
,, σ
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡⎟⎠⎞
⎜⎝⎛+⋅++=
23
32112cxM
cxM
cxM
xW aaaa π
( )
( )
( )aaa
a
a
MMM
FFQ
M
FFQ
M
213
102
011
1
1590604
818304
++−=
+−=
−−=
π
π
( )( )⎩
⎨>+ − 1,464.11 65.1 caca
⎧ ≤+=
1,464.11 65.1 cacaQ
Glinka (1991, 1998)
σ(x) is the stress distribution on the crack surface in the uncrackedbody
F0, F1 are normalized reference solutions
0: uniform tension1: linear bend stress
15
New Bivariant WF Method
• Developed by Yi-Der Lee (SwRI)– Uses Orynyak PWF as basic term– Three corrective terms to account for finite boundary effect– Details published:
• R. C. McClung, M. P. Enright, Y.-D. Lee, L. J. Huyse, S. H. K. Fitch, "Efficient fracture design for complex turbine engine components," Proceedings, 49th ASME International Gas Turbine & AeroengineTechnical Congress, ASME, Vienna, Austria, June 14-17, 2004, ASME Paper GT2004-53323.
• Advantages:– Relatively fast– Highly accurate– Robust—no geometry limitations
• Disadvantage:– Requires large number of accurate reference solutions
• 3 solutions per geometry, many geometry combinations
16
Development of WF Reference Solutions
• SwRI WF methods are based on a large number of highly accurate “reference solutions”– Numerical K solutions for crack face tractions
• Uniform, linear stress profiles
• Boundary element methods appear to be a superior approach– Simple meshing requirements: surfaces only– Highly accurate results with relatively coarse meshes
• FADD3D code (Prof. Mark Mear, UT-Austin) employed– 3D version of NASBEM
• FADD3D analysis compared against independent 3D finite element calculations in some cases
17
FADD-3D Models forCorner Cracks at Holes
• Initial solution matrix– R/t = 0.25, 1.0, 2.0– a/t = 0.1, 0.2, 0.5, 0.8,
0.9– a/c = 0.5, 1.0, 2.5, 5, 10
• Total of 150 meshes– For each mesh…
• 2 reference solutions (Uniform tension, linear stress gradient)
• 1 validation solution (typical hole gradient)
18
FADD-3D Model for Surface Crack at a Hole
2b
2t
2h
R
19
FADD-3D Solutions for Cracks at Holes in Finite Geometries
• Complete problem has 6 major degrees of freedom– R/t, c/a, T/t, a/(t-T), B/b, c/(b-(B+R))
• Comprehensive matrix would require ~13,500 solutions
• Simplified approach based on 192 limiting cases
c
2aT
t
2t
R
Bb
2b
20
FADD-3D Reference Solutionsfor Bivariant Corner Crack
• Analysis matrix:– c/W = 0.1, 0.2, 0.5, 0.8, 0.9– a/t = 0.1, 0.2, 0.5, 0.8, 0.9– c/a = 1, 1.25, 1.667, 2.5, 5, 10
• (1, 0.8, 0.6, 0.4, 0.2, 0.1)– σref = 1, 1-x/c, 1-y/a
• Totals– 150 geometries– 3 reference loads– 450 solutions
21
NASGRO v5 WF Solutions
• Currently implemented in v5.0 β:– Bivariant corner crack at hole (CC10)– Univariant surface crack at hole (SC18)
• Planned for v5.x development:– Bivariant surface crack in plate (SC19)– Bivariant embedded crack in plate– Bivariant surface crack at hole– Surface, corner, through crack at edge notch– Surface crack on curved (convex, concave) surface– Through crack in variable thickness plate
22
NASGRO K Solution Summary
• Extensive library of models!• NASSIF can be used to compute
stress intensity factors.• NASCCS can be used to compute
critical crack sizes.
23
NASGRO Spectrum Input
• Definitions• Spectrum Input Files• Spectrum Visualization• Spectrum Editing• Spectrum Generation
24
Definitions
• Cycle– The load step between a specified minimum and
maximum point– The end points of a cycle should be reversal
points• Block
– A group of cycles• Schedule
– The largest unit of load repetition composed by assembling blocks
25
Spectrum Input Files
A variety of flexible options are available:• Traditional NASGRO steps & blocked format:
• N, S01, S02, S11, S12, S21, S22, S31, S32• N, S01, S02, S11, S12, S21, S22, S31, S32
• Long block file formats:• NASGRO format• Peak-valley• Max, Min, N or Min, Max, N• Multi-block
• Manual (keyboard) input• Time-mean-range• TWIST, Mini-TWIST, FALSTAFF• Vibration test spectra• Scale Factors on stress components
26
Spectrum Visualization
• Display current block– Statistical analysis (S0-S3)– Exceedance diagrams (S0 only)– Stress or R-value histograms (S0 Only)– Plot min & max values (S0-S3)– View a text file in original or NASGRO
format (S0-S3)
• Select “Visualize current block” button on Load Blocks tab
27
Spectrum VisualizationGraphs
• Exceedance Diagram:– Shows plots for minimum,
maximum, range, and mean– Bin size is 2 ksi
• Graphical Min-Max values:– Plots S(t1) & S(t2)– Plot range can be defined– Plot can be printed to screen or
file
28
Spectrum VisualizationHistograms
• Stress Histogram– Shows plots for minimum,
maximum, range, and mean
– Bin size is 2 ksi• User selection for bin size is
currently not available
• R-value Histogram– Bin size is 0.1
• User selection for bin size is currently not available
29
Spectrum Statistics
• Statistical Analysis– Number of Steps– Number of Cycles– For each non-zero stress quantity
• Scale Factor• S(t1),S(t2),Smean
– Min,Max values and step IDs• Stress Ratio (R)
– Min,Max values and step IDs– Average
• ΔS– Min,Max values and step IDs– Average– RMS– Standard Deviation
30
Spectrum Editing
• Spectrum editing functions available for the NASGRO spectrum format– Clipping– Truncation– Rainflow cycle counting– Range-pair cycle counting
• One of the stress scale factors must be non-zero
• Spectrum must be defined as single cycles
• To access spectrum editing functions, choose “Edit Spectrum” button
Access Spectrum Editing Functions
31
Spectrum Generation
• The “Spectrum File Generator” tool converts load time-history data (time series) to a NASGRO long block spectrum file.
• Turning points are identified (peak-picked).• Intermediate points are removed.• Points with load pair ranges below a user-defined
threshold (filter level) can be removed.
32
NASGRO Results
• Tabular• Graphical• End of Analysis• Summary of Output Variables
33
NASGRO Results
View, Print, Save & PlotResults
Many options!
Spreadsheet Word processor
34
Tabular Results• Results Window
– Highlight details are presented in text window
• Save contents to a Microsoft Word file
• Print contents directly to printer
Schedule Block Step Cycles Blocks a c Blk max K Blk max K F0(a) F0(c) G0 da/dN dc/dN DKth(a) DKth(c) DKth/DK(a DKth/DK(c U(a)0 0 0 0 0 5.00E-02 5.00E-02 - - - - - - - - - - - -
431 1 - 4310 431 5.50E-02 5.48E-02 5.47 6.01 0.658 0.723 0 1.23E-06 1.20E-06 1.92 1.92 0.35 0.35 0.67815 1 - 8150 815 6.00E-02 5.97E-02 5.7 6.28 0.657 0.723 0 1.38E-06 1.35E-06 1.92 1.92 0.34 0.34 0.67
• All data to “csv” file– Comma delimited file with results and column headers
35
Graphical Results
• Plot Options– Plot limits may be
defined by user– If plot limits are blank,
plot will be auto-sized to display results
– Plot destination• Screen• Printer• Text File• Various graphics
formats– Plot is created by
choosing “Show plot for:” button
36
Final Results Output
• Final Results– Reason for end of
calculation– Cycle, Load Step,
Block, and Schedule at end of calculation
– Crack size at end of calculation for current geometry (transition may have occurred)
– Total Cycles & Flights– Execution Time
37
Summary of Output Variables
• Cycle count– Cycle number at output step
• Crack size– Crack dimensions at output
step• Max K
– Largest K in block at output step
• Beta Factor, F – Non-dimensional SIF
• Net Stress Factor, G– Function of geometry and
crack length used to compute net-section stress
• da/dN– Crack growth rate for each
tip at output step• DKth
– Threshold ΔK• DKth/DK
– Ratio of threshold ΔK to applied ΔK
• U (=DKeff/DK)– Ratio of effective ΔK to
applied ΔK• Residual strength
– Amount of load carrying capacity when a crack is present
38
Advanced Analysis Capabilities
• Load Interaction Effects• Small Crack Effects• Temperature Dependant FCG• Shakedown• Elastic Plastic Fracture
Support Pad Example Problem
Pad. 2Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Support Pad Radius Crack
• Material:– 17-4PH, H1025 plate
• Force-time history, F(t), available from test results
• FEA stress analysis computed gradient at radius location for a unit load (4-point bending)
• W = 1.88 inches• t = 0.36 inches Consider a surface
crack located in the radius of the pad.
F
W
t
Pad. 3Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Analysis Outline
• Stress Gradient from FEM Analysis • Geometry Definition (SC02)• Material Selection• Spectrum Development• Analysis Results• Repeat Analysis with Weight Function Model
(SC17)
Pad. 4Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Support Pad FE Analysis
• FEA through-thickness stress gradient at radius:
Norm NormDistance Stress
0.0000 1.0000.0694 1.0000.1389 1.0000.2083 1.0000.2778 0.7950.3472 0.7440.4167 0.6920.4861 0.5850.5556 0.5250.6250 0.4450.6944 0.3290.7639 0.2310.8333 0.1450.9028 0.0600.9722 -0.0261.0000 -0.128
Section thru Pad FEM at Radius
Pad. 5Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Geometry DefinitionSC02 – Surface Crack in Plate with Nonlinear Stress
Define geometry and initial flaw size.
Manual entry or cut & paste stress gradient.
Pad. 6Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Material Selection
Pad. 7Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Load Spectrum Development from Time History Data Using NASGRO
• Time history file contains over 4500 data points.• These pairs of (force, time) data need to be converted
to stress cycles (Smax, Smin) for crack growth analysis.
Force-Time History
-4,000
-2,000
0
2,000
4,000
6,000
8,000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Time (sec)
Forc
e (lb
)
Pad. 8Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Load Spectrum Development from Time History Data
• NASGRO Spectrum File Generator Tool:
Pad. 9Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Load Spectrum Development from Time History Data Using NASGRO
• Remove cycles with +/- 100 lb • Determine reversals & rainflow count• Results in a spectrum containing 27 max-
min cycles.• One pass thru this spectrum represents
one loading event. • Spectrum peak load is 7340 lbs.• Peak stress is 110 ksi (from FEA)• Spectrum can then be easily scaled for
crack growth analyses:• SF = Smax/Fmax = 110/7340 = 0.015
Cycle Max MinNumber (lb) (lb)
1 21 -82 213 623 2,300 1,9434 4,648 4,2645 4,992 4,7586 5,225 4,7997 5,280 4,6358 5,816 5,6379 6,598 6,420
10 6,804 6,42011 7,093 6,96912 7,189 6,73613 7,148 6,95514 3,371 2,84915 7,340 -15816 -1,395 -2,07417 -807 -1,01818 -370 -58119 -490 -1,48620 -204 -1,72721 48 -5322 144 -2,07423 1,009 63924 -143 -30925 -128 -27926 1,064 -2,81327 7 -339
Pad. 10Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Load Spectrum Development from Time History Data Using NASGRO
• NASGRO Spectrum File Editor Tool:
Pad. 11Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Specify Spectrum File UsingLoad Blocks Tab
Pad. 12Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Analysis Results (SC02)
Pad. 13Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Geometry DefinitionSC17 – Surface Crack in Platewith Weight Function Solution
Manual entry or cut & paste stress gradient.
Select input of stress gradient on crack plane.
Pad. 14Support Pad Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Analysis Results (SC17)
Fastener Hole Example Problem
Hole. 2Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
• Corner Crack at Hole:W = 8.0 inchest = 0.50 inchesB = 1.25 inchesD = 0.28 inchesai = ci = 0.005 inches
• 7075-T73 plate (L-T)• Wing stress spectrum
(tension) loading, S0
Hole. 3Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Define geometry and initial flaw size.
Hole. 4Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Select material.
Hole. 5Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Examine
Examine Spectrum File
One pass thru the spectrum file = 1000 flight hours
Hole. 6Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Display spectrum statistics.
Hole. 7Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Plot spectrum.
Hole. 8Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Plot spectrum,zoom in.
Hole. 9Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Results show that corner crack (a, c) transitions to a through crack (c) before failure occurs.
Hole. 10Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
NASGRO corner crack model automatically transitions to a through crack model.
Hole. 11Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
• Examine printed output– Transition message– End of life message
• Display plots of other results• Comparison runs:
– Different spectrum– Load Interaction (retardation) analysis using
Generalized Willenborg model
Hole. 12Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Repeat previous analysis using Generalized Willenborgload interaction (retardation) model with a Shut-Off Overload Ratio, RSO, of 2.15.
RSO = KOLmax/Kmax
Hole. 13Fastener Hole Example ProblemCopyright 2006, Southwest Research Institute.All Rights Reserved.
Corner Crack at Offset Fastener Hole in Plate under Aircraft Spectrum Loading
Analysis using Generalized Willenborg retardation model predicts 3X longer life than previous analysis that did not consider load interaction.
Material Modeling Using NASMAT
2Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Outline
• The Distinction Between NASMAT and NASFLA
• Content of the NASMAT Database• da/dN-ΔK Material Selection Process• Plot/Examine/Export Data• da/dN Curve Fitting Options • Fitting the NASGRO Equation• Entering New da/dN-ΔK Data into the User
Database
3Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Outline
• Toughness Database• NASGRO Model for Thickness Effect on
Fracture Toughness• Entering New Toughness Data into the User
Database
4Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
The Distinction Between NASMAT and NASFLA
• NASMAT– NASMAT contains the database of “raw” material property data
(da/dN vs ΔK, Kc).– Allows user to fit NASGRO or Walker equation to data.– Allows user to determine fit of toughness vs thickness.– There are more data sets in NASMAT than have been fit to the
NASGRO equation in NASFLA.
• NASFLA– NASFLA is the main crack growth analysis module. – Use NASFLA to specify material properties for use in a fatigue
crack growth analysis.– NASFLA provides access to the library of NASGRO equation curve
fits.
5Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Content of the NASMAT Database
• Fatigue Crack Growth Rate (FCG) Data:– da/dN vs ΔK data sets for multiple R values– Specimen types, geometries, environment, etc.– References
• Toughness Data:– Data from multiple specimen types (including dimensions)– “Valid” Kc data distinguished from Kq and other Kc data– Yield and ultimate strengths– References
• NASMAT database cannot be modified and is encrypted.
• Users can define their own FCG and toughness databases.
• Material ID code system is identical to that used in NASFLA.
6Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
NASMAT Opening Screens
Click on “Material Data Processing”radio button on main NASGRO screenand then on “NASMAT program” buttonto enter the NASMAT module. Choose radio button for either
database, then click continue.
NASMAT function tabs
7Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔKMaterial Selection Process
2024-T3 was selected. 30 data sets found.
Click OK to continue…..
8Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔKMaterial Selection Process
In this example the NASA da/dN Delta K database was chosen and the data ID is M2EA11AB01. Then the Show Data Sets button was clicked and all the data sets that have matching identification codes are displayed. The user may choose the data sets of interest (i.e., the data sets to be used in curve fitting, plotting or otherwise examined) by clicking on their data identifications.
9Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔKMaterial Selection Process
Three Data ID’s have been clicked to select them (all 0.09” sheet data). The Load Selected Data button changes color to red to indicate it is the next button to click.
10Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔKMaterial Selection Process
• Once the “Load Selected Data” button has been clicked, the following page is displayed and you can proceed to plot and fit the data.
11Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔK Data Plotting
For each material ID, choose to plot the R = 0, 0.5 and 0.7 data sets and click “New CurveFit/Plot” button to plot.
12Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
da/dN-ΔK Data Plotting
13Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Examine da/dN-ΔK Data
• Clicking on the material ID code button activates the “Examine/Edit Data” window for that data set (as shown on next chart).
14Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Examine/Edit da/dN-ΔK Data
Clicking on “Show Data” button for a specific R value displays the da/dN-ΔK data set for that R in the grid to the right.Material
DescriptionOptions to plot or write data to text file.
15Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
• NASMAT has three curve fitting options:– Walker Equation– NASGRO Equation– Spline Fit
• Data sources:– NASMAT database– User-supplied:
• Text file• Clipboard • Digitizer
• Click on the “CurveFit/Plot” tab.
da/dN-ΔKCurve Fitting Options
16Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
• After selecting and plotting your data sets, decide which sets you will use in the curve fitting process.
• Check the corresponding Fit boxes on the “Choose Plot/Fit Data”page. R = 0, 0.5 and 0.7 have been chosen for fitting below.
• Click on the “CurveFit/Plot” tab.
da/dN-ΔKCurve Fitting Options
17Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Clicking on the “CurveFit/Plot” tab activates the fitting GUI:
da/dN-ΔKCurve Fitting Options
Choose Equation
18Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
The NASGRO Equation is complicated and fitting it requires a number of key, interrelated steps:– Fitting or defining the threshold region (ΔK0, ΔK1, Cth)– Fitting or defining toughness as a function of thickness– Making initial assumptions on key parameters (p & q)– Performing the least squares fit to obtain C and n– Using your “engineering judgment” to obtain an acceptable
result.
19Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
1. Click NASGRO button2. Click Least Squares
Fit button3. Enter Stress Ratio
(S.R.) and Alpha4. Specify threshold
region parameters 5. Enter initial values for
p and q6. Specify toughness,
yield strength, and how toughness varies with thickness
7. Enter R values for curves to be drawn
8. Click “Fit/Plot”
20Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
3. Enter Stress Ratio (S.R. = Smax/σ0 ) and Alpha
These parameters are used in computing the crack closure function, f.
Use: Smax/σ0 = 0.3
andα = 2.0unless you havebetter information.
21Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
4. Specify threshold region parametersThere are two options:
Calculates a fit using a set of (R, ΔKth) data to obtain ΔK0, ΔK1, and Cth.
Enter any two of the parameters (ΔK0, ΔK1, Cth) and calculate the third.
or
22Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
4. Specify threshold region parameters (using fit):
Enter values of ΔKth for each R obtained from examining da/dN data.
23Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
4. Specify threshold region parameters (using fit):The threshold fit can then be displayed and the parameters are automatically entered into their cells in the GUI.
24Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
5. Enter initial values for p and q:
p and q are constants describing curvature near threshold and instability and must be determined by iteration.
25Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
6. Specify toughness directly using the “Enter Kc”button:
or …
26Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
6. Specify toughness, yield strength, and how toughness varies with thickness using the “Calculate Kc” button:
• Select KIc from toughness database or other sources.
• Enter Yield Strength
• Select Ak and Bk to fit upper region of da/dN curve or use the NASMAT tougness database to determine them.
27Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Use as typical estimate Ak = 1 & Bk = 1 Increase Bk to raise Kc
Decrease Ak to flatten curve
Example Behavior of Ak and Bk
28Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
7. Enter R values for curves to be drawn
8. Click “Fit/Plot”
29Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
NASGRO parameters are displayed on plot.
30Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
• Completed screen following curve fit.
• Values obtained for C and n.
• Are you happy with the curve fit results?
• If not, you can edit or adjust any of the parameters as you desire using:
31Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
• For the previous example, assume we would like a more conservative fit and want to adjust the threshold exponent, p.
• Click on • Enter C = 1.0e-08• Enter p = 0.50• Click on “Fit/Plot” again to
plot revised fit.• Iterate until you are
satisfied!
32Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Fitting the NASGRO Equation
Initial fit has been modified to provide a more conservative fit and have a more gradual transition to the threshold region.
33Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Entering New da/dN-ΔK Data into the User Database
• NASMAT provides the capability to enter data into the user database using six sources:– Text file– Clipboard– Keyboard– FTA file format– Digitizer– Digitized file
• The user can then fit their own data.
These two methods are discussed in this presentation.
34Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Entering New da/dN-ΔK Data into the User Database
“Enter New Data” tab activates user data entry form:
35Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Entering New da/dN-ΔK Data into the User Database
Enter data from text file:
• Click on “Text File”
• Enter text file format data
For this example, the text file is described as follows:
• 2 header lines
• da/dN values in column 4
• ΔK values in column 5.
• Blank or blanks between columns
36Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Entering New da/dN-ΔK Data into the User Database
Save data to user database; plot if desired
37Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Entering New da/dN-ΔK Data into the User Database
Enter data from clipboard:
• Click on the “Show Data”button for the R value of the data set.
• Use text editor or spreadsheet to copy data to clipboard.
• Return to NASMAT and click the “Clipboard” button. Data is pasted into NASMAT.
• Repeat for other R data sets.
38Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• Selecting “Toughness data” as the data type from the main NASMAT screen activates the toughness database window shown on the next page.
39Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
Specify or Select Material ID
Clicking “Show Entries for ID”displays number of data sets for each specimen type.
40Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• 7075-T76351 (M7GJ11AB01) has been selected
41Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• The “Search Criteria” column lists the types of toughness data (Kc, KIc, Kq, etc.).
• The “Num” column lists the corresponding number of data sets (toughness values) in the database for the selected material and the type of toughness data.
• This example shows that there are 8 KIc values, 3 Kq values and 3 Kcvalues in the NASMAT database for the selected material.
42Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• The “Specimen Type” column lists laboratory specimen types used to obtain the data sets (toughness values) in the database for the selected material.
• Specimen types in the database for the selected material are highlighted in green. This example shows that the NASMAT database contains toughness data obtained from M(T), C(T) and SE(B) specimens for the selected material.
• Definitions of specimen types and their ASTM standards are on the next chart.
43Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Specimen Definitions
SpecimenType Definition ASTM StandardPS(T) partially cracked surface
(tension)unknown
M(T) middle cracked (tension) E561, E338
M(T)S stiffened M(T) unknown
DC(T) disk-shaped C(T) E399, E1820
C(T) compact (tension) E399, E561, E1820, E1290
MC(T) modified (wider) C(T) unknown
SE(B) single edge notched (bend) E399, E1820
SE(T) single edge notched (tension) E1290
DE(T) double edge notched (tension) E338
R-BAR(T) circumferentially notched (tension)
unknown
A(T) arc shaped (tension) E399, like pipe wall segment, E1823 terminology
UNK unknown n/a
44Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• There is no relation between the rows of the “Search Criteria” and “Num” columns to the “Spec Type” column!
• This row alignment is only an artifact of the GUI.
• These are really two separate display windows.
45Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• Click on data type in “Search Criteria” column.• “Valid Kc data” has been chosen below.
46Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• Click on multiple data types in “Search Criteria” column.• “Number of Entries” box sums all selected data entries.
Click “Show Selected Data” to display database contents.
47Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
Click on Toughness values to toggle selection.
Scroll to right to display references for each set of data.
48Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• After toggling on toughness values in the database display grid, you can compute the average and standard deviation.
• Write all data in the display grid to a comma-delimited text file.
49Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Toughness Database
• Plot Kc vs thickness using the toggled toughness values in the database display grid.
50Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
NASGRO Model for Thickness Effect on Fracture Toughness
( )K K B ec Ic kAk
tt/ = + −1 0
2 ( )t KIc ys0
22 5= . / σ
0
10
20
30
40
50
60
0 2 4 6 8 10
Kc,
[MP
a*sq
rt(m
)]
Thickness, [mm]
t0 = 1.62
t0 = 1.62 Ak = 0.35 Bk = 0.5
Kc = 40.32
C(T) - KIcM(T) - KcPS(T) - KIeKIc = 28Kc
Beryllium-Copper Alloy
Use the NASMAT toughness database to determine Ak and Bk.
51Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
NASGRO Model for Thickness Effect on Fracture Toughness
• Manual entry of data to estimate Ak and Bk:
• Average KIc and YS
• Edit KIc and YS
• Click on “Enter Ak and Bk”
• Enter Ak and Bk
• Plot Points and Curve and iterate
52Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
NASGRO Model for Thickness Effect on Fracture Toughness
• Calculate Ak and Bk:• Average KIc and YS
• Edit KIc and YS
• Click on “Calc Ak and Bk”
• Use mouse to pick Thk1 and Thk2
• Plot Points and Curve and iterate
53Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
NASGRO Model for Thickness Effect on Fracture Toughness
54Material Modeling Using NASMATCopyright 2006, Southwest Research Institute.All Rights Reserved.
Click the Enter/Edit Data for ID button on the Toughness Notes page to display the Enter/Edit Data page. When changes are entered the Save Changes button will be enabled to allow writing to the user toughness database.
Entering New Toughness Data into the User Database
Craig McClungSouthwest Research Institute
San Antonio, Texas
DARWIN® Overview
UTMIS Spring MeetingMay 31, 2006
Background
Undetected anomaliescan reduce rotor reliability
Multiple causesInherent in the materialInduced by manufacturing
Very rare occurrencesSome famous accidentsNot addressed by safe life design practices
Engine industry developing an enhanced life management processRequested by Federal Aviation Administration (FAA) following Sioux City accidentDeveloped by industry through AIA Rotor Integrity Sub-Committee (RISC)Probabilistic damage tolerance methods and opportunity inspectionsProcess now documented as FAA Advisory Circular 33.14
“Turbine Rotor Material Design”(TRMD) Program
Funding from FAAGoal is to support FAA guidelines
Enhanced predictive tool capabilitySupplementary material/anomaly behavior characterization and modeling
SwRI is program managerU.S. engine companies are steering committee, major subcontractors
General ElectricHoneywellPratt & WhitneyRolls-Royce Corp.
Activities coordinated with RISC
Anomaly Types
Inherent material anomaliesTitanium Hard Alpha (HA)
Small brittle zone in microstructure
Induced anomaliesSurface damage due to manufacturing or maintenance
DARWIN® Analysis ModesInherent Material Anomalies vs. Surface Damage
Inherent Anomalies Surface Damage
Zone-Based Risk (Volume) Feature-Based Risk (Area)
2D finite element models 3D finite element models
initial crack location
Random Defect
Probabilistic Fracture Mechanics Methodology
Size DistributionInclusion
CyclesPr
obab
ility
Life Prediction
Thermal & StressAnalysis
InclusionFrequency
Probabilistic Analysis
Fracture MechanicsStressed volume/areaInclusion incubationStatistical Integration
Mission Analysis
Prob
abilit
y
Size
Crack Growth
Stress intensity
Gro
wth
rate
MISSYDD
Cyclic UsageAnomaly Distribution- Size and Frequency
Probability of Fracture
Inspection POD
Part Inspection Distribution
Probabilistic Fracture Mechanics
Statistical Integration
DARWIN® OverviewDesign Assessment of Reliability With INspection
Probabilistic Fracture Mechanics
Probability of DetectionAnomaly Distribution
Finite Element Stress Analysis
Material Crack Growth Data
NDE Inspection Schedule
Pf vs. Cycles
Risk Contribution Factors
Zone-Based Risk Assessment
Define zones based on similar stress, inspection, anomaly distribution, lifetimeTotal probability of fracture for zone:
(probability of having an anomaly) x (POF given an anomaly)
Anomaly probability determined by anomaly distribution, zone volumePOF assuming an anomaly computed with Monte Carlo sampling or advanced methods
POF for disk = sum of zone probabilitiesAs individual zones become smaller (number of zones increases), risk converges down to “exact” answer
1
2 3 4
m
5 6 7
Fracture Mechanics Model of Zone
m
7
Retrieve stresses along line
Finite Element ModelZone life calculated from plate idealization
User specifies initial crack location and size/orientation of fracture mechanics plate
Crack placed at “worst-case” location in zone
DARWIN Interface with FE Models
Input FE geometry and stress files and view in DARWIN GUI
Build fracture modelDefine initial crack locationDraw a plate for the fracture modelExtract stresses from FE info
Zones and Fracture Models
The plate dimensions and orientation define a gradient path
Stresses and temperatures are extracted along this path
The zone relates global coordinates of the FE model to local plate coordinates
x
y
θ1
θ2
θ1
θ1
SC02
EC02
CC01
r
z
x y
Fracture Mechanics Model
hx
hy
x
Y
grad
ient
dire
ctio
n
1
2
3
4
5
Defect
(Not to Scale)
Zoned Impeller Model
Surface Damage Zone DefinitionExtract 3D Finite Element Model Results
Load 3D Model
Compute Slice
1. Import 3D Finite Element Model2. Select surface node and associated
principal stress plane3. Adjust cutting plane, create 2D slice
Surface Damage Zone Definition Specify Zone Properties based on 2D Slice
Feature idealized as rectangular plateStresses extracted from FEM results
Multiple load stepsMultiple missions
Remaining properties defined using existing surface damage libraries
DARWIN® 3D Finite Element Models
20 node brick 10 node tetrahedron
8 node prism 20 node pyramid 20 node tetrahedron
20 node prism
GUI supports all 3D element types commonly used in 3D rotor FE models
ANS2NEU Element Filtering
ANS2NEU translator converts ANSYS input and output files into DARWIN format
Can be executed directly from GUI
Rotor/disk finite element analysis often performed as part of engine assembly model
Time-consuming to manually extract rotor/disk model for DARWIN analysis
ANS2NEU includes element filtering capabilityUser can include/exclude specific elements based on specified ranges of element ID, material ID, or load case
! example.flt! this is a comment*VERSION ! required1.0
*MATERIAL_IDINCLUDE1 2 4
*ELEMENT_IDINCLUDE200-500EXCLUDE300-350 401 422
*LOAD_CASEINCLUDE13
Stress Processing
FE Stresses and zone definition
stress gradient
Stress gradient extraction
FE Analysis
0.0 0.2 0.4 0.6 0.8 1.0Normalized distance from the notch tip, x/r
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
σ/σo
(σz)relax
(σz)residual
(σz)elastic
Shakedown module
Computed relaxed stressσelastic - σresidual
σ0/σ
Residual stress analysis
3 4 5 6 7 0 1 2 3Load Step
01020304050607080
Hoo
p S
tress
(ksi
)
Rainflow stress pairing
Output: Risk vs. Flight Cycles
Output: Risk Contribution Factors
Identify regions of component with highest riskRefine zone breakup as needed to achieve convergence
www.darwin.swri.orgwww.darwin.swri.org