nasgro fatigue crack growth analysis software -...

NASGRO®

Fatigue Crack Growth Analysis SoftwarePresented at

UTMIS Spring MeetingFinspang, Sweden

May 31, 2006

Joseph W. CardinalSouthwest Research Institute®

San Antonio, Texasjcardinal@swri.org

(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

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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®

(210) 522-3323www.nasgro.swri.org

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)

NASGRO® Features

• K Solutions• Material Property Database• Crack Growth Algorithms• Spectrum Input• Output Features• Other Special Features

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)

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

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®

NASGRO® Use at NASA

Payloads

NSTS Ground Test Facilities

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

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.

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.

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

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

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

NASGRO Awards

“One of the 100 Most Technologically Significant New Products of 2003” (R&D Magazine)

NASA Software of the Year Award (2003)

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

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

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

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

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

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

• 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

NASGRO® GUI for Selection of K Solutions

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

1 10 100

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.)

NASMAT GUI(Material Selection)

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

q=−−

⎛⎝⎜

⎞⎠⎟

⎣⎢

⎦⎥

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

NASGRO Database Contains NASGRO Equation Material Constants

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

q=−−

⎛⎝⎜

⎞⎠⎟

⎣⎢

⎦⎥

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

Parameters in the NASGRO crack growth equation:

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.

q=−−

⎛⎝⎜

⎞⎠⎟

⎣⎢

⎦⎥

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

Parameters in the NASGRO crack growth equation:

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

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

Output Features

View, Print, Save & PlotResults

Many options!

Spreadsheet Word processor

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

NASMAT Curve Fitting

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

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

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

• 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 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

• 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)

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

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®

• Understanding the NASGRO Equation• NASFLA Material Selection Process • Display of NASGRO Equation Fits• User Defined Tabular Data Input• Additional Options

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

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

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

Effect of Mean Stress

• FCG rates generally increase with increasing mean stress (increasing R)

R = 0.8R = 0.5R = 0.1

• NASGRO 4.0 Equation:

• f = stress ratio correction (based on crack closure theory)

• p, q are empirical constants describing curvature near threshold and instability

q=−−

⎛⎝⎜

⎞⎠⎟

⎣⎢

⎦⎥

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

Near-threshold factor

Stress ratio factor

Near-instability factor

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

NASGRO Threshold Equations

• NASGRO determines the threshold as a function of R and crack size:p

th ARf

RKK )1(0

)1(*1 )1/(

][11 −

−⎥⎦

⎤⎢⎣

⎡−−

)1(*1 )1/(

][11 m

th ARf

RKK −+

−⎥⎦

⎤⎢⎣

⎡−−

*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

– 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

Threshold as a Function of R

-2 -1.5 -1 -0.5 0 0.5 1

Stress Ratio, R

DK1 = 0.98 Smax/Sflow = 0.30 Alfa = 2.00 Cth+ = 1.6 Cth- = 0.20

DataCurve

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 2 4 6 8 10

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

0 50 100 150 200

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

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.

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

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

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.

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.

The “View curve fit” button first displays a plot options utility:

Default “show plot”

• 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.

• Example exercise:– Display NASGRO

equation fit for 7075-T73511 Ext (L-T)

– Plot curve fit– Save data to text file– Examine references

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

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

logΔK

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

m16m25

R4 R3 R2 R1

da/dN1

da/dN2

da/dN3

da/dN4

da/dN5

da/dN6

da/dN7

da/dN8

da/dN9

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.

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.

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.

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

⎥⎦

⎤⎢⎣

⎡−Δ

= −1)1(

Key NASGRO® Features

Outline

• NASGRO K Solutions• NASGRO Spectrum Input• NASGRO Results• Advanced Analysis Capabilities

NASGRO K Solutions

• Overview• GUI for Selection of K Solutions• Tabular Solution Input• Weight Function Models

• 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

Selection of model for a corner crack at an offset hole in a plate (CC02)

Input screen for corner crack at an offset hole in a plate (CC02)

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)

Tabular Solution Input

1D table of user-supplied geometry factors plotted and fit using linear interpolation option

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.

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).

-1.0-0.5

0.00.5

-1.0-0.5

0.00.5

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

• Univariant weight function K solutions– TC13 (through crack at hole)– CC08 (corner crack at hole)– SC17 (surface crack in plate)

• 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)

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

⎥⎥

⎢⎢

⎡⎟⎠⎞

⎜⎝⎛+⋅++=

32112cxM

xW aaaa π

( )aaa

1590604

818304

++−=

−−=

( )( )⎩

⎨>+ − 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

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

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

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)

FADD-3D Model for Surface Crack at a Hole

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

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

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

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.

NASGRO Spectrum Input

• Definitions• Spectrum Input Files• Spectrum Visualization• Spectrum Editing• Spectrum Generation

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

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

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

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

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

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

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

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.

NASGRO Results

• Tabular• Graphical• End of Analysis• Summary of Output Variables

NASGRO Results

View, Print, Save & PlotResults

Many options!

Spreadsheet Word processor

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

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

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

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

Advanced Analysis Capabilities

• Load Interaction Effects• Small Crack Effects• Temperature Dependant FCG• Shakedown• Elastic Plastic Fracture

Support Pad Example Problem

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.

Analysis Outline

• Stress Gradient from FEM Analysis • Geometry Definition (SC02)• Material Selection• Spectrum Development• Analysis Results• Repeat Analysis with Weight Function Model

(SC17)

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

Geometry DefinitionSC02 – Surface Crack in Plate with Nonlinear Stress

Define geometry and initial flaw size.

Manual entry or cut & paste stress gradient.

Material Selection

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

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Time (sec)

Load Spectrum Development from Time History Data

• NASGRO Spectrum File Generator Tool:

• 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

• NASGRO Spectrum File Editor Tool:

Specify Spectrum File UsingLoad Blocks Tab

Analysis Results (SC02)

Geometry DefinitionSC17 – Surface Crack in Platewith Weight Function Solution

Manual entry or cut & paste stress gradient.

Select input of stress gradient on crack plane.

Analysis Results (SC17)

Fastener Hole Example Problem

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

Define geometry and initial flaw size.

Select material.

Examine

Examine Spectrum File

One pass thru the spectrum file = 1000 flight hours

Display spectrum statistics.

Plot spectrum.

Plot spectrum,zoom in.

Results show that corner crack (a, c) transitions to a through crack (c) before failure occurs.

NASGRO corner crack model automatically transitions to a through crack model.

• 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

Repeat previous analysis using Generalized Willenborgload interaction (retardation) model with a Shut-Off Overload Ratio, RSO, of 2.15.

RSO = KOLmax/Kmax

Analysis using Generalized Willenborg retardation model predicts 3X longer life than previous analysis that did not consider load interaction.

Material Modeling Using NASMAT

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

Outline

• Toughness Database• NASGRO Model for Thickness Effect on

Fracture Toughness• Entering New Toughness Data into the User

Database

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

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.

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

da/dN-ΔKMaterial Selection Process

2024-T3 was selected. 30 data sets found.

Click OK to continue…..

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.

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.

• Once the “Load Selected Data” button has been clicked, the following page is displayed and you can proceed to plot and fit the data.

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.

da/dN-ΔK Data Plotting

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).

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.

• 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

• 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.

Clicking on the “CurveFit/Plot” tab activates the fitting GUI:

Choose Equation

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.

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”

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.

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.

4. Specify threshold region parameters (using fit):

Enter values of ΔKth for each R obtained from examining da/dN data.

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.

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.

6. Specify toughness directly using the “Enter Kc”button:

or …

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.

Use as typical estimate Ak = 1 & Bk = 1 Increase Bk to raise Kc

Decrease Ak to flatten curve

Example Behavior of Ak and Bk

7. Enter R values for curves to be drawn

8. Click “Fit/Plot”

NASGRO parameters are displayed on plot.

• 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:

• 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!

Initial fit has been modified to provide a more conservative fit and have a more gradual transition to the threshold region.

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.

“Enter New Data” tab activates user data entry form:

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

Save data to user database; plot if desired

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.

Toughness Database

• Selecting “Toughness data” as the data type from the main NASMAT screen activates the toughness database window shown on the next page.

Toughness Database

Specify or Select Material ID

Clicking “Show Entries for ID”displays number of data sets for each specimen type.

Toughness Database

• 7075-T76351 (M7GJ11AB01) has been selected

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.

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.

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

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.

Toughness Database

• Click on data type in “Search Criteria” column.• “Valid Kc data” has been chosen below.

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.

Toughness Database

Click on Toughness values to toggle selection.

Scroll to right to display references for each set of data.

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.

Toughness Database

• Plot Kc vs thickness using the toggled toughness values in the database display grid.

( )K K B ec Ic kAk

tt/ = + −1 0

2 ( )t KIc ys0

22 5= . / σ

0 2 4 6 8 10

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.

• 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

• 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

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

Life Prediction

Thermal & StressAnalysis

InclusionFrequency

Probabilistic Analysis

Fracture MechanicsStressed volume/areaInclusion incubationStatistical Integration

Mission Analysis

abilit

Crack Growth

Stress intensity

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

Fracture Mechanics Model of Zone

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

Fracture Mechanics Model

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

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

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

nasgro fatigue crack growth analysis software -...

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