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Copyright 2010 Southwest Research Institute
Advanced Software for Integrated Probabilistic Damage Tolerance Analysis
Including Residual Stress Effects
R. Craig McClungMichael P. Enright
Yi-Der LeeWuwei Liang
Southwest Research InstituteSimeon H. K. Fitch
Mustard Seed Software
AeroMat 2010Bellevue, Washington
June 21-24, 2010
Copyright 2010 Southwest Research Institute2
Acknowledgments
• Funding provided byFederal Aviation Administration (FAA)• Grant 05-G-005
Air Force Research Laboratory (AFRL)• DUS&T Contract No. F336150325203• SBIR Contract No. FA8650-10-M-5110
–Via Scientific Forming Technologies Corporation
Copyright 2010 Southwest Research Institute3
Introduction
• Damage tolerance analysis plays an increasingly important role in assuring integrity and reliability of components
Address threat of potential manufacturing or material anomalies
• Increasing requirement for accurate, efficient fatigue crack growth (FCG) life analysis methods
• Special challenge: Many possible locations for fatigue cracks to appear
For example, hard alpha anomalies in titanium rotors
• Probabilistic damage tolerance methods can address this threat, but introduce additional efficiency challenges
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“Engineering” Approach to Damage Tolerance Analysis
• CharacteristicsPre-programmed SIF solutions for simple geometriesSophisticated FCG equations with load interaction models
• AdvantagesVery fast execution timesDetailed load history analysis
• DisadvantagesSIF solutions are often for simple constant or linear stress profilesMust manually transfer (and interpret) stress and geometry information from component model to fracture model
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New Computational Approach
• Goal: User-friendly balance of accuracy and efficiency• Sophisticated GUI with direct interface to 2D/3D FE
models to extract and visualize geometry/stress information
• Automated construction of optimum simple fracture model geometry
• New weight function SIF solutions to address complex stress gradients
• Residual stresses (surface or bulk) addressed via weight function solutions
• Advanced FCG algorithms directly integrated with probabilistic analysis algorithms to calculate reliability
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2D Finite Element Model Interface in DARWIN
• Import, visualize 2D FE model & stresses
• Use mouse to build engineering FCG model
Place initial crackLocate and size plate
• GUI extracts all stress and dimension information for fracture calculation
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3D Finite Element Model Interface
1. Load 3D FE model
2. Select crack location & show principal stress plane
3. Slice 3D model to reveal 2D crack growth plane
4. Build 2D fracture model
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Automatic Fracture Model Generation: Goal and Motivation
• GoalGiven…
• 2D FE model with stress results• Initial crack location
Automatically determine (no user input)• Initial crack type• Orientation & size for idealized fracture
mechanics plate model giving accurate FCG life results
• FCG life for specified initial crack size
• MotivationReduce variability and errors in the analysis process introduced by the human operatorReduce human time for analysis
• Especially important for large numbers of calculations
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Automatic Fracture Model Strategy
• General rules that can be applied to any initial crack location in any general 2D model, set within a rigorous logical framework
• Addresses the effects of finite component boundariescurved front and side surfacescorners of various anglescrack transitionscomplex stress fieldsembedded, surface, and corner cracks
• GUI provides visualization for user review of the generated models
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Automatic Fracture Model Examples
Automatically generated fracture mechanics plates for six representative crack locations
Circles are estimates of critical crack size
2D axisymmetric finite element mesh
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Automatic Fracture Model Examples
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x
y
• QR(ξ0, η)
• Q(ξ, η)
• Q*(0, η)
• Q’(ξ0, η0)yQ (-ξ, η) •
• xQ (ξ, -η)
c
a t
W
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New Weight Function Stress Intensity Factor Solutions
• Calculate effect of actual FE stress field on SIF• New family of univariant & bivariant SIF solutions developed
Embedded, surface, corner, and through cracks in plates
• Calibrated with accurate 3D numerical reference solutions • Special algorithms to improve computational efficiency
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Life Contour Maps
• Use auto-plate capability to build FM model at every node in the FE model
• Calculate FCG life for user-specified (fixed) initial crack size at each node
Stress Contours Life Contours
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Life Contour Maps
• Life contour maps provide guidance for calculation of reliability as well as for design revision
• Stress contour hot spots and life contour hot spots may be different, due to geometry influences
Stress Contours Life Contours
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DARWIN® Overview Design 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 FactorsLife Scatter
Stress Scatter
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Zone-Based Risk Assessment
• In probabilistic damage tolerance, we need to calculate not merely the FCG life, but the overall probability of fracture for the component, given all the potential locations that a crack could occur
• Discretize component into zones based on similar anomaly distribution, stress, lifetime
Place crack at life-limiting location in the zone• Total probability of fracture for zone:
(probability of having an anomaly) x (POF given an anomaly)
“Anomaly probability” determined by anomaly distribution, zone volume“POF given an anomaly” is probabilistic FCG calculation
• POF for disk = sum of zone probabilities• As individual zones become smaller (number
of zones increases), risk converges down to “exact” answer (~numerical integration)
1
2 3 4
m
5 6 7
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Next Automation Step: Reliability Calculation
• Use “auto-plate” to generate FCG model at many locations in the component
• Use life contour map to guide automated zone breakup• Give special attention to efficiency: do as few FCG life
calculations as possible for adequate accuracy
ac
a
NTarget N
P(a)
P(N)
Pf
ac
a
NTarget N
P(a)
P(N)
Pf
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Residual Stress Issues
• Residual stresses can introduce significant uncertaintyWhat are the magnitudes of the residual stresses?How might these residual stresses change with cycles/temperature?How might the fracture critical locations change with RS effects?What are the anticipated fatigue lifetimes at these locations?
• Challenges:Assess fatigue life at many different locationsCombine complex service stress fields with complex RS fieldsAddress uncertainty in residual stressesIntegrate total risk of fracture over the entire component
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-80
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-60
-50
-40
-30
-20
-10
0
10
0 0.02 0.04 0.06 0.08 0.1
Depth (inches)
Res
idua
l Str
ess
(ksi
)
baseline200 min60 min10 min600 minaverageupperlower
Variability in Residual Stress SP and LSP in Ti-6Al-4V
Prevey et al., Proc. 17th Heat Treating Society Conf./Expo.
and 1st Int. Heat Treating Symp., ASM, 1998, pp. 3-12.
±8 ksi envelope
-140
-120
-100
-80
-60
-40
-20
0
20
0 0.002 0.004 0.006 0.008 0.01 0.012
Depth (inches)
Res
idua
l Str
ess
(ksi
)
baseline10 min
60 min200 min
600 minaverageupper
lower±10 ksi envelope
Shot Peening Laser Shock Peening
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Effect of Residual Stress Variability on Fatigue Life
R = 0.1 Ti-6Al-4V
60
70
80
90
100
110
120
10000 100000 1000000
Cycles to Failure
Max
Stre
ss (k
si)
LPBSPDARWIN SP .003DARWIN LPB .003LPB -9 ksiLPB +9 ksiSP -9 ksiSP +9 ksi
These life calculations assume zero initiation life and include a small-crack model 20
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(Local) Residual Stress Regions in DARWIN
RS Region
• The RS region is defined by the gradient distance and orientation 21
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Exploratory Study of Local RS Variability
Shot Peening
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 50000 100000 150000 200000 250000 300000 350000 400000
Crack Growth Life, Flights
Prob
abili
ty
CDF (90 ksi Max Stress)CDF (80 ksi Max Stress)CDF (70 ksi Max Stress)Estimated Values (90 ksi)Estimated Values (80 ksi)Estimated Values (70 ksi)
• Residual stress is currently modeled as a deterministic quantity in DARWIN
• The influence of residual stress variability on crack growth life was explored by linking the NESSUS probabilistic code with DARWIN
• Stress amplitude was modeled as a normally distributed random variable
-140
-120
-100
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-60
-40
-20
0
20
0 0.002 0.004 0.006 0.008 0.01 0.012
Depth (inches)
Res
idua
l Str
ess
(ksi
)
baseline10 min
60 min200 min
600 minaverageupper
lower
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Effect of Local Residual Stress Variability on Fatigue Life for LSP
Laser Shock Peening
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 200000 400000 600000 800000
Crack Growth Life, Flights
Prob
abili
ty
CDF (110 ksi Max Stress)CDF (100 ksi Max Stress)CDF (90 ksi Max Stress)Estimated Values (110 ksi)Estimated Values (100 ksi)Estimated Values (90 ksi)
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DARWIN Treatment of Material Processing Residual Stresses
• USAF SBIR phase I program currently in progressProject Title – “Integrated Processing and Probabilistic Lifing Models for Superalloy Turbine Disks”Project Manager – Rollie Dutton, Air Force Research LaboratoryPrime Contractor – Ravi Shankar, Wei-Tsu Wu, Scientific Forming Technologies Corporation (SFTC)
• Primary objective: Establish link between DARWIN and SFTC DEFORM software
Phase 1 focus for DARWIN – demonstrate proof of concept model for linking residual stress predictions from DEFORM with probabilistic fracture risk assessment capability in DARWINWill also evaluate links with other DEFORM variables (microstructure, defect location/orientation) in preparation for potential Phase II project
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DEFORM-DARWIN SBIR
• Phase 1 statusA residual stress interface is being established between DEFORM and DARWIN
• Residual stress files are transferred from DEFORM to DARWIN using SIESTA neutral file standard
• Service stress files can be transferred from DEFORM or other FE codes (e.g., ANSYS, ABAQUS, MARC) using existing DARWIN capabilities
The interface has been successfully implemented in DARWIN
DEFORMDARWIN
Service StressNeutral file
Residual StressNeutral file
ANSYS
DEFORMDARWIN
Service StressNeutral file
Residual StressNeutral file
ANSYS
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DARWIN Stress Superposition Approach for Residual Stresses
Service StressNeutral file
Residual StressNeutral file
stress gradient
Service Stress
0.0 0.2 0.4 0.6 0.8 1.0-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
Residual Stress
Combined stress
Residual stress analysisDARWIN Stress ExtractionNormalized Distance
Nor
mal
ized
Stre
ssService StressNeutral file
Residual StressNeutral file
stress gradient
Service Stress
0.0 0.2 0.4 0.6 0.8 1.0-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
Residual Stress
Combined stress
Residual stress analysisDARWIN Stress ExtractionNormalized Distance
Nor
mal
ized
Stre
ss
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DARWIN Enhancements for Material Processing Residual Stresses
Input
Output
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DARWIN Enhancements for Material Processing Residual Stresses (cont)
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DARWIN Demonstration Example
• The DARWIN residual stress superposition capability was demonstrated for a realistic engine disk
• Objectives:Demonstrate that DARWIN could correctly combine service and residual stress values from files that were in the SIESTA format (i.e., format used for DEFORM output files)Correctly apply combined stress values to deterministic crack growth life and fracture risk computations
• To verify the result, crack growth life and fracture risk values were computed for two sets of input data
Service and “residual” stresses combined in a single set of SIESTA formatted files prior to use in DARWINService and “residual” stresses in separate sets of SIESTA formatted files that were combined during run time using the enhanced version of DARWIN developed under this projectAgreement was observed, which indicates that DARWIN is ready for use with DEFORM output files
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Influence of “Residual Stress” on Life Contour Values in DARWIN
Without Residual Stress With Residual Stress
Stress
Life
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Some Potential Future Steps
• Develop formal methods to treat residual stress variability in DARWIN (and effects on fracture risk)
• Develop probabilistic models for residual stress variability as a function of uncertainties in manufacturing processes
• Address residual stress relaxation and redistribution due to thermal, monotonic load, cyclic load, and crack growth mechanisms
McClung, FFEMS 30 (2007):173-205
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Summary
• DARWIN provides an accurate, efficient, user-friendly method to perform structural reliability assessments of 2D and 3D components
Automated fatigue crack growth analysisProbabilistic damage tolerance analysis
• DARWIN facilitates analysis of engineered (local) residual stress effects on fatigue crack growth life
• Development of a DEFORM-DARWIN interface is underway to address bulk residual stress effects on fatigue crack growth life and reliability
• Residual stresses introduce multiple uncertainties into structural reliability analysis
These can be addressed through probabilistic analysis, but more work is needed