Harry Millwater The University of Texas at San Antonio Michael Enright
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Transcript of Harry Millwater The University of Texas at San Antonio Michael Enright
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A Convergent Probabilistic Technique for Risk Assessment of Gas Turbine Disks Subject to
Metallurgical Defects
Harry Millwater
The University of Texas at San Antonio
Michael Enright
Southwest Research Institute
Simeon Fitch
Mustard Seed Software
April 2002
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Rotor Burst Severing Plane Hydraulics
Fatigue Crack Missed During Inspection
Crack Initiated From Metallurgical Defect
Accident in Sioux City, 1989
NTSB Report
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Hard Alpha Defect In Titanium
Brittle Inherent Defect - Site for Fatigue Crack Initiation
Titanium Matrix
Hard AlphaDefect
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1990: FAA Post-crash Report Recommended Probabilistic Damage Tolerance Approach to Reduce Risk of Failure Due To Metallurgical Defects in Future Designs of Titanium Rotors
AIA Rotor Integrity Subcommittee (RISC) formed to address these (and other) issues
Improved Materials
Improved Inspection Methods
Improved Design Methods
FAA/Industry Response
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Advisory Circular 33.14
FAA Advisory Circular 33.14 Requests Risk Assessment Be Performed for All New Titanium Rotor Designs
New Designs Must Pass Design Target Risk for Rotors
ComponentsComponents
RiskRisk
AA BB
MaximumMaximumAllowableAllowable
RiskRisk
1010-9-9
RiskRiskReductionReductionRequiredRequired
CC
1E-9 - Component
5E-9 - Engine
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DARWIN OverviewDesign Assessment of Reliability With INspection
Probabilistic Fracture Mechanics
Material Crack Growth Data
Finite Element Stress Analysis
Anomaly Distribution Probability of DetectionNDE Inspection Schedule
Risk Contribution Factors
Pf vs. Flights
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Anomaly Distribution
How Likely Is Defect in a Rotor?What is the Distribution of Defect Sizes?
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Risk Assessment Results
Risk of Fracture on Per Flight Basis
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Risk Contribution Factors
Identify Regions of Rotor With Highest Risk of Failure
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Random Variables
Probability of having an anomaly in the disk,
Possibility that a hard alpha anomaly developed during the titanium melt process could be in any location of the disk,
Initial size distribution of the anomaly,
Randomness in the time of inspection time, probability of detection, finite element stresses and fracture mechanics analysis.
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Zone-based Risk Assessment
1
2 3 4
m
5 6 7
Collect material exhibiting a like fracture mechanics behavior into a zone
Place flaw in the life limiting locationAssume risk constant over the zone
Akin to stratified sampling methodology -- assures sampling of small but high stressed areas.
Finite element mesh used as a framework for defining zones.
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Zone-based Risk Assessment
1
2 3 4
m
5 6 7
Define zones based on similar stresses, inspections, defect distributions, lifetimes
Defect probability determined by defect distribution, zone volume
Probability of failure assuming a defect computed using Monte Carlo sampling or advanced methods
Pi = Pi[A] * Pi[B|A] - zone
PfDISK Pi - disk
Prob. of having a defect
Prob. of failure given a defect
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AC Test Case
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Mesh Size Dependence
Life from a 10x10 mil Flaw “Coarse” Mesh Overlay
36,000 Cycles
28,000 Cycles
Greater than 20% change in life across single “element”
Courtesy GEAERisk variation > Stress Variation
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Element Subdivision
Selected elements subdivided 2 x 2
Modified mesh only used for risk zone creation (not FE analysis)
Elements may be subdivided (repeatedly) to provide the desired resolution for zone creation.
Element subdivision from original FE mesh
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Onion Skinning
A thin layer of elements is required to model surface zones Subdivide surface elements to develop a layer of
elements of desired thickness, e.g., 20 mils
After Onion Skinning
Before Onion Skinning
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Convergence Issues
Constant variation in risk throughout the disk. Risk approximated as constant in each zone.Defect located in life limiting location of zone.Convergence in disk POF depends on number of zones
and zone breakup. (although will converge from the high side)
A zone refinement strategy has been developed and
implemented to facilitate obtaining a converged solution
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Zone Refinement Capability
Features
Robustness
Should always work for any well posed problem
Solution should converge to correct solution
Simple - easy to understand, not hidden nor confusing
Extension of current approach
Quality of the risk solution obtained should not be dependent on the experience of the user
Quality of the risk solution obtained should not be dependent on the initial zone breakup
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Zone Refinement Methodology
Identify zones that contribute significantly to the overall risk
Automatically subdivide these zones into smaller subzones
Generate new input file and rerun
(results for unmodified zones read from database - coming in risk assessment code)
Check convergence
Iterate
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Risk Contribution Factors
Identify Regions of Rotor With Highest Risk of Failure
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Zone Selection
User defines initial zones (corner, surface, embedded)
Risk assessment carried outSelect potential zones to be refined
based on Risk Contribution Factor(RCF) RCF (w or w/o inspection) > , e.g.,
5%Zone RCF < , no refinementZone RCF > , possible refinement
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Create Potential Subzones
The new “subdivide” button on the zone editor panel will automatically create subzones from any parent zones.
This function will automatically:Subdivide material into 4 (or 3) zones for
subsurface, 2 zones for surfacePlace flaw in subzones geometrically closest to
location in parent zoneAdjust plate if necessaryInherit other properties from parent
All POTENTIAL subzones may be edited by user
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Generate Potential Subzones
Determine material in each subzone Use centroid equation (based on stress)Embedded -> 4 (or 3) zones, surface -> 2 zonesUses plate coordinates to define quadrants
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Subdivide Elements
Zones that have only a few elements, subdivide into more elements as previously described
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Generate Potential Subzones
Place flawGeometrically closest to flaw in parent zone
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Generate Potential Subzones
Define plateUse same plate as parent zone (new crack is inside
existing plate), same gradient directionClip front and back along gradient line if necessaryIf new flaw location is outside parent plate, move
plate if possible. If not possible, warn user.
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Generate Potential Subzones
Inherit the following properties from parent
volume multiplier, inspection schedules, material no., crack type, crack plane, defect distribution, # samples
Note: ALL generated potential subzones may be edited by user before analysis.
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Zone Refinement Procedure
GUI
Risk Assessment
ResultsDatabase
InputFile
Read/Write Results
Input File
SubsequentIterations
Iterative procedure until convergence
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Convergence Criteria
Examine stop criteria - user implemented If risk < L (target risk) All RCFs < target If (disk risk(i+1) - disk risk(i))/disk risk(i) < E
0.0E+00
4.0E-09
8.0E-09
1.2E-08
1.6E-08
2.0E-08
2.4E-08
2.8E-08
3.2E-08
3.6E-08
0 1 2 3 4 5 6
ITERATION NUMBER
PR
OB
AB
ILIT
Y O
F F
RA
CT
UR
E P
ER
FL
IGH
T C
YC
LE
Pf no inspection
Pf with inspection
1.90 E-9
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Example: AC Test Case
Initial Zone Breakup Converged Zone Breakup
Zone breakup closely matches risk variation
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Mesh Size Dependence
Life Contour Zone Breakup
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Retrieval of Zone Results
For any zone in the input file, compare the zone’s properties with those on the database. If a match is found, the results are retrieved. If not, the results are calculated.
Impeller1
22 Zones - 13 retrieved from impeller0.ddb
Impeller0
16 Zones
Zone numbers do not have to match
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Zone Comparison Checks
Global checks - if these are not satisfied, risk results cannot be retrieved (other information possible, e.g., stress results) Probabilistic method
(Monte Carlo vs. Importance sampling)
Local checks Material Defect distribution # samples Volume multiplier
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Zone Properties Checks
Local checks (cont’) Life scatter - median & COV Crack type, plane, r & z coordinates Plate: stress directions, dimensions (xd, hx, yd, hy) Elements:
All element numbers must match exactly Inspection schedules
All inspection schedule numbers and type (top, bottom, left, right) must match exactly
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Example
Impeller model - 6 iterations
16 Zones
0 Retrieved
3:57 (3:57)
22 Zones
13 Retrieved
3:08 (7:08)
34 Zones
12 Retrieved
10:24 (17:32)
53 Zones
24 Retrieved
14:12 (31:44)
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Example
Risk for 6th iteration is ~10% of initial risk
1
0.12 0.120.11
0.1
0.170.3
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Iteration Num ber
Ris
k a
s p
erc
en
t o
f in
itia
l
mo
de
l
62 Zones
48 Retrieved
7:30 (39:14)
70 Zones
59 Retrieved
6:09 (45:23)
73 Zones
68 Retrieved
2:58 (48:21)
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Summary and Conclusions
A number of significant new features have been developed and implemented to facilitate zone development and refinement.
Element subdivision implemented in an easy-to-use manner to allow risk zone dimensions of any size.
Onion skinning to easily develop surface zones
Zone refinement strategy delineated and tools implemented to provide the user an approach to consistently and conveniently converge on the risk solution.
Subzone visualization and selectionSubzone creation
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Summary and Conclusions
Zone refinement strategy (cont’)
Subzones may be edited by the userResults for unmodified zones retrieved from results
database and integrated with new subzone results(database can be used for archiving)
Provides the user an approach to consistently and conveniently converge on the risk solution.
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The Future
FAA Phase II Grant Awarded to SwRIin April 1999 – Five Year Duration, $9M
Extend To Cast, Wrought,Powder Nickel
Extend To Surface Defects:Induced Defects(as opposed to inherent) byMachining, Maintenance, etc.
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Zoned Impeller Model
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Example: AC Test Case
6 Zones 10 Zones
Note: Red zones contribute > 1% of (total) disk risk
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Example: AC Test Case (cont)
Note: Red zones contribute > 1% of (total) disk risk
91 Zones 192 Zones
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Element Refinement Example
Subsequent DARWIN analysis with improved crack transitioning, fine mesh and 70 zones yields a solution within AC limits.
Pf wo insp = 1.79E-9
Courtesy Pratt & Whitney
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Coloring All Zones by RCF
Set Threshold Value to 0.0
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Probability of Detection Curves
Defines Probability of Detecting Flaw as Function of Flaw Size
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Inspection
DARWIN Simulates Inspection of Rotor for Metallurgical Defects and Removal of Rotor if Defect Detected
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Material Properties
Fatigue Crack Growth Properties – How Fast CrackGrows and Critical Crack Size
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FAA Advisory Circular
AC 33.14 Damage Tolerance for High Energy Turbine Engine Rotors, 1/8/01
Damage Tolerance - Recognizes the potential existence of component imperfections
Probabilistic Based - Design Target Risk (DTR)Augments, not replaces, existing safe life approach
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Fracture Mechanics Model
GUI Developed To Graphically Define DARWIN Input
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Summary
FAA and industry recognize role of a probabilistically-based damage tolerance analysis method for Titanium Rotors
DARWIN software developed as an Acceptable Means To Assess Rotors for Compliance With Design Target Risk
Industry Expects Risk Reduction of Three Times or More
SwRI/Industry Team Under Extending DARWIN To Other Rotor-Integrity Issues
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DARWINTM Status
3.3 Delivered Jan 2000 GUI enhancements, web site distribution of code
3.4 - April 2001 Improved K solutions Inspection transition with defect, e.g., embedded -> surface
3.5 - Summer 2001 Element subdivision Zone refinement
4.0 - End of 2001 Initial version for surface damage (maintenance/machining
induced defects)
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Severity of Problem
RotorRotor
Engine Rotor Is Major Structural Carrying Member of Engine
Rotors Seldom Fail but, . . . if Rotor Fractures, Too Much Mass-Energy To Prevent Penetrating Fuselage
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Why Probabilistic?
Defects Seldom Occur (but Consequences Severe If They Do). Difficult to Analyze other than probabilistically.
Damage Tolerance
Explicitly Considers Behavior of Structure Subjected To Imperfections (Cracks)
Addresses This Situation Through Incorporation of Fracture-Resistant Design, and/or Nondestructive Inspection
FAA/Industry Response
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Compute Risk for New Zones
Read risk results from unchanged zones <-- Restart Capability
Compute risk for new zonesSum risks and compute new risk contribution factors
Risk Assessment
ResultsDatabase
Retrieve Results for Unchanged
Zones
New Zones
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Potential Future Efforts
Provide feedback to the GUI regarding the life for a particular crack location. Ensures crack is in the life limiting location.
Potential crack locations placed in zone. Flight_life evaluates life and returns the solution. GUI ranks the crack locations.
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Potential Future Efforts
Make the GUI scriptable so that the GUI would execute a list of commands. Zone refinement then becomes automated - zone
refinement could be carried out without human intervention.
Scripts could be generated for common tasks like report generation.
GUI would generate a script of operations at any time which may be replayed at a later date.
Automated search for the life limiting location in the zone