Transcript DARWIN GUI 3.4.5 - College of Engineering

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
Accident in Sioux City, 1989
NTSB Report
 Rotor Burst Severing
Plane Hydraulics
 Fatigue Crack Missed
During Inspection
 Crack Initiated From
Metallurgical Defect
2
Hard Alpha Defect In Titanium
Hard Alpha
Defect
Titanium Matrix
 Brittle Inherent Defect - Site for Fatigue Crack Initiation
3
FAA/Industry Response
 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
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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
Risk
Reduction
Required
Risk
10-9
Maximum
Allowable
Risk
 1E-9 - Component
 5E-9 - Engine
A
B
C
Components
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DARWIN Overview
Design Assessment of Reliability With INspection
Anomaly Distribution
NDE Inspection Schedule
Probability of Detection
Finite Element Stress Analysis
Probabilistic Fracture Mechanics
Pf vs. Flights
Material Crack Growth Data
Risk Contribution Factors
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
3
2
4
5
6 7
 Collect material exhibiting a like fracture
mechanics behavior into a zone
 Place flaw in the life limiting location
 Assume 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.
m
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Zone-based Risk Assessment
1
3
2
4
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
Prob. of having
a defect
Prob. of failure
given a defect
Pi = Pi[A] * Pi[B|A] - zone
m
PfDISK   Pi - disk
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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”
Risk variation > Stress Variation
Courtesy14
GEAE
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
Before Onion
Skinning
After 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 20
Zone Selection
 User defines initial zones
(corner, surface,
embedded)
 Risk assessment carried
out
 Select potential zones to be
refined based on Risk
Contribution Factor(RCF)
 RCF (w or w/o
inspection) > , e.g., 5%
Zone RCF < , no
refinement
Zone 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 surface
Place flaw in subzones geometrically closest to
location in parent zone
Adjust plate if necessary
Inherit 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 zones
Uses 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 flaw
Geometrically closest to flaw in parent zone
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Generate Potential Subzones
 Define plate
Use same plate as parent zone (new crack is inside
existing plate), same gradient direction
Clip front and back along gradient line if necessary
If 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
Iterative procedure until convergence
GUI
Subsequent
Iterations
Input File
Results
Database
Read/Write
Results
Input
File
Risk
Assessment
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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
3 .6 E -0 8
3 .2 E -0 8
P R O B A B IL IT Y O F F R A C T U R E P E R F L IG H T C Y C L E
P f n o in s p e c tio n
2 .8 E -0 8
P f w ith in s p e c tio n
2 .4 E -0 8
2 .0 E -0 8
1 .6 E -0 8
1 .2 E -0 8
8 .0 E -0 9
4 .0 E -0 9
1 .9 0 E -9
0 .0 E + 0 0
0
1
2
3
4
5
6
IT E R AT IO N N U M B E R
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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.
16 Zones
22 Zones - 13
retrieved from
impeller0.ddb
Zone numbers
do not have to
match
Impeller0
Impeller1
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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
22 Zones
0 Retrieved
13 Retrieved
3:57 (3:57)
3:08 (7:08)
34 Zones
53 Zones
12 Retrieved
24 Retrieved
10:24 (17:32)
14:12 (31:44)
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Example
62 Zones
70 Zones
48 Retrieved
59 Retrieved
7:30 (39:14)
6:09 (45:23)
68 Retrieved
2:58 (48:21)
1 .2
1
m o d el
73 Zones
R is k a s p e r c e n t o f in it ia l
 Risk for 6th
iteration is
~10% of initial
risk
1
0 .8
0 .6
0 .4
0 .3
0 .1 70 .1 2 0 .1 20 .1 1
0 .2
0 .1
0
0
1
2
3
4
5
6
7
It e r a t io n N u m b e r
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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 selection
Subzone creation
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Summary and Conclusions
 Zone refinement strategy (cont’)
Subzones may be edited by the user
Results 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 SwRI
in April 1999 – Five Year Duration,
$9M
 Extend To Cast, Wrought,
Powder Nickel
 Extend To Surface Defects:
Induced Defects
(as opposed to inherent) by
Machining, Maintenance, etc.
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)
91 Zones
192 Zones
Note: Red zones contribute > 1% of (total) disk risk
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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
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Courtesy Pratt & Whitney
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
Inspection
 DARWIN Simulates Inspection of Rotor for Metallurgical
Defects and Removal of Rotor if Defect Detected
Material Properties
 Fatigue Crack Growth Properties – How Fast Crack
Grows and Critical Crack Size
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
Fracture Mechanics Model
 GUI Developed To Graphically Define DARWIN Input
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
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
Rotor
 Engine Rotor Is Major Structural Carrying Member
of Engine
 Rotors Seldom Fail but, . . . if Rotor Fractures, Too
Much Mass-Energy To Prevent Penetrating Fuselage
FAA/Industry Response
 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
Compute Risk for New Zones
 Read risk results from unchanged zones <-- Restart
Capability
 Compute risk for new zones
 Sum risks and compute new risk contribution factors
New Zones
Results
Database
Retrieve Results
for Unchanged
Zones
Risk
Assessment
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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
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