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

2

Rotor Burst Severing Plane Hydraulics

Fatigue Crack Missed During Inspection

Crack Initiated From Metallurgical Defect

Accident in Sioux City, 1989

NTSB Report

3

Hard Alpha Defect In Titanium

Brittle Inherent Defect - Site for Fatigue Crack Initiation

Titanium Matrix

Hard AlphaDefect

4

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

5

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

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

7

Anomaly Distribution

How Likely Is Defect in a Rotor?What is the Distribution of Defect Sizes?

8

Risk Assessment Results

Risk of Fracture on Per Flight Basis

9

Risk Contribution Factors

Identify Regions of Rotor With Highest Risk of Failure

10

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.

11

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.

12

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

13

AC Test Case

14

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

15

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

16

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

17

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

18

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

19

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

20

Risk Contribution Factors

Identify Regions of Rotor With Highest Risk of Failure

21

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

22

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

23

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

24

Subdivide Elements

Zones that have only a few elements, subdivide into more elements as previously described

25

Generate Potential Subzones

Place flawGeometrically closest to flaw in parent zone

26

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.

27

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.

28

Zone Refinement Procedure

GUI

Risk Assessment

ResultsDatabase

InputFile

Read/Write Results

Input File

SubsequentIterations

Iterative procedure until convergence

29

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

30

Example: AC Test Case

Initial Zone Breakup Converged Zone Breakup

Zone breakup closely matches risk variation

31

Mesh Size Dependence

Life Contour Zone Breakup

32

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

33

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

34

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

35

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)

36

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)

37

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

38

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.

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.

40

Zoned Impeller Model

41

Example: AC Test Case

6 Zones 10 Zones

Note: Red zones contribute > 1% of (total) disk risk

42

Example: AC Test Case (cont)

Note: Red zones contribute > 1% of (total) disk risk

91 Zones 192 Zones

43

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

44

Coloring All Zones by RCF

Set Threshold Value to 0.0

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 CrackGrows 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

51

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)

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

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

54

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

55

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.

56

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