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DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES

THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS ANACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCHINSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THEORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM:

(A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I)WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, ORSIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESSFOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON ORINTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUALPROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'SCIRCUMSTANCE; OR

(B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER(INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVEHAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOURSELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD,PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT.

ORGANIZATION(S) THAT PREPARED THIS DOCUMENT

Structural Integrity AssociatesEPRI Repair and Replacement Applications Center

ORDERING INFORMATION

Requests for copies of this report should be directed to the EPRI Distribution Center, 207 Coggins

Drive, P.O. Box 23205, Pleasant Hill, CA 94523, (800) 313-3774.

Electric Power Research Institute and EPRI are registered service marks of the Electric PowerResearch Institute, Inc. EPRI. POWERING PROGRESS is a service mark of the Electric PowerResearch Institute, Inc.

COPYRIGHT 1999 ELECTRIC POWER RESEARCH INSTITUTE, INC. ALL RIGHTS RESERVED.

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iii

CITATIONS

This report was prepared by

Structural Integrity Associates3315 Almaden Expressway, Suite 24San Jose, California 95118-1557

Principal InvestigatorsD. Rosario

P. RiccardellaS. Tang

EPRI Repair and Replacement Applications Center1300 W.T. Harris BoulevardCharlotte, NC 28262

Principal InvestigatorsD. GandyR. Viswanathan

This report describes research sponsored by EPRI.

The report is a corporate document that should be cited in the literature in the following manner:

Development of an LP Rotor Rim-Attachment Cracking Life Assessment Code (LPRimLife),EPRI, Palo Alto, CA: 1999. TR-110407.

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v

REPORT SUMMARY

Report SummaryMost of the domestic turbine fleet has reached the 50,000-hour range of service operation.Unfortunately, above this level of operational hours, a number of turbines have begun toexperience low-pressure (LP) rim-attachment cracking. A computer code developed by EPRI,LPRimLife, provides utilities with a methodology for assessing the remaining life of LP rimattachments with known or suspected cracking.

BackgroundThe first documented incidence of stress corrosion cracking in blade rim attachments in nuclearLP steam turbine discs occurred in the late 1970s in a U.S. pressurized water reactor (PWR)power plant. Since that occurrence, EPRI has performed two surveys (one in 1980 and the mostrecent in 1995) to review industry experience with rim-attachment cracking. The latterdocumented that of 109 boiling water reactor (BWR) and PWR operating units surveyed, 38%had experienced cracking. Based upon this experience, EPRI, along with the input and directionof several key utilities, began the development of a life assessment tool (LPRimLife) to assist inaddressing rim-attachment cracking.

Objectives

To develop a software package with which utility personnel can determine the probability offailure for low-pressure rotor rim attachments

To provide utilities with a tool for evaluating the condition and disposition of LP rotor rimattachments for their turbines

To acquire geometry and dimensional information for both straddle-mount (GE) and axial-entry (Westinghouse) style attachments to be used in generating a library of individual stresssolutions

ApproachThe development of the life assessment code, LPRimLife, was split into two phases to separately

address cracking for the two rim-attachment configurations. Phase I addressed the straddle-mount attachments and is now complete. Phase II is currently in development and addressesWestinghouse axial-entry attachments. The methodology employed for development of the codewas to generate individual modules to address specific aspects of the cracking problem. Themodules include the following:

Built-in stress solutions for problematic GE/Westinghouse rim attachments

Materials properties (unit-specific or default values)

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vi

Crack initiation and growth

Operating and inspection data inputs

Fracture mechanics

Load redistribution and ligament overload checks

Deterministic and probabilistic analysis options

Each module was then integrated into a single package (LPRimLife) for predicting remaininglife.

ResultsLPRimLife integrates a variety of factors to assess critical crack size, to address loadredistribution between individual steeples/ligaments, and to predict remaining life of LP rotorrim attachments with known or suspected cracking. Geometrical and dimensional data have beenobtained for a number of different problematic straddle-mount and axial-entry designs. From thisinformation, specific finite element stress solutions have been developed for each design.

EPRI PerspectiveThe LPRimLife computer code combines the appropriate stress analysis information, materialproperty data, and fracture mechanics algorithms with applicable material degradation data intoan integrated methodology to assess the remaining life of LP rotors with rim-attachmentcracking. For the first time, utilities can now predict the remaining life of rim attachments fromboth a deterministic and a probabilistic standpoint. Critical crack size can be assessed, andmaintenance/repair schedules can be more effectively planned. In conjunction with recentadvances made in ultrasonic inspection of rim attachments using phased array technologies,LPRimLife provides utilities with the ability to more effectively monitor their turbines.Furthermore, it assists utilities in planning effective maintenance strategies for continued

operation of LP rotor rim attachments with known or suspected cracking.

TR-110407

KeywordsSteam turbinesLow-pressure steam turbinesRim attachment crackingBlade attachment crackingLPRimLife

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EPRI Licensed Material

vii

ABSTRACT

Stress corrosion cracking (SCC) in the blade attachment region of low-pressure (LP) turbinerotors has emerged as one of the most significant problems affecting steam turbine rotors today.In response to an expressed utility need for a life prediction tool, EPRI has sponsored thedevelopment of an easy-to-use PC-based computer program, LPRimLife, which enables utilitypersonnel to perform a rapid remaining life assessment of LP rotors with known or suspectedcracking. The first phase of development, incorporating the methodology for evaluating crackingin GE dovetail (straddle-mount) attachments, is complete. The next phase, to address cracking inWestinghouse axial-entry attachments, is currently in development.

The LPRimLife computer code, developed for EPRI by Structural Integrity Associates, combinesthe necessary stress analysis, material property data, and fracture mechanics algorithms withapplicable material degradation data into an integrated methodology to assess the remaining lifeof LP rotors with rim-attachment cracking. Features built into the PC-based code include thefollowing:

Easy-to-use Windows graphical user interface with pull-down menus and dialog boxes

Built-in library of stress solutions which can easily expand to incorporate user-specificattachment geometries

A fracture mechanics stress intensity factor calculator for arbitrary crack aspect ratios

Material properties module with built-in fracture toughness data

An algorithm to account for redistribution of load between top, middle, and bottom hookswith cracking

An algorithm to check for overload of a cracked ligament in addition to fracture toughnesslimit

SCC threshold to simulate crack arrest if stress intensity factors drop below the threshold

Deterministic and probabilistic calculation options and built-in graphics and plottingcapability to view and modify presentation of results

With comprehensive on-line help, the program facilitates rapid life assessments and parametricstudies to be performed by non-experts with minimal introduction to the software.

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ix

ACKNOWLEDGMENTS

The authors would like to thank all the tailored collaboration utility participants who funded thisprogram and provided valuable input, guidance and feedback from the initial stages of theprogram development through the testing and release of the of the first phase software.

T. Alley Duke Power CompanyG. Beckerdite Kansas City Power and LightR. Bundt Southern NuclearJ. Johnson Alliant/IES Utilities

P. Klein Baltimore Gas and ElectricM. Metzger Nebraska Public Power DistrictA. Mosquada Pacific Gas and ElectricD. Wright Baltimore Gas and Electric

The authors would also like to thank members of the TurboCare team which has partnered withEPRI in a sister program, Development of Repair Technology for Shrunkon Discs andMonoblock Rotors. Dimensional information generated under that program and independentlyby TurboCare has been incorporated into this report and into the LPRimLife program. Specificmembers of the TurboCare team involved in this project include the following:

J. BeverlyB. CatlowP. DiCristoforoS. Hecker

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xi

CONTENTS

1INTRODUCTION.................................................................................................................. 1-1

2METHODOLOGY................................................................................................................. 2-1

3PROGRAM MODULES........................................................................................................ 3-1

3.1 Stress Analysis.......................................................................................................... 3-1

3.2 Crack Initiation and Growth ....................................................................................... 3-5

3.3 SCC Growth Threshold (KISCC

) ................................................................................... 3-6

3.4 Critical Crack Size..................................................................................................... 3-6

3.4.1 Load Redistribution............................................................................................... 3-7

3.5 Remaining Life (Deterministic Versus Probabilistic)................................................... 3-8

4GEOMETRICAL AND DIMENSIONAL MEASUREMENTS ................................................. 4-1

5LPRIMLIFE SOFTWARE..................................................................................................... 5-1

5.1 Description ................................................................................................................ 5-1

5.2 Analysis .................................................................................................................... 5-3

5.3 Results...................................................................................................................... 5-3

6CONCLUSIONS .................................................................................................................. 6-1

7FUTURE DEVELOPMENTS................................................................................................ 7-1

8REFERENCES .................................................................................................................... 8-1

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LIST OF FIGURES

Figure 1-1 Rim Attachment Cracking in Nuclear Units by Reactor Type and Manufacturer ..... 1-2

Figure 1-2 Rim Attachment Cracking in Fossil Units by Steam Type (Supercritical orSubcritical) ...................................................................................................................... 1-3

Figure 2-1 Schematic of Rim-Attachment Configurations Illustrating Typical Locations ofCracking.......................................................................................................................... 2-2

Figure 2-2 Flowchart of LPRimLife Software........................................................................... 2-3

Figure 3-1 Typical FE Analysis Model of Disk and Blade Attachment Region With Non-

Linear Contact (Gap) Elements ....................................................................................... 3-2Figure 3-2 Geometry and Loading Data for a Built-In Attachment Geometry ........................... 3-4

Figure 3-3 Stress Gradients Normal to Crack Incorporated in Built-In Library of FE StressResults ............................................................................................................................ 3-4

Figure 3-4 Critical Crack Size Determination Flow Diagram.................................................... 3-7

Figure 3-5 Illustration of Load Redistribution as a Function of Crack Depth (a) to HookWidth (W) Ratio. .............................................................................................................. 3-8

Figure 3-6 Flowchart for Probabilistic Calculations.................................................................. 3-9

Figure 4-1 Axial-Entry (Westinghouse) Root Types................................................................. 4-6

Figure 4-2 Axial-Entry (Westinghouse) Steeple Groove Dimensions....................................... 4-7

Figure 5-1 LPRimLife Splash Screen and Main Menu Options................................................ 5-1

Figure 5-2 Typical Solution Procedure .................................................................................... 5-2

Figure 5-3 Calculation and Print Controls Data Input Window................................................. 5-3

Figure 5-4 Deterministic Analysis Results Output Window ...................................................... 5-4

Figure 5-5 Probabilistic Analysis Results Output Window........................................................ 5-4

Figure 5-6 Cumulative Probability of Failure Plot Option From the View Main Menu............... 5-5

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xv

LIST OF TABLES

Table 3-1 Phase I Straddle-Mount (GE) Dovetail Geometries ................................................. 3-3

Table 3-2 Phase 2 Axial-Entry (Westinghouse) Geometries.................................................... 3-3

Table 4-1 Summary of Straddle-Mount (GE) Dimensional and Loading Data.......................... 4-2

Table 4-2 Summary of Axial-Entry (Westinghouse) Dimensional and Loading Data................ 4-4

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1-1

1INTRODUCTION

The problem of stress corrosion cracking (SCC) in the blade attachment region of nuclear lowpressure steam turbine disks was first identified in the United States at a nuclear pressurizedwater reactor (PWR) plant around the late '70s. Additional discoveries of cracking in disk rimattachments, bores and keyways, and hub and web locations in nuclear LP turbines led to thedevelopment of EPRI Research Project 1398 [1]. Task 5 of this project included a survey of U.S.and foreign experience with LP disk cracking as of mid-1980. The 1980 survey documented diskrim attachment cracking instances in Westinghouse LP turbines of seven nuclear units and noinstances of cracking in General Electric nuclear turbines.

Industry concern with regard to LP rotor rim cracking has increased over the last five to ten yearswith an increasing number of rotors requiring repair or replacement. These concerns led to therecent data collection effort on LP rotor rim cracking which was performed under EPRI ResearchProject 9005-01 [2]. Data was collected through 1995 to document the location, extent, andmechanism of cracking; to document repair methods used; and to investigate possiblerelationships between cracking experience and various design and operating parameters. Diskcracking experience in U.S. nuclear utilities and several fossil utilities was determined from areview of literature data and a questionnaire survey mailed to the utilities. Information on rotorrepair methods was obtained from a separate survey of repair vendors and original equipmentmanufacturers (OEMs).

Reflecting industry concerns, the 1995 survey reported a significant increase in the incidence ofrim cracking compared with the 1980 survey. Nuclear utility operators surveyed reported LPrim-attachment cracking in 41 of 109 currently operating units in the United States(see Figure 1-1) [2]. The cracking mechanism reported was predominantly stress corrosioncracking with a few instances of corrosion-fatigue and one incident of high-cycle fatigue. Basedon the survey data, the incidence of cracking did not appear to be related to generator or turbinemanufacturer or power rating. Higher incidences of cracking were reported in units with longerlast stage blades. Data was insufficient to establish a relationship between the incidence of rimcracking and operating variables, such as operating time, number of startups, type of watertreatment, oxygen levels, condenser cooling water, and condenser leakage rate. Limited rim-attachment crack growth data suggested that use of an equation first proposed by Clark et al of

Westinghouse [3] to estimate crack growth rates is adequate for the purpose of life prediction.Compared with the results of the 1980 survey, the new data showed a significant shift in thenumber of cracks by row number to downstream rows and a significant rate of cracking inGeneral Electric rotors which was not reported in the earlier survey.

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Introduction

1-2

Figure 1-1Rim Attachment Cracking in Nuclear Units by Reactor Type and Manufacturer

Of the 757 fossil units surveyed, the incidence of cracking was ten times higher in supercriticalunits with once-through boilers (26%) than in subcritical units (3%) (see Figure 1-2).

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Introduction

1-3

Figure 1-2Rim Attachment Cracking in Fossil Units by Steam Type (Supercritical or Subcritical)

The cracking mechanism reported was predominantly SCC, with a few instances of corrosionfatigue and reportedly excessive attachment stress. In GE units, more instances of rim crackingwere reported in the L-1 and L-2 rows; in Westinghouse units, more cracking was reported in theL-0 and L-1 rows.

Life prediction methods have been successfully applied to rim attachments by OEMs andconsultants. However, until now no analytical tool has been available that would allow utilitypersonnel to perform these assessments. Therefore, several utilities expressed the need for a user-friendly integrated software code that would allow utility personnel to perform a remaining lifeassessment for LP rotors with known or suspected rim-attachment cracking. The 1989 EPRIguidelines [4] provided a step in this direction, but the lack of an integrated software tool for useby utility personnel was still apparent.

In response to utility concerns with regard to rim cracking, EPRI initiated Tailored Collaborationprogram RP4597-01 [5] to develop a computer code that would combine the necessary stressanalysis and fracture mechanics algorithms with applicable material degradation data into anintegrated methodology to assess the remaining life of LP rotors with rim-attachment cracking.The resulting computer program, LPRimLife [6] is described in this report.

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2-1

2METHODOLOGY

The development effort for the life assessment code, LPRimLife, was split into two phases toaddress separately rim-attachment cracking for the two configurations shown in Figure 2-1.Phase I, which includes the assessment of straddle-mount attachments (see Figure 2-1b), iscomplete; and Phase II, which addresses cracking in Westinghouse axial-entry attachments (seeFigure 2-1a), is currently in development.

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Methodology

2-2

Figure 2-1

Schematic of Rim-Attachment Configurations Illustrating Typical Locations of Cracking

A flow chart of the LPRimLife computer code is provided in Figure 2-2.

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Methodology

2-3

Geometry

- Select

Dimensions

- View/Scale

Loading/Stresses

- View/ScaleNDE Data

- Location, Size

Material

Properties

Operating Data

- Temperature

- Hrs, OverspeedCrack Initiation

Model

Crack Growth

Model

Time-to-Failure

- Deterministic

- Probabilistic

Predefined

Geometries: -GE (Phase I)

- Westinghouse

(Phase II)

Finite ElementStress Analyses

Develop Library of Rim Attachment Geometries

and Stresses

Critical Crack Size

(Toughness, Overload,

Vibratory)

Load

Redistribution

Algorithm

Vibratory

Threshold

Figure 2-2Flowchart of LPRimLife Software

A brief description of the inputs and calculation procedures is given below.

Geometry and Stresses

1. First, the user defines the type of attachment to be evaluated (GE straddle-mount or

Westinghouse axial-entry).

2. Next, the user has the option of (1) selecting appropriate geometry and stress data from a pre-defined (built-in) library of geometry and finite element stress solutions or (2) inputtingappropriate geometry and stress data for the attachment to be evaluated.

3. In addition, using scale factors, pre-defined geometry and loading data can be modified toapproximate the desired geometry.

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Methodology

2-4

Other Inputs

4. Next, the user defines various inputs required for the life assessment calculation. Theseinputs fall into the following major categories:

Operating Data

Inspection Data

Material Properties

Initiation and Crack Growth Data

Calculation/Print Controls

Calculations

5. Once all the necessary inputs have been defined, the user has the option of performing theremaining life calculations either deterministically or probabilistically. Remaining life is the

sum of initiation time (if applicable) and time to reach critical size. Calculations performedinclude the following:

Estimate initiation time (if cracking was not detected).

Simulate growth of initiated or detected cracks due to stress corrosion cracking (SCC).

Account for redistribution of loading between hooks as crack growth progresses.

Check for crack arrest below defined SCC threshold.

Determine minimum critical crack size for fracture toughness limit, remaining ligamentoverload, or user-defined depth limit.

Results

6. After the calculations are completed, detailed results are available for review in an outputtext file along with the option to plot key inputs and results. Results include the following:

Stresses, including the effect of load redistribution due to cracking

Stress intensity factors (without and with scale factors and load redistribution)

Crack size versus time

Remaining life

Initiation and Failure Probabilistic results

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3-1

3PROGRAM MODULES

To facilitate the assembly of the LPRimLife software, a number of interlinked modules weredeveloped. Key modules include the following:

Stress analysis

Crack initiation and growth

Stress corrosion cracking (SCC) growth threshold

Critical crack size

Remaining life (deterministic and probabilistic)

Each of these modules will be discussed in this section of the report.

3.1 Stress Analysis

The program incorporates a built-in library of finite element (FE) stress results required forevaluation of rim-attachment cracking. This eliminates the complexity associated withperforming a typical FE analysis using non-linear contact elements (see Figure 3-1).

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Program Modules

3-2

Figure 3-1Typical FE Analysis Model of Disk and Blade Attachment Region With Non-Linear Contact(Gap) Elements

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Program Modules

3-3

Stress analysis results for the Phase I dovetail geometries shown in Table 3-1 are built into thesoftware program.

Table 3-1Phase I Straddle-Mount (GE) Dovetail Geometries

Turbine Size/Rating LP Configuration1

Row

GE 920 MW TC6F38 L-2, L-3

GE 1300MW TC6F43 L-2, L-3

GE 540 MW TC4F38 L-2, L-3

GE 858 MW2

TC4F43 L-2, L-3

GE 1220 MW2

TC6F43 L-2, L-3

Notes1: TC6F38 = Tandem-Compound, 6-Flows (3 LPs), with 38-inch last blades2: To be incorporated in next software release.

Phase II is currently in development and will incorporate the axial-entry stress analysis resultsshown in Table 3-2.

Table 3-2Phase 2 Axial-Entry (Westinghouse) Geometries

Turbine Size/Rating LP Configuration Row

WH 1080MW, BB81 TC6F44 L-0, L-1

WH 764MW, BB81 TC4F44 L-0, L-1

WH BB281 TC6F44 L-0, L-1

WH 893MW, BB276 TC4F28 L-0, L-1

Key geometry and loading information are incorporated in the built-in library and can be viewedby the user (see Figure 3-2). Appropriate stress gradient results normal to the crack (see Figure3-3) are also built into the library. These stresses are defined for locations away from the notch-entry position. The local stress increase at the notch-entry position must be accounted for using aload/stress scale factor which can be modified by the user. For example, to increase stresses at

the notch-entry position by 50%, this factor must be changed to 1.5. A separate Library moduleallows the user to expand the existing library to include additional attachmentgeometry/loading/stress data.

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Program Modules

3-4

Figure 3-2Geometry and Loading Data for a Built-In Attachment Geometry

Figure 3-3Stress Gradients Normal to Crack Incorporated in Built-In Library of FE Stress Results

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Program Modules

3-5

3.2 Crack Initiation and Growth

An industry review of available stress corrosion cracking (SCC) initiation data and models isprovided by Rosario [7]. Since no quantitative model currently exists to predict SCC initiation asa function of the principal governing material, stress, and environment variables, the software

allows the user to specify an industry experienced-based statistical probability of initiation as afunction of total operating time for a given fleet or design of low-pressure (LP) rotor.

Crack growth due to SCC is the dominant crack growth mechanism simulated within thesoftware. Low cycle fatigue due to unit start/stops is typically very small relative to SCC growthrates. The most widely accepted model for SCC crack growth rate [3] is expressed by thefollowing equation:

y0.0278+(7302/T)-C=)dt

da( 1ln (Eq. 3-1)

where

C1 = Material constant with a mean value of -4.968 and a standard deviation of 0.587

T = Operating temperature of the disk in R (F+460)

y = Yield strength in ksi

da/dt = Growth rate in inches/hour

The 1995 EPRI survey of rim-attachment cracking [2] has shown that this equation also providesreasonable estimates of crack growth rates for disk rim attachments. Data presented by

Holdsworth [8] and Speidel [9] at the most recent EPRI Steam Turbine Stress CorrosionCracking Conference in March 1997 also confirms that SCC growth rates, for typical disk steelswith yield strengths below 160 ksi, are a function of only yield strength and temperature.

To allow flexibility in defining the SCC growth rate, the following generic form of eq. 3-1 isincorporated in the software program:

yC+T)(C-C=)dt

da( 321 /ln (Eq. 3-2)

where the material constants C1, C

2, and C

3can be defined by the user.

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Program Modules

3-6

3.3 SCC Growth Threshold (KISCC

)

Eq. 3-1 applies to the SCC growth region, called the plateau region, which is independent ofthe stress intensity factor [9]. However, for stress intensity factors below the threshold (K

ISCC),

which is in the range of 10 to 20 ksi inch, crack growth is insignificant [9]. With loadredistribution, stress intensity factors may fall below the threshold, and SCC crack growth willcease. To incorporate this effect, SCC crack growth is terminated when, K

I< K

ISCC. To activate

this threshold effect, the user must define a mean and standard deviation for KISCC

; this featurecan be deactivated by setting both mean and standard deviation values to zero.

3.4 Critical Crack Size

The critical crack size computed by the software is the minimum value for the following failurecriteria:

The applied stress intensity factor (KI) exceeding the material toughness (KIc)

Plastic overload of the remaining ligament

The crack depth exceeding a user-specified limit

In future software releases, a vibratory limit will be included to address the possibility ofterminal high cycle fatigue failure. A flow diagram for critical crack size determination is shownin Figure 3-4.

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Program Modules

3-7

Figure 3-4Critical Crack Size Determination Flow Diagram

Stress intensity factor solutions for a semi-elliptic surface-connected crack in finite width plate[10] are incorporated in the software. Any combination of user-specified depth (a) and length (l)can be evaluated. Unit-specific disk fracture toughness values can be specified by the user, ordefault values in the software code from literature data [11] can be used. The lower bound disktoughness values are estimated based on a startup temperature for the disk and are input by theuser. Plastic overload of the remaining ligament is calculated based on the combined membrane,bending, and shear stresses in the ligament using a similar approach to that given by Cipolla et al

[12].

3.4.1 Load Redistribution

An algorithm to account for load redistribution between the hooks due to cracking has beendeveloped and incorporated into the software program. This algorithm uses a numericalinterpolation scheme to predict load redistribution based on the results of several FE analyses

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Program Modules

3-8

simulating various combinations of cracks depths in the top, middle, and bottom hooks. Agraphical illustration of this load redistribution feature is shown in Figure 3-5 for the special caseof single cracks in each of the hooks. Load redistribution is computed for any arbitrarycombination of crack sizes in the top, middle, and bottom hooks.

Load Redistribution with Cracking

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(Crack Depth/Hook Width) = (a/W)

Load

Relativeto

Uncracked

Value

Top

Mid

Bot

Figure 3-5Illustration of Load Redistribution as a Function of Crack Depth (a) to Hook Width (W)Ratio.

3.5 Remaining Life (Deterministic Versus Probabilistic)

For a deterministic analysis, remaining life (trem) is computed using the following relationship:

da/dt

a-at=t

icrinirem + (Eq. 3-3)

where

tini

= Remaining initiation time (if applicable)

ai = Initiated or detected crack size

acr = Critical crack size

da/dt = Crack growth rate

Because of the non-linear dependency of load redistribution on crack size, crack-growthsimulations must be performed in small increments of crack size, and critical size must bedetermined when one of the above failure criterion is met.

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Program Modules

3-9

Deterministically predicted remaining lives typically yield a large scatter in results for worst-caseversus mean data, suggesting that variability in modeled data cannot be adequately characterizeddeterministically. The use of worst-case assumptions stacks conservatisms with results in anoverly pessimistic estimate of remaining life and does not represent a realistic outcome. It isunlikely that all of the worst case conditions would occur simultaneously; therefore, aprobabilistic analysis that considers position in the scatterband can provide a more realisticassessment of remaining life.

A probabilistic evaluation requires identification of appropriate random variables anddetermination of a statistical distribution associated with each variable. The generation ofprobabilistic results can then be accomplished using a technique such as Monte Carlo, whichinvolves successive deterministic remaining life calculations using randomly selected values ofinputs. The probabilistic approach is illustrated schematically in Figure 3-6.

Figure 3-6Flowchart for Probabilistic Calculations

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Program Modules

3-10

Probabilistic calculations are performed using the Monte Carlo technique for a user-specifiednumber of iterations. A summary of random variables, which can be defined using the varioussub-menus under the Input main menu option, is provided below:

1. Scale factor for load/stresses (normal distribution)

2. Overspeed level (normal distribution)3. Disk startup temperature (normal distribution)4. Disk steady-state operating temperature (normal distribution)5. Crack depth (normal distribution)top6. Crack depth (normal distribution)middle7. Crack depth (normal distribution)bottom8. Crack aspect ratiodepth/length (normal distribution)top9. Crack aspect ratiodepth/length (normal distribution) middle10. Crack aspect ratiodepth/length (normal distribution)bottom11. Yield strength (normal distribution)12. Lower Bound Fracture Toughness (normal distribution)

13. FATT (normal distribution)14. Fracture Toughness (normal distribution) vs. (T-FATT)15. Crack initiation time (user-defined tabular)16. SCC Growth Rate Constant, C

1(log normal distribution)

17. SCC Growth Threshold, KISCC

(normal distribution)

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4-1

4GEOMETRICAL AND DIMENSIONAL MEASUREMENTS

One of the keys to the successful development of the LPRimLife software was to secure accurategeometrical and dimensional information for blade attachments. This information would be usedto develop the library of built-in finite element stress results required for the evaluation of rim-attachment cracking. For the straddle-mount (GE) blade attachments, this information was madeavailable by the tailored collaboration participants who funded the EPRI program. However, forthe axial-entry blade attachments, this information was not readily available and had to besecured through measurements. Participants were asked to remove or provide spare blades whichwere, in turn, forwarded to an aftermarket vendor for dimensioning.

As mentioned in Section 3.1, five different geometries were incorporated into the stress analysismodule for the straddle-mount (GE) attachments. For each of these five geometries, two rowsL-2 and L-3 rowswere incorporated. L-2 and L-3 represent the most problematic attachmentslocations to date. The dimensional data for the straddle-mount attachments is shown inTable 4-1.

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Geometrical and Dimensional Measurements

4-2

Table 4-1Summary of Straddle-Mount (GE) Dimensional and Loading Data

SUMMARY OF GE DOVETAIL DIMENSIONAL AND LOADING DATA

1 Type

2 MW3 Turbine Mfg.4 Turbine Type

Nuclear

1300GETC6F43

Nuclear

920GETC6F38

Nuclear

538GETC4F38

5 Stage/Row # L-2 L-3 L-2 L-3 L-2 L-3

DESCRIPTION PARA-METER

1Inches Inches Inches Inches Inches Inches

Dovetail6 Disk Outside

RadR0 45.5 46.375 44.887 45.75 45.5 45.75

7 Base Width dZ7 5.125 4.462 4.45 3.877 4.691 3.88Top Lug

8 Lug Width dZ1 2.015 1.6695 1.685 1.478 1.68 1.4759 Neck Width dZ2 1.3655 1.0645 1.0906 1.104 1.1 1.01

10 Fillet Radius r1 0.0938 0.0781 0.1181 0.063 0.094 0.06311 Radial Coord. R1 44.915 45.888 44.414 45.381 45 45.3512 Max. Crack W1 0.74 0.6 0.61 0.5 0.6 0.45

Middle Lug13 Lug Width dZ3 3.0475 2.578 2.5787 2.226 2.595 2.22514 Neck Width dZ4 2.363 1.989 1.9882 1.764 2.008 1.7615 Fillet Radius r2 0.0938 0.0781 0.1181 0.063 0.094 0.06316 Radial Coord. R2 43.915 44.903 43.446 44.663 44.03 44.6817 Max. Crack W2 0.77 0.68 0.68 0.5 0.6 0.45

Bottom Lug18 Lug Width dZ5 4.049 3.484 3.5157 2.976 3.5 2.97419 Neck Width dZ6 3.373 2.92 2.9134 2.5 2.91 2.49920 Fillet Radius r3 0.0938 0.0781 0.1181 0.063 0.094 0.06321 Radial Coord. R3 42.915 43.918 42.477 43.945 43.07 43.9322 Max. Crack W3 0.77 0.68 0.68 0.5 0.7 0.53

Side Tang23 Tang Width dZ_tang 0.38 0.336 0.35 0.287 0.447 0.324 Fillet Radius r4 0.0938 0.0938 0.09 0.09 0.094 0.06325 Radial Coord. R4 42.4675 43.436 41.8973 43.445 42.56 43.4926 Tang Height H_tang 0.3 0.248 0.2 0.2 0.253 0.25

Blade27 Height to foils H_blade 4.575 4.483 4.687 3.533 4.5 3.628 Width at Top dZ0 4.005 3.51 3.758 3.265 3.8 3.3

Rim Load29 # blades --- --- 135 170 136 15730 Blade Wt (lbs) --- --- 19.53 9.558 17.88 931 Rim Load (kips) 10,000 6,000 11,787 7,068 11,277 6,34932 % Top Hook 44.40% 42.40% 40.60% 41.40% 41.63% 39.91%33 % Middle Hook 31.10% 31.70% 32.40% 31.40% 31.26% 32.32%34 % Bottom Hook 24.50% 25.80% 27.00% 27.20% 27.11% 27.77%

Note: Refer to Figure 3-2 for a description of each parameter.

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4-3

Measured geometrical information recorded for the axial-entry (Westinghouse) attachmentsincluded three separate machine designs:

BB81

BB281

BB276

Dimensional data for the BB81 and BB276 designs are shown in Table 4-2. At the printing ofthis document, blades had been secured, and the BB281 dimensional/geometrical informationwas being obtained through direct measurements.

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4-4

Table 4-2Summary of Axial-Entry (Westinghouse) Dimensional and Loading Data

SUMMARY OF WH STEEPLE DIMENSIONAL & LOADING DATA

1 Type: Fossil Nuclear

2 MW 740 1137 (Unit 1),

1164 (Unit 2)3 Turbine Mfg.: WH WH

4 Turbine Type: TC4F28 TC6F44

5 Stage/Row #: L-1 L-0 L-4 (new) L-3 (new) L-4 L-3

DESCRIPTION PARAMETER

Disk Overall Dimensions (inches):

6 Disk Outside Dia. OD 59.372 - - - -

7 Disk Width W 4 - 2.309

8 Root Type (S=Straight, SK=Skewed, C=Curved) Curved Skewed Skewed Curved Curved

8a Skew Angle (SK) Alpha - n/a - - - - n/a - - n/a -

8b Radius of Curvature (C) Rc 4.8 - n/a - - n/a - - 3.162

8c Offset from Disk Inlet Face (C) Wo 0.7 - n/a - - n/a - - 0.495

Groove Angles (degrees): Groove Angles Same for Th

9 Overall Angle Theta1 13.2 28.3208

10 Lug Angle Theta2 58.2 26.7072

Groove Width Dimensions (inches): Groove Dimensions Same fo

11 Blade: Top Neck A 0.702 0.702

12 Steeple: Top Neck B 1.025 1.025

13 Blade: Middle Neck (2) C2

14 Blade: Middle Neck C 0.518 0.518

15 Steeple: Middle Neck D 0.826 0.826

16 Blade: Bottom Neck (2) E2

17 Blade: Bottom Neck E 0.354 0.354

18 Steeple: Bottom Neck F 0.636 0.636

Groove Height Dimensions (inches):

19 Blade: Top Neck G 0.122 0.122

20 Steeple: Top Neck J 0.239 0.239

21 Blade: Middle Neck (2) H2

22 Blade: Middle Neck H 0.545 0.545

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Geometr

Table 4-2 (continued)Summary of Axial-Entry (Westinghouse) Dimensional and Loading Data

SUMMARY OF WH STEEPLE DIMENSIONAL & LOADING DATA

1 Type: Fossil Nuclear

2 MW 740 1137 (Unit 1),

1164 (Unit 2)3 Turbine Mfg.: WH WH

4 Turbine Type: TC4F28 TC6F44

5 Stage/Row #: L-1 L-0 L-4 (new) L-3 (new) L-4 L-3

DESCRIPTION PARAMETER

23 Steeple: Middle Neck K 0.635 0.635

24 Blade: Bottom Neck (2) I2

25 Blade: Bottom Neck I 0.925 0.925

26 Steeple: Bottom Neck L 1.011 1.011

27 Overall Groove Depth M 1.168 1.168

Groove Radii (inches):

28 Blade Top Fillet R1 0.062 0.062529 Blade Middle Fillet R2 0.031 0.0312

30 Blade Bottom Fillet R3 0.031 0.0312

31 Steeple Top Fillet R4 0.031 0.0312

32 Steeple Middle Fillet R5 0.031 0.0312

33 Steeple Bottom Fillet R6 0.031 0.0312

34 Steeple Top R7 0.157 0.1406

35 Steeple Bottom of Groove R8 0.167 0.120

Rim Load Data:

36 # blades 120 114 - - - -

37 Blade Wt (lbs) 6.01 - - - -

38 Rim Load (kips) 7368 - - - -39 % Top Hook 33.17% - - - -

40 % Middle Hook 33.29% - - - -

41 % Bottom Hook 33.54% - - - -

Figures 4-1 and 4-2 provide the steeple details that correspond to Table 4-1.

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4-6

Figure 4-1Axial-Entry (Westinghouse) Root Types

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4-7

Figure 4-2Axial-Entry (Westinghouse) Steeple Groove Dimensions

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5-1

5LPRIMLIFE SOFTWARE

The LPRimLife software program was written in Microsoft C++ for operation on a personalcomputer (PC) in a Windows environment (see Figure 5-1).

Figure 5-1LPRimLife Splash Screen and Main Menu Options

5.1 Description

The software program incorporates an easy-to-use graphical user interface with comprehensiveon-line help. Main menu options (see Figure 5-1) and their use are as follows:

The Fileoption should be selected by the user when the program is first executed to definewhether a new analysis is to be performed or an existing analysis file is to be opened.

The Edit option is currently limited to searching for text (using Find) in the standard outputfile once an analysis has been performed.

The Input option contains all of the necessary inputs that must be defined by the user prior toperforming an analysis.

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LPRimLife Software

5-2

The Analysis option offers the user the choice of performing a deterministic or probabilisticanalysis and starts the calculations.

The View option allows the user to view the output of the analysis in text or graphical form.

The Library option is a special tool that allows the user to add or modify items in the default

library of geometry and stress data. The Help option allows the user to access Help Topics, which cover the entire content of the

software users manual, and to invoke the About LPRimLife pop-up window, which providesdetails about the version number of the program and software support. Context-specific helpcan also be accessed using the F1 function key from any dialog box.

A typical solution procedure, consisting of defining inputs, selecting an analysis type, andviewing results, is illustrated in Figure 5-2.

Inputs Analysis View Results

Figure 5-2Typical Solution Procedure

An example of the input data format for calculation and print controls is shown in Figure 5-3.

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LPRimLife Software

5-3

Figure 5-3Calculation and Print Controls Data Input Window

Before proceeding to the Analysis option, the user must define the calculation and print controlsshown in Figure 5-3. The Total Simulation Time is the total number of operating hours into the

future over which remaining life calculations will be performed. A Calculation Increment of 100to 500 hours is recommended for accuracy because the failure criteria and stress corrosioncracking (SCC) threshold feature are a non-linear function of crack size. To limit the size of theoutput file, a Print Increment in excess of 1000 hours should be used. For a probabilisticanalysis, the number of iterations should be at least one order of magnitude greater than thereciprocal of the desired failure probability level; that is, to demonstrate a failure probability lessthan 10

-3, the number of iterations should be at least 10

4.

5.2 Analysis

A deterministic analysis takes only a few seconds to run on a personal computer with a Pentiumprocessor. A probabilistic analysis with 104iterations runs in about 5 to 10 minutes.

5.3 Results

After an analysis is completed, results can be viewed either in a detailed output text file or ingraphical format. Sample output file results for deterministic and probabilistic analysis runs areshown in Figures 5-4 and 5-5.

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LPRimLife Software

5-4

Figure 5-4Deterministic Analysis Results Output Window

Figure 5-5Probabilistic Analysis Results Output Window

Various key inputs and results can also be plotted using a graphics capability built into thesoftware code. The user can modify any of the plot elementssuch as title, legend, andmarkersby clicking the right mouse button anywhere within the plot. For example, the tabular

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LPRimLife Software

5-5

probabilistic analysis results shown in Figure 5-5 are plotted in Figure 5-6 using the Failure Plotoption from the View main menu.

Figure 5-6Cumulative Probability of Failure Plot Option From the View Main Menu

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6-1

6CONCLUSIONS

A Windows-based personal computer software program, LPRimLife, has been developed forperforming a remaining life assessment of disk rim attachments with known or suspectedcracking. The code combines the necessary stress analysis, fracture mechanics algorithms, andmaterial degradation data into an easy-to-use software tool to predict the appropriate failuremode and remaining life of rim attachments with cracking. The first phase of softwaredevelopment, which includes the methodology for evaluating cracking in GE dovetailattachments, is complete. The next phase, to evaluate cracking in Westinghouse axial-entryattachments, is currently in development with completion expected in 1999. With comprehensive

on-line help and built-in graphics and plotting capability, the program facilitates rapid lifeassessments by non-experts with minimal introduction to the software.

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7-1

7FUTURE DEVELOPMENTS

Future developments will include the evaluation of cracking in GE finger-pinned attachmentsand the addition of an economics-based decision analysis module to assist with run/repair/replacedecision-making.

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8-1

8REFERENCES

1. EPRI Report NP-2429, Steam Turbine Disk Cracking Experience, Volumes 1 through 7,Research Project 1398-5, June 1982.

2. D. A. Rosario, C. H. Wells, G. J. Licina, LP Rotor Rim-Attachment Cracking Survey ofUtility Experience, EPRI Research Project 9005-01, Final Report TR-107088, January1997.

3. W. G. Clark, B. B. Seth, and D. M. Shaffer, Procedures for Estimating the Probability of

Steam Turbine Disc Rupture from Stress Corrosion Cracking, presented at JointASME/IEEE Power Generation Conference, October 1981.

4. EPRI Report NP-6444, Guidelines for Predicting the Life of Steam Turbine DisksExhibiting Stress Corrosion Cracking, Volumes 1 and 2, Research Projects 1929-16/14,2518-1, July 1989.

5. LP Rotor Rim-Attachment Cracking - Development of a Life Assessment Code, ProjectAgreement WO4597-01 between Electric Power Research Institute (EPRI) and StructuralIntegrity Associates, Inc., May, 1997.

6. LP Rotor Rim-Attachment Cracking Computer Code (LPRimLife) Software UsersManual, prepared for EPRI by Structural Integrity Associates, Inc., Report No. SIR-97-111,Rev.1, November 1998.

7. D. A. Rosario, R. Viswanathan, C.H. Wells and G. J. Licina, Stress Corrosion Cracking ofSteam Turbine Rotors, 1998 NACE International, CORROSION- Vol.54, No. 7, pp. 531-545.

8. S. R. Holdsworth, et al, Laboratory Stress Corrosion Cracking Experience in Steam TurbineDisc Steels, Proceedings of the EPRI Steam Turbine Stress Corrosion Cracking Workshop,March 1997.

9. M. O. Speidel and R. Magdowski, Major Influences on the Growth Rates of StressCorrosion Cracks in Steam Turbine Rotor and Blade Materials, Proceedings of the EPRISteam Turbine Stress Corrosion Cracking Workshop, March 1997.

10. pc-CRACKfor Windows, Version 3.0-3/27/97, Structural Integrity Associates, 1997.

11 R. C. Schwant and D. P. Timo, Life Assessment of General Electric Large Steam TurbineRotors, EPRI CS-4160, Proceedings of the Seminar on Life Assessment and Improvement

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References

of Turbo-Generator Rotors for Fossil Plants, September 12-14, 1984, Raleigh, NorthCarolina.

12. R. C. Cipolla, J. F. Lesiuk, M. A. Melton and T. J. Szumski, Safe-Life Evaluation andRepair Acceptance Criteria for Dovetail Cracking in Low Pressure Rotors, Proceedings ofthe 5

thEPRI Steam Turbine/Generator Workshop, July 29-August 1, 1997, Lake Buena Vista,

Florida.

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