NUREG/CR-68 17

PNNL-14268

A Generalized Procedure for

Generating Flaw-Related

Inputs for the FAVOR Code

Pacific Northwest National Laboratory

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
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NUREG/CR-6817

PNNL-14268

A Generalized Procedure for

Generating Flaw-Related

Inputs for the FAVOR Code

Manuscript Completed: April 2003

Date Published: March 2004

Prepared by

F.A. Simonen, S.R. Doctor,

G.J. Schuster, P.G. Heasler

Pacific Northwest National Laboratory

P.O. Box 999

Richland, WA 99352

D.A. Jackson, NRC Project Manager

Prepared for

Division of Engineering Technology

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code Y6604
NUREG/CR-6817, has been reproduced

from the best available copy.
ABSTRACT

The U.S. Nuclear Regulatory Commission (NRC) has supported research to re-evaluate regulations for

pressurized thermal shock. In addition to a severe overcooling transient and an embrittled material, a

factor critical to reactor pressure vessel (RPV) failure is a crack-like flaw near the inner vessel surface.

This report documents research on fabrication flaws performed at Pacific Northwest National Laboratory

as part of a larger multiyear program sponsored by the NRC to address issues related to the reliability of

ultrasonic testing and the development of improved programs for inservice inspection. These studies

have generated data on flaws in RPVs in terms of flaw densities, flaw locations, and flaw sizes (throughwall depth dimensions and lengths). This report describes data from these studies, results from an expert

judgment elicitation on RPV fabrication practices, and probabilistic models that characterize flaws that

may exist in RPVs. A procedure is described for generating flaw-related parameters for use as inputs to

probabilistic fracture mechanics calculations.

iii
CONTENTS

A B STRA CT ............................................................................................................................................ ......... iii

EXECUTIVE SUMMARY .................... xiii

ACKNOWLEDGEMENTS..................................................................................................................... xv

ABBREVIATIONS ..................... xvii

1 ITRODUCTON . .1.1

1.1 Probabilistic Fracture Mechanics Codes .1.1

1.2 Domestic Reactor Pressure Vessel Fabrication .1.3

1.3 Historical Sources of Fabrication Flaw Data .1.3

1.4 Overview of Report ................ 1.4

2 OVERVIEW OF FLAW ESTIMATION PROCEDURE .... 2.1

2.1 Vessel Regions and Flaw Categories . . .2.1

2.1.1 Seam Welds .. 2.1

2.1.2. Base Metal . . .2.2

2.1.3 Repair Welds .. 2.2

2.1.4 Cladding .. 2.3

2.1.5 Underclad Cracking .................. 2.3

2.2 Treatment of Flaws by FAVOR Code ............................. .. 2.3

2.3 Monte Carlo Simulation ........................... 2.4

2.4 Estimation Procedure for Welds ........................... 2.4

2.5 Estimation Procedure for Base Metal ................... ........... :.!..2.5

2.6 Estimation Procedure for Clad/Surface Flaws. . . ................................ 2.6

2.7 Flaw Locations..................................... 2.6

2.8 Treatment of Uncertainties ....................... : 2.7

2.9 Sample Flaw Distributions ......................... 2.7

2.10 Summary and Conclusions ......................... 2.8

3 EXAMINATIONS OF VESSEL MATERIAL........ .................................................................. 3.1

3.1. Procedures Used to Detect and Size Flaws ....................................... 3.2

3.2 Characterization of Flaws for Fracture Mechanics Models .. . .3.6

3.3 Treatment of Large Repair Flaws .... ..... 3.7 3.3 Treatme t of L rge epair Raws ......................:.............................................................. 37

3.4 Validated Flaw Densities and Size Distributions ....................................... 3.9

3.4.1 Shielded Metal Arc Weld .3.10

3.4.2 Submerged Arc Weld .................. 3.10

3.4.3 Repair Weld .................. 3.10

4 EXPERT JUDGMENT PROCESS FOR FLAW DISTRIBUTION . ............................................... 4.1

4.1 Expert Judgment Process .............................. 4.1

4.1.1 Selection of Issues and Experts . 4.1

4.1.2 Presentation of Issues to the Experts .4.1

4.1.3 Elicitation Training .4.1

4.1.4 Preparation of Issue Analyses by the Experts ................................... 4.2

V
4.1.5 Discussion of Issue Analyses ............................... 4.2

4.1.6 Elicitation of the Experts ............................... 4.2

4.2 Recomposition and Summary of Results ............. .. ................ 4.2

4.2.1 Documentation ............................... 4.3

4.3 Quantitative Characteristics ................................ 4.3

4.4 Qualitative Characteristics ................................ 4.4

4.5 Discussion ................................ 4.4

5 PRODIGAL WELD SIMULATION MODEL . . .............................. 5.1

5.1 Types of Defects ............................... 5.1

5.2 Defect Density ............................... 5.3

5.3 Defect Characteristics ............................... 5.3

5.4 Inspection Model ............................... 5.3

5.5 Computer-Based Implementation ............................... 5.3

5.6 Calculations and Results ................................ 5.4

5.7 Flaw Characterization by PRODIGAL Code .. ............................. 5.6

5.8 Discussion and Conclusions.................................................................................................... 5.6

6 WELD FLAWS - DATA AND STATISTICAL CORRELATIONS . .6.1

6.1 Approach and Assumptions .............................. 6.1

6.2 Statistical Functions for Flaw Distributions .............................. 6.4

6.2.1 Flaw D ensities ................................................................. 6.5

6.2.2 Conditional Depth Distribution for Small Flaws ................................................. ........ 6.7

6.2.3 Conditional Depth Distribution for Large SAW and SMAW Flaws ........... ................ 6.9

6.2.4 Conditional Depth Distribution for Large Repair Flaws .............................................. 6.10

6.2.5 Length Distribution for Small SAW Flaws in PVRUF Vessel ............... ..................... 6.12

6.2.6 Length Distribution for Small SMAW and Repair Flaws in PVRUF Vessel .............. 6.13

6.2.7 Length Distribution for Small SAW Flaws in Shoreham. Vessel ................................. 6.14

6.2.8 Length Distribution for Small SMAW and Repair Flaws in Shoreham Vessel ........... 6.17

6.2.9 Length Distribution for Large SAW Flaws in PVRUF Vessel ............... ..................... 6.18

6.2.10 Length Distribution for Large SMAW and Repair Flaws in PVRUF Vessel .............. 6.18

6.2.11 Length Distribution for Large SAW Flaws in Shoreham Vessel ................................. 6.19

6.2.12 Length Distribution for Large SMAW and Repair Flaws in Shoreham Vessel ........... 6.19

7 BASE METAL FLAWS - DATA AND STATISTICAL CORRELATIONS . ...................... 7.1

7.1 Approach and Assumptions ................................................................. 7.1

7.2 Inputs from Expert Elicitation ................................................................. 7.3

7.3 Flaw Data from PNNL Base Metal Examinations ................................................................. 7.3

7.4 Flaw Estimation Procedure for Plate Materials ................................................................. 7.4

8 CLAD FLAWS - DATA AND STATISTICAL CORRELATIONS ................................................ 8.1

8.1 Approach and Assumptions ............................. 8.1

8.2 Sources of Information Cladding Flaws ............................ 8.1

8.2.1 PVRUF Data ............................ 8.2

8.2.2 Data from Bettis Laboratory ............................ 8.3

8.2.3 Expert Judgment Elicitation ............................ 8.3

8.2.4 PRODIGAL Predictions ............................ 8.3

8.2.5 Vessel-Specific Considerations ............................ 8.5

8.3 Flaw Length Distribution for Clad Flaws ............ ................ 8.6

vi
8.4 Flaw Inputs to Fracture Mechanics ............................................ 8.8

8.5 Probabilistic Fracture Mechanics Calculations ............................................ 8.11

8.5.1 Fracture Mechanics Methodology ............................................ 8.11

8.5.2 Description of Reference Vessel ............................................ 8.12

8.5.3 Results of Probabilistic Fracture Mechanics Calculations . 8.13

8.6 Concluding Discussion ........................... 8.13

9 ALGORITHM TO GENERATE FLAW INPUT FILES FOR FAVOR .9.1

9.1 Input Files Required by FAVOR Code .......................... 9.1

9.2 Computer Code for Generating Flaw Input Files ........................................ 9.1

9.2.1 Input File to PNNL Algorithm ............................................ 9.3

9.2.2 Output File from PNNL Algorithm ............................................ 9.5

9.2.3 Output File from PNNL Algorithm for Inputs to FAVOR .......................................... 9.6

9.3 Procedure for Weld Regions ....... ...................................... 9.6

9.3.1 Treatment of Weld Flaws ............................................ 9.6

9.3.2 Flow Chart for Welds ................... . ... . . . 9.7

9.3.3 Sample Input File for Welds ........................... 9.9

9.4 Procedure for Base Metal Regions ..................... 9.12

9.4.1 Treatment of Base Metal Flaws ........................... 9.12

9.4.2 Flow Chart for Base Metal ........................... 9.12

9.4.3 Sample Input File for Base Metal ........................... 9.13

9.5 Procedure for Surface/Clad Flaws .. 9.13

9.5.1 Treatment of Surface/Clad Flaws . 9.13

9.5.2 Flow Chart for Surface/Clad Flaws . 9.13

9.5.3 Sample Input File for Surface/Clad Flaws . 9.16

10 CONCLUSIONS ...... :10.1

11 REERENCES.S11.1

Appendix A - STATISTICAL EQUATIONS FOR FLAW DISTRIBUTION

FUNCTIONS AND UNCERTAINTY ANALYSIS .A.1

vii
FIGURES

1.1 Elements of Computational Model for Predicting Vessel Failure Probabilities and its

Application to Regulations for Pressurized Thermal Shock .......................................................... 1.2

2.1 Conceptual View of Material Regions of a Vessel and the Categories of Flaws

That Can Impact Structural Integrity ........................................................... 2.1

2.2 Metallographic Cross Section of a Circumferential Weld Showing Adjacent Regions

of Base Metal and Cladding ........................................................... 2.2

2.3 Flaw Locations Relative to Vessel Inner Surface ........................................................... 2.7

2.4 Sample Flaw Distribution for Use in Probabilistic Fracture Mechanics Calculations .......... ........ 2.8

3.1 Sequence of Techniques Used To Detect and Size Flaws ........................................................... 3.2

3.2 Techniques Used for Detailed Characterization of Flaws ........................................................... 3.2

3.3 Metallographic Cross Section of a Circumferential Weld from PVRUF Vessel

Showing Adjacent Regions of Base Metal and Cladding ........................................................... 3.2

3.4 Location of Flaw in the Fusion Zone of a Weld with the Base Metal .3.2

3.5 Inside View of the PVRUF Vessel During SAFT-UT Inspections ............................................ 3.3

3.6 Weld Normal Inspections ............................................ 3.4

3.7 Examinations of Plate Specimens ............................................ 3.4

3.8 Image of a Fabrication Flaw Using Conventional Radiography ............................................ 3.4

3.9 Micrograph of 25-mm Cube Containing a Failed Weld Bead ............................................ 3.5

3.10 Electron Microscope Image of Cracked Weld Bead . 3.5

3.11 Composition of a Complex Flaw . 3.7

3.12 Shape and Orientation of 14-mm PVRUF Flaw - Relevant to Structural Integrity

Assessment.................................................................................................................................... .3.8

3.13 Shape and Orientation of 32-mmn Shoreham Repair Flaw with Less Conservative

Treatment B of Flaw Dimensions . 3.9

3.14 SMAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities . 3.11

3.15 SAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities . 3.11

viii
3.16 Repair Metal, Through-Wall Size Distribution of Cumulative Flaw Densities ............................. 3.12

3.17 Comparison of Through-Wall Size Distributions of Cumulative Flaw Densities ........... .............. 3.12

4.1 Relative Flaw Densities of Base Metal Compared to Weld Metal as Estimated

by Expert Judgment Process ................................................................. 4.4

5.1 Types of Crack-Like Defects ................................................................. 5.2

5.2 Cross Section of Thickness Transition Single V Weld for PVRUF Vessel .............. .................... 5.4

5.3 Model of Thickness Transition Single V Weld for PVRUF Vessel ...................... ......................... 5.5

5A Calculated Flaw Frequencies for PVRUF Weld Showing Effects of Inspection and Repairs ...... 5.6

5.5 Distributions of Flaw Aspect Ratio and Flaw Length as Predicted by PRODIGAL

Weld Simulation ................................................................. 5.7

6.1 Uncertainty in Flaw Densities for Flaws in PVRUF Vessel ............................... I ............................ 6.7

6.2 Uncertainty in Flaw Densities for Flaws in Shoreham Vessel ...................................................... 6.7

6.3. PVRUF Weld Metal Specimen Cut into 25-mm Plate .................................................................. 6.8

6.4 Depth Distribution for Small Flaws Including Uncertainty Analysis ............................................ 6.9

6.5 Uncertainty Evaluation for Complementary Conditional Depth Distribution

for Large SAW and SMAW Flaws ........................ 6.11

6.6 Uncertainty Evaluation for Complementary Conditional Depth Distribution

for Large Repair Flaws ........................ 6.11

6.7 Lengths of Small Flaws in SAW and SMAW Welds of PVRUF Vessel ....................................... 6.13

6.8 Lengths of Small Flaws in SAW Welds of PVRUF Vessel Showing Exponential

Distribution Along with Uncertainties ............................................... 6.13

6.9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel Showing Exponential

Distribution Along with Uncertainties .......................... 6.14

6.10 Lengths of Small Flaws in SAW and SMAW Welds of Shoreham Vessel ...................................... 6.14

6.11 Lengths of Small Flaws in SAW Welds of Shoreham Vessel Showing Exponential

Distribution Along with Uncertainties ................................................. 6.17

6.12 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham Vessel

Showing Exponential Distribution Along with Uncertainties ................................................. 6.17

ix
6.13 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel

Showing Exponential Distribution Along with Uncertainties ....................................................... 6.19

6.14 Lengths of Large Flaws in SAW Welds of Shoreham Vessel Showing

Exponential Distribution Along with Uncertainties .................................. ....................... 6.20

7.1 A Flaw Detected in Plate Material ......................................................... 7.2

7.2 Flaw Frequencies for Plate Materials with Comparisons to Data for Weld Flaws ........................ 7.4

8.1 Examples of Flaws in Cladding of PVRUF Vessel ............................... .......................... 8.1

8.2 Summary of Data on Flaws in Vessel Cladding ......................................................... 8.2

8.3 Lengths of Clad Flaws in PVRUF and Hope Creek II Vessels ..................................................... 8.7

8.4 Proposed Curves for Estimating Number and Sizes of Flaws in Vessel Cladding . 8.10

8.5 Probability of Flaw Initiation in Vessel with Axial Welds as Limiting Material .......................... 8.13

8.6 Probability of Flaw Initiation in Vessel with Plates as Limiting Material ..................................... 8.13

9.1 Input Instructions for Flaw Distribution Algorithm ................................ ........................ 9.2

9.2 Flow Chart for Weld Flaws ........................................................ 9.8

9.3 Sample Flaw Distribution Input File for Weld Region ........................................................ 9.9

9.4 Sample from Flaw Distribution File for Weld Region ........................................... ............. 9.10

9.5 Sample Flaw Data Output File for Weld Region ........................................................ 9.11

9.6 Flaw Distribution for Various Vessel Regions . 9.12

9.7 Sample from Flaw Distribution Input File for Base Metal Region . 9.14

9.8 Sample Flaw Distribution Output File for Base Metal Region . 9.14

9.9 Sample Flaw Data from Output File for Base Metal Region . 9.15

9.10 Sample Flaw Distribution Input File for Surface/Clad Flaws . 9.17

9.11 Sample Flaw Distribution Output File for Surface/Clad Flaws . 9.17

9.12 Sample Flaw Data from Output File for Surface/Clad Flaws . 9.18

x
TABLES

3.1 Weld Material Evaluated To Generate'Data on Flaw Rates .......................................................... 3.1

3.2 Base Metal Material Evaluated To Generate Data on Flaw Rates ................................................. 3.1

3.3 Presence of Metallic and Nonmetallic Oxides in Failed Weld Bead ............................................. 3.6

3.4 Flaw Dimensions, Validated by Use of Multiple Techniques ........................................................ 3.6

6.1 Flaw Density Parameters ................................................................... 6.6

6.2 Gamma Distribution Used To Sample'for Parameter of Poisson Distribution

for Flaw Densities ................................................................... 6.7

6.3 Weld Bead Dimensions for PVRUF and Shoreham Welds ........................................................... 6.7

6.4 Data from Radiography of 25-mm Thick Plates from PVRUF Welds ................. ......................... 6.9

6.5 Data and Parameters of the Uncertainty Distribution for Depth Distribution

for Small Flaws ......... 6.10

6.6 Large SAW and SMAW Flaws in PVRUF and Shoreham Vessels .................... .......................... 6.11

6.7 Large Repair Flaws in PVRUF and Shoreham Vessels .................................................................. 6.12

6.8 Lengths of Small Flaws in SAW Welds of PVRUF Vessel .......................................................... 6.13

6.9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel ....................................................... 6.14

6.10 Lengths of Small Flaws in SAW Welds of Shoreham Vessel .................................. ..................... 6.15

6.11 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham Vessel ................ 6.18

6.12 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel .............. ...................... 6.19

6.13 Lengths of Small Flaws in SAW Welds of Shoreham Vessel ......................................................... 6.20

7.1 Flaws Detected and Sized in PNNL Examinations of Inner 1 Inch of Plate Material .......... ......... 7.4

8.1 Flaws in Cladding of PVRUF Vessel ................................................................... 8.2

8.2 Parameters of Representative PWR Reactor Pressure Vessel for PRODIGAL Calculations ........ 8.4

8.3 RR-PRODIGAL Predictions for Surface-Breaking Flaws in Cladding

by Submerged Arc Process (with and without PT) ................................................................... 8.5

xi
8.4 RR-PRODIGAL Predictions for Buried Flaws in Cladding Applied

with Manual Metal Arc and Submerged Arc Process .............................................................. 8.5

8.5 Clad Product Form and Inspection Results .............................................................. 8.7

8.6 Dimensions of Flaws in Cladding as Reported in Appendix A of Schuster et al. (1998) .............. 8.7

8.7 Validated Dimensions of Flaw in Cladding as Reported in Schuster et al. (2000) ........................ 8.7

8.8 Amount of Multi-Wire Clad in Specimen HC2A2B .............................................................. 8.8

8.9 Length of Flaws in Cladding for Specimen HC2A2B .............................................................. 8.8

8.10 Amount of 4 in. Strip Clad in Specimen 5-IOD ................................... ........................... 8.8

8.11 Length of Flaws in Cladding for Specimen 5- OD.8.8

8.12 Data Used to Develop Length Distribution for Clad Flaws .8.9

xii
EXECUTIVE SUMMARY

Pacific Northwest National Laboratory (PNNL) is conducting a multiyear program for the U.S. Nuclear

Regulatory Commission (NRC) to assess the reliability of ultrasonic testing (UT) in detecting flaws in

piping and pressure vessels and to develop improved programs for inservice inspection (ISI). This

involves establishing the accuracy and reliability of UT for ISI and includes efforts to apply improved

methods to ensure the integrity of vessels and piping at commercial nuclear power plants. This report

summarizes studies that have measured and characterized fabrication flaws in the welds and base metal of

reactor pressure vessel (RPV) materials.

The present work is coordinated with other research by the NRC that is re-evaluating regulations for

pressurized thermal shock (PTS) of RPVs. In determining the significance of a PTS event, the critical

factors for the integrity of an RPV are the severity of the overcooling transient, the level of material

embrittlement, and the presence of a crack-like flaw near the inner vessel surface. This report documents

research on fabrication flaws that has generated data on flaws in RPVs covering the vessel fabrication

permit from the late 1960s through the early 1980s when most vessels in commercial operation were

fabricated. The fabrication flaw data was developed to quantify the flaw densities, flaw locations, and

flaw sizes (through-wall depth dimensions and lengths). In addition to data from vessel examinations, the

report presents results from an expert judgment elicitation on RPV fabrication practices and presents

probabilistic models that characterize the flaws that may exist in vessels. Also described is a procedure

for generating flaw-related parameters for use as inputs to probabilistic fracture mechanics calculations.

PTS events consist of a severe overcooling along with an increase in pressure in the RPV, which

challenges the integrity of the reactor vessel's 'inrier'wall. Such transients are a significant concern as

plants approach the end of their operating license and for periods of license renewal because the material

of the vessel wall can become increasingly embrittled at elevated levels of neutron fluence. PNNL has

participated in research to address PTS issues by performing examinations of RPV materials to detect and

measure the numbers and sizes of fabrication flaws in weld cladding and base metal. Experimental work'

has provided fabrication flaw data from nondestructive and destructive examinations using material from

vessels fabricated for cancelled nuclear power plants.

The current treatment of fabrication flaws considers different vessel regions including seam welds, base

metal, and cladding. Welding processes include submerged metal arc, shielded metal arc, and repair

welding procedures. Depending on known details for the fabrication process, the resulting flaw

distributions can, if desired, be generated to apply to a particular vessel. Most of the smaller flaws, which

can be significant to the integrity of highly embrittled vessels, are related to common lack-of-fusion

defects and slag that occurs from the normal welding process. The largest observed flaws are, however,

associated with repair welding. The probabilistic model realistically assumes that flaws are at random

locations through the thickness of the vessel wall rather than being conservatively placed at the inner

vessel surface. Inner surface-breaking flaws are those associated with only the vessel cladding process.

Measured flaw data show vessel-to-vessel differences regarding the numbers and sizes of flaws.

Consequently, the flaw treatment allows the application of data trends from either the Pressure Vessel

xiii
Research User Facility (PVRUF) vessel' or the Shoreham vessel. Because the limited data did include

occurrences of very large flaws, the treatment truncates flaw distributions at flaw depths that significantly

exceed the maximum observed depths. Flaw lengths (or aspect ratios) are not assumed to be very large as

has been the practice in past treatments, with flaw lengths being assigned on the basis of the measured

lengths of observed flaws.

The number and sizes of flaws in base metal regions are assigned using the limited flaw data from

PNNL's examinations of plate and forging materials, as well as by applying insights gained from the

expert judgment elicitation. Flaws in base metal, compared to weld material, have significantly lower

densities in terms of flaws per unit volume of material. In addition, the maximum possible depth

dimensions of base metal flaws are significantly less than the corresponding maximum depths of weld

flaws.

To supplement the limited data from flaw measurements, PNNL has applied an expert judgment

elicitation process and has applied the PRODIGAL flaw simulation model developed in the United

Kingdom by Rolls-Royce and Associates. Using these data, PNNL has developed statistical distributions

to characterize the number and sizes of flaws in the various regions of RPVs. The available data have

been applied in combination with insights from the expert elicitation and PRODIGAL flaw simulation

model to generate computer files using a Monte Carlo simulation that generates flaw-related inputs for

probabilistic fracture mechanics calculations. The end objective of the PNNL work on flaw distributions

has therefore been to support research at Oak Ridge National Laboratory that has developed the

probabilistic fracture mechanics code titled FAVOR fracture Analysis of Vessels: Oak Ridge). This

computer code predicts failure probabilities for embrittled vessels subject to PTS transients.

This report begins with a summary of the available empirical inspection and validated data on flaws in

seam welds, repair welds, base metal, and cladding materials and describes the treatment of these data to

estimate flaw densities, flaw depth distributions, and flaw aspect ratio distributions. In each case, there

are statistical treatments of uncertainties in the parameters of the flaw distributions, which have been

included as part of the inputs to the probabilistic fracture mechanics calculations. The report concludes

with a presentation of some sample inputs for flaw distributions that have supported NRC evaluations of

the risk of vessel failures caused by PTS events.

a The PVRUF vessel was fabricated by Combustion Engineering but was never put into use after

fabrication was completed in December 1981. The vessel was later transported to Oak Ridge National

Laboratory and was used for research programs related to the structural integrity of RPVs.

xiv
ACKNOWLEDGMENTS

The authors wish to thank the U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory

Research for supporting this work and, in particular, the NRC Program Manager, Ms. Deborah A.

Jackson.

The authors thank Dr. Lee Abramson, Dr. Mark Kirk, and Dr. Ed Hackett of the U.S. Nuclear Regulatory

Commission Office of Nuclear Regulatory Research for discussions and guidance during the development

of the generalized procedure for estimating vessel-specific flaw distributions. Terry Dickson of Oak

Ridge National Laboratory provided constructive interactions that ensured that the flaw estimation

procedure was compatible with current fracture mechanics developments. Finally, we acknowledge the

insights gained from discussions with the members of the expert elicitation panel.

The authors also acknowledge the contributions of PNNL staff members Ms. Kay Hass for assistance in

preparing this manuscript and Ms. Andrea Currie for editorial support.

xv
ABBREVIATIONS

ASME American Society of Mechanical Engineers

BWR boiling water reactor

CCDF complementary conditional depth distribution

CT later

EPRI Electric Power Research Institute

ESW electro slag welding

FAVOR Fracture Analysis of Vessels: Oak Ridge

GDF generalized flaw distribution

GMAW gas metal arc welding

GTAW gas tungsten arc welding

HAZ heat-affected zone

ISI in-service inspection

LQ lower quartile

NDE nondestructive evaluation

NDT nondestructive testing

NRC U.S. Nuclear Regulatory Commission

ORNL Oak Ridge National Laboratory

PFM probabilistic fracture mechanics

PNNL Pacific Northwest National Laboratory

PRA probabilistic risk assessment

PTS pressurized thermal shock

PVRUF Pressure Vessel Research User Facility

PWR pressurized water reactor

RPV reactor pressure vessel

RRA Rolls-Royce and Associates

RT radiographic testing

RVID reactor vessel integrity data

SAFT-UT synthetic aperture focusing technique for ultrasonic testing

SAW submerged arc welding

SMAW shielded metal arc welding

xvii
UQ upper quartile

UT ultrasonic testing

xviii
1 INTRODUCTION -

The U.S. Nuclear Regulatory Commission (NRC)

has supported research to re-evaluate the

regulations for pressurized thermal shock (PTS)

within the framework of modern probabilistic risk

assessment techniques (Dickson et al. 1999). A

PTS event or transient consists of a severe

overcooling along with an increase in pressure in

the reactor pressure vessel (RPV), which

challenges the integrity of the reactor vessel's

inner wall. Such transients are a significant

concern as plants approach the end of their

operating license and for periods of license

renewal because the material of the vessel wall

can become increasingly embrittled at elevated

levels of neutron fluence. In addition to the

severe overcooling transient and embritttled

vessel material, a factor critical to vessel failure is

the presence of a crack-like flaw within the - -- ..

embrittled material of the inner surface region of

the vessel. This report focuses on the fabrication

flaws in RPVs in terms of the number of flaws

(flaw density), the locations of flaws (relative to

the vessel inner surface), the sizes of the flaws

(through-wall depth dimensions and lengths), and

orientations of flaws (axial or circumferential).

Pacific Northwest National Laboratory (PNNL)

has participated in research to address PTS issues

by performing examinations of RPV materials to

detect and measure the numbers and sizes of

fabrication flaws in welds and base metal. To

supplement the limited data from'flaw detection

and measurements, PNNL has applied an expert

judgment elicitation process (Jackson and Doctor

2000; Jackson and Abramson 2000) and the

PRODIGAL flaw simulation model (Chapman

and Simonen 1998) developed in the United

Kingdom by Rolls-Royce and Associates. The'

experimental work on flaw distributions has

provided fabrication flaw data from

nondestructive and destructive examinations. ;

Using these data, PNNL has developed statistical

distributions to characterize the number and sizes

of flaws in the various regions of RPVs. The

work on flaw distributions has been coordinated

with another research program at Oak Ridge

National Laboratory (ORNL) that has developed a

probabilistic fracture mechanics (PFM) code titled

FAVOR (fracture Analysis of Vessels: Oak

Ridge) (Dickson 1994). This computer code

predicts failure probabilities for embrittled vessels

subject to PTS transients. Critical inputs to

FAVOR are the number and sizes of fabrication

flaws in the vessels of interest. To this end,

PNNL has provided computer files to ORNL that

describe the flaws in various vessel regions. The

present report describes how PNNL applied the

available data on fabrication flaws in combination

with insights from the expert elicitation and

PRODIGAL flaw simulation model to computer

files that serve as inputs to the FAVOR.

1.1 Probabilistic Fracture

Mechanics Codes

Since the early to mid 1980s, there have been'

significant advancements and refinements in the

relevant technologies associated with the physics

of PTS events that impact RPV integrity

assessment. Updated computational models have

evolved through interactions among experts in the

relevant disciplines of thermal hydraulics,

probabilistic risk assessment, statistics, material

embrittlement, fracture mechanics, and inspection

(flaw detection and characterization). These'

updated models have been integrated into the

FAVOR computer code, which is an applications

tool for performing risk-informed structural

integrity evaluations of aging reactor pressure

vessels. Figure 1.1 diagrams the major elements

that enter into a PFM evaluation' of a RPV

subjected to conditions of pressurized thermal

shock. Each of these elements has been reviewed

and revised as part ofan effort to update the

technical bases for revision of current NRC

regulations for PTS. In this methodology, the

loads due to thermal and pressure transients come

from detailed probabilistic risk assessments

(PRAs) and thermal hydraulic calculations.

1.1
Figure 1.1. Elements of Computational Model for Predicting Vessel Failure Probabilities and its Application

to Regulations for Pressurized Thermal Shock

Material properties (fracture toughness

estimates)are based on calculated neutron fluence

maps, embrittlement correlations, databases on

fracture toughness measurements, and vessel

parameters from reactor vessel fabrication records

(RVID).

The model used in the previous PFM analyses,

from which the current PTS regulations were

derived, conservatively postulated that all

fabrication flaws were inner-surface breaking

flaws. It was also recognized that the fabrication

flaw data had the greatest level of uncertainty of

the inputs required for the PTS evaluations. This

report discusses an improved model that PNNL

developed for postulating fabrication flaws in

RPVs and describes the treatment of that data by

the FAVOR code. The discussion presents a

methodology that has been developed to estimate

the number and sizes of fabrication flaws in

RPVs. The methodology has been applied to

generate flaw-related inputs for probabilistic

fracture mechanics calculations that have been

performed as part of an effort to update

pressurized thermal shock regulations.

NRC-funded research at PNNL has generated

data on fabrication flaws from nondestructive and

destructive examinations of RPV material

(Crawford et al. 2000; Schuster et al. 1998, 1999,

2000a,b). Statistical distributions have been

developed to describe the flaws in each material

region (Jackson and Doctor 2000; Jackson and

Abramson 2000; Jackson et al. 2001). Results

from an expert elicitation (Jackson and Abramson

2000) helped to fill gaps in the measured data on

fabrication flaws. The regions include the main

seam welds, repair welds, base metal of plates and

forgings, and the cladding at the inner surface of

the vessel.

This report includes a summary of the available

data on fabrication flaws in seam welds, repair

welds, base metal, and cladding materials and

describes the treatment of these data to estimate

flaw densities, flaw depth distributions, flaw

aspect ratio distributions, flaw orientation, and

flaw location. In each case, there have been

statistical treatments of uncertainties in the

parameters of the flaw distributions, which have

been included as part of the inputs to the PFM

1.2
calculations. The report includes a presentation

of some sample inputs for flaw distributions that

have supported evaluations by NRC of the risk of

vessel failures caused by PTS events.

1.2 Domestic Reactor Pressure

Vessel Fabrication

The fabrication process involves a number of

variables or characteristics that must be

considered, some of which have a significant

bearing on the introduction of flaws into the RPV.

There were three major maniufacturers of

domestic RPVs: Combustion Engineering, which

fabricated approximately 45% of the domestic

RPVs; Babcock and Wilcox, which fabricated

about 35%; and Chicago Bridge and Iron, which

fabricated the remaining 20%. Although each

vessel was inspected to American Society of

Mechanical Engineers (ASME) standards prior to

operation, the fabrication and inspection

processes were different for each manufacturer.

The fabrication processes for pressurized water

reactors (PWRs) and boiling water reactors

(BWRs) is very similar, but PTS is a concern only

for PWRs.

Most RPVs in the United States were constructed

by welding together plate material and forgings.

The shell courses of the RPVs were constructed

either by welding'three sections of formed plate,

resulting in axial weldments, or using forged rings

for the shell courses.' The base metal materials

used for most plates and forgings were A533B

and A508, respectively. The welding process

used in the fabrication of the reactor vessels

varied with each manufacturer. For the vast

majority of PWRs, three welding processes were

used in assembling the reactor vessels: shielded

metal arc welding (SMAW), gas metal arc

welding (GMAW), and submerged arc welding

(SAW). The rarely used GMAW process was for

cladding repairs. Both SMAW and SAW were

used for axial and circumferential welds. A

fourth process, electroslag, is an automatic

process that was used mainly for axial welds in a

few BWR vessels. Before, during, and following

the welding, both surface and volumetric

inspections were performed. A stainless steel

cladding was applied to the inside of each shell

course. The formed rings were then stacked and

welded to form the cylinder. These

circumferential weld preparation surfaces were

inspected prior to welding, and the welds were

subjected to inspections during and following

welding. Finally, cladding was applied to the

inside of the vessel to cover the newly formed

circumferential weld, and the clad surface was

then inspected.

1.3 Historical Sources of

Fabrication Flaw Data

The current rules that govern the generic PTS

screening limit and plant-specific vessel

evaluations were derived from models that

utilized the Marshall distribution for flaws in the'

welds of RPVs. The documents on the Marshall -

study (Marshall Committee 1982) indicate that

the flaw distribution was based on'flaw data from

a limited population of nuclear vessels and many

non-nuclear vessels. 'The flaw measurements

were part of the customary nondestructive

preservice examinations as performed 25 or more

years ago'at vessel fabrication shops. Due to

limitations of the nondestructive evaluation

(NDE) technology, the Marshall flaw distribution'

provides a reasonable representation only for

flaws having depth dimensions of about I in.

(25.4 mm) or greater. The Marshall distribution

has nevertheless been applied to PTS evaluations

by extrapolation of curves to the much smaller

flaws of concern to PTS calculations (flaw depths

of 0.25 in. [6 mm] and smaller).

The objective of the recent NRC research on

vessel flaws has been to examine RPV materials

using more sensitive NDE techniques and to

collect data on flaws of all sizes, including those

with depth dimensions as small as a few

millimeters. These efforts have exploited

advanced NDE methods with high levels of

sensitivity. Another advantage came from the use

of material from surplus RPVs from cancelled

plants. In this regard, ultrasonic scans were not

limited to access from the cladded inner surface

1.3
of the vessels but exploited the use of smaller

samples of material removed from intact vessels

along with high-resolution synthetic aperture

focusing technique for ultrasonic testing

(SAFT-UT) scans from sectioned surfaces that

were optimized to detect flaws with orientations

normal to the vessel inner surface. The current

database provides dimensions for a large number

of relatively small flaws of the sizes identified as

the major contributors to potential vessel failures

for PTS events. Such flaw sizes were not

addressed by the data used to develop the

Marshall distribution.

Other papers have described the methods used to

examine RPV materials and have documented the

actual detection and sizing of the flaws in these

materials. The flaw measurements have included

through-wall depth dimensions, flaw lengths

(aspect ratios), and locations of inner flaw tips

relative to the inner surface of the vessel. Where

limitations in the measured data were identified,

other approaches, including expert elicitation

(Jackson and Doctor 2000; Jackson and

Abramson 2000) and the PRODIGAL weld

simulation model (Chapman and Simonen 1998),

were applied to supplement the measured data or

to otherwise guide the development of flawrelated inputs to the fracture mechanics model.

The objective of the current report is to describe

how new sources of information on RPV flaws

were used to support the improved model for

postulating fabrication flaws in RPV. The

discussion describes the conceptual framework of

the PFM in terms of vessel regions and the types

of flaws that are important to each region.

In the PTS evaluations, the flaws of concern are

assumed to be present at the time of vessel

fabrication but not detected and repaired before

the vessel was placed into service. The

evaluations assume that there are no credible

mechanisms to cause service-related cracking of

the RPV materials. It is also assumed that crack

growth mechanisms of fatigue and stress

corrosion cracking can be neglected due to the

relatively benign operating conditions of

pressurized water reactors.

1.4 Overview of Report

This report provides a systematic documentation

of how flaw-related inputs have been generated

for the FAVOR probabilistic fracture mechanics

code. Section 2 describes the basic structure of

the flaw estimation model, with a focus on key

assumptions made in developing the

methodology. Section 3 presents experimental

work on examinations of vessel material that

provided a database on fabrication flaws in welds,

base metal, and cladding. Section 4 describes the

expert judgment process used to augment the gaps

in the empirical database and Section 5 provides a

detailed description of and results from the

PRODIGAL model. The treatment of these data

to develop statistical distribution functions is

documented in Sections 6, 7, and 8 for weld

metal, base metal, and cladding, respectively.

Integration of the flaw estimation model into a

computer algorithm to generate input files for the

FAVOR code is described in Section 9, and

Section 10 provides conclusions.

1.4
2 OVERVIEW OF FLAW ESTIMATION PROCEDURE

This section provides an overview of the flaw

estimation model and summarizes a number of

assumptions made in the development of the

model.

2.1- Vessel Regions and Flaw

Categories

Figure 2.1 depicts the various regions of a RPV

and the flaws that are addressed by the PFM

model. This conceptual cross-sectional view

shows axial welds in a vessel. A corresponding

cross section to show circumferential welds

would illustrate the same categories of flaws but

with flaw orientations rotated by 90 degrees.

Figure 2.2 is a metallographic cross section of a

circumferential weld from a RPV. This view

shows all the major material regions of concern to

vessel integrity, which include weld metal, base

metal, weld fusion lines, and the cladding at the

vessel inner surface. The flaws of concern are

those present at the time of vessel fabrication and

not detected and repaired before the vessel is

placed into service. It is'assumed that there are no

credible mechanisms to cause service-related

Fusion Una Wok

Flaw (E nv

Repailm to

Base metal -.

cracking and that crack growth mechanisms of

fatigue and stress corrosion cracking can be

neglected.

In developing inputs for fracture mechanics

calculations, the vessel material regions described

in Sections 2.1.1 through 2.1.5 were addressed.

2.1.1 Seam Welds

Major weld regions of concern to RPV integrity

are the axial and circumferential seam welds in

the high neutron fluence region of the vessel

beltline. These welds can be fabricated by the

SAW process or by the SMAW process.

Typically, a given seam weld will have some

welding from both processes but the largest

fraction (e.g., >90%) of the weld would be

deposited by the automatic SAW process. The

improved flaw model accounts for separate flaw

densities and flaw size distributions for each weld

process. However, the identification of specific

local weld regions as being produced by particular

processes requires information not generally

available from vessel fabrication records.

Calculations with the FAVOR code have

Structurally SignHfiant

) Bass Metal Flaw

Benign Base Metal Flaw

- SAWWeld

Large Flow

at End of

Structurally RepalrZone

Figure 2.1. Conceptual View of Material Regions of a Vessel and the Categories of Flaws That Can Impact

Structural Integrity -

2.1
Figure 2.2. Metallographic Cross Section of a

Circumferential Weld Showing Adjacent Regions of

Base Metal and Cladding

flaws for circumferential welds are assumed to

have circumferential orientations.

2.1.2 Base Metal

Flaws within base metal are observed to occur at

much lower rates (per unit volume of metal) than

in welds. Figure 2.1 shows two flaw categories

that were identified. It is well known that the

largest flaws in plate and forging materials have

orientations parallel to the surface of the vessel.

This orientation comes from the rolling and other

operations used to fabricate the vessel plates and

forged rings. Although such flaws can be quite

large, their orientations are such that they have no

significance to vessel integrity. As indicated in

Figure 2. 1, the only base metal flaws of concern

are those that have some through-wall dimension.

Data from limited examinations at PNNL of plate

materials indicate that such flaws occur at lower

rates per unit volume (by a factor of ten or

greater) in plate materials than in welds

(Crawford et al. 2000; Schuster and Doctor

2001a).

Another significant feature of the flaw model for

plate materials relates to the fusion line flaws

located at the region between the base metal and

weld metal. The FAVOR code assumes that these

fusion line flaws can propagate into either

embrittled weld metal or into embrittled plate

material, depending on which material has the

lower level of fracture toughness

2.1.3 Repair Welds

Although repair welds make up only a small

percentage of the weld metal in a typical vessel,

most of the larger flaws (depth dimensions greater

than a weld bead) have been observed in weld

repairs. As depicted in Figure 2.1, typical repairs

consist of a ground-out region that has been filled

by a manual welding process. The repairs can be

entirely within seam welds, entirely within base

metal, but will most typically span both weld

metal and base metal because repairs are

generally made to defects along the weld fusion

therefore been based on an assumption of a

random mixture of SAW and SMAW materials

along with a small fraction of repair welding. The

fractions have been based on trends observed

from examinations of vessels at PNNL.

Flaws in seam welds can be located randomly

within the volume of deposited weld metal or

along the fusion lines between the weld metal

from the adjoining base metal (plate or forging

material). Although some flaws are distributed

within the volume of the weld joint, the measured

data have shown very few of these flaws to have

significant through-wall dimensions. Most flaws

are located along the weld fusion line. These

flaws (lack-of-fusion or entrapped slag) are

usually relatively small. However, a small

fraction of these flaws has through-wall

dimensions approaching or exceeding the size of a

single weld bead. Based on observed flaw

locations, the probabilistic fracture mechanics

analysis assumes that all weld-related flaws are

located along weld fusion lines. Flaws for axial

welds are assumed to have axial orientations, and

2.2
lines. Repairs have been observed to occur at

both the inside and the outside of vessels.

Flaws in repair welds have been observed along

fusion lines between the metal of the weld repair

and the original vessel material. These flaws will

usually impinge on both seam welds and base

metal. The largest flaws found during PNNL

examinations have been located at the ends of

repair cavities and have been attributed to the

difficulties in manual welding within the confined

spaces at the ends of the ground-out cavities.

In modeling of weld repairs with the FAVOR

code, it has not been practical to identify specific

locations of repairs such as may be documented

by construction records. The repairs have been

assumed to occur at random locations, such that

the repair flaws are blended into the other

population of flaws associated with the normal

welding processes. The small amount of material

from repair welding nevertheless makes a

disproportionate contribution to the estimated

numbers of larger flaws.

2.1.4 Cladding

The number and size of surface-breaking flaws at

the inner surface of a vessel have been estimated

from data on flaws that have been detected during

examinations of vessel cladding (Simonen et al.

2001).' As indicated in Figure 2.1, such flaws can

occur randomly in the cladding applied over both

weld and base metal. Because the vessel inner

surface consists mostly of base metal, all but a8,

small fraction of the clad (or surface-related) : ;

flaws will be associated with base metal rather

than with weld metal.

Figure 2.1 shows four categories of clad flaws.

The FAVOR code assumes that the fracture

toughness of the cladding material is sufficiently

high such that flaws entirely within the cladding

will not propagate. Hence, some configurations

of clad flaws labeled in Figure 2.1 are benign.

Structurally significant flaws are only those flaws

(either buried flaws or large through-clad flaws)

that extend to the clad-to-base metal interface.

The vessel examinations show that the majority of

such structurally significant flaws are of the

buried type because the probability for the larger

through-clad flaws is low and because shop

examinations of clad surfaces will detect and

repair most of the surface-breaking flaws that may

occur from the weld depositing of cladding. All

flaws in cladding are assumed to have

circumferential orientations because cladding is

applied using weld beads that have a

circumferential orientation.

2.1.5 Underclad Cracking

A final type of flaw, not yet addressed by the

FAVOR code, is iuiiderclad cracks resulting from

unfavorable conditions' during the weld deposition

of the cladding material.' Underclad cracks have -

been observed in some vessels, particularly within

the base metal of forged rings. Such flaws are

precluded for most PWR vessels by consideration

of the chemical compositions of the base metal.

2.2 Treatment of Flaws by FAVOR

Code

The FAVOR code simulates the sizes and

locations of flaws and makes use of three input

files for (1) flaws in weld regions, (2)'flaws in

base metal regions, and (3) surface-related flaws

in the vessel cladding. In each case, the number

of flaws per unit volume of material is specified

using numerical tables of data. Statistical uncertainties in the estimated flaw-related parameters

are treated by generating 1000 possible tables to

characterize the estimated uncertainties in the

flaw distributions. The elements of the tables

correspond to flaws with given depth dimensions

as a percentage of the vessel wall thickness and

given aspect ratios (flaw length divided by flaw

depth). The locations of flaws'in weld and base

metal regions are assumed to be'randomly

distributed through the thickness of the vessel

wall.

All of the planar-type flaws that have been

observed durin'g the vessel examinations are

treated by FAVOR as exhibiting ideal crack-like

2.3
behavior. For planar flaws, it was not possible to

consider the morphology of cracks in detail such

as to account for flaws whose tips were somewhat

blunted relative to idealized cracks such as

sharpened by fatigue crack growth.

User input data to FAVOR PFM analyses

includes the volume of metal for each of the RPV

subregions. Each of these subregions has its own

embrittlement-related properties. From the

assigned metal volumes and the inputs for the

number of flaws per unit volume of each size

category, the total number of flaws in each weld,

base metal region, or clad region is calculated.

Flaw locations relative to the vessel inner surface

are assigned randomly. The FAVOR code also

divides the vessel wall thickness into regions with

the first region being the inner one-eighth of the

wall thickness, and the second region being the

region from one-eighth to three-eighths of the

vessel wall thickness. FAVOR assumes that

flaws located beyond three-eighths of the wall

thickness make negligible contributions to the

vessel failure probabilities.

2.3 Monte Carlo Simulation

A computer code was developed by PNNL to

generate input files for probabilistic fracture

mechanics calculations. The flaw distribution

code decomposed the data on measured flaws into

a set of flaw categories (large and small flaws,

SAW, SMAW, and repair welds) and separated

the data measured from the Pressure Vessel

Research User Facility (PVRUF) and Shoreham

vessels. The objective was to allow vesselspecific flaw distributions to be estimated by

consideration of the actual processes used to

complete the welds, the sizes and number of weld

beads for each weld, and the statistical

uncertainties in the parameters that describe the

characteristics of each category of welds.

To address uncertainties in the parameters of the

statistical correlations that characterize the

densities and sizes of the various categories of

flaws, a Monte Carlo simulation was used to

generate a large number of possible flaw

distributions that are consistent with the

uncertainties arising from the limited amount of

data. The FAVOR code takes samples from these

datasets in calculating vessel failure probabilities.

2.4 Estimation Procedure for Welds

The procedure assumes that seam welds consist of

various amounts of weld metal deposited by

different welding processes (SAW, SMAW, and

manual repair welding). However, the FAVOR

code does not attempt to identify the specific

locations of materials from each process but

assumes that each weld process can occur

randomly within the volume of the completed

weld. The procedure therefore blends the

contributions from the three welding processes in

accordance with the relative volume fractions of

material deposited by each process. User inputs

are required for the fraction of weld metal from

each welding process. Characterization of welds

in the PVRUF and Shoreham vessels indicates

that at least 90% of the weld volume will be of the

SAW type, 5% to 10% of the SMAW type, and

1% to 2% will consist of repair welding.

In evaluating the data from weld examinations,

the flaw dimensions were first normalized with

respect to the estimated thickness of the weld

beads to account for vessel-to-vessel differences

in welding procedures. This approach permitted

the data from PVRUF and Shoreham vessels to be

applied to welds with smaller or larger bead sizes.

The first step in the estimation procedure assigns

values for the flaw densities (e.g., flaws per cubic

meter) for each of the weld types. Each sampling

of the Monte Carlo simulation assigns six values

of flaw density corresponding to the two flaw size

categories (large and small) and the three weld

processes (SAW, SMAW, and repair). The

estimation procedure also includes a specification

that determines if flaw densities should be based

on the observed densities from the PVRUF vessel

or from the Shoreham vessel.

The second step in the estimation procedure

addresses the through-wall depths of simulated

2.4
flaws. As part of this step, a user input is required

to specify a through-wall bead size for each weld

process.' These bead sizes are used as the basis

for-distinguishing "small flaws" from "large

flaws." There are potentially six statistical

distributions for the through-wall dimensions of

flaws corresponding to the small and large flaws

and the three welding processes. Because there

were limited data from high-accuracy -

measurements for the sizes of very small flaws, a

single'depth distribution was assumed to apply'to

all three welding processes. For large flaws, there

was a clear difference in the depth distributions.:

for flaws in repair welds as compared to'the flaw

depths for SMAW and SAW welds. Two depth

distribution functions were developed for large

flaws.' Given the relatively small number of large

flaws, 'the uncertainties in the parameters of the '

distribution functions (exponential distributions)

were relatively large, and these parameter

uncertainties were an important element of the

Monte Carlo simulation.

The next step of the flaw estimation procedure

addressed flaw lengths (or aspect ratios). Again

the procedure allows separate consideration of the

trends from the PVRUF and Shoreham vessels .'

and deals separately with'the six flaw categories

corresponding 'to small and large flaws and three'.

weld processes (SAW, SMAW, and repair welds).

The data indicated that flaw dimensions are best

described in terms of flaw length rather than in

terms of flaw aspect ratios (i.e., ratio of flaw

length to flaw depth dimension). The important

parameter was the amount by which the flaw

lengths exceeded the flaw depth dimensions. This

procedure produced distributions of flaw aspect

ratios that were a function of the depth -

dimensions. The data showed interesting trends

for flaw lengths. For example, small flaws in the

SAW welds of the PVRUF vessel were all nearly

1:1, whereas the corresponding flaws in the

Shoreham vessel had relatively large aspect ratios.

Another significant trend was that flaws with

relatively large through-wall depth dimensions,

had small aspect ratios. -Flaws with large aspect

ratios were primarily those with relatively small

depth dimensions

A final step in the estimation procedure allows a

truncation 'on the possible through-wall depths of

'large flaws. The truncation values of flaw depths

are user inputs to the estimation procedure. - -

Different truncation values can be specified for

each of the three welding processes. For

example, the maximum depth dimension for

repair flaws can be set at a much larger value than

the maximum value for flaws associated with

SAW welds

Consistent with the flaw orientations observed

during the PNNL examinations of vessel welds,

the orientations of flaws in axial welds are treated

as having axial orientations.' Similarly, flaws in

circumferential welds were treated as

circumferential flaws.

2.5 Estimation Procedure for Base

Metal

The base metal flaws of interest were those with

sufficient through-wall dimensions to potentially'

impact the structural integrity of an RPV. This

consideration excluded the common types of.

planar flaws seen in plate and forging material

(e.g.,jlaminations) that may be relatively large but

whose through-wall dimensions are negligible.

Therefore, the examinations of vessel base metal

specimens at PNNL were designed to detect and

size flaws with measurable through-wall

dimensions.

In summary, the inputs for flaws within the

volume of base metal regions (plate and forging

materials) were estimated by applying reduction

factors to the flaw densities for weld metal. A

factor of 10 reduction was applied for densities of

small flaws (depth dimensions less than or equal

to 6 mm) and a factor of 40 reduction for large

flaws. A truncation of the distribution is applied

to flaws greater than 11 mm in depth dimension,

which depth corresponrds to about 5% of a PWR

vessel wall thickness. The resulting inputs for

base metal flaws are otherwise identical to those

for weld flaws, including the elements of flaw

aspect ratios and uncertainty distributions applied

to flaw densities. The procedure allows the

2.5
parameters of the flaw density and depth

distributions to be based on either the data from

the PVRUF or the Shoreham vessels. Because the

flaw aspect ratios observed during PNNL's base

metal examinations had consistently small values,

the assigned distribution of aspect ratios had

values of 2:1 or less.

The reduction factors of 10 and 40 corresponded

to values from an expert elicitation (Jackson and

Abramson 2000). These values are also generally

consistent with preliminary data from

nondestructive examinations of plate materials.

Future work will provide additional validated

flaw data for plate materials and will also address

forging material. Data from plate taken from four

different vessels show considerable variation in

the number and sizes of flaws. However, the

reduction factors of 10 and 40 have been found to

be generally consistent with the range of the data

obtained from the various samples of vessel plate

material. It should also be noted that the FAVOR

code assumes that failures caused by lowtoughness plate and forging materials are

potentially associated with (1) flaws distributed

within the volume of the base metal itself,

(2) flaws located along the fusion line between

base metal and weld metal, or (3) clad/surface

flaws within the clad material that extend up to

the clad/base metal interface. The relative

importance of each of these flaw categories will

be determined by future vessel-specific

calculations with the FAVOR code.

There was no consistent trend in the observed

base metal flaw orientations during the PNNL

examinations of base metal materials. Therefore,

in the probabilistic fracture mechanics model, it

was assumed that half of the base metal flaws had

axial orientations and the other half was assigned

circumferential orientations.

2.6 Estimation Procedure for

Clad/Surface Flaws

Flaws located in the clad/inner surface region are

addressed using the methodology described in

another paper (Simonen et al. 2001). There is no

quantitative treatment of uncertainties in the

inputs for surface flaws. Flaw aspect ratios are

assigned by application of data on flaw lengths as

measured for clad flaws detected in the cladding

of the PVRUF vessel. The estimation procedure

can address specific clad configurations as

defined by the number of clad layers along with

the thickness and width of the weld beads that

make up the cladding.

All of the observed flaws in the cladding had

circumferential orientation. This trend was

consistent with expectations because welddeposited cladding is applied to vessel inner

surfaces as a series of circumferential weld

passes. The fracture mechanics-model treated all

inner surface flaws as being in the circumferential

direction. Inputs for clad/surface flaws have been

generated for the FAVOR code. Inputs for both

buried clad flaws and surface-breaking flaws were

developed to match the fracture mechanics model

used in FAVOR, which addresses only the

contributions of surface-breaking flaws. Because

the flaws detected by PNNL in vessel cladding

were exclusively buried flaws, the number of such

flaws was reduced to values consistent with the

FAVOR fracture mechanics model that treats only

flaws that penetrate the full thickness of the clad.

Based on sensitivity calculations (Simonen et al.

2001), only about one of a thousand buried clad

flaws was estimated to impact vessel integrity as

much as the limiting surface flaw having a depth

equal to the full clad thickness. The FAVOR

code expresses the density of surface-breaking

flaws as the number of surface flaws per unit

volume of underlying material of the vessel wall.

This required another conversion of flaw densities

to go from flaws per unit area of the vessel inner

surface to an equivalent density of flaws per unit

volume.

2.7 Flaw Locations

Figure 2.3 presents data on the observed locations

of flaws in the welds of the Shoreham vessel as

measured relative to the inner surface of the

vessel. There was a similar trend for flaw

locations in the PVRUF vessel. There were no

2.6
0.0 1.0 2.0 3.0 4.0 5.0 6.0

Flaw Location Relative to Vessel ID, Inch

Figure 2.3. Flaw Locations Relative to Vessel Inner Surface

observed flaws from the PNNL examinations that

were true inner-surface brealdng. All observed

flaws near the inner vessel surface could be

classified as buried flaws. These data had

important implications to the fracture mechanics

calculations because there was no indication that

flaws occur preferentially at the locations at or

near the embrittled inner surface of the vessel.'

Based on the trends such as shown by Figure 2.3,

it was assumed that weld flaws occur at random

locations within the thickness of the weld.

2.8 Treatment of Uncertainties

Two broad areas of uncertainty were identified in

the treatment and application of the PNNL flaw

data. One area of uncertainty was how well the

flaws in other vessels are described by the flaws

that were observed in the PVRUF or'Shoreham

vessels. The second area of uncertainty is that the

measurements from the PVRUF and Shoreham'

vessels provide only a finite number of data.

points for use in establishing the parameters of

statistical distributions that descrbe the densities

and sizes (through-wall depth dimensions and

aspect ratios) for each of the flaw categories of

interest (large and small flaws, SAW, SMAW,

and repair flaws). The uncertainty analyses

focused on this second area of uncertainty.

The uncertainty analysis selected an appropriate

distribution function and used the available data

to establish the numerical parameters for the

selected distribution functions that provided the

best fit of the data. If the number of data'points

was'relatively small, the established distribution is

subject to large uncertainties. A formal procedure

(described in Appendix A) quantified the

uncertainties in the estimated parameters of the

statistical distributions making use of a Bayesian

methodology based on unbiased previous

distributions.

2.9 Sample Flaw Distributions

The methodology as described above is a

generalized procedure for generating a flaw

distribution applicable to a specific vessel.

Figure 2A presents some sample flaw

distributions coming from applications of the

generalized procedure. Presentations of these

results become somewhat complicated because

the uncertainty analysis provides not one

distribution but a series of sample distributions,

2.7
1.E+03 1.E+03 .FIA!PEtCD?4Ic, :OIFtC4OpCpKLtNPJI,::'.Ft 11AVAIX,:PICt CD-VO 20 '00 1. Pt-:,T20FOPKL IN PUT O

A

0.

Q

0

0

UU0I..

GI

T.

aUU0

L..

.0

E

Z

I.E.02

I.E+01

I. E '00

I.E.01 I:

1.E-02

I.E.03 1

I.E-04I

Bas e 1M14

Wall Thickniess = 214 min

etal

Well Mletal

Suirface/Clad

I.E-05

I.E.06

0 5 10 15 20 25 30

a = Flaw Depth, Percent Wall

Figure 2.4. Sample Flaw Distribution for Use in Probabilistic Fracture Mechanics Calculations

with each distribution being consistent with the

statistical variability of the observed data.

Figure 2.4 presents 50th percentiles of the

uncertainty analyses. These flaw distributions

were based on the trends of the data from the

Shoreham vessel, which gave a somewhat more

conservative estimate of the number and sizes of

flaws than would estimates based on the PVRUF

data. It was assumed that the weld of interest

consisted of a mixture of SAW, SMAW, and

repair welding with volume fractions for these

weld processes being 93%, 5%, and 2%,

respectively. The depth distributions were

truncated to avoid unreasonable extrapolations

beyond the flaw depths actually observed in the

vessel examinations. The curves for SAW and

SMAW flaws were truncated at a depth of

25 mm, which is a depth about two times greater

than the measured depth of any flaws detected in

either the Shoreham or PVRUF vessel. The

depths for repair flaws were truncated at a depth

of 50 mm, which is a factor of two or more

greater than any observed flaws in repair welds.

The 50-mm depth is also a physical limitation on

the largest repair flaw imposed by the width

dimensions of a large cavity associated with a

large weld repair. A final curve of Figure 2.4 is a

plot of the flaw distribution for surface or cladrelated flaws. The maximum possible flaw depth

is constrained by the thickness of the cladding.

2.10 Summary and Conclusions

The objective was to develop fracture mechanics

inputs for the number, sizes, and locations of

fabrication flaws that may exist in the belt-line

regions of reactor pressure vessels. The approach

has been to maximize the use of data on vessel

flaws obtained from examinations of material

taken from cancelled nuclear power plant RPVs

fabricated from the late 1960s to the early 1980s.

The examined material is therefore believed to be

typical of the material in vessels at currently

operating plants in the United States that are of

concern for potential failure due to PTS events.

The improved model for postulating fabrication

flaws in RPVs addresses three broad categories of

vessel material regions and the flaws within these

2.8
regions, namely (1) weld flaws, (2) base metal

flaws, and (3) cladding flaws. A separate set of

input data corresponding to each of these flaw

categories is provided as input to the probabilistic

fracture mechanics calculations. These input files

describe the number of flaws per cubic volume,

the distribution of flaw depth dimensions, and the

distribution of flaw aspect ratios. Other key

features of the flaw model are as follows:

(1) The flaw model treats the flaw locations as

uniformly distributed through the thickness of

the vessel wall and does not assume, as in

previous PTS calculations, that the flaws are

inner-surface breaking.

(2) Weld flaws are assumed to lie along the weld

fusion line between weld and base metal;

fracture mechanics calculations then allow

these fusion line flaws to grow into either the

weld material or into the base metal,

whichever is more limiting from the

standpoint of fracture toughness.

(3) Flaws of potential concern to failure of base

-metal regions are (1) flaws within the base

metal itself, (2) flaws associated with the

weld fusion line, and (3) flaws associated

with the cladding.

(4) Clad materials are assumed to have sufficient

fracture toughness to preclude the growth of

flaws if the flaws are entirely within the

cladding material; clad flaws are therefore

structurally significant only if they extend up

to or penetrate beyond the clad-to-base metal

interface.

(5) Underclad cracks in base metal are not

addressed; the present model would need to

be enhanced in the future to evaluate vessels

for which underclad cracking is considered to

be a credible source of flaws.

Data files have been prepared for use by ORNL

for PTS calculations with the FAVOR code.

Calculations have been performed for several

representative vessels that will address plants

from the major nuclear steam supply system

(NSSS) suppliers and with various levels of

embrittlement. Although most calculations have

been for vessels, for which the weld material is

the most limiting material from the standpoint of

embrittlement, other calculations address a vessel

that has base metal as the most limiting material.

2.9
3 EXAMINATIONS OF VESSEL MATERIAL

Recent NRC research on vessel flaws has

examined RPV materials using sensitive NDE

techniques and has collected data on flaws with

depth dimensions as small as a few millimeters.

This research has exploited advanced NDE

methods with high levels of sensitivity and has

used material from surplus RPVs from cancelled

plants. Ultrasonic scans were not limited to

access from the clad inner surface of the vessels

but used smaller samples of material removed

from intact vessels. High-resolution SAFT-UT

has scanned from sectioned surfaces in a manner

optimized to detect flaws with critical orientations

normal to the vessel inner surface.

The examinations of vessel welds and base metal

used vessel materials from cancelled plants as

listed in Tables 3.1 and 3.2. The examined weld

metal (Table 3.1) totaled about 50% of the

beltline weld material for the Shoreham and

PVRUF vessels; for the Hope Creek II and River

Bend II vessels, only relative samples of weld

metal was examined. The sampling of plate

material was limited to the inner I in. of the

vessel wall because this region of the vessel is the

primary concern for PTS fracture mechanics

calculations. The total volume of examined plate

material as listed in Table 3.2 approached 10% of

the plate material of the beltline of a typical PWR

vessel.

The newly developed database provides

dimensions for a large number of smaller flaws of

the sizes identified to be the major contributors to

potential vessel failures for PTS events. Several

reports and papers have described the methods

used to examine RPV materials and have

documented the detection and sizing of the flaws

in these materials (Schuster et al. 1998, 1999,

2000a,b; Crawford et al. 2000; Jackson and

Doctor 2000; Jackson and Abramson 2000;

Jackson et al. 2001; Pardini et al. 2000; Schuster

and Doctor 200 lb).

TaHbl 31- WePM Material Evalnuatd Tn GPnPratP Data nn Flnw nRate

Total Weld Indication

Length Volume of Density,

Cancelled Reactor Years of Available for Weld Metal Indications/

Plant Manufacturer .- Type Construction Examination, m Examined, m3 m 1 3

Shoreham CE BWR 1968 to 1974 24 0.15 30,000

Hope Creek II CB&I BWR 1971 to 1975 3 0.004 40,000

River Bend II CB&I BWR 1974 to 1978 - 15 0.04 10,000

PVRUF CE PWR 1976 to 1981 20 0.17 . 9,000

Table 3.2. Base Metal Material Evaluated To Generate Data on Flaw Rates

Volume of Volume of

Plate or Material Material

Cancelled Forging Year of Available for Available for

Plant Vendor Fabrication Material Examination, m3 Examination, m3

Shoreham Lukens 1968 A533B Plate 0.9 0.016

Hope Creek U Lukens 1971 A533B Plate 6.8 0.009

River Bend II Lukens 1974 A533B Plate 1.0 0.024

PVRUF Marrel Freres 1976 A533B Plate 0.6 0.014

Midland Ladish 1969 A508 Forging 0.4 pending

3.1
3.1 Procedures Used to Detect and

Size Flaws

PNNL's methodology for flaw detection and size

measurements consisted of four stages of 12 .1 13

increasing refinement. The first two stages form a apt;

general category wherein PNNL selected material

for the later stages for more refined measurements. The final two stages produced the S .- 39cm

validated measurements for best estimates of flaw 2 to 3 Rows

densities and distributions. 4.,

% -_22^X;T cm,

A combination of techniques was applied as D, ,

indicated in Figures 3.1 and 3.2. A cross section 13 Layers

of an examined circumferential weld of the

PVRIJF vessel is shown in Figure 3.3. The

validation results showed that most flaws were

located in the fusion zone of the weld to the

adjacent base metal (Figure 3.4) and that the

largest flaws were associated with repairs. The Clad . 8mm Clad - 5mm

X-ray computed tomography gave good shape

information for the complex repair flaws. Figure 3.3. Metallographic Cross Section of a

Circumferential Weld from PVRUF Vessel

gb. Xma IShowing Adjacent Regions of Base Metal and

Stage4 Validated Cladding

S 3dimensions

at 3 f ~~hin plate.o ^ -- -

accuracy

Stage 2 I Conservative

Clasizing

Stage I s 91io 

Figure 3.1. Sequence of Techniques Used To Detect

and Size Flaws

SEM and Spec ClPQii~

X( r y CT of Dimensions, -. Oship, and

(2~-:TOI Orlentation validated

Figure 3.4. Location of Flaw in the Fusion Zone of

Figure 3.2. Techniques Used for Detailed a Weld with the Base Metal

Characterization of Flaws

3.2
Metallography provided good information on flaw

composition. Electron microscopy confirmed the

metallographic results and provided additional

magnification. The X-ray computed tomography

gave additional shape information for the

complex repair flaws. Metallography provided

information on flaw composition. Electron

microscopy confirmed the metallographic results

and provided additional magnification. X-ray

spectroscopy provides chemical composition.

The repair flaws were shown to be a combination

of cracks, lack of fusion, porosity, and slag.

X-ray spectroscopy provides chemical

compositions.

The initial inspections of the PVRUF vessel were

performed by SAFT-UT from the clad inner

surface as shown in Figure 3.5. Data from these

inspections were analyzed, and sizing rules as

reported by Schuster et al. (1998), were

consistently applied for two purposes. Most

importantly, the material that contained the largest

indications was identified for later validation.

The sizing rules were needed to generate the

tabulation of 2500 flaws inspected with

10 modalities in a reproducible way. These rule

statements and the results of their application to

SAFT-UT inspections formed PNNL's two-part

conservative sizing methodology.

The second stage in developing validated flaw

rates for RPVs used weld-normal SAFI-UT

inspections (see Figure 3.6) of weld bearing

specimens removed from the vessels (Schuster

et al. 1999). The amount of vessel material

examined with weld-normal testing was reported

in Schuster et al. (1999). For the weld normal

inspections, it was assumed that no large flaws

were missed. Of equal importance, the flawed

material was rank-ordered to set priorities of the

subsequent validation testing.

The measurements of the final validated

dimensions of the larger fabrication flaws in the

PVRUF vessel began with radiographic

inspections of thin, weld-bearing plates as shown

in Figure 3.7. The weldments were sectioned into

25-mm thick plates and radiographed using a

450-kV X-ray machine. The flaws in the welds

were centered within the plate thickness, and the

through-wall dimensions were recorded.

Figure 3.8 shows an example of a digitized

radiograph of a fabrication flaw using

conventional radiography.

Figure 3.5. Inside View of the PVRUF Vessel During SAFT-UT Inspections

3.3
I 7-, -'-. a NM 4

i~ M Mf t In

4z.}r -d.w

.. I

,1

a

Figure 3.6. Weld Normal Inspections

Figure 3.8. Image of a Fabrication Flaw Using

Conventional Radiography

Figure 3.7. Examinations of Plate Specimens

Dimensions for the lack-of-fusion flaws were

recorded to the nearest 1.0 mm. The shapes and

orientations were evident in the image of the flaw,

and the lack of fusion could be observed to follow

the fusion zone between the weld and the

basemetal. The composition of the flaw was

evidenced by a low-density shape in the

radiograph. Rounded and linear features of the

radiographic testing (RT) indication separated

porosity from lack of fusion. However, tight

cracks not in a single plane were not imaged on

the radiographic film.

The fourth and last stage of the validation was

accomplished by centering flaws in small cubes as

shown by Figure 3.4. Dimensions for the flaws in

the cubes were measured by ultrasonic,

radiographic, computer-assisted tomographic

(CAT) scans, and metallography techniques. In

cube form, the measurements by each technique

confirmed the measurements in the other

techniques. Because of the small variance in

measurements from the cubed flaws, PNNL was

3.4
able to dispense with the conservative sizes

established in stages one and two of the

validation.

The cubes were inspected in an immersion tank

with 10-MHz high-resolution SAFT (Schuster

et al. 2000b). The horizontal resolution for the

probe was 1 mm, and the images were full-;

volume focused. The scanner's steps were

0.25 mm in both scan and increment directions.

The majority of the flaws examined were lick of

fusion. The inspection surface was chosen to

favorably orient the flaw to the ultrasonic beam.'

The location and dimensions of the flaws in the

cubes were determined to within ±0.5 mm'and '

recorded to the nearest 1.0 rmrn. The shapes and

orientations were evident in the image of the flaw,

and the lack of fusion could be observed to follow

the fusion zone of the weld with the base metal.

Changes in composition of the flaw were evident

where the lack of fusion contained more or less

slag.

Small specimens were sent to the Electric Power

Research Institute NDE Center for characterizing

the shape and orientation of the flaws. The

specimens contained large flaws from the ends of

weld repairs, and small flaws from the fusion

zone of SAW material with the base metal. The

data showed that X-ray CAT can image complex

flaws and give the flaws extent as it followed the

3-dimensional contour of the end of the repair

(Jackson and Doctor 2000).

Six cubes were examined with metallography.

The micropolish produced a surface finish of

approximately 1 ju (a mirror finish). The etchant

was a solution of 20% nitric acid and 80% ethyl

alcohol. Lighting sources were adjusted to

produce the necessary contrast for the - -

photomicrographs. Dimensions for the'flaws

were recorded to the nearest 1.0 mm. The

composition of the flaws was generally shown to

be lack of fusion and cracks. 'Figure 3.9 shows a

micrograph of SMAW weld passes at the inner

near surface zone of a vessel. A cracked weld

pass can be seen in the micrograph.

Figure 3.9. Micrograph of 25-mm Cube Containing

a Failed Weld Bead

Figure 3.10 shows an image from one of PNNL's

electron microscopes. A portion of the cracked

weld pass was imaged using 20-kV electrons, and

the magnification is shown with a l00-L scale.

The crack morphology is shown in the image to

be branched and filled with segregates.

.... I .

Figure 3.10. Electron Microscope Image of

Cracked Weld Bead

3.5
Table 3.3 shows the distribution of atomic elements

in the cracked portion of the SMAW weld pass

shown in Figure 3.10. The measurements were

made with the electron microscope using the X-ray

emissions from the electron bombardment and the

spectroscopic features of the microscope. The

concentrations of elemental oxygen, aluminum, and

silicon are evidence of metallic and nonmetallic

oxides in the failed weld bead.

mechanics calculations. Flaws in repairs were

particularly irregular and unique in shape. In the

case of fusion line flaws in the normal seam welds

(Figure 3.4), it nevertheless was reasonable to

approximate the flaws as planar elliptical cracks.

However, flaws in repairs were determined to be

trapped impurities along the irregular shape of the

fusion zone, most notably for the flaws located at

the ends of the repairs.

- -

Table 3.3. Presence of Metallic and Nonmetallic

Oxides in Failed Weld Bead

Proportions In Crack

Element Weight % Atomic %

C 3.73 9.30

Mn1.22 0.66

Fe 55.62 29.83

0 22.57 42.25

Al 1.65 1.84

Si 14.80 15.78

S 0.14 0.13

K 0.26 0.20

3.2 Characterization of Flaws for

Fracture Mechanics Models

The purpose of characterizing flaws was to

provide accurate data for developing flaw density

and size distributions for use in probabilistic

fracture mechanics calculations. The final

characterization used a combination of techniques

for measurements of location, dimensions, shape,

and orientation. The data showed that most flaws

are located in the weld fusion zone and that repair

regions contained the largest flaws. The measured

dimensions of the flaws were consistent across all

techniques used to validate through-wall

dimensions, lengths, and widths. The flaws were

not truly elliptical as assumed in fracture

Metallography provided the best information for

flaw characterization. A 17-mm repair flaw was

shown to be a continuous flaw composed of a

combination of cracks, lack of fusion, elongated

tubular gas pocket (blow hole), and slag.

Metallography provided the only clear evidence

of the crack. The crack was detected because it

was associated with nearby lack of fusion, slag,

and contamination.

Figure 3.4 showed the location of a small flaw in

the fusion zone of an SAW weld. The weld is to

the right in Figure 3.4, and the heat-affected zone

(HAZ) of the base metal is just right of image

center. The flaw is located in the weld metal,

where fusion occurs with the heat-affected zone.

Flaw dimensions in the coordinate system of the

vessel were recorded for the small specimens

removed from three product forms. Table 3.4

lists depth (relative to the vessel inner surface)

locations and dimensions of flaws with values

listed for metallography, radiography, and

ultrasound. Good agreement was found in the

validated flaw dimensions as measured by the

independent techniques.

Figure 3.11 shows the composition of a complex

flawed region as measured by metallography.

Table 3.4. Flaw Dimensions, Validated by Use of Multiple Techniques

Vol 1 name: HAZ V1

Vol I TWD: 7 mm

Metallography RT UT of Cubes

Depth location 20 mm 19mnun 22 mm

TWD 4 mm 4 mm 5 mm

Length NotMeasured 17mmnu 16mm

Width 6 nun6mm | 6 mm

3.6
d fission line

1) crack

B s;t,.

2) lack of fiision

lcont=IIiua tion

Figure 3.11. Composition of a Complex Flaw

The two images shown are'from the same region

of a vessel but are different micropolished and

etched cross sections. The flawed region is

shown to be composed of a crack, lack of fusion,

contamination, and slag.

3.3 Treatment of Large Repair

Flaws

The large repair flaws found in the PVRUF and

Shoreham vessels were subjected to special

detailed evaluations. In all cases, these flaws

occurred at the ends of repair cavities, and the

SAFT-UT images showed complex flaw

geometries. Figure 3.12 exemplifies such a flaw,

designated as the "14-mm Shoreham repair flaw"

because of initial examinations showing it to have

a 14-mm through-wall dimension. The flaw was

clearly not a planar elliptical crack with a radial.

orientation. Additional evaluations addressed the'

size, shape, and orientation of the flaw. The

treatment of this flaw illustrates the approach used

for all large repair flaws. In all cases, the'

characterizations made use of refined SAFT scans

that were performed after the flaws had been ,

removed from the welds and placed into the form

of small cube samples.

idealization of the flaw as potentially an axial or

circumferential planar flaw. The sketch of the

flaw labeled Treatment A shows an estimate of

shape and orientation where the ultrasonic

indication is assumed to be one connected flaw.

The sketch labeled Treatment B shows a

characterization of the indication as two separate

flaws oriented at approximately 60 degrees from

surface normal. The dimensions as measured

along the orientation of the flaw (rather than the

coordinates of the cylindrical vessel) are

considered to be the most useful for structural

integrity assessments.

The nominal flaw sizes (in terms of through-wall

extent) were established to be conservative

relative to the subsequent measurements made

during the validation. The initial sizing

measurements did not necessarily show the

presence of a single planar crack as opposed to a

cluster of cracks or other NDE indications such as

due to inclusions or material'contamination. The

images use to draw the sketches such as

Figure 3.12 showed more detail as to the structure

of the flaws and defined dimensions of possible

multiple flaws and their relative proximity to each

other.

The sketches of Figure 3.12 represent projections:

of the complex flaw onto a radial plane for .-

3.7
MMML

14 anm Shorem ReWr Flaw-Tretnrnt A 14 nin Shorehm Rqalr Flgw-T Tnent B

V

Figure 3.12. Shape and Orientation of 14-mm PVRUF Flaw - Relevant to Structural Integrity Assessment

The original measurements of the flaw in

Figure 3.12 characterized this flaw as

approximately circular with a maximum throughwall dimension of about 14 mm. The more

refined SAFT examinations showed a more

complex shape having two major subregions that

could be connected (Figure 3.12 -Treatment A)

or unconnected (Figure 3.12 - Treatment B).

Fracture mechanics calculations would show that

the flaw interpretation of Figure 3.12b would

have a significantly smaller impact on structural

integrity because the critical flaw dimensions

have been reduced from a single flaw of 14 mm to

separate flaws with dimensions of 4 mm and

5 mm. However, there are significant

uncertainties regarding the separation distance

between the legs of the complex flaw and with the

structural soundness of the region joining the ends

of the two subregions. Therefore, the

recommendation for this particular flaw was to

describe the flaw with the same dimension of

14 mm as originally estimated.

A very different result was obtained from the

detailed characterization for the "32-mm

Shoreham repair flaw" as shown by Figure 3.13.

The original measurements characterized this flaw

as approximately circular with a maximum

3.8
through-wall dimension of about 32 mm. The

more refined SAFT examinatiorii showed a

flawed region bounded by dimensions of 12 mm

and 44 nmm. The 32-mm maximum through-wall

extent was confirmed. However, the images did

not show evidence of the circular flaw but rather

an elongated flaw at an angle of about 45 degrees.

The proper characterization of this flaw for

fracture mechanics calculations of stress intensity

factors was a smaller flaw with a depth of 12 mm

and a length of 44 mm. There remained

uncertainties regarding the possible separation of

the single elongated flaw into separate flaws as

indicated in Figure 3.13 - Treatment B.

However, the dimension of the ligament between

the separate flaws is subject to uncertainties such

that ASME Code flaw proximity rules would

need to combine the two flaws into one flaw. The

recommendation was to describe the flaw as a

32 mm Shoreham Repair Flaw - Treatment A

Tw 2

32m

single flaw with dimensions of 12 mm and

44 mm. This charcterization removes'a large

measure of conservatism from the earlier

evaluation by dealing with the large apparent'

through-wall dimension of 32 mm with'

recognition of the 45-degree flaw orientation or

rotation. The rotation increases the measured

maximum through-wall dimension of the flaw but

does nothing to increase the value of the

calculated crack-tip stress intensity factor.

In summary, the validation effort generally

confirmed the original characterizations of many

of the large repair flaws but, in most cases, the

flaw dimensions recommended for fracture

mechanics calculations were significantly

reduced. The primary consideration for the less

conservative treatments was recognition of the

importance of flaw orientation, and how a rotated

orientation can impact the measured through-wall

dimension of a flaw. The validation

measurements significantly reduced the

dimensions of the 32-mm Shoreham repair flaws

as well as the dimensions of a number of other

flaws.

3.4 Validated Flaw Densities and

Size Distributions

Best estimates of flaw density and size

distributions were made using the validated flaw

characteristics for larger flaws combined with the'

measured characteristics for smaller flaws. The

smaller flaws were validated on a more limited

sampling basis. Distributions are given here for

flaw through-wall dimensions for the different

product forms. The discussion presents the data

as collected from the vessel exams without the

use of statistical evaluations."Sections 6, 7, and 8'

present the statistical analyses of the data along

with the development of statistical distribution

functions to describe the data trends and the

uncertainties in the derived statistical

distributions.

The construction of best estimates of flaw

distributions required that measurements to

determine that large flaws are not present in the

32 mm Shoreham Repair Flaw - Treatment B

Figure 3.13. Shape and Orientation of 32-mm

Shoreham Repair Flaw with Less Conservative

Treatment B of Flaw Dimensions

3.9
bulk of the examined material and that the larger

detected flaws are accurately characterized. For

this reason, the larger flaw indications from

PNNL's conservative sizing methodology were

selected for the validation cubes. Eighteen such

flaw-bearing cubes were removed from the welds.

The cubes were approximately 25 mm on a side.

This specimen size permitted accurate

measurement of flaw characteristics using

ultrasound, radiography, computed tomography,

and metallography.

Consideration of pressurized thermal shock

dictated that the inner near surface zone material

receive special emphasis in the selection of the

validation cubes. Fourteen cubes were removed

from the SMAW of the inner near surface zone.

Three of these cubes were removed from repair

metal. One cube and 30 thin plates were removed

from the SAW material.

The results illustrated in Figures 3.14 through

3.17 show the impact of the validation on the flaw

distributions for the three product forms. Flaw

densities are shown before and after validation.

Because all of the small flaws were not selected

for the validation with cubes, separate densities

are shown with and without the cube data.

3.4.1 Shielded Metal Arc Weld

Figure 3.14 compares three flaw distributions for

SMAW material. The first distribution, shown by

circles, is from the validation cubes. The second

uses the data given in Jackson and Abramson

(2000) and is labeled Best (for best estimate).

The third is labeled Step 1 and is taken from the

SAFT-UT inspections as performed through the

vessel's cladded surface (Schuster et al. 1998).

As shown in Figure 3.14, no flaws were validated

to be 6 mm in size or greater. Reasonable

agreement is evident between 3 mm and 5 mm in

through-wall size. The density of small flaws in

SMAW was not selected for validation in the

cubes, so the 2-mm data point for the cubes is

artificially low. The data from Jackson and

Abramson (2000) is PNNL's best estimate for the

flaw rate in SMAW material of the PVRUF

vessel's inner near surface zone.

3.4.2 Submerged Arc Weld

Figure 3.15 compares three flaw density

distributions for SAW. The first uses the

validated data from the thin plates given (Schuster

et al. 1998). The second, labeled Best (for best

estimate), uses the plate data plus the flaw

indications that were not available for validation.

PNNL received all flaw-indications that were 8

mm in through-wall size or larger in the SAW

material. A third flaw distribution data set,

labeled Step 1, is taken from Schuster et al.

(1998). All flaw indications were confirmed to be

smaller than 8 mm. For flaws between 1 mm and

4 mm in through-wall size, reasonable agreement

can be seen in Figure 3.15.

3.4.3 Repair Weld

Figure 3.16 compares flaw distributions for repair

metal. The first distribution uses the through-wall

dimensions from the three validation cubes. The

second uses the cube data plus four flaw

indications as given in Jackson and Abramson

(2000). The third data set is from Schuster et al.

(1998) for SAW material including the HAZ. No

flaws larger than 17 mm were found in the vessel.

For flaws 12 mm to 17 mm in through-wall size,

the flaw density is high for repair metal compared

to the unvalidated (Step 1) SAW flaw densities.

Smaller flaws in repair metal were not selected

for the validation cubes, making the data point at

4 mm appear artificially low.

Figure 3.17 shows a comparison of PNNL's best

estimates of flaw density distributions for the

three product forms and the rate estimated by the

Marshall Committee (1982). The density

distribution for SMAW and SAW are in

reasonable agreement with each other. The

distribution of flaws in repair metal is shown to be

significantly different from those of the other two

product forms.

3.10
E

(.2

U

0.

@2

0

E

C,

-*--Cubes

- -A* -Best

- -I -Step 1

0 2 4 6

Through-wall Size (mm)

8

FA, T

Figure 3.14. SMAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

aV

n

62

E

i-0.

S.

0

-a

Z%

to

c,

--- Thin plates

. -A- -Best

..- -I - Step I

0 10 20 30 40

Through-wall Size (mm)

Figure 3.15. SAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

3.11
1.E+04

'I

CD

E

.0

M

U

1...

0

0

a,

E

(a

dk ---

--- Sk __ --- %6

E - __ -LLA.--_- --

" a--- -%., 1.E+03

II

- Cubes

- -A- - Best

-...--- Step 1

'.0.

1 .E+01

1.E+00

0 10 20 30

Through-wall Size (mm)

40

Figure 3.16. Repair Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

1.E+05

@ 1.E+04 a,

a,

E

.2 1.E+03

.0

U

4c 1.E+02

4-

>s

c 1.E+01

a,

a

,Z 1.E+00

E

L 1.E-01

1.E-02

- SMAW

-_- Repair

Ai SAW

e Marshal data

0 5 10 15 20

Throuah-wall Size (mm)

25 30

Figure 3.17. Comparison of Through-Wall Size Distributions of Cumulative Flaw Densities

3.12
The results of the selected application of four

techniques to the characterization of flaws in

25-mm cubes showed that accurate validated

dimensions were achieved. The conservative

oversizing, used for the long metal paths of the

preliminary inspections, was not needed for the

measurements of flaw dimensions in the cubes.

X-ray computed tomography was able to show a

complex three-dimensional shape for a repair flaw

and revealed that the flaw followed the fusion

surface between the repair metal with the base

metal. Metallography was able to show the

complex composition of fabrication flaws.

Sizes for lack-of-fusion flaws were easily

measured by all of the techniques used. For one

flaw, a weld bead solidification crack was

validated. A recommendation for use of CAT is

made to overcome the alignment limitations of

only the three viewing directions used in RT.

Porosity was reliably detected in weld-normal

ultrasound but was excluded from the cubes

because it was small and its volumetric nature

reduced the importance to structural integrity

assessment. Validated flaw distributions were

achieved using the best data for each point in the

distribution. Best estimates are based on the

validated dimensions in the 25-mm cubes, from

weld-normal testing, and from ultrasonic flaw

indications.

For SMAW, the flaw indications from the early

exams had a density distribution that was in

reasonable agreement with the validated

distribution. This shows that the rule statements

used in the analysis of the inspections through the

vessel's cladded surface worked reasonably well.

3.13
4 EXPERT JUDGMENT PROCESS FOR FLAW DISTRIBUTION

This section provides an overview of an expert

judgment process that was used to support the

development of flaw distributions. An expert

judgment elicitation was used in conjunction with

the empirical data from PNNL vessel

examinations and the PRODIGAL model for weld

flaws to develop a generalized approach to flaw

distributions. A report prepared by NRC staff

documents details of the elicitation (Jackson and

Abramson 2000).

4.1 Expert Judgment Process

The formal use of expert judgment (sometimes

referred to as expert opinion) has been extensively

applied to a number of major studies in the

nuclear probabilistic risk assessment area.

Scientific inquiry and decision-making have

always relied informally on expert judgment, but.

the formal use of expeir judgment is a welldocumented systematic process. For the

development of a generalized flaw distribution,

17 experts participated as the panel. The panel

was needed to review, interpret, and supplement

the available information on vessel fabrication

processes and the data on vessel flaw

distributions. The experts also reviewed the

comprehensive work to date by PNNL.

The expert judgment process involved eight steps:

(1) selection of issues and experts,

(2) presentation of issues to the experts,

(3) elicitation training, (4) preparation of issue

analyses by the experts, (5) discuss of issue

analyses, (6) elicitation of the experts,:

(7) recomposition, and (8) documentation.

4.1.1 'Selection of Issues and Experts

The selections of issues and experts were closely

related. The initial selection of issues was',

developed by NRC and PNNL staff and was used -

to guide the selection of experts. The experts

reviewed an initial list of issues and proposed

additions, deletions, or modifications to the list.

It was essential that the experts be knowledgeable

about the state of the art in their respective fields.

The expert panel was chosen to represent a

diversity of backgrounds, with a wide variety of

viewpoints (e.g., academic, consulting, vessel

fabricators, forging manufacturers). The specific

areas of needed expertise were ASME Code for

construction, failure analysis, forgings,

metallurgy, NDE, reactor vessel fabrication,

statistics, and welding. The 17 experts were

selected on the basis of their recognized expertise

in the issue areas, as demonstrated by their work

experience, publications, and professional

reputations. In most cases, the experts were

individuals, many retired, who were'employed by

organizations involved during the 1960s, 1970s,

and 1980s in the fabrication of the RPVs that are'

in service at currently operating nuclear power

plants in the United States.

4.1.2 Presentation of Issues'to the Experts

Presentation of issues to the experts provided a

mechanism to discuss the state of the art for each

issue. An essential aspect of issue presentation

was a decomposition of the issues, which allowed

the experts to make a series of simpler

assessments rather than one overall assessment of

a complex issue. This step was crucial, as the

decomposition of an issue can vary by expert and

can thereby significantly affect its assessment.

Upon initial review of the issues, extensive

feedback was provided by the experts. This

feedback was critical to NRC and PNNL staff in

making revisions to the format in which the issues

were presented to the experts during their

individual elicitation sessions.

4.1.3 Elicitation Training

Elicitation training assisted the experts with

encoding their knowledge and beliefs into a

quantitative form. Such training can significantly

improve the quality of the expert's assessments by

avoiding psychological pitfalls that can lead to

4.1
biased and/or other overconfident assessments.

The training was conducted by a normative expert

who was knowledgeable about decision theory

and the practice of probability elicitation. In

addition to elicitation training, NRC and PNNL

staff gave presentations on the background of the

PTS work and the empirical NDE data from RPV

inspections. The definition of a flaw for use

during the expert judgment process was

developed. A flaw was defined as an

unintentional discontinuity that has the potential

to compromise vessel integrity and is present in

the vessel after pre-service inspection.

4.1.4 Preparation of Issue Analyses by the

Experts

In order to perform a comprehensive issue

analysis, the experts were given time and

resources to analyze all of the issues before their

individual elicitation sessions. If an expert's

preparation required additional technical support,

it was provided by NRC and PNNL staff. Each

expert was given a set of documents to review,

which supplemented the information presented

during the three-day orientation meeting.

4.1.5 Discussion of Issue Analyses

Before the elicitation session, the experts were

invited to discuss their issue analyses and to

present the results of their analyses and research.

Some of the experts engaged in discussions of the

characteristics of vessels and flaws prior to their

individual elicitation sessions. The ensuing

discussions served to ensure a common

understanding of the issues and available data.

4.1.6 Elicitation of the Experts

The experts were elicited by a team consisting of

a normative expert, two substantive experts, and a

recorder. The elicitation team met separately with

each expert, to avoid pressure to conform and

other group dynamic interactions that might occur

if the expert judgments were elicited in a group

setting. The elicitation focused on a number of

quantitative and qualitative characteristics (see

Sections 4.3 and 4.4). The experts were asked to

rank each characteristic in order from highest to

lowest in terms of contributing to or having a flaw

after preservice inspection. They were then asked

for a quantitative assessment, if appropriate. For

example, the experts were asked which product

form is most likely to have a flaw remaining after

preservice inspection. Suppose the response was

that weld metal is the most likely to have a flaw

remaining, followed by cladding, plate, and

forgings. The expert was then asked to assess the

relative likelihood of a flaw in cladding, plate,

and forgings, each compared with the likelihood

of a flaw in weld metal. For each relative

likelihood (expressed as a ratio or percentage

change), the expert was asked to supply low, high,

and median values. For characteristics for which

the ranking or quantitative assessment did not

apply, the experts were asked what effect the

characteristic would have on the introduction of a

flaw. They were asked which vessels are more

likely to have a large number of flaws and what

elements of fabrication are most affected by field

versus shop fabrication.

As the sessions continued, it became apparent to

the members of the elicitation team that the

experts were not able to provide quantitative data

such as ranking of the characteristics and/or

pairwise comparisons for all characteristics. For

example, welder skill and inspector skill are

dominated by human factors issues, and

quantitative data was not easily provided. The

experts also provided the elicitation team with

feedback that some of the characteristics should

be further subdivided to accurately classify a

particular characteristic. Flaw size and cladding

process are examples of two characteristics that

needed further division.

4.2 Recomposition and Summary of

Results

Recomposition and summaries of results was

performed by the normative and substantive

experts who recomposed the results into a form

suitable for further analysis. This was completed

after each session. Upon completion of the

4.2
17 elicitation sessions and a preliminary review of

the responses, it was apparent that the

characteristics had to be divided into quantitative

and qualitative categories. There was a need to

re-elicit the experts on a number of quantitative

characteristics and obtain additional information

on flaw size. The experts were re-elicited to

obtain responses regarding flaw size, density of

large flaws versus small flaws, flaw density in

cladding versus weld metal, flaw density in base

metal versus weld metal, repaired versus

nonrepaired weld metal and base metal for small

and large flaws, underclad cracking, flaw density

of SAW and electro slag welding (ESW) versus -

SMAW, flaw density of three cladding processes

(strip, multi-wire, and single-wire) versus

SMAW.

Quantitative characteristics were those for which

the experts were able to provide numerical

comparisons. In most cases, records and data are

available to verify information for quantitative

characteristics. The quantitative characteristics

were product form, weld process, flaw

mechanisms, repairs, and flaw size. Qualitative

characteristics were those for which the experts

could not provide any meaningful numerical

comparisons. Records and corresponding

information are not readily available. The

qualitative characteristics are field versus shop

fabrication, weld procedure, weld materials,

welder skill, inspection procedure, inspection

skill,-base metal properties, surface parameters

and preparation, and flaw location.

4.2.1 Documentation

The final step in the expert judgment process was

to document the entire process. Documentation

had several purposes. First, it can be used by the

experts involved to assure them that their

judgments were correctly reflected. Second, it

can be used by potential users of the results to

enhance their understanding. Third, it can be

used by peer reviewers of the process to provide

an informed basis for their review. And finally,

documentation can be extremely useful to update

the analyses, when future research on other vessel

material becomes available. Technical rationales

for the responses from each expert were recorded

during the elicitation sessions.

4.3 Quantitative Characteristics

Information on the quantitative characteristics can

also be obtained from construction and QA

records for most vessels. Many experts provided

similar or identical rationales to justify their

assessments. Some of the vessel fabrication

characteristics addressed whose effects were

addressed on a quantitative basis by the elicitation

were as follows:

* flaw size

* product form - base metal ring forgings

* product form - base metal plate

* product form - cladding

* product form - weld metal

* repairs to weld metal

* repairs to base metal

* repairs to cladding

* weldprocess--SMAW..'-

* weld process - SAW

* weld process - ESW (used mainly in BWRs

but information was provided by experts)

* weld process- cladding

* flaw location.

Figure 4.1 shows a typical set of results (from

Jackson and Abramson 2000). In this example

the experts were asked to estimate the number of

flaws in plate and forging materials. The

estimates were expressed as flaw densities (flaws

per unit volume) relative to flaw densities for

weld metal. Figure 4.1 indicates individual

estimates along with minimum, maximum,

median, lower quartiles (LQ) and upper quartiles

(UQ) from the group of experts. For example, the

median values indicate one-tenth as'many'small

flaws in plates as in welds. The corresponding

ratio for large flaws (>6 mm) was even smaller

(40:1). Similar estimates were provided for ring

forgings, with a consensus that the occurrence of

large flaws is more likely in forgings than in plate

materials.

4.3
3.0-

V,

0

LL

_0

0

0

:D

a)3

m

V0

Al

2.5-

2.0-

1.5-

1.0-

0.5-

0.0.

V

V A

A

A

P3'C1 P3i2

Plate

Sm Flaws Lg Flaws

-- P3C3 P34

Ring Forging

Sm Flaws Lg Flaws

Base Metal vs. Weldmetal

Plate vs. Welds Ring Forgings vs. Welds

Small Large Flaws Small Flaws Large Flaws

Flaws

MIN .0004 .001 .001 .002

LQ .015 .01 .02 .007

MED .1 .025 .1 .07

UQ .3 .09 .2 .6

MAX 12.0 1.0 .9 2.0

Figure 4.1. Relative Flaw Densities of Base Metal Compared to Weld Metal as Estimated by Expert

Judgment Process (from Jackson and Abramson 2000)

4.4 Qualitative Characteristics

For qualitative characteristics, it is not possible to

quantify the effect the characteristic will have on

the introduction of a fabrication flaw, and no

records are readily available to document

information on these characteristics. However,

qualitative knowledge can help guide application

of existing data to other vessels. Some of the

technical rationales for the qualitative

characteristics are as follows:

4.5 Discussion

The expert judgment process was not a consensus

process. Responses and data were obtained from

each expert during individual elicitation sessions.

The entire set of data and responses from the

process will be published in an upcoming

NUREG report which will contain the generalized

flaw distribution (GFD) for the entire fleet of

domestic reactor vessels along with uncertainty

and sensitivity studies. In addition, comments

and questions received by NRC related to data

acquisition, the process used for the expert

judgment process and development of the GFD,

flaw depth location, PVRUF flaw sizing and

characterization accuracy, flaw distribution

development and destructive examination

techniques will be addressed in the upcoming

NUREG.

0

0

S

0

0

0

0

field versus shop fabrication

weld procedure

weld materials

welder skill

inspection procedure

inspector skill

base metal properties

surface preparation and parameters.

4.4
5 PRODIGAL WELD-SIMULATION MODEL

This describes a method originally developed at

Rolls-Royce and Associates (RRA) in the mid

1980s to create an expert system (PRODIGAL)

that generates a defect size distribution and

density for multi-pass welds up to approximately

four inches in thickness (Chapman 1993). The

model accounted for fabrication factors such as

differences in welding processes, materials being

welded, restraint, access, welding position, and

shop versus field conditions. Parameters to

quantify the effects of each factor were

established by an'elicitation process that involved

experts on welding processes and the procedures

used to fabricate vessels. On an NRC-funded

research program, PNNL collaborated with RRA

to extend the PRODIGAL method to address

welds in thick section reactor pressure vessels as

built for the nuclear power industry in the United

States (Chapman et al. 1996; Chapman and

Simonen 1998).

A number of specific benefits were gained from

the PRODIGAL model:

(1) physical insights into the nature of welding

defects

(2) a basis for estimating flaw densities and size

distributions for cases for which no data are

available

(3) a basis for extrapolating the data from

detailed characterizations studies such 'as that

for the PVRUF vessel-one such ' extrapolation is needed to estimate the

probabilities for large flaw sizes greater than

the sizes observed in the examination of the

limited volume of PVRUF and Shoreham

weld material

(4) a basis for extrapolating the data from vessels

such as PVRUF and Shoreham to other

vessels.

The discussion below describes the extension of

the PRODIGAL model to U.S. vessels, explains

the role of this model as a complement to data on

welding flaws (Schuster et al. 2000b) and to

perform expert elicitations that address vessel

fabrication practices (Jackson and Doctor 2000),

presents results of some applications to predict

distributions of flaws in vessel welds made using

particular welding and inspection processes, and

proposes further development of the model to

better simulate inspection and repair procedures.

A detailed description of PRODIGAL along with

example applications of the code are given in

Chapman and Simonen (1998).

5.1. Types of Defects

The PRODIGAL model addresses defects that

occur and that may or may not be detected and

repaired during the buildup of a weld. The

methodology is based on the concept that a weld

is made of individual weld runs (beads) and

layers. Figure 5.1 shows the specific defects of

concern to welds in reactor pressure vessels as

identified by the experts.

Most flaws are confined to a single weld layer,

and the characteristic flaw sizes are related to the

bead dimensions. Larger flaws are associated

with processes that cause the forward propagation

of a given defect from one weld layer into the

next layer as the weld is built up. Based on

discussions with stress engineers and fracture

mechanics experts; defect types such as single

pores that are unlikely to impact structural

integrity were excluded from consideration in the

modeling of the defect distributions. In

addressing vessel welds, the original list of

defects identified by the RRA experts was

reviewed and modified by a group of experts on

U.S. vessel fabrication. These experts were

individuals from the major U.S. vessel

manufacturing facilities and who were involved

on a first-hand basis during the 1960s and 1970s

5.1
HAZ Crack Centerline Crack

Lack of Sidewall Fusion

Sidewall Slag Lack of Interrun Fusion

Interrun Slag

Pore with Tail

Figure 5.1. Types of Crack-Like Defects

with the welding and inspection of the vessels that

are currently in use at operating nuclear power

plants.

The defect types for reactor vessel welds as

indicated in Figure 5.1 include the following:

* centerline cracking - As a weld solidifies and

contracts, any impurities tend to collect at the

top center of the bead. The stresses present

may then cause a centerline crack to initiate

along the weld bead due to the presence of

low strength or low melting point phases.

* heat-affected zone cracking - During the

formation of a weld, hydrogen is usually

absorbed on cooling. The hydrogen may

form hydrogen gas, which exerts a bursting

pressure within the metal. If this effect is

combined with the formation of a hardened

structure, cracking may result. This usually

occurs in the heat-affected zone (HAZ).

* lack of fusion - The lack of fusion defect is a

lack of union between the weld metal and the

parent plate or (in multi-run welds) between

successive weld runs.

* nonmetallic slag inclusions - Linear slag

inclusions are normally due to incomplete

slag removal between weld runs but may

occasionally be caused by slag laminations

within the parent plate. Isolated slag

inclusions can be caused by mill scale or rust

on the plate, or damaged electrode coatings

that denude the weld metal of slag-forming

elements of adequate floatability; i.e., slag is

left within the weld bead rather than floating

to the top for removal.

* porosity - A welded joint usually will contain

gas-forming elements; these evolve into

phases as the temperature decreases and result

in formation of cavities or porosity.

5.2
5.2 Defect Density

The defect occurrence frequencies (per unit length

of weld bead) for the resulting set of crack-like

defect types were estimated by welding

metallurgists and inspection engineers. The

experts were asked to rank the defects from 1 to

10 against the factors that define the specific

welding process used in constructing a weld. The

ranking numbers were intended to quantify the

relative rates of occurrence of each type of defect

as a function of each welding condition (e.g.,

process, restraint). In this step of the evaluation,

the occurrence rates are those prior to any

inspection and repair of defects. The welding

conditions were selected to be attributes for

welding processes (e.g., shop versus field weld)

that could be assigned by a structural analyst

without access to detailed data from archived

shop records. The data for the different scorings

under different conditions for a given type of

defect should be added or multiplied. It was

decided that the individual scorings reflected

independent probabilities of producing the defect,

and multiplication was appropriate.

5.3 Defect Characteristics

The first step in developing the model was to

estimate the numbers of each type of defect,

without defining the various characteristics (e.g.,

size, location) of these defects. The principal

parameters and defect types for thick vessels are

described by Chapman and Simonen (1998). -

Through-wall and length dimensions are defined'

for purposes of fracture mechanics calculations.

Defect location within the vessel wall is defined

by application of the simulation model with the

assumption that defects occur randomly within

the individual runs that make up the completed

weld.

A significant question was the probability that a

defect, once initiated, would propagate on to the

next layer or additional layers of the weld. -An

important part of the model was designed to

predict the number of small defects initiated early

in the welding process that would grow to become

larger defects before the weld was completed.

5.4 Inspection Model

A final aspect of the weld simulation model

addresses the effects'of inspections that are

performed in the shop both during the welding

process and after the welding process is

completed. The details of the inspection models

are not documented here. The original RRA

model included methods for calculating'

inspection efficiency curves for each type of

defect in the weld of interest, with the inspection

efficiency being a function of the defect size and

its through-wall location. Both radiographic and

surface (dye penetrant) inspection methods are

addressed. Radiography is simulated using the

model of Halmshaw and Hunt (1975).

5.5 Computer-Based Implementation

The expert system model of weld buildup, as

adapted to address reactor pressure'vessel welds,

uses a Monte Carlo simulation procedure.' A

computer code (PRODIGAL) has been written for

application on'a UNIX-based workstation with

the parameters for the simulated welds specified

through interactive menu-driven inputs

A weld is described as a series of activities. One

type of activity consists of the stepwise process of

constructing the weld as a set of building blocks,

with each block corresponding to a single pass of

the multi-pass weld; Other activities are' as

follows:

* inspections - Radiographic or surface

inspections can be performed at any stage,

' either during the partial weld buildup or after

all weld runs have been completed. It is

assumed that all detected defects are repaired.

-It is assumed in PRODIGAL that new flaws

are not introduced by the repair process.

* machining - Post-weld machining is

considered as a factor for the surface finish

that impacts the effectiveness of surface

5.3
inspections. Machining can also expose nearsurface buried defects and thereby increase

the number of surface-breaking defects.

* post-weld heat treatment - The sizes of heataffect-zone cracks can be extended by the

effects of post-weld heat treatment.

* code outputs - Data outputs from the RRA

PRODIGAL simulation model currently

include information on flaw depth, flaw

length or aspect ratio, and flaw locations

within the vessel wall. All outputs are in the

form of frequency distributions that indicate

the number of flaws in each category per

meter of finished weld (after inspections and

weld repairs).

5.6 Calculations and Results

The flaw simulation model of the PRODIGAL

computer code has been used to estimate the

numbers and sizes of flaws in the welds of reactor

pressure vessels. The cross section of a single V

weld taken from the PVRUF vessel (Figure 5.2)

was idealized for the PRODIGAL calculations as

the configuration of weld layers and individual

beads shown by Figure 5.3. Further details of the

model and the input used to describe the welding

and inspection processes are described in

Chapman and Simonen (1998).

All comparisons of predicted versus observed

flaw densities are made on a per unit volume or

unit length basis. The simulated flaw densities

were calculated using the PRODIGAL code for

the submerged arc weld as described Figures 5.2

and 5.3. A weld cross-sectional area of 0.0054 m2

was used to convert the calculated flaw densities

from flaws per meter of weld length to flaws per

cubic meter.

Figure 5.4 shows the results of the PRODIGAL

calculations expressed as the number of flaws

greater than a given depth per meter of weld

length. This plot shows the predicted effects of

various assumptions regarding radiographic

Figure 5.2. Cross Section of Thickness Transition

Single V Weld for PVRUF Vessel

examinations and the associated repairs. It is

noted that the PRODIGAL code simulates the

detection of flaws and then assumes that all

material with detected flaws is replaced with

material that has no flaws. Computer runs were

made first for the limiting assumption of

radiographic examinations and then by assuming

there were no radiographic examinations. The

difference in the flaw distributions predicted by

these two limiting cases was calculated outside

the PRODIGAL code to establish the depth and

length dimensions of the flaws that were detected

by the RT examinations.

The family of curves of Figure 5.4 corresponding

to various repair criteria was then generated. It is

noted that the repair criteria of the ASME

Section HI and XI Codes require repairs of flaws

between 19 and 33 mm in measured length. It

was recognized, however, that there are

uncertainties in both the ability of radiographic

5.4
In comparing results of PRODIGAL calculations

with measured data, several observations can be

made:

* The observed data show a much larger

number of very small flaws (1- to 2-mm

range) than predicted by PRODIGAL. This

occurs because the scope of the PRODIGAL

model is limited to crack-like flaws that have

a potential to affect structural integrity. Flaws

of very small sizes (less than about half a

weld bead in depth dimension) were excluded

from the predicted flaw distribution.

* The measured and predicted flaw

distributions are in relatively good agreement

'for flaw sizes of about 5 mm, which

corresponds to about the dimensions of weld

beads.

* If flaws associated with weld repairs are

excluded from the PVRUF data, no data

remain to make comparisons for flaw depths

greater than 7 mmn.

* With the inclusion of the larger measured '

flaws associated with repairs, the measured

data are seen to follow the upper bound curve

of the PRODIGAL calculations (effects of

radiography neglected), rather than following

a trend between the two limiting curves from

PRODIGAL. This disagreement with the

expected trend is likely the result of the

assumption in PRODIGAL that weld repairs

are made without introducing any new flaws

in the repaired material. In contrast, the

PNNL examinations show that the largest

detected flaws have been associated with

-weld repairs.

The comparisons of PVRUF data with

PRODIGAL predictions show a reasonable level

of agreement. Observed differences are within

the level of accuracy expected, based on the fact

that PRODIGAL was designed to predict the

average flaw distribution for populations of welds

and was not intended to address random weld-toweld differences.

Figure 53. Model of Thickness Transition Single V

Weld for PVRUF Vessel

methods to'accurately measure flaw lengths and

the ability of the PRODIGAL code to predict the'L'

distribution of flaw lengths. Therefore, the range'

of the curves from L = 0 mm to 33 mm is

believed to represent the range of how much the

flaw depth distribution can be influenced by

inspections and repairs. Accordingly, a best

estimate from the PRODIGAL calculations would

be somewhere intermediate to the two limiting

curves of Figure 5.4.

5.5
1.E+02

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1.E-01 -

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I\ RR-Prodigal

/AII Regions

-^~ , WVIth X-Ray)

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L = Length of Flaw Indication for Repair

ASME Sectlon III: L -1 i-rnrm

ASME Section Xl: L - 33-m

FJIr. I

0 5 10 15 20 25 30 35 40

Flaw Depth, a, mm

Figure 5.4. Calculated Flaw Frequencies for PVRUF Weld Showing Effects of Inspection and Repairs

5.7 Flaw Characterization by

PRODIGAL Code

PRODIGAL provides detailed outputs for both

flaw lengths and locations within the vessel wall

that can provide a source of input data for

probabilistic fracture mechanics calculations.

Figure 5.5 shows predictions of flaw lengths and

aspect ratios (ratio of total flaw length to total

flaw depth dimension). It is seen that the

predicted aspect ratios become significantly

smaller as the flaw depths become larger. The

same data, when plotted in terms of flaw lengths,

show that the predicted lengths of shallow flaws

are about the same as the corresponding lengths

of much deeper flaws. This trend differs from the

(conservative) assumption commonly used in

probabilistic fracture mechanics models, which

assigns the same aspect ratios to deep flaws as for

shallow flaws. Trends as seen in Figure 5.5 are a

direct result of an assumption in the PRODIGAL

model that grows flaws in the depth direction

from one weld bead to the next bead but provides

for no corresponding increase in the flaw length.

Data on flaw lengths such as from the PVRUF

and Shoreham vessels (as described in Section 6)

is consistent with the PRODIGAL assumption of

flaw length being relatively independent of the

through-wall depth of the flaw.

5.8 Discussion and Conclusions

The PRODIGAL code provides a simulation

model to estimating flaw densities and size

distributions for welds in reactor pressure vessels.

This model is founded on empirical knowledge of

the flaws that have been observed by the welding

and inspection experts who were responsible for

the fabrication of the vessels now in use at

operating nuclear power plants. Efforts to

validate the simulation model with data from

inspections of vessel welds have shown relatively

good agreement between the NDE and destructive

examination data for the PVRUF vessel.

5.6
ASPECT RATIO - CUMULATIVE DISTRIBUTION

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generation of flaw.estimates without reference to

PRODIGAL calculations. Nevertheless, the

PRODIGAL methodology had an important role

in the final methodology of estimating flaw

distributions as follows:

o s 10 15 20 25 30

ASPECT RATIO

FLAW LENGTH - CUMULATIVE DISTRIBUTION

C0 00 Z

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(1) Quantitative predictions of flaw densities and

size distributions from PRODIGAL provided

an independent benchmark for comparisons

with flaw distributions generated on the basis

of examinations of the PVRUF and Shoreharn

vessels. The estimates from PRODIGAL

were based on an independent set of

judgments from welding experts drawn from

organizations in the United Kingdom. In

addition, the PRODIGAL model was based in

part on data for welding flaws not covered by

the examinations performed at PNNL.

(2) Insights from the PRODIGAL model guided

the interpretation of the data from the PVRUF

and Shoreham vessels. The depth dimensions

of flaws were normalized with respect to weld

bead dimensions, and the data were separated

in terms of flaws less than a weld bead in size

and those greater than a weld bead in size.

The data for measured flaw lengths were

described in terms of a distribution of flaw

lengths independent of the flaw depth

dimensions rather than as a distribution of

flaw aspect ratios, as had been the past

practice in the treatment of flaws in

probabilistic fracture mechanics.

(3) The PRODIGAL model provided a

systematic approach to relate flaw occurrence

rates and size distributions to the parameters

of welding processes that can vary from

vessel-to-vessel. Application of the model

showed the sensitivity of calculated flaw

distributions to changes in the welding

process conditions. Calculations with

PRODIGAL and consideration of known

differences in fabrication procedures used to

manufacture U.S. vessels indicated that data

from PVRUF and Shoreham can reasonably

be applied to all vessels at U.S. plants.

20 40 0o BO 100 120

FLAW LENGTH. MM

Figure 5.5. Distributions of Flaw Aspect Ratio and

Flaw Length as Predicted by PRODIGAL Weld

Simulation

NRC's interest in the PRODIGAL methodology

began before data from examinations of the

PVRUF and Shoreham vessels were available,

and the flaw simulation model was viewed as a

parallel and/or alternative approach for estimating

flaw distributions should examinations of vessel

materials prove to be impractical. As the work at

PNNL moved forward, both with PRODIGAL

and with examinations of vessel welds, the

quantity and quality of the flaw data from vessel

examinations became sufficient to support the

5.7
(4) Insights from the PRODIGAL model

supported the assumption that locations of

flaws relative to the vessel inner surface

should be described by a uniform or random

distribution.

(5) The development of distributions for

clad/surface flaws was in large measure

guided by the insights and quantitative

predictions of PRODIGAL calculations. As a

result, the probability of a clad flaw (in a

multilayer clad) having depth dimension

greater than the thickness of a single layer

was assigned very small values. A tendency

of clad flaws to be originated at the clad-tobase metal interface was based largely on the

approach used in the PRODIGAL model. An

approach for estimating densities of clad

flaws using observed flaw densities for flaws

in seam welds came from the approach used

in the PRODIGAL code.

(6) The assumption that essentially all larger

flaws in seam welds are along the weld fusion

line was reinforced by the insights provided

by the PRODIGAL model.

5.8
6 WELD FLAWS - DATA AND STATISTICAL CORRELATIONS

The flaw distribution model was designed to

generate three input files for the FAVOR code

with one file used to describe flaws in seam

welds, another file to describe flaws in base metal

regions, and a final file to describe surfacebreaking flaws that reside in the vessel cladding.

This section addresses flaws in seam welds and

describes the measured flaw data along with the

correlations that characterize the data.

6.1 Approach and Assumptions

The basic considerations that apply to the

development'of flaw distributions for weld

regions are described in the following paragraphs.

Scope of Generalized Distribution -'Although

the data available to PNNL for weld flaws were

from two'specific vessels (PVRUF aid

Shoreham), the flaw distribution model was

developed to allow some specific attributes of

other vessels to be addressed if the attributes

differ from the attributes of the two reference

vessels.

Evaluations of data on observed flaws took

several steps to allow for the construction of

generalized flaw distributions. PNNL did not

combine the data from the PVRUF and Shoreham

vessels. In developing statistical correlations, all

flaw dimensions were normalized by the..

estimated dimensions of the weld beads for the

weld regions of interest.

Inputs to the computer code that generates input

files to FAVOR allow the following vessel-.

specific considerations to be addressed:

of welding by the SAW, SMAW, and repair

welding processes;

(3) The user can specify dimensions for the

through-wall dimensions of weld beads, with

independent inputs allowed for bead sizes of

SAW, SMAW, and repair welds.

(4) The user can specify maximum flaw depths at

- which the extrapolations of flaw distributions

for SAW, SMAW, and repair welding

material regions are to be truncated.

In most cases, the user will lack the detailed

knowledge needed to make vessel-specific inputs

for the above factors. The suggested approach

would be to use the same values of inputs used to

characterize the welds in the PVRUF or

Shoreham vessels, thereby allowing the flaw

distribution model to produce a distribution of

flaws as measured for either the PVRUF or

Shoreham vessel.

Flaws per Unit Volume Versus Flaw per Unit

Area - Traditional approaches, including that of

the FAVOR code,'quantify flaw densities in terms

of flaws per unit volume. PNNL's weld

examinations, however, indicated that essentially

all of the flaws with 'significant through-wall - ' dimensions were located along weld fusion lines.'

Therefore, it was recognized that it would be best'

to describe weld flaw densities in terms of flaws

per unit area of fusion zone.'The flaw distribution

algorithm allows the user to specify which

measure of flaw density is to be used in

generating the input for files for the probabilistic

fracture mechanics code. The flaw distribution of

algorithm makes appropriate transformations

(based on the average widths of the weld joints)

of the PVRUF and Shoreham daia to go from

flaws per unit of volume to flaws per unit area.

The transformation used weld widths of 1.61 in.

and 1.52 in. for the PVRUF and Shoreham

vessels, respectively.

(1) The user can specify if the desired flaw ;

distribution should be based on data trends

from the PVRUF vessel or from trends from .

the Shoreham vessel.

(2) The user can-specify volume fractions for the

amount of the total seam weld that is made up

6.1
Use of Data Versus Models and Expert

Elicitation - In developing flaw distributions,

measured data were used to the maximum extent

possible. The PRODIGAL flaw simulation model

and results of the expert judgment elicitation were

used only when the data were inadequate. In the

case of seam welds, there was a relatively large

amount of data, and the PRODIGAL model and

expert elicitation were not used to quantify

estimates of flaw densities and sizes. The

PRODIGAL model did, however, suggest the

normalization of flaw dimension by the

dimensions of weld beads and the separation of

data into subsets corresponding to small and large

flaws (as defined by flaw depth dimensions

relative to the weld bead dimensions). In

addition, the expert elicitation and the

PRODIGAL model helped to justify the

application of data from the PVRUF and

Shoreham vessels to the larger population of

vessels at U.S. nuclear plants.

Rule of Mixtures - PNNL's examinations

showed that final welds will typically consist of

weld metal deposited by the SAW, SMAW, and

repair welding processes. In most cases, the weld

consists mainly of SAW-deposited material with a

few percentage of SMAW and repair weld. The

flaw distribution algorithm uses a "rule of

mixtures" that first calculates flaw densities and

size distributions for each of the three weld types

and then combines these contributions in

proportion to the relative volumes of material

coming from each process. In estimating the flaw

locations relative to the vessel inner surface, the

resulting flaws are assumed to occur randomly

within the volume of the weld. In application of

the FAVOR code, the level of knowledge of the

welds has made it necessary to assume random

locations for the flaws coming from the various

welding processes. However, the generalized

flaw model can be used to generate inputs that

identify specific weld regions produced by given

welding processes. For example, such a model

could, for example, identify a region of SMAW

weld with relatively low levels of embrittlement

and then assign an appropriate distribution of

flaws for the region of interest.

Decomposition of Flaw Data - The flaw data

from PNNL's examinations were separated into

subsets according to the following three

attributes:

* PVRUF versus Shoreham vessel

* small flaws versus large flaws based on

through-wall flaw dimensions relative to the

estimated sizes of the weld passes

* flaws in SAW, SMAW and repair-welded

material.

This approach is more detailed than that of other

studies (such as that of the Marshall Committee

[1982]) that have combined the data and

approximated the trends with a single statistical

distribution function such as an exponential

distribution. The current approach avoids

difficulties of using single distribution functions

to achieve good statistical fits over wide ranges of

flaw sizes. The current approach allowed each

subset of data to be described by a simple

statistical function such as an exponential

distribution, with the overall distribution coming

from a summation of distributions from the

subsets of data.

Use of Combined Datasets - In some cases, it

was necessary and/or desirable to work with

combined datasets from PVRUF and Shoreham in

developing statistical distributions to describe the

data. In estimating flaw densities, it was not

necessary to combine data from the various

subsets of flaws. However, for flaw size

distributions, the data were more limited because

the flaw sizes were measured with a high level of

accuracy for only a small number of flaws. As

one example, the flaw size measurements

combined SAW and SMAW data to establish the

statistical size distribution for small flaws.

Approach to Statistical Correlations - Once the

flaw data were separated into subsets

corresponding to relatively narrow categories of

flaws, it was possible to describe the data in terms

of simple statistical distribution functions. The

6.2
evaluations also characterized the uncertainties in

the parameters of the distributions associated with

the finite number of data points in the samples.

The Poisson distribution was used to treat the

flaw density. Exponential distributions were.

found to be suitable to characterize distributions

of flaw depths and lengths. The exception was

the use of a multi-nomial distribution for the

depth dimensions of small flaws (flaws one weld

bead size or smaller).

The use of statistical distribution functions served

two purposes that could not be accomplished by

simple numerical histograms or binning of the

flaw data. Common statistical functions allowed

uncertainties associated with small sample sizes

to be quantified with a Bayesian approach as

described in the appendix to this report. The

statistical functions also provided a consistent

basis for extrapolating flaw distributions to flaws

larger than could be observed in the limited --

volume of vessel material that could be examined.

Vessel-to-Vessel Variability - The PNNL

examinations of vessel material focused on two

vessels (PVRUF and Shoreham), with only

limited examinations of material from other

vessels (Hope Creek, River Bend, and Midland).

The Shoreham flaws showed some clear

differences from the PVRUF flaws with

somewhat greater flaw densities and longer flaws

(larger aspect ratios). However, there was no

basis for relating these differences in flaw

densities and sizes to other vessels. With only

two examined vessels it was not possible to

statistically characterize vessel-to-vessel

differences such that the differences could be

simulated as a random factor in Monte Carlo

calculations. The decision -was to develop

separate procedures to generate flaw distributions

for the PVRUF and Shoreharn vessels. Following

the conservative approach taken in other aspects

of the PTS evaluations where data and/or

knowledge is lacking, it was recommended that

the Shorehamn version of the flaw distribution be

used in PTS calculations, which served to ensure

conservatism in the predictions of vessel failure

probabilities.

Locations of Flaws Relative to Vessel Inner

Surface - Weld flaws were assumed to be buried

flaws with the locations of their inner tips relative

to the vessel inner surface distributed in a random

manner. The limiting case would be a flaw with

its inner tip at the clad-to-base metal interface,

which would statistically have a zero probability

of occurrence. A separate flaw distribution was

defined for the flaws in the vessel cladding.

Fusion Line Flaws -PNNL's examinations of

vessel material showed that most weld flaws of

significant size were located at weld fusion lines

and had orientations to follow weld fusion lines.

This trend occurred for flaws in original seam

welds and for flaws associated with weld repairs.,

This information was used to modify assumptions

used in fracture mechanics calculations performed

with the FAVOR code. Flaws associated with

seam welds or repair welds are assumed to

propagate into either weld metal or base metal.

Cracks are assumed to propagate into the material

with the lowest level of fracture toughness.

Crack Shape - All flaws are to be crack-like

flaws, which is consistent with the generally.

planar nature of the flaws observed in the PNNL

examinations. There was no detailed

consideration of the truly sharp nature of flaw

tips. It was recognized that the treatment of flaws

by the FAVOR code assumes planar flaws having

ideal elliptical shapes. The plane of the cracks

and the major and minor axes in FAVOR of the

flaws are aligned with the radial and axialcoordinates of the vessel. The PNNL

measurements of flaws gave dimensions of the

flaws in terms of a "box" that would contain the

flaw. In the case of fusion line flaws in seam

welds, the dimensions of this box provide a

realistic representation of the flaw for the fracture

mechanics calculations. However, complex repair

flaws tended to have major and minor axes that

did not align with the vessel coordinate system.

PNNL described these flaws in terms of

dimensions of major and minor axes (relative to

the orientation of the flaw) to preclude an overly

conservative treatment of such flaws by the

FAVOR code.

6.3
Flaw Proximity Considerations - The weld

examinations by SAFT-UT gave special

consideration to indications that would give the

appearance of one or more flaws that may in fact

be one larger flaw. Subsequent validation efforts

focused on these regions for more accurate

characterization of flaw dimensions. ASME Code

flaw proximity rules were then applied to the

refined NDE results. The dimensions of multiple

flaws were tabulated as a single larger flaw if so

dictated by application of the code proximity

rules. The database on flaws should therefore be

considered as accounting for random occurrences

of small flaws that are sufficiently close to each

other to be properly treated as a single larger flaw

in fracture mechanics calculations. The flaws as

given by the input files from generalized flaw

distribution procedure should be treated as single

isolated flaws. There should be no further steps

in the fracture mechanics models to simulate

random locations of flaws in order to identify

occurrences of adjacent flaws that should be

treated as a single larger flaw.

Flaw Orientation - Flaws in axial seam welds are

assumed to have axial orientations, and flaws in

circumferential seam welds are assumed to have

circumferential orientations. These orientations

correspond to the assumptions made in the

development of the FAVOR code and are

consistent with the orientations of flaws as

observed in the PNNL examinations. These

orientations were imposed without regard to

whether the flaw was associated with the original

seam weld or with a subsequent repair to the

weld. Given the complex geometries and

orientations of repair flaws, these assumptions

may be overly simplified and could be subject to

revision as more refined fracture mechanics

models are developed in the future.

Truncation of Flaw Distributions -Flaw inputs

for use in the FAVOR code calculations were

truncated to avoid excessive extrapolations of the

statistically based depth distributions. The

truncations were such to preclude flaws that are

greater than about two times the depth dimensions

of any of the observed flaws upon which the

statistical correlations were based. This approach

was a compromise that allowed consideration of

low-probability flaws larger than could be

detected in the limited volume of examined

material addressed by the PNNL work. On the

other hand, the truncations avoided arbitrary

extrapolations to larger flaw depths outside the

range of the cracking mechanisms covered by the

databases.

Service-Related Flaws - The flaw distribution

methodology addresses only fabrication flaws,

with no consideration of service-initiated cracks

or service-induced growth of fabrication flaws (by

fatigue or stress corrosion cracking). In this

regard, the material examined by PNNL was from

vessels that had never been placed into operation.

Inservice inspections of PWR vessels and fracture

mechanics calculations provide no reason to

believe that crack initiation or growth for flaws in

the vessel beltline region are likely.

6.2 Statistical Functions for Flaw

Distributions

Statistical distribution functions were developed

to describe the data obtained from PNNL's

examinations of vessel weld material. The

evaluations were also to address the uncertainties

in the parameters for the distribution functions.

The following matrix identified the potential need

for a total of 36 functions (3 x 2 x 3 x 2) as

follows:

Variable Values N

Flaw Flaw Density 3

Characteristics Through-Wall Depth

Flaw Length (Aspect Ratio)

Source of Flaw PVRUF 2

Data Shoreham

Weld Process SAW 3

SMAW

Repair Weld

Flaw Depth Small 2

Category Large

In many cases, one function served more than one

purpose, which reduced the number of

independent statistic correlations that were

6.4
needed. The following commonality in the

functions was employed:

* 'One conditional depth distribution described

the small flaws in both the PVRUF and

Shoreham vessels, including all three welding

processes.

* One conditional depth distribution described

all large repair flaws in the PVRUF and

Shoreham vessels;.

* One conditional depth distribution described

all large SAW and SMAW flaws in both the

.PVRUF and Shoreham vessels.

* One length distribution described all large

flaws in the PVRUF and Shoreham vessels,

including all three welding processes.

* One length distribution described the small

SMAW and repair flaws in the PVRUF

vessel.

* One length distribution described the small

SMAW and repair flaws in the Shoreham

vessel.

This commonality reduced the number of

independent functions to 20, including

12 functions to describe flaw densities. In all

cases, flaw density was described by a Poisson

distribution. Exponential distributions were used

to describe flaw depth dimensions and flaw .

lengths, except that a multi-nomial distribution

was used for the depth dimensions of small flaws.

The distribution functions that described the

measured dimensions of flaws included the

following considerations:

(1) Flaw dimensions were first normalized with

respect to the estimated through-wall

dimensions of the weld bead associated with

the flaw being addressed.

(2) Only datasets for which the flaw dimensions

were measured with the highest degree of

accuracy were used to develop the statistical

distribution functions; in many cases this

approach resulted in a relatively small

collection of data for use in the statistical

evaluations.

(3) Whenever possible, a single distribution

function were used to address (1) both the

PVRUF and Shoreham vessels, (2) several

weld types (SAW, SMAW, and repair) and

(3) ranges of flaw sizes (large and small

flaws). In some cases, the data indicated

common trends for the normalized.

dimensions of two or more categories of

'flaws; in other cases, the very limited amount

of data dictated that datasets be combined for

the statistical evaluations. -

The discussion below describes the derivation of

the individual distribution functions. The data

used to establish the parameters of each

distribution are listed. Mean values of the

distribution parameters are given along with the

parameters use to simulate the uncertainties in the

estimated parameters. Appendix A provides

equations for the distribution- functions and the.

equations used to simulate the uncertainties in the

* parameters of the distribution functions.

6.2.1 Flaw Densities

Flaw densities were expressed in terms of flaws

per cubic meter. An option with PNNL's_-

algorithm for generating flaw input files for

FAVOR converts the output to units of flaws per

cubic foot. It should also be noted that the

development of the distribution functions was

originally performed in terms of flaws per unit

volume based on data from the PVRUF and

Shoreham vessels. It was later recognized that

flaws per unit area of the weld fusion zone is a

better measure of flaw density. The algorithm has

the option for output files in units of flaws per

unit area. Conversion factors for the PVRUF and

Shoreham vessels are embedded in the algorithm

to make the conversion from a volume basis to an

area basis. For the PVRUF and Shoreham

vessels, the ratio of weld area (square meters) to

6.5
-

weld volume (cubic meters) is a factor of 45.84.

This accounts for two fusion surfaces along each

seam weld. The weld was assumed to have an

average width (or gap) of 1.61 in. for the PVRUF

vessel and 1.52 in. for the Shoreham vessel.

Table 6.1 lists the flaw data and corresponding

examined material volumes as reported by

Jackson and Abramson (2000), which were used

to calculate flaw densities. The parameter

uncertainty for the Poisson distribution was

calculated from a gamma distribution

(Appendix A) on the basis of the volume of

material inspected and the number of flaws found.

Each Monte Carlo trial of the flaw distribution

algorithm samples from the gamma distribution to

calculate a parameter for the six flaw densities of

Table 6.1. Table 6.2 gives the values used to

define the gamma distribution for sampling of the

parameters of the Poisson distribution.

Table 6.3 lists the assumed through-thickness

dimensions for weld beads that were used to

identify small flaws versus large flaws. These

same bead dimensions were used to normalize

flaw dimensions in the development of statistical

distributions to characterize the through-wall

depths and lengths of flaws.

Figures 6.1 and 6.2 are plots of the calculated

flaw densities as calculated from the parameters

of Table 6.2, with the relative uncertainties in the

calculated densities indicated by the relative

slopes of the curves. The densities for small

flaws are 2 to 3 orders of magnitude greater than

the densities for large flaws. There are greater

statistical uncertainties in the estimated densities

for large flaws than for small flaws. Consistent

with the relatively small number of observations,

the uncertainties are greater for repair flaws than

for the SAW and SMAW material.

Table 6.1. Flaw Density Parameters

Examined Flaw lensity, Flaws per Cubic Meter

Weld Flaw Number Volume, 25t75t

Vessel Type Size of Flaws M3 Mean Median Quartile Quartile

PVRUF SAW Small 1419 0.180 7883 7881 7741 8023

PVRUF SMAW Small 197 0.014 14071 14047 13382 14734

PVRUF Repair Small 12 0.00123 9756 9486 7738 11480

PVRUF SAW Large 4 0.180 22.2 20.4 14.1 28.4

PVRUF SMAW Large 4 0.014 285 262 181 364

PVRUF Repair Large 7 0.00123 5671 5422 4132 6958

Shoreham SAW Small 3160 0.137 23065 (a) (a) (a)

Shoreham SMAW Small 741 0.0105 70571 .. _.._..

Shoreham Repair Small 45 0.0030 15.0 .. _.._..

Shoreham SAW Large 32 0.137 234 ..

Shoreham SMAW L 8 0.0105 761

Shoreham Repair L 6 0.0030 2000 .. .. ..

(a) Available data analyses did not provide these numbers.

6.6
Table 6.2. Gamma Distribution Used To Sample for Parameter of Poisson

Distribution for Flaw Densities - _-

Examined Parameters for

Weld Number Volume, Gamma Distribution

Vessel Type Flaw Size of Flaws m3 ; a2 

PVRULF SAW Small - 1419 0.180 0.180 .1419

PVRUF SMAW Small . 197 0.014 0.014 197

PVRUF Repair Small 12 0.00123 0.00123 12

PVRUF SAW Large 4 0.180 - 0.180. 4

PVRUF SMAW Large 4 0.014- 0.014 4

PVRUF Repair Large 7 0.001 0.001 4

Shoreham SAW Small . . 3160 0.137 0.137 3160

Shoreham SMAW Small 741 0.0105 0.0105 741

Shoreham Repair Small 45 0.0030 0.0030 45

Shoreham SAW Large 32 0.137 0.137 32

Shoreham SMAW Lg 8 0.0105 0.0105 8

Shoreham Repair L 6 0.0030 0.0030 6

Table 63. Weld Bead Dimensions for

PVRUF and Shoreham Welds

Weld Bead

Vessel Weld Type Thickness, mm

PVRUF SAW 6.5

PVRUF SMAW 3.5

PVRUF Repair 3.5

Shoreham. SAW 5

Shoreham SMAW 3.5

Shoreham Repair 3.5

0.01 0.10 1.00 10.00 100M 1000.00 1000.0

Flaw Density. Flaws per Cubic Foot

Figure 6.2. Uncertainty in Flaw Densities for Flaws

in Shoreham Vessel

6.2.2 Conditional Depth Distribution for

Small Flaws

A single distribution was developed to describe

the through-wall dimensions of small flaws. In

this report, small flaws are defined as flaws

having depths that are less than or equal to the

weld bead size. One depth distribution was

applied to small flaws for all three weld types

(SAW, SMAW, and repair) and for the PVRUF

1.00 0.00 100.00 1000.0 - 10."

Flaw Density. Flaws per Cuble Foot :

Figure 6.1. Uncertainty in Flaw Densities for Flaws

in PVRUF Vessel

6.7
and Shoreham vessels. The distribution was

based on sets of flaw size data that were measured

by radiography of 25-mm plate specimens cut

from welds of the PVRUF vessel (Figure 6.3).

These specimens had only a small fraction of the

small flaws detected by SAFT-UT during the

examinations of the PVRUF and Shoreham

vessels. However, the sizing accuracy for these

flaws by RT was significantly better than the

sizing accuracy possible with the SAFT-UT

scans, which had an accuracy of no better than

2 mm. Limitations associated with the relatively

small number of data points were addressed with

the uncertainty analysis for parameters of the

distribution function used for simulating flaw

type. The estimated bead size ranged from 3.5

mm for SMAW welds to 6.0 mm for SAW welds.

Because similar data from RT examinations were

not available for the Shoreham vessel, the depths

of flaws for the Shoreham vessel were assumed to

be described by the same conditional distribution

as the PVRUF vessel. Schuster et al. (1999,

Figure 6.1) compare flaw depth distributions for

the PVRUF and Shoreham welds. Whereas the

Shoreham vessel has about three times the

number of flaws per cubic meter more than the

PVRUF vessel, the conditional depth distributions

of the flaws for the two vessels were shown to

follow similar trends.

depth dimensions. Before a distribution function was developed, the

data on flaw depths were normalized relative to

the size of the weld bead for each flaw. A

multinomial distribution (see Appendix A)

<' described the complementary cumulative

e'C^ distribution of flaw depths. The uncertainties in

the three parameters of this distribution were

Ad described by a Dirichlet distribution. The

r 6 normalized flaw depths (bounded 0.1 and 1.0 for

small flaws) were described as discrete sizes with

three bins of width 0.3 of the bead thickness and

centered at values of 0.25, 0.55, and 0.85. The

three discrete flaw sizes described by the

multinomial distribution had probabilities of

occurrence given by a three-element vector f3;.

The probability density function is defined as

' 'I I SI I .I ! I, 1 I .' ,: -,; 1-i . ' i4 i | I I

 11,

- - "  - - ': -,;.  .1 _.

Figure 63. PVRUF Weld Metal Specimen Cut into

25-mm Plate

Randomly selected material from the PVRUF

welds was prepared in the form of plate samples

and examined by RT. A total of 43 small flaws

were detected in the examined plates, with

measured sizes (through-wall depth dimensions)

ranging from 0.5 to 7.0 mm (see Table 6.4). The

location of each flaw relative to the inner surface

of the vessel was established. This location was

used to determine if the weld metal at the flaw

location was most likely SAW or SMAW. Most

of the flaws were in SAW weld material. Flaws

for both weld types were combined into one

dataset. However, the size of the weld bead for

each flaw was assigned according to the weld

f (a/A) = 13/0.3 (6.1)

where a is the flaw through-wall depth dimension

and A is the bead thickness.

From the data of Table 6.4, the mean, median, and

quartiles of the distribution parameters of

Table 6.5 were derived. The flaw distribution

algorithm generates uncertainty distributions by

sampling from the Dirichlet distribution using the

parameters Uj listed as in Table 6.5. Figure 6.4 is

a plot of curves based on the parameters from

Table 6.5, which shows curves for various

percentiles of the flaw depth distribution as

obtained by sampling of the uncertainty

distributions.

6.8
Table 6A. Data from Radiography of 25-mm

Thick Plates from PVRUF Welds.

Flaw

Bead Flaw Depth

ID Size, Depth, Fraction Fraction

Number Plate mm mm of Bead >X

20 5-IC-8 6.50 0.50 0.077 1.000

2 5-IAB-2 6.50 1.00 0.154 0.977

S 5-lAB-S 6.50 1.00 0.154 0.953

10 5-IAB-7 6.50 1.00 0.154 0.930

13 5-lAB-11 6.50 1.00 0.154 0.907

34 5-lOB-10 6.50 .1.00 0.154 0.884

37 5-12BA-2 6.50 1.00 0.154 0.860-

17 5-1C-2 6.50 1.10 0.169 0.837

6 5-lAB-5 6.50 1.20 0.185 0.814

1 5-IAB-2 6.50 1.30 0.200 0.791

27 5-IC-14 6.50 1.30 0.200 0.767

3 5-IAB-3 6.50 1.50 0.231 0.744

14 5-IAB-12 6.50 1.50 0.231 0.721

15 5-IAB-12 6.50 1.50 0.231 0.698

19 5-IC-6 6.50 1.50 0.231 0.674

21 5-1C-8 6.50 1.50 0.231 0.651

22 5-IC-10 6.50 1.50 0.231 0.628

24 5-1C-12 6.50 1.50 0.231 0.605

32 5-I iOB-7 6.50 1.50 0.231 0.581

33 5-IOB-8 6.50 1.50 0.231 0.558

35 5-12BA-1 6.50 1.50 0.231 0.535

-36 5-12BA-1 6.50 1.50 0.231 0.512

42 5-12BA-1 1 6.50 1.75 0.269 0.488

4 5-IAB-5 6.50 1.80 0.277 0.465

25 5-IC-13 3.50 1.00 0.286 0.442

8 5-IAB-6 6.50 2.00 0.308 0.419

9 5-1AB-7 6.50 2.00 0.308 0.395

11 5-1AB-9 6.50 2.00 0.308 0.372

29 5-IOB-4 6.50 2.00 0.308 0.349

39 5-12BA-4 6.50 2.00 0.308 0.326

30 5-lOB-5 3.50 1.10 0.314 0.302

31 5-1OB-5 - 6.50 2.20 0.338 0.279

41 5-12BA-8 6.50 2.20 0.338 0.256

43 5-12BA-13 6.50 2.50 0.385 0.233

1 8 5-1C-4 3.50 1.50 0.429 0.209

7 5-IAB-6 6.50 3.00 0.462 0.186

12 5-lAB-1 1 6.50 3.00 0.462 0.163 .

23 5-IC-Il 6.50 3.00 0.462 0.140

38 5-12BA-3 6.50 3.00 0.462 0.116

28 5-IOB-2 6.50 3.50 0.538 '0.093

40 5-12BA-6 6.50 3.50 0.538 0.070

26 5-IC-13 6.50 4.00 0.615 0.047

16 5-IAB-14 3.50 4.50 1.286 0.023

t ;,aima srLawa OJO tPVRUF Data * RT of Plates

K 0.70 Percentits Based on

Flaw Deph of a ISW

- . '5%

e, Larg S

.0 04025%

0.40

0.10. 0

0.00

0.0 Ci2 GA 0.6 0.s 1.0 1.2 1.4

x a Flaw Depth Fraction of Bead St

Figure 6.4. Depth Distribution for Small Flaws

Including Uncertainty Analysis

6.2.3 Conditional Depth Distribution for

Large SAW and SMAW Flaws

Two conditional distributions were developed to

describe the through-wall dimensions of large

flaws. Large flaws are defined as flaws having

depths that are greater than the weld bead size.

The data showed that the depth distribution for

large repair flaws had a significantly different

trend (larger sizes) than the large flaws in SAW

and SMAW welds. Depth distribution for large

repair flaws was addressed by a separate

evaluation.'

The depth distributions for large SAW and

SMAW flaws were based on data from weld

normal examinations of welds that had been

sectioned from the intact vessel. The size

measurements by. SAFT-UT were of relatively

high accuracy but not as accurate as the

measurements performed later during the

validation effort for repair flaws that employed a

combination of SAFI-UT of small cubes,

radiography, and destructive sectioning.

6.9
Table 6.5. Data and Parameters of the Uncertainty Distribution for

De th Distribution for Small Flaws

pi - Parameters of Multinomial Distribution

Normalized Number 2 5 tb 5 0 th 7 5 tb

Index i Flaw Depth of Flaws U, Mean i Percentile f3 Percentile 01 Percentile A,

1 0.25 34 34 0.79 0.75 0.80 0.83

2 0.55 8 8 0.19 0.14 0.18 0.22

3 0.85 1 1 0.02 0.01 0.02 0.03

Table 6.6 presents a combined dataset for large

SAW and SMAW flaws from both the PVRUF

and Shoreham vessels. Because of the relatively

small number of observed flaws, the data from the

PVRUF and Shoreham vessels were combined to

develop a distribution for flaw depths. A review

of a sample of flaws from Schuster et al. (1999)

indicated that about 81% of these flaws were in

SAW material and the remaining 19% in SMAW

material. For developing complementary conditional depth distributions (CCDF), the approach

of Jackson and Abramson (2000) combined the

flaw size data for the two weld types. However,

the flaw distribution algorithm did include

separate treatments of flaw densities for SAW and

SMAW welds as well as separate flaw densities

for the PVRUF and Shoreham vessels.

Figure 6.5 presents flaw distribution curves that

are based on the data of Table 6.6. An

exponential distribution function was found to

provide a relatively good description of the data.

Flaw depth dimensions were normalized with

respect to the weld bead thickness to develop the

CCDF correlations indicated in Figure 6.5. An

evaluation included the uncertainty in the

parameter of the exponential distribution as

indicated by the percentiles displayed on

Figure 6.5. The distribution was calculated from

parameters of the gamma function are based on

the data of Table 6.6. The values were

established to be a, = 21.68 and a 2 = 52, where

(from Table 6.6) the parameter a, is calculated as

the sum of the 52 values of the quantity (d/A - 1)

and a2 corresponds to the number of data points

in Table 6.6.

6.2.4 Conditional Depth Distribution for

Large Repair Flaws

A second conditional distribution was developed

to describe the through-wall dimensions of large

repair flaws, using the same approach as used for

large flaws in SAW and SMAW welds. Because

of the relatively small number of observed flaws,

data from the PVRUF and Shoreham vessels were

combined for developing a distribution for flaw

depths. Large repair flaws had first been sized by

weld normal examinations. These measured

dimensions were subsequently replaced by more

accurate dimensions coming from the validation

effort that used a combination of SAFT-UT of

small cubes, radiography, and destructive

examinations.

Table 6.7 presents the combined the dataset for

repair flaws. Figure 6.6 presents flaw distribution

curves based on the data of Table 6.7. An

exponential distribution function was again found

to provide a relatively good description of the

data. The flaw depth dimensions were

normalized with respect to the weld bead

thickness as indicated in Figure 6.6. The

evaluation addressed the uncertainty in the

parameter of the exponential distribution as

indicated by the percentiles displayed on

Figure 6.6. The distribution was calculated from

Equation (6.2) as described in Section 6.2.3.

N(>d/A) = p e - ) (6.2)

where N(>d/A) is the number of flaws per cubic

meter with the normalized depth dimensions

greater than d/A and j3 is the parameter of an

exponential distribution assigned to provide a best

fit of the data. Using equations from the Bayesian

methodology as described in the Appendix, a

gamma distribution function was established to

describe the uncertainty in the value of P3. The

6.10
Table 6.6. Large SAW and SMAW Flaws In

PVRUF and Shoreham Vessels

11.01

Bead Flaw Depth,

Size, Depth, Frac

Index ID No. mm mm Bead

1 10 6.0 5.50 1.00

2 11 - 6.0 5.50 1.00

3 20 5.0 5.00 1.00

4 22 5.0 5.00 1.00

5 24 5.0 5.00 1.00

6 26 5.0 5.00 1.00

7 28- 5.0 5.00 1.00

8 30 5.0 5.00 1.00

9 32 5.0 5.00 1.00

10 34 5.0 5.00 1.00

11 1 3.5 4.00 1.14

12 2 3.5 4.00 1.14

13 12 6.5 7.50 1.15

14 13 6.5 7.50 1.15

15 14 6.5 7.50 1.15

16 15 6.5 7.50 1.15

17 36 5.0 6.00 1.20

18 38 5.0 6.00 1.20

19 40 5.0 6.00 1.20

20 42 5.0 6.00 1.20

21 44 5.0 6.00 1.20

22 46 5.0 6.00 1.20

23 16 6.0 7.50 1.25

24 17 6.0 7.50 1.25

25 49. 5.0 7.00 1.40

26 50 5.0 7.00 1.40

27 52 5.0 7.00 1.40

28 3 3.5 5.00 1.43

29 4 3.5 5.00 1.43

30 21 3.5 5.00 1.43

31 23 3.5 5.00 1.43

32 25 3.5 5.00 1.43

33 '27 3.5 5.00 1.43

34 29 3.5 5.00 1.A3

35 31 3.5 5.00 1.A3

36 33 3.5 5.00 1.43

37 53 5.0 8.00 1.60

38 56 5.0 8.00 1.60

39 35 3.5 6.00 1.71

40 37 3.5 6.00 1.71

41 39 3.5 6.00 1.71

42 41 3.5 6.00 1.71

43 43 3.5 6.00 1.71

44 45 3.5 6.00 1.71

45 57 5.0 9.00 1.80-

46 58 5.0 9.00 1.80

47 59 5.0 9.00 1.80

48 51 3.5 7.00 2.00

49 62- 5.0 10.00 *2.00

50 54 3.5 8.00 2.29

51 55 3.5 8.00 229

52 60 3.5 9.00 2.57

1Ed

i 1141

* r

2 1142

I.E.03

Large Flaws

PVRUF + Shoreham Data

SAW and SMAW Flw

f.V

W%

50%

. 20%

S'

1.W E4

0.0 1.0 - 2.0 - O 4.0

- Crack Depth. Fraction o Bead Thcknns

*.0

Figure 6.5. Uncertainty Evaluation for Complementary

Conditional Depth Distribution for Large SAW and

SMAW Flaws

0 2 4 6

Flaw Depth. Fraction of Bead

I 10

Figure 6.6. Uncertainty Evaluation for

Complementary Conditional Depth Distribution

for Large Repair Flaws

Parameters of the gamma function are based on

the data of Table 6.7. The values were

established to be &a = 17.58 and a2 = 13 where

(from Table 6.7) the parameter a, is calculated as

the sum of the 17 values of the quantity (d/A - 1)

and °X2 corresponds to the number of data points

in Table 6.7.

6.11
-

Table 6.7. Large Repair Flaws in PVRUF and Shoreham Vessels

Bead Nominal Measured Measured

Size, Flaw Depth, Flaw Depth, Flaw Length, No. Flaws

Index mm mm mm mm > x

1 3.5 11.50 2.5 12.00 13

2 3.5 5.50 5.50 - 12

3 3.5 5.50 5.50 11

4 3.5 5.50 5.50 . 10

5 3.5 5.50 5.50 9

6 3.5 5.50 5.50 - 8

7 3.5 7.00 6.00 18.00 7

8 3.5 21.00 7.00 30.00 6

9 3.5 7.00 10.00 13.00 5

10 3.5 10.00 10.00 11.00 4

11 3.5 32.00 12.00 44.00 3

12 3.5 14.00 14.00 14.00 2

13 3.5 17.50 17.00 18.00 1

6.2.5 Length Distribution for Small SAW

Flaws in PVRUF Vessel

Flaw aspect ratios (the ratio of flaw length to flaw

depth) are an important input to the probabilistic

fracture mechanics calculations of the FAVOR

code. Considerable effort was applied to develop

a method to define these flaw aspect ratios on the

basis of the flaw lengths measured for the PVRUF

and Shoreham vessels. PNNL adopted the

approach of the PRODIGAL model (Chapman

and Simonen 1998) for describing flaw aspect

ratios, which assumed that the distribution of flaw

lengths is independent of the depth dimension of

the flaws. An evaluation of the length data from

the PVRUF and Shoreham flaws showed that this

was a reasonable assumption for the current work.

The model established the statistical distributions

for amounts by which normalized flaw lengths

exceeded the normalized flaw depths.

The available data indicated different trends of

flaw lengths for the PVRUF and Shoreham

vessels and different trends for SAW versus

SMAW welds. There appeared to be sufficient

data for small flaws to address four flaw

categories corresponding to two vessels and two

weld processes. Lacking sufficient data for small

repair flaws, it was assumed that the lengths of

small repair flaws can be described by the same

distribution function as for flaws in SMAW

welds.

This section addresses the lengths of small SAW

flaws in the PVRUF vessel. The next three

sections address small flaws in SMAW welds and

the Shoreham vessel. The selected dataset

included only those small SAW flaws in the

PVRUF welds that were subjected to the most

complete of the validation efforts (Schuster et al.

2000a, Table 9 and Figure 4). This selection

excluded small flaws that were detected only by

the examinations performed with the early SAFTUT examinations at ORNL. Also excluded were

the flaws that were validated only by the weld

normal ultrasonic (UT) examinations but not

further validated by RT and destructive

evaluations. These restrictive requirements

resulted in the most accurate measurements of

flaw dimensions but meant that only 9 small flaws

remained upon which to base a flaw length

distribution.

Figures 6.7 and 6.8 show all of the length data for

small and large flaws in the PVRUF vessel. The

length distribution was characterized by the

exponential distribution. The distribution was

calculated from

P[>(e - a)/A] = e"e- allA (6.3)

6.12
A SUAW

16.

Sm.0 Il 4 S.-) SAW

F.0d6)

PeFigure 6.7. Lengths of Small Flaws in SA

SMAW Welds of PVRUF Vessel

-:where P>(t'- a-/A] is the fraction of flaws with

the normalized length dimensions greater than

- - a)/A and P3 isthe parameter of an exponential _, distribution assigned to provide a best fit of the

data. Using equations from the Bayesian

methodology as described in the Appendix, a '

gamma distribution function was established to

describe the uncertainty in the value of P. The

parameters of the gamma function were'based on

the data of Table 6.8. The values were

established to be a, = 0.53846 and a2 = 9, where

4. to (from Table 6.8) the parameter a, is calculated as

the sum of the nine values of the quantity

- a)/A and a2 corresponds to the number of

LW and data points in'Table 6.8. The resulting

distribution function is shown in Figure 6.8 along

with the data and results of the uncertainty

PVRUF Small Fl,aws | evaluation.'

11

i

Z

P

.0

I

A.

0.e

0.e

6.7

a..

0.5

6.4

0.2

02

0.1

,S%

SAW

. I

_ II

6.2.6 Length Distribution for Small

SMAW and Repair Flaws in PVRUF

Vessel

This section addresses the lengths of small

SMAW flaws in the PVRUF vessel. Lacking

sufficient data for small repair flaws, it was

assumed that the lengths of small repair flaws

could be described by the same distribution

function as used for SMAW flaws. The length

distribution was calculated from Equation (6.3) as

described in Section 6.2.5. The parameters of the

gamma function are based on the data of

Table 6.9. The values were established to be a, =

10.857 and a2 = 6, where (from Table 6.9) the

.1.e 0.0 1.0 2.0 se 4.6 5t

Lreigth. DopthU)Bad

Figure'6.8. Lengths of Small Flaws In SAW Welds

of PVRUF Vessel Showing Exponential Distribution

Along with Uncertainties

Table 6.8. Lengths of Small Flaws In SAW Welds of PVRUF Vessel |

Bead Flaw Flaw Depth- Length Minus

Weld Size, Depth, Length, Length Minus Frac Depth Frac Fraction

Label Type mm mm mm - Depth, mm Bead Bead > x

5-IC-13 SAW 6.50 4.0 3.5 -0.50 0.615 -0.077 1.000

5-IOB-2 SAW 6.50 3.5 3.5 0.00 0.538 0.000 0.875

5-12BA-1 SAW 6.50. 3.5 3.5 0.00 0.538 0.000 0.750

5-IAB-6 SAW 6.50 3.0 3.5 0.50 0.462 0.077 0.625

5-lAB-1l SAW 6.50 3.0 3.5 0.50 0.462 0.077 0.500

5-IC-1l SAW 6.50 3.0 3.5 0.50 0.462 0.077 0.375

5-12BA-1 SAW 6.50 3.0 3.5 0.50 10.462 0.077 0.250

5-12BA-1 SAW 6.50 2.0 35 * L 1.50 0.308 0.231 0.125

6.13
Table 6.9. Lengths of Small Flaws in SMAW Welds of PVRUF Vessel

Flaw Flaw Length Depth Length Minus

Weld Bead Depth, Length, Minus Depth, Frac Depth, Frac Fraction

Label Type Size, mm mm mm mm Bead Bead > x

5-7HIiibiic SMAW 3.50 3.0 4.0 1.00 0.857 0.286 1.000

5-4Bliidiie SMAW 3.50 3.0 5.0 2.00 0.857 0.571 0.833

5-lOB5ibic SMAW 3.50 3.0 9.0 6.00 0.857 1.714 0.667

5-lOECliibiic SMAW 3.50 3.0 11.0 8.00 0.857 2.286 0.500

5-IOEAliiibiiic SMAW 3.50 3.0 12.0 9.00 0.857 2.571 0.333

5-lOECiidiie SMAW 3.50 3.0 15.0 12.00 0.857 3.429 0.167

parameter a, is calculated as the sum of the six

values of the quantity (-e - a)/A and a2

corresponds to the number of data points in

Table 6.9. The resulting distribution function is

shown in Figure 6.9 along with the data and

results of the uncertainty evaluation.

1.E00-

VRUF Small Flaws

SMAW

AX95

0 50%

I.E.01

10. 0.0 1.0 20 30 4.0

(Lenth. -Dpth)/Bad

Figure 6.9. Lengths of Small Flaws in SMAW

Welds of PVRUF Vessel Showing Exponential

Distribution Along with Uncertainties

requirements for the data resulted in a relatively

large number of measurements of flaw

dimensions, which gave a total of 105 small flaws

upon which to base a flaw length distribution.

Figure 6.10 shows the available length data for

small and large flaws in the Shoreham vessel.

Length distributions were calculated from

Equation (6.3) as described in Section 6.2.5.

Parameters of the gamma function for small flaws

SAW welds of the Shoreham vessel were based

on the data of Table 6.10. The values were

established to be a, = 286 and a2 = 105, where

(from Table 6.10) the parameter a, is calculated

as the sum of the 105 values of the quantity

(E - a)/A and a2 corresponds to the number of data

points in Table 6.10. Figure 6.11 shows the

length distribution along with the data used to

establish the distribution function and the

No statistical uncertainty in the correlation.

6.2.7 Length Distribution for Small SAW

Flaws in Shoreham Vessel

This section addresses the lengths of small SAW

flaws in the Shoreham vessel. The selected data

set addressed only a sample of the small SAW

flaws in the Shoreham welds (Schuster et al.

2000a). This selection included small flaws that

were detected and sized by the examinations

performed with the weld normal UT examinations

but not further validated by SAFT-UT and

destructive evaluations. These less restrictive

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 10.0

fLangth - DepthY84ad

Figure 6.10. Lengths of Small Flaws in SAW and

SMAW Welds of Shoreham Vessel

6.14
Table 6.10. Lengths of Small Flaws in SAW Welds of Shoreham Vessel

Bead Flaw Flaw Length Depth Length Minus

Weld Size, Depth, Length, Minus Frac Depth Frac Fraction

Label Type mm mm .,mm Depth, mm Bead Bead >_ _

208 SAW 5.0 5.0 7.0 2.0 1.000 0.400 1.000

144 SAW 5.0 5.0 7.0 2.0 1.000 0.400 0.990

11 . SAW 5.0 5.0 7.0 2.0 1.000 0.400 0.981

68 SAW 5.0 5.0 8.0 3.0 1.000 0.600 0.971

153 SAW 5.0 5.0 8.0 3.0 1.000 0.600 0.962

132 SAW 5.0 5.0 9.0 4.0 1.000 0.800 0.952

124 SAW 5.0 5.0 9.0 4.0 1.000 0.800 0.943

64 SAW 5.0 4.0, 9.0 5.0 0.800 1.000 0.933

30 SAW 5.0 4.0 9.0 5.0 0.800 1.000 0.924

177 SAW 5.0 4.0 9.0 5.0 0.800 1.000 0.914

8 SAW 5.0 5.0 .10.0 5.0 1.000 .1.000 0.905

184 SAW 5.0 5.0 10.0 5.0 1.000 1.000 0.895

2 SAW 5.0 5.0- 10.0 5.0 1.000 1.000 0.886

37 SAW 5.0 5.0' 10.0 5.0 1.000 1.000 0.876

262 SAW 5.0 4.0 10.0 6.0 0.800 1.200 0.867

258 SAW -5.0 4.0. 10.0 6.0 0.800 1.200 0.857

100' SAW 5.0 4.0 10.0 6.0 0.800 1.200 0.848

48 - SAW 5.0 4.0- 10.0 6.0 0.800 1.200 0.838

98 SAW 5.0 4.0 10.0 _ 6.0 0.800 1.200 0.829

23 SAW 5.0 4.0 10.0 .6.0 0.800 1.200 0.819

160 SAW 5.0 4.0 10.0 &6.0 0.800 1.200 0.810

233 SAW 5.0 4.0 10.0 6.0 0.800 '1.200 0.800

180 SAW 5.0 4.0 10.0 6.0 0.800 1.200 0.790

231 SAW 5.0 4.0 10.0 6.0 0.800 1.200 0.781

123 SAW 5.0 4.0 10.0 6.0 0.800 1.200 0.771

38 SAW 5.0 4.0 10.0 _ 6.0 0.800 1.200 0.762

67 SAW 5.0 4.0 11.0 7.0 0.800 1.400 0.752

42 SAW 5.0 4.0 11.0 7.0 0.800 IA.00 0.743

112 SAW 5.0 4.0 11.0 .7.0 0.800 1.400 0.733

158 SAW 5.0 4.0 11.0 7.0 0.800 1.400 0.724

52 SAW 5.0 4.0 11.0 .7.0 0.800 1.400 0.714

16 SAW 5.0 4.0 11.0 7.0 0.800 1.400 0.705

18 SAW 5.0 4.0 11.0 7.0 0.800 1.400 0.695

107 SAW 5.0 5.0 12.0 7.0 1.000 1.400 0.686

34 SAW 5.0 4.0 12.0 8.0 0.800 | 1.600 0.676

105 SAW 5.0 4.0 12.0 8.0 0.800 1.600 0.667

12 SAW 5.0 4.0 12.0 8.0 0.800 1.600 0.657

293 SAW 5.0 4.0 12.0 8.0 0.800 1.600 0.648 7

317 SAW 5.0 4.0 12.0 8.0 0.800 1.600 0.638

338 : SAW 5.0 4.0 12.0 8.0 0.800 1.600 0.629

256 SAW 5.0 5.0 13.0 8.0 1.000 1.600 - 0.619

74 SAW 5.0 5.0 13.0 8.0 1.000 1.600 X 0.610

126 SAW 5.0 5.0 13.0 - 8.0 1.000 1.600 0.600

111 SAW 5.0 5.0 13.0 8.0 1.000 1.600 . 0.590

38 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.581

47 SAW 5.0 4.0 13.0 9.0 0.800- 1.800 0.571

65 SAW 5.0 4.0 13.0 - 9.0 0.800 - 1.800 0.562

222 SAW 5.0 4.0 13.0 - 9.0 0.800 1.800 0.552

6.15
Table 6.10. Lengths of Small Flaws in SAW Welds of Shoreharm Vessel (contd)

Bead Flaw Flaw Length Depth Length Minus

Weld Size, Depth, Length, Minus Frac Depth Frac Fraction

Label Type mm mm mm Depth, mm Bead Bead > x

125 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.533

94 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.524

17 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.514

26 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.505

51 SAW 5.0 4.0 13.0 9.0 0.800 1.800 0.495

51 SAW 5.0 5.0 14.0 9.0 1.000 1.800 0.486

39 SAW 5.0 5.0 14.0 9.0 1.000 1.800 0.476

47 SAW 5.0 5.0 14.0 9.0 1.000 1.800 0.467

21 SAW 5.0 4.0 14.0 10.0 0.800 2.000 0.457

274 SAW 5.0 4.0 14.0 10.0 0.800 2.000 0.448

196 SAW 5.0 5.0 15.0 10.0 1.000 2.000 0.438

58 SAW 5.0 5.0 15.0 10.0 1.000 2.000 0.429

73 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.419

45 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.410

49 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.400

299 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.390

124 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.381

310 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.371

334 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.362

98 SAW 5.0 4.0 15.0 11.0 0.800 2.200 0.352

284 SAW 5.0 5.0 16.0 11.0 1.000 2.200 0.343

119 SAW 5.0 5.0 16.0 11.0 1.000 2.200 0.333

39 SAW 5.0 4.0 16.0 12.0 0.800 2.400 0.324

4 SAW 5.0 4.0 16.0 12.0 0.800 2.400 0.314

22 SAW 5.0 4.0 16.0 12.0 0.800 2.400 0.305

17 SAW 5.0 5.0 18.0 13.0 1.000 2.600 0.295

206 SAW 5.0 5.0 18.0 13.0 1.000 2.600 0.286

32 SAW 5.0 4.0 18.0 14.0 0.800 2.800 0.276

151 SAW 5.0 4.0 18.0 14.0 0.800 2.800 0.267

95 SAW 5.0 4.0 18.0 14.0 0.800 2.800 0.257

29 SAW 5.0 4.0 18.0 14.0 0.800 2.800 0.248

173 SAW 5.0 4.0 18.0 14.0 0.800 2.800 0.238

55 SAW 5.0 4.0 19.0 15.0 0.800 3.000 0.229

24 SAW 5.0 5.0 22.0 17.0 1.000 3.400 0.219

17 SAW 5.0 4.0 22.0 18.0 0.800 3.600 0.210

286 SAW 5.0 4.0 22.0 18.0 0.800 3.600 0.200

83 SAW 5.0 5.0 23.0 18.0 1.000 3.600 0.190

22 SAW 5.0 4.0 23.0 19.0 0.800 3.800 0.181

79 SAW 5.0 5.0 25.0 20.0_ 1.000 4.000 0.171

65 SAW 5.0 4.0 25.0 21.0 0.800 4.200 0.162

153 SAW 5.0 4.0 28.0 24.0 0.800 4.800 0.152

239 SAW 5.0 4.0 30.0 26.0 0.800 5.200 0.143

164 SAW 5.0 4.0 30.0 26.0 0.800 5.200 0.133

102 SAW 5.0 4.0 30.0 26.0 0.800 5.200 0.124

318 SAW 5.0 4.0 30.0 26.0 0.800 5.200 0.114

345 SAW 5.0 4.0 30.0 26.0 0.800 5.200 0.105

112 SAW 5.0 5.0 33.0 28.0 1.000 5.600 0.095

18 SAW 5.0 4.0 33.0 29.0 0.800 5.800 0.086

6.16
Table 6.10. Lengths of Small Flaws in SAW Welds of Shoreham Vessel (contd)

Bead Flaw Flaw Length Depth Length Minus

Weld Size, Depth, Length, Minus Frac Depth Frac Fraction

Label Type mm mm mm - Depth, mm Bead Bead > x

139 SAW 5.0 5.0 36.0 . 31.0 .1.000 6.200; .0.076

22 SAW 5.0 4.0 36.0 32.0 0.800 6.400 0.067

113 - SAW 5.0 4.0 41.0 37.0 0.800 7.400 -0.057

81 SAW- 5.0 4.0 51.0 47.0 0.800 9.400 0.048

40 SAW 5.0 5.0 61.0 56.0 1.000 11.200 0.038

28 SAW -5.0 4.0 64.0 60.0 0.800 12.000 0.029

149 SAW -5.0 4.0 76.0 72.0 0.800 14.400. 0.019

78 SAW 5.0 5.0 81.0 76.0 1.000 15.200 0.010

.Shoreham Small Flaws

'' SAW .

1 2 3 4 5 * * 7 * 9 if 1 12 13 14 tS I

* avid

:Lfgt- .Opth ,ad

Figure 6.11. Leniths of Small Flaws in SAW Welds

of Shoreham Vessel Showing Exponential

-Distribution Along with Uncertainties

6.2.8 Length Distribution for Small

SMAW and Repair Flaws in'-

Shoreham Vessel

acceptance requirements for the data resulted in a

total of 16 small flaws upon which to base a

*distribution function for flaw lengths.

The flaw lengths were calculated from

Equation (6.3) as described in Section 6.2.5. The

parameters of the gamma function for small SAW

in the Shoreham vessel were based on the data of

Table 6.1 1. The values were established to be a,

= 46.3 and a2 = 16, where (from Table 6.11) the

parameter a, was calculated as the sum of the

25 values of the quantity (4? - a)/A'and a2

corresponds to the number'of data poinits' in

Table 6.11. The resulting distribution function is

shown in'Figure 6.12 along with the data and

results of the uncertainty evaluation.

This section addresses the lengths of small

SMAW flaws in the Shoreham vessel., A review

of the available data (Schuster et al. 1999)

indicated that length measurements for small,

flaws were insufficient to support a length . --

distribution, whereas a combined dataset covering.

both small and large SMAW and repair flaws

provided an adequate database. The dataset .

included only larger flaws for which the length

measurements were made with a reasonable level

of accuracy. These flaws were detected and sized

by the weld normal UT examinations. None of

these measurements had been further validated by

SAFT-UT and destructive evaluation. The

AP:

0

_ I . . e 1 2-3 4 5 * 7 o' * 10 11 12

(Length Depth)eBad : I

13 14 15 1f

Figure 6.12. Lengths of Small and Large Flaws in

SMAW and Repair Welds of Shoreham Vessel

Showing Exponential Distribution Along with

Uncertainties

6.17.
-

Table 6.11 . Len2ths of Small and Lare Flaws in SMAW and ReDair Welds of Shoreham Vessel

TW- Bead Depth

Size, Length, Length- Size, Frac Length-TW

ID Table Specimen Length Figure mm mm TW mm Bead Frac Bead

13 i.1 COG 58.4 1.6 7.0 9.0 2.0 3.5 2.0 0.6

14 D. I Bl8OC-2 41.5 D.3 7.0 9.0 2.0 3.5 2.0 0.6

47 T._ C270D 117.4 T.9 8.0 11.0 3.0 3.5 2.3 0.9

59 D.1 B 18OC-2 41.5 D.4 9.0 12.0 3.0 3.5 2.6 0.9

32 G.1 COE 55.2 G.i 6.0 10.0 4.0 3.5 1.7 1.1

5 _ T.1 C270D 117.4 T.3 4.0 10.0 6.0 3.5 1.1 1.7

36 F.1 COD 19.4 F.1 4.0 11.0 7.0 3.5 1.1 2.0

37 G. COE 55.2 G.5 4.0 11.0 7.0 3.5 1.1 2.0

50 G.l COE 55.2 G.4 4.0 12.0 8.0 3.5 1.1 2.3

60 T.1 C270D 117.4 T.11 4.0 13.0 9.0 3.5 1.1 2.6

80 I.1 COG 58.4 1.1 5.0 14.0 9.0 3.5 1.4 2.6

96 T. I C270D 117.4 T.8 4.0 16.0 12.0 3.5 1.1 3.4

97 T.1 C270D 117.4 T.13 4.0 16.0 12.0 3.5 1.1 3.4

98 T.1 C270D 117.4 T.12 4.0 16.0 12.0 3.5 1.1 3.4

114 M.A C120E 53.6 M.9 7.0 20.0 13.0 3.5 2.0 3.7

142 P.1 C180B 71.7 P.7 4.0 57.0 53.0 3.5 1.1 15.1

6.2.9 Length Distribution for Large SAW

Flaws in PVRUF Vessel

This section addresses the lengths of large flaws

in SAW welds of the PVRUF vessel. The

selected dataset addressed only those flaws in the

PVRUF welds that were subjected to the most

thorough of the validation efforts (Schuster et al.

2000a, Table 9 and Figure 4). The selection

excluded small flaws that were detected only by

the examinations performed with the early

SAFT-UT examinations at ORNL. The selection

also excluded flaws that were validated by the

weld normal UT examinations but not further

validated by RT and destructive evaluations.

These restrictive requirements for validation

resulted in the most accurate measurements of

flaw dimensions but meant that only 9 small flaws

remained upon which to base a flaw length

distribution. The relatively small number of flaws

with high-accuracy length measurements was

judged to be insufficient to develop separate

length distributions for large versus small flaws.

Therefore, a single depth distribution was used to

describe the lengths of both small and large flaws

in SAW welds of the Shoreham vessel.

Figure 6.7 showed the length data for small and

large SAW flaws in the PVRUF vessel. The

length distribution was calculated from

Equation (6.3) as described in Section 6.2.5. The

parameters of the gamma function are based on

the data of Table 6.6. The values were

established to be al = 0.53846 and a 2 = 9, where

(from Table 6.8) the parameter al is calculated as

the sum of the nine values of the quantity (t - a)/A

and Ct2 corresponds to the number of data points

in Table 6.8.

6.2.10 Length Distribution for Large

SMAW and Repair Flaws in PVRUF

Vessel

This section addresses the lengths of large flaws

in SMAW and repair welds of the PVRUF vessel.

The selected dataset addressed only those large

SMAW and repair flaws in the PVRUF welds

(Schuster et al. 1999). This selection excluded

large flaws that were detected and sized by the

examinations performed with the weld normal UT

examinations but not further validated by SAFTUT and destructive evaluations after being

removed as cube samples. The dataset resulted in

6.18
a relatively small number of measurements of

flaw lengths, which gave a total of 5 large flaws

upon which to base a flaw length distribution.

The length distributions were calculated from '

Equation (6.3) as described in Section 6.2.5. The

parameters of the gamma function were based on

the data of Table 6.12 The values were

established to be a, = 5.428 and a2 = 5, where

(from Table 6.12) the parameter a, is calculated

as the sum of the five values of the quantity

- a)/A and a2 corresponds to the number of data

points in Table 6.12. The resulting distribution

function is shown in Figure 6.13 along with the

data and results of the uncertainty evaluation.

6.2.11 Length Distribution for Large SAW

Flaws in Shoreham Vessel

This section addresses the lengths of large flaws

in SAW welds in the Shoreham vessel. The

selected data are reported in Schuster et al.

-(1999). These large flaws were detected and

sized by the examinations performed with the

weld normal UT examinations but not further

validated by SAFT-UT and destructive

evaluations. The dataset gave a total of 25 large

flaws upon which to base a flaw length

distribution.

-The length distributions was calculated from

Equation (6.3) as described in Section 6.2.5. The

parameters of the gamma function for small SAW

in 'the Shoreham vessel 'were based on the data of

Table 6.13. The values were established to be a,

= 47.80 and a2 = 25, where (from Table 6.13) the

parameter al is calculated as the sum of the

25 values of the quantity (,e - a)/A and a2

corresponds to the number of data points in

Table 6.13. The resulting distribution function is

shown in Figure 6.14 along with the data and

results of the uncertainty evaluation.

6.2.12 Length Distribution for Large

SMAW and Repair Flaws in

Shoreham Vessel

The available length measurements for small and

large SMAW and repair flaws were combined

into a single dataset. The resulting distribution

including uncertainties is described in

Section 6.2.8.

A

I.

1.541 1-

.1.0 0.0 1.0 2.0 o

(Length - Depth)/Bad

so so

Figure 6.13. Lengths of Large Flaws in SMAW and

Repair Welds of PVRUF Vessel Showing

Exponential Distribution Along with Uncertainties

Table 6.12. Lengths of Large Flaws In SMAW and Repair Welds of PVRUF Vessel

Frac >

Bead TW- . - TW L-TW L-TW

Size, Size, Length, Aspect L-TW, Frac Large=2 Frac Frac

Label mm mm mm Ratio mm Bead Small=1 Bead Bead

5-12AC5&6 REPAIR 3.50 17.0 14.0 0.8235 -3.00 4.8571 2 -0.8571 1.0000

5-12AC3 REPAIR 3.50 5.0 5.0 1.0000 0.00 1.4286 2 0.0000 0.8000

5-lAB14ibic SMAW 3.50 5.0 8.0 1.6000 3.00 1.4286. 2 0.8571 0.6000

5-12AC2 REPAIR 3.50 12.0 15.0 1.2500 3.00 3.4286 2 0.8571 0.4000

5-11OEB3ibiic SMAW 3.50 4.0 17.0 4.2500 13.00 1.1429 2 3.7143 0.2000

6.19
Table 6.13. Lengths of Small Flaws in SAW Welds of Shoreham Vessel

Bead Flaw Flaw Depth Length Minus

Weld Size, Depth, Length, Length Minus Frac Depth Frac Fraction

Label Type mm mm mm Depth, mm Bead Bead > x

200 SAW 5.0 7.0 8.0 1.0 1.400 0.200 1.000

39 SAW 5.0 9.0 10.0 1.0 1.800 0.200 0.960

197 SAW 5.0 8.0 10.0 2.0 1.600 0.400 0.920

123 SAW 5.0 9.0 11.0 2.0 1.800 0.400 0.880

42 SAW 5.0 9.0 11.0 2.0 1.800 0.400 0.840

116 SAW 5.0 6.0 9.0 3.0 1.200 0.600 0.800

272 SAW 5.0 6.0 10.0 4.0 1.200 0.800 0.760

207 SAW 5.0 6.0 11.0 5.0 1.200 1.000 0.720

65 SAW 5.0 6.0 11.0 5.0 1.200 1.000 0.680

7 SAW 5.0 7.0 12.0 5.0 1.400 1.000 0.640

31 SAW 5.0 8.0 13.0 5.0 1.600 1.000 0.600

2 SAW 5.0 10.0 15.0 5.0 2.000 1.000 0.560

5 SAW 5.0 32.0 38.0 6.0 6.400 1.200 0.520

6 SAW 5.0 6.0 13.0 7.0 1.200 1.400 0.480

112 SAW 5.0 6.0 13.0 7.0 1.200 1.400 0.440

13 SAW 5.0 21.0 28.0 7.0 4.200 1.400 0.400

32 SAW 5.0 6.0 15.0 9.0 1.200 1.800 0.360

8 SAW 5.0 6.0 18.0 12.0 1.200 2.400 0.320

148 SAW 5.0 7.0 20.0 13.0 1.400 2.600 0.280

214 SAW 5.0 6.0 20.0 14.0 1.200 2.800 0.240

186 SAW 5.0 10.0 25.0 15.0 2.000 3.000 0.200

103 SAW 5.0 14.0 30.0 16.0 2.800 3.200 0.160

101 SAW 5.0 6.0 25.0 19.0 1.200 3.800 0.120

157 SAW 5.0 6.0 38.0 32.0 1.200 6.400 0.080

111 SAW 5.0 6.0 48.0 42.0 1.200 8.400 0.040

A

3t

a:

o 1 2 3 4 5 4 7 8 9 10 11 12 13 14 15 16

(Length - Depth)yBead

Figure 6.14. Lengths of Large Flaws in SAW

Welds of Shoreham Vessel Showing Exponential

Distribution Along with Uncertainties

6.20
7 BASE METAL FLAWS -DATAAND.STATISTICAL

CORRELATIONS

The flaw distribution model provides a total of

three input files for the FAVOR code, with one of

these files describing flaws in base metal regions.

The treatment of base metal flaws is documented

-in this section along with a discussion of the

available flaw data and other sources of

information that support the model.

7.1 Approach and Assumptions

Basic considerations and assumptions related to

the development of the flaw distributions for base

metal regions'are described in this section.

Scope of Generalized Distribution - Available

data to PNNL for base metal flaws were 'obtained

from plate material from four specific vessels

(PVRUF, Shoreham, River Bend II, and Hope

Creek II). The flaw distribution model, however,

was developed to be applied on a generic basis for

any vessel constructed with rolled plates. The''

model was not intended to apply to vessels

constructed with forged rings. Flaw distributions

as predicted by the model were intended to apply

to material of the surface regions of plates down

to a depth of about 1 in., because this material

region is of primary concern to vessel integrity for

conditions of pressurized thermal shock.

The FAVOR code addresses three categories of

flaws that have the potential to impact the

integrity vessels that have low-toughness base

metal:

(1) flaws distributed within the volume of the

base metal with their origins from the

production processes for the plates or

forgings-These flaws are addressed here in

this section.

(2) weld flaws located along the fusion zone,

which can propagate into embrittled base

metal-These flaws were addressed in.

Section 6 on distributions of weld flaws.

(3) flaws within cladding material, which can

extend to the clad-to-base metal interface

' such to have a potential to propagate into the

base metal-These flaws are addressed in

Section 8 as clad flaws.'

The present methodology does not address underclad cracks in the base metal that originate during

the cladding process.

Flaws per Unit Volume Versus Flaws per Unit

Area - The FAVOR code describes flaw densities

in terms of flaws per unit volume. This approach

is consistent with PNNL's treatment of flaws in

base metal regions. The input files for FAVOR

are based on flaws per unit volume.

Use of Data Versus Models and Expert

Elicitation - The approach taken in developing

base metal flaw distributions was to use measured

data to the maximum extent possible and to use

results of the expert judgment elicitations only

when data are inadequate. For base metal flaws,

there were only a limited amount of data on

observed flaws. The quantity of data was limited

because PNNL could examine only a small

volume 'of base metal relative to the volume of

such material in the beltline of a typical vessel. In

addition, there were relatively few flaws in

volumes of the examined base metal. Lacking an

adequate body of data, the expert elicitation

(Jackson and Abramson 2000) was an important

element that was used to estimate flaw densities

and size distributions. In this regard, the

measured data were used mainly as a benchmark

against the inputs derived from the expert

judgment elicitation.

Vessel-to-Vessel Variability - Examinations of

plate material from the four vessels showed

significant vessel-to-vessel variations in flaw

7.1
densities. However, flaw depth distributions in

the four vessels were found to follow a common

trend. The approach was to develop a single flaw

distribution that was consistent with both the

inputs from the expert elicitation and trends of the

available data. The objective was to describe the

flaws in the plate material of a so-called average

vessel.

Locations of Flaws Relative to Vessel Inner

Surface - Weld flaws were assumed to be buried

flaws with the locations of the flaw inner tips

relative to the vessel inner surface distributed in a

random manner. As a limiting case, a flaw could

have its inner tip at the clad-to-base metal

interface, a condition that would have a

statistically zero probability of occurrence.

Information from the expert elicitation clearly

indicated that, compared to near-surface regions,

the midsections of rolled plates consistently have

larger flaw densities and larger flaw sizes. The

plate flaw distribution was developed to address

only the near-surface region because of the

concerns for this region from the standpoint of

pressurized thermal shock. It was assumed that

flaws in the plate mid-section, even with their

greater densities and sizes, are relatively

unimportant to vessel integrity.

Flaw Orientation - The base metal flaw

distribution was intended to address only flaws

with significant through-wall dimensions. The

approach was to neglect flaws of no structural

significance, which have orientations parallel to

the vessel surfaces. The PNNL inspections of

plate materials selected techniques for the

SAFr-UT examinations that were optimized to

detect and size small flaws with through-wall

dimensions rather than larger flaws that are

parallel to the vessel surface.

Crack Shape - All plate flaws were assumed to

be crack-like flaws without detailed consideration

of the sharp nature of flaw tips. It was recognized

that the treatment of flaws by FAVOR assumes

planar flaws of ideal elliptical shape. In FAVOR,

the plane of the cracks and the major and minor

axes of the flaws are aligned with the radial and

axial coordinates of the vessel. The PNNL

measurements of plate flaws by SAFT-UT

provided dimensions of flaws in terms of an

enclosing box that would contain the flaw.

A typical plate flaw is shown in Figure 7.1. As in

the case of weld flaws, the dimensions of the

enclosing box provide a realistic representation of

the overall flaw dimensions. However, the

FAVOR assumption of idealized elliptical cracks

is a conservative treatment of flaws, as shown by

Figure 7.1. The flaw of Figure 7.1 is a cluster of

crack-like flaws with complex interactions

between the individual features of the flaw.

Current fracture mechanics models do not permit

treatment of detailed geometries of the complex

flaws such as shown in Figure 7.1; consequently,

the use of simplified fracture mechanics models is

believed to be necessary and reasonable. Other,

less conservative fracture mechanics models

could be developed in the future, particularly if

the flaws within base metal are the most limiting

type of flaw to the integrity of vessels with an

embrittled plate material.

TW

1

Figure 7.1. A Flaw Detected in Plate Material

Flaw Orientation - Flaws in base metal were

assumed to have both axial and circumferential

orientations. FAVOR assigns an axial orientation

to 50% of the base metal flaws and a

circumferential orientation to the remaining 50%

of the flaws.

7.2
Truncation of Flaw Distributions - Flaw inputs

for use with the FAVOR code wereiruncated to

avoid excessive extrapolations of the statistically

based flaw depth distributions. The truncations

for base metal flaws were such to preclude flaws

that were greater than about two times the depth

dimensions of any of the flaws observed in

PNNL's examinations of base metal. This

truncation value has been assigned as 11 mm.

Service Related Flaws -IThe flaw distribution

methodology for base metal flaws addresses only

fabrication flaws, with no consideration of i- -

service-initiated cracks or service-induced growth

of fabrication flaws (by fatigue or stress corrosion

cracking). In this regard, the material examined

by PNNL was from vessels that had never been

placed into operation. However, inservice

inspections of PWR vessels and fracture

mechanics calculations of fatigue crack growth -

provide no reason to believe that crack initiation

or growth for flaws in the vessel beltline region

are likely.

7.2 Inputs from Expert Elicitation

Part of the expert elicitation (Jackson and

Abramson 2000) addressed the subject of flaws in

base metal regions, including both plate and

forging materials. Many of the questions covered

qualitative factors such as details regarding

processes used to manufactuiie plates and

forgings. Other questions related to mechanisms

that are most likely to cause flaws in base metal

and the most likely locations relative to the inner

surface of the vessel for various flaw types to

occur.

The experts also were requested to make '

quantitative estimates of flaw occurrence rates.

These questions were posed inmterms of relative -

estimates. During the expert solicitation process,

PNNL described the examinations and flaws

observed for the PVRUF vessel. It was therefore

convenient to make the relative 'estimates in terms

of the PVRUF vessel. Estimates provided by the'

experts for the numbers and sizes of flaws in

plates and forging relative to the flaws observed

in the welds of the PVRUF vessel are shown

earlier inmFiguir'e 4.1. Large base metal flaws were

defined as flaws with through-wall depth

dimensions greater than a typical bead dimension

(6 mm for SAW welds).

The chart of Figure 4.1 'indicates the rather large

orange of individual estimates'provided by

members of the expert panel. Using standard

practices to evaluate the variability in data from

the elicitation processes, the data were evaluated

in terms of minimum and maximum values,

median values, and quartiles'('which indicate the

range of values that cover estimates from 50% of

the experts).- Experience has shown that, even

with a wide range of estimates from experts on a

panel, the median values of estimates tend to

provide a reasonable and consistent basis for

decision-making.

The flaw distribution model used the median

values of relative flaw densities from Figure 4.1.

The density of small flaws (<6 mm) in plate

material was a factor of 10 less than the flaw

density for the PVRUF welds. The density of

small flaws (>6 mm) in plate material was a

factor of 40 less than the flaw density for the

PVRUF welds. These estimates were compared

for consistency with the data for plate flaws from

the PNNL examinations of plate materials from

various vessels.

7.3 Flaw Data from PNNL Base

Metal Examinations

Table 7.1 presents data from PNNL's

examinations of plate materials from the PVRUF,

Shoreham, Hope Creek II, and River Bend 1I

vessels. These examinations detected a total of

175 flaws in 0.063 m3 (2.2 f10) of examined

material: Only 9 flaws had through-wall depth

dimensions as large as 4 mm. No observed flaws

had depth dimensions as large as 6 mm.

Figure 7.2 is a plot of the base metal flaw rates as

a function of the measured through-wall depth

dimensions. Also shown are thetflaw rates for

welds from the examinations in the PVRUF and

7.3
- -

Table 7.1. Flaws Detected and Sized in PNNL Examinations of Inner 1 Inch of Plate

Matprial (frnm DPePmhPr 72Di mnnthiv rennrt SAT.rr-TTT erxmin-atinn nfhaep metfals

Shoreham Hope Creek River Bend

Cum Cum Cum PVRUF Cum Combined Data

Flaw Depth, Indication Indication Indication Indication Cum Indication

mm Rate, per m Rate, per n3 Rate, per m3 Rate, per n3 Rate, per in

1.0 250 5000 1420 7000 2783

4.0 0.0 222 83 357 142

6.0 0.0 0.0 0.0 0.0 0.0

Volume

Examined, m3 0.016 0.009 0.024 0.014 0.063

I 10,000 Avenge of Base Metal

E

1 ,000\ PVRUF Wold

100ld h 

* 100 4 10 12 1

n: Base Metal Rivor Be W

10

0 2 4 a S 1a 12 14

Flaw Depth, mm

Figure 7.2. Flaw Frequencies for Plate Materials

with Comparisons to Data for Weld Flaws

Shoreham vessel. The flaw rates for all the plate

materials were less than the flaw rates for welds.

There was a wide range of flaw rates for the plate

materials with a factor of 30 difference between

the highest rate (PVRUF plate material) and the

lowest rate (Shoreham plate material). The

average rate indicated in Figure 7.2 was obtained

by combining the data from all four vessels. This

rate was a factor of about 5 less than the flaw rate

for the PVRUF welds.

The average flaw rate from the plate examinations

is generally consistent with the factor of 10 ratio

of flaw rates from the median of the estimates

from the expert elicitation. It is also noted from

Figure 7.2 that the slopes of the curves for plate

materials are nearly the same as for the weld

metal of the PVRUF and Shoreham vessels. It

was therefore concluded that the 10:1 ratio of

flaw rates of welds versus plates, as provided by

the expert elicitation, is consistent with the

limited amount of data. This 10:1 ratio was used

to generate flaw distributions for use as inputs to

the FAVOR code.

There were no observed flaws greater than 6 mm

from the PNNL examinations of plate material.

Extrapolation of the flaw rate curves of Figure 7.2

would predict that no flaws would be expected

from the examination of 0.063 m3 of plate

material. Therefore, the 40:1 ratio from the

expert elicitation for densities of large flaws in

welds versus plate material is not inconsistent

with the available data. However, the data do not

allow a quantitative evaluation of the 40:1 ratio

from the expert elicitation.

7.4 Flaw Estimation Procedure for

Plate Materials

Flaw frequencies for use as inputs to the FAVOR

code were generated using simple adjustments to

the flaw rates that were estimated on the basis of

the data for flaws in the PVRUF vessels. In these

calculations, it was assumed that the welds

consisted of SAW, SMAW, and repair weld

material in the percentages of 93, 5 and 2,

respectively. The weld bead dimensions were

assigned as 6 mm, 3.5 mm, and 3.5 mm,

respectively, for the SAW, SMAW, and repair

welds. Flaw densities for small and large flaws

were reduced by factors of 10 and 40. Flaw depth

distributions were assigned using the same

distribution functions developed for the PVRUF

vessel welds. A truncation was made for large

flaws by assigning a zero flaw rate for all flaws

7.4
-. I,

with depth dimensions greater than 11 mm in

through-wall depth dimension.

Aspect ratios for base metal flaws were assigned

to be the same aspect ratios that were established

on the basis of the PVRUF data. The flaw rates

for small weld flaws are dominated by the

contribution from SAW materials, for which the

PVRUF data indicated flaws of relatively small

aspect ratios (a distribution with most flaws

having aspect ratios of about 1:1). This 1:1 aspect

ratio turns out to be generally consistent with the

observed flaws in plate material, as shown by

Figure 7.1. In the case of large flaws, the aspect

ratio distributions based on the PVRUF data

predicted flaws with greater aspect ratios than the

1:1 trend of the small flaw data. The PNNL

examinations did not detect any large flaws

(>6 mm) in plate material. There is, therefore, no

empirical basis to evaluate the extent to which the

assignment of aspect ratios >1:1 is conservative

for large flaws.

The treatment of uncertainties in flaw distribution

inputs to FAVOR for base metal regions is the

same as that for the weld regions as established

for the PVRUF flaw regions. The development of

an uncertainty treatment based on evaluations of

data for base metal flaws could be performed in

the future. This evaluation is recommended, once

PNNL's examinations of base metal materials and

the validations of the observed flaws are

completed.

7.5
8 CLAD FLAWS - DATA AND STATISTICAL CORRELATIONS

The flaw distribution model provides three input E 7 -l, 

files for the FAVOR code; one of these files

describes surface-breaking flaws-the flaws in.,

the clad metal of the vessel. The treatment of clad

flaws is documnen'ted in this section, as are the a 4'

available flaw data and other sources of

information that support the model.

8.1 Approach and Assumptions

The objective was to estimate the expected

number and sizes of fabrication flaws in the

beltline cladding of a PWR vessel. Consistent

with the assumptions of the FAVOR code, the

clad material was assumed to have sufficient

toughness to preclude fracture for flaws located

entirely within the clad. Attention was therefore

directed to (1) surface-breakirg flaws that

penetrate the full thickness of the clad and extend

up to the underlying embrittled weld metal or

base metal and (2) large buried flaws in the

cladding that extend up to the clad/base metal

interface but do not entirely, penetrate the

thickness of the clad. An example of the second

category of clad flaw is shown in Figure 8.1 as

seen in a cross section of clad from the PVRUF

vessel.

8.2 Sources of Information

Cladding Flaws

The estimates for flaws in cladding were based on

four sources of information:

(1) data on observed flaws from destructive and

nondestructive examinations of the PVRUF

vessel (Schuster et al. 1998, 1999, 2000a)

(2) simulations of clad flaws with thei'

PRODIGAL computer code (Chapman and

Simonen 1998) ' -

Figure 8.1. Examples of Flaws in Cladding of

PVRUF Vessel

(3) examinations of cladding material performed

at Bettis Laboratory (Li and Mabe 1998)

(4) an NRC expertjudgment elicitation on vessel

flaws (Jackson and Abramson 2000).

The measured data and/or estimated occurrence

frequencies of clad flaws are summarized in

Figure 8.2. The data in Figure 8.2 were

normalized to compare information from various

sources on a common basis. Flaw depths were

expressed as a fraction of the through-wall

dimensions of weld beads. The numbers of flaws

were expressed as flaws per meter of weld bead

length. This approach followed the methodology

of the PRODIGAL flaw simulation model.

Significant variability is seen in the curves of

Figure 8.2, which reflects the uncertainties in flaw

occurrence rates.

8.1
I

la

U.

1.1.02 -

1.E.01 i

1.1-01 -

1.5-02 -

I.E-42 -

1.E-04 -

1.E-05-

1.1-06

1.E471 1.5-00

IPVRL Cad If. l_ -3 MA. .I W.M .- 4

"w UW _ (D

-~ d~ p.. PS" EK- aPOOWO 0.1

a. X--G/SIG

(SAW Wma PT

. | | * @ * | * | * | | * | |

. 0.2 0.4 s U 1.0 1a2 1.4 1.6 1.6

Through-WalI Extent. Fraction of Bead Size

Figure 8.2. Summary of Data on Flaws in Vessel

Cladding

8.2.1 PVRUF Data

Data in Figure 8.2 for the PVRUF vessel were

reported in Schuster et al. (1998). For

comparison purposes, flaw data for the seam

welds of the PVRUF vessel also are displayed in

Figure 8.2. The volume of examined PVRUF

clad was 0.027 in3 . The clad consisted of

submerged arc strip clad, manual metal arc clad,

and multi-wire clad. Table 8.1 presents the flaw

data for the PVRUF clad material. Two PVRUF

data points in Figure 8.2 at larger flaw depths

corresponded to the two largest flaws observed in

the PVRUF clad. The single data point at zero

flaw depth represents the large number of small

flaw indications that were observed but were too

small for accurate size measurements. The

PVRUF data included a large number of flaws

less than 2 mm in depth, for which it was not

possible to measure flaw sizes with any degree of

accuracy.

Although a large numbers of flaws were detected

in the PVRUF cladding, none of these flaws was

of the surface-breaking category. The occurrence

frequency of surface-breaking flaws is much

lower than the frequency for buried clad flaws. It

was inappropriate, however, to assign an

occurrence frequency of zero for surface flaws

because of the limited amount of examined vessel

cladding.

Two bounding approaches were used to estimate

flaw frequencies for the PVRUF cladding, which

gave estimates of flaw densities that differed by a

factor of about 10. The first approach assumed

that all of the clad was deposited by manual metal

arc welding. The total length of weld bead was

calculated accordingly to establish the lower

curve of Figure 8.2. The second approach was

based on the observation that the majority of

flaws, including all of the flaws having depths

greater than 2 mm, were found within a relatively

small region where the PVRUF clad was applied

by the multi-wire process. This region was at a

thickness transition between the component rings

of the vessel. Local areas of changing diameter

evidently presented difficulties to the automatic

welding procedure, which resulted in lack-offusion flaws between adjacent weld runs. Such

flaws were not observed in cladding deposited

over vessel regions of uniform diameter.

Table 8.1. Flaws in Cladding of PVRUF Vessel

Number of Flaws Number of Flaws

Flaw Depth Number of Depth > a, per Depth > a, per

Flaw Depth, Fraction of Number of Flaws with Meter of Examined Meter of Beltline

mm Bead Flaws Depth > a Weld Bead Weld Bead

0.00 0.000 0 1204 5.35 0.447

0.10 0.017 1200 1204 5.35 0.447

3.00 0.500 3 4 0.0177 0.00148

4.00 0.667 1 1 0.0044 0.00037

Data from NUREG/CR-6471 Vol. 3 Length of Examined Clad Bead = 222 meters

Clad Thickness = 6 mm Length of Beltline Clad Bead = 2690 meters

Width of Strip Clad Bead = 20 mm

8.2
8.2.2 Data from Bettis Laboratory

Li and Mabe (1998) described tests performed on

two types of weld-deposited cladding. The

examined cladding was not from actual vessels

but was fabricated to simulate a range of cladding

qualities that might occur in practice. The

examinations were performed destructively on

relatively small samples of material (9.5 cm3). In

one case, the cladding was deposited by shielded

metal arc welding. This material was intended to

represent a bounding case of poor quality

cladding, with steps being taken (e.g., no special

grinding at the locations of weld stop/starts) to*

increase the potenitial for flaws: In the other case,

the cladding was deposited by a gas tungsten arc

process (GTA-HW) that was intended to decrease

the potential for flaws.

Figure 8.2 shows data points and data correlations

from the Li and Mabe work Very few flaws were

found in the higher quality GTA-HW welds. The

curve for this clad material as shown in Figure 8.2

was a correlation based on the data for the very

small flaws that were detected. An extrapolationof this curve falls between the two curves for the

PVRUF cladding.' In contrast, the data for flaw

occurrence rate in the shielded metal arc cladding

are more than a factor of 10 above the observed

number of flaws in the PVRUF cladding.

8.2.3' Expert Judgment Elicitation

As part of the NRC expert judgment elicitation

(Jackson and Abramson 2000), the members of

the expert panel were asked to estimate the

number and sizes of flaws in cladding relative to

the flaws in the main seam welds of a vessel.'

Although the experts provided awide range of

estimates, a significant subset of the experts

provided estimates'inia mid range between the

extreme values. The data were treated in a

statistical manner to establish median values,

which served as the basis for establishing best-'

estimate distributions of flaw occurrence rates.

The scatter in the data provided an indication of

the uncertainty in the estimates. The rationale for

the best-estimate'values as expressed by the

experts were as' follows:

(1)'Cladding should have fewer flaws than the

corresponding amount of seam weld material

by a factor of about 2. The experts explained

that welding of cladding to a vessel surface is

performed under relatively favorable ' '

conditions of good access, compared to the

more difficult access for the narrow gaps of

the weld geometries for seam welds. --

i(2) The-cladding should have essentially no'flaws

greater than the dimension of a single weld

bead. Therefore, the'decrease in slope of the

flaw depth distribution curve for the seam

welds (as seen in Figure 8.2) should be absent

for clad flaws.

Although Figure 8.2 does not present a specific

curve from the expert judgment process, such acurve could be constructed by adjusting the curve

labeled "PVRUF seam weld." This curve would

be a straight line with a constant slope, equal to

the slope of the seam weld curve for the flaw

'depths ranging from 0 to 0.5 of the weld bead

'size. In addition, the curve for clad flaws would

be shifted downward by a factor of 2 relative to

the PVRUF curve for seam welds. A curve from

the'expert judgment process would fall between

of the two bounding curves of Figure 8.2 based on

the PVRUF data for clad flaws. -

8.2.4 PRODIGAL Predictions

Calculations were performed with the'

PRODIGAL code (Chapman and Simonen 1998)

to estimate flaw sizes and densities for cladding ' material.' The model of this code includes

predictions that'specifically address flaws in'

cladding.' The development of a clad model was a

significant pa'rt of building the PRODIGAL code

(Chapman and Simonenl 998).'. Parameters used

to quantify"the frequencies for flaws in cladding

were established through detailed discussions'

with a panel of U.S. experts on welding and

vessel fabrication.

8.3
8.2.4.1 Scope of Calculations

The PRODIGAL calculations reported here

addressed both manual metal arc cladding and

submerged arc (strip) cladding. Table 8.2 lists

parameters for the PWR vessel addressed by the

PRODIGAL calculations. Calculations were first

performed by assuming no dye penetrant

examination of the clad surface and then by

simulating a dye penetrant examination (assuming

repairs of the detected surface-breaking defects).

from the PVRUF vessel. The exact configuration

of weld beads is not critical to the present

evaluations because the results were normalized

such that flaw depths were expressed as fractions

of weld bead thickness. Flaw frequencies were

expressed in terms of flaws per unit length of

weld bead. This allowed combinations of clad

thickness and weld bead dimensions as they exist

in other vessels to be addressed.

8.2.4.2 Results for PRODIGAL Runs

Table 8.2. Parameters of Representative PWR

Reactor Pressure Vessel for PRODIGAL

Calculations

Parameter Value

Vessel Inner Diameter 4.4 m

Beltline Height 4.4 m

Number of Axial Welds in Beltline 3

Number of Circumferential Welds in 1

Beltline

Width of Weld at Vessel Inner Surface 5 cm

Total Beltline Surface Area _ 60.8 __

Length of Circumferential Welds in 13.8 m

Beltline

Surface Area of Circumferential 0.69 m

Welds in Beltline

Length of Axial Welds in Beltline 13.2 m

Surface Area of Axial Welds in 0.66 rn

Beltline

Total Clad Thickness 11 mm

Number of Clad Layers 2

Number of Runs per Layer Over Weld 7

Number of Clad Start/Stops per Meter 26

of Weld (manual clad)

Results from the PRODIGAL calculations for the

selected region of cladding are given in Tables 8.3

and 8.4. These calculations addressed both

submerged arc and manual metal arc clad along

with the benefits of dye penetrant (PT)

examinations of the clad inner surface. The PT

examinations were predicted to reduce the

number of surface-breaking flaws by a factor

approaching 100. The predicted densities of

buried flaws were much higher than the densities

for surface-breaking flaws (Table 8.3 versus

Table 8.4), which is consistent with the data from

examinations of clad in the PVRUF vessel.

8.2.4.3 Comparison of Observed Flaw

Data with PRODIGAL Predictions

Figure 8.2 shows comparisons of flaw frequencies

as predicted by PRODIGAL with data from

experimental studies. All comparisons were made

on the basis of flaw depths expressed as a fraction

of the weld bead thickness. Flaw occurrence rates

were expressed in terms of flaws per linear meter

of weld bead. For flaw depths greater than about

half a weld bead thickness, the data are seen to

generally agree with the PRODIGAL predictions.

It was not appropriate to make comparisons for

flaws having depths less than about half a weld

bead because the PRODIGAL methodology was

not intended to address these very small flaws.

Figure 8.2 shows (for flaw depths greater than

about 50% of the clad thickness) that PRODIGAL

predicts flaw frequencies that are consistent with

the range based on the PVRUF data.

All calculations assumed a total clad thickness of

11 mm, consisting of two weld layers. The

modeled region of the clad surface was assumed

to be 52 mm wide. This region of clad included

7 weld beads for each weld layer. For the manual

metal arc weld, there were 26 start/stops during

the cladding of the modeled region that had a

width of 52 mm and length of 1 m (surface area of

0.05208 m2), giving a total weld bead length of

14m.

The number and sizes of weld beads for the

PRODIGAL calculations were based on

dimensions as observed on cross-sectioned welds

8.4
Table 83. RR-PRODIGAL Predictions for Surface-Breaking Flaws in Cladding by Submerged Arc

____ Process (with an without PT)

No PT Inner Surface, With PT Inner Surface,

Depth, Flaws per Meter of Flaws per Meter of Bead

N Flaw Depth, mm Fraction of Bead Bead Depth > a with Depth > a

I 1.1 0.208 2.743E-04 5.486E-06

2 3.4 0.623 2.486E-04 4.971E-06

3 5.7 1.038 5.714E-06 1.143E-07

4 8.0 1.453 0.000E+00 0.000E+00

5 10.3 1.869 0.000E+00 0.OOOE+00

6 12.6 2.284 0.000E+00 0.000E+00

7 14.8 2.699 - 0.000E+00 0.000E+00

8 '17.1 3.114 0.000E+00 0.OOOE+00

9 19.4 3.530 0.000E+00 0.000E+00

a10 - 21.7 3.945 0.000E+00 0.OOOE+00

Table 8.4. RR-PRODIGAL Predictions for Buried Flaws In Cladding Applied with Manual Metal Arc

'__ '__'_ _ _; and Submerged Arc Process

Submerged Arc Shielded Metal Arc

i Buried Flaw, Buried Flaw, Flaws per

Depth, Flaws per Meter of Meter of Bead

N Depth, mm Fraction of Bead Bead Depth > a with Depth > a

1 1.1 0.208 1.999E-03 9.736E-03

2 3.4 . 0.623 1.760E-03 8.074E-03

3 5.7 1.038 5.143E-05 1.369E-03

4 8.0 1.453 5.714E-06 3.286E-05

5 10.3 1.869 0.000E+00 0.000E+00

6 12.6 2.284 0.OOOE+00 0.000E+00

7 14.8 2.699 0.000E+00 0.000E+00

8 17.1 3.114 0.000E+00 0.000E+00

9 19.4 3.530 0.000E+00 0.000E+00

10 21.7 3.945 0.000E+00 0.000E+00

8.2.5 Vessel-Specific Considerations

The data in' Figure 8.2 indicate considerable

variability and uncertainty associated with

estimates of cladding flaws. Some of the

variability is due to effects of the different

processes used to apply clad to vessel surfaces.,

Because cladding is considered in'design to make

no contribution to vessel integrity, more

variations in the quality of clad welding may

occur than for other welds. -

The data from the PVRUF vessel show significant

variability in clad quality, eveni within a'given '

vessel. The PRODIGAL model (based on an

elicitation of welding experts) indicates that

machine-welded strip clad should have fewer

welding defects than manual cladding. It has

been observed that one region of the PVRUF

vessel (thickness transition) had an unusually

large number of flaws. The greater number of

flaws in this region is not considered to be

particularly significant because the embrittled

region of the PVRUF vessel beltline would be

outside the thickness transition region.

An important consideration is that of flaw

orientation. For machine-deposited strip clad, the

significant flaws (as evidenced by the PVRUF

data) are circunferen'tial in orientation. Such

flaws should have a minimal impact on the'

integrity of axial welds (and also the plate

8.5
regions) of a vessel. Manual cladding to

circumferential welds also will have

circumferential flaws as the expected orientation.

Manually applied cladding can have a large

number of small axial flaws associated with

start/stops of the stick-welding process, while

machine-deposited cladding is likely to produce

fewer flaws because such cladding usually

consists of only one weld layer. On the other

hand, there is a much greater likelihood of

through-clad flaws for single-layer clad than for

clad with two or more layers. Manual cladding

inevitably has more than one layer, which reduces

the likelihood of through-clad flaws in manual

clad. However, as indicated by the PVRUF data,

manual clad often had a greater thickness than the

machine cladding. As such, a through-clad flaw

in the manual clad would have a greater impact on

structural integrity than a through-clad flaw in a

single-layer machine-deposited clad.

8.3 Flaw Length Distribution for

Clad Flaws

It was initially assumed that all clad flaws had

large aspect ratios (infinity) because observed

clad flaws tended to be relatively long. Later

worka compiled data on more exact measurements

for the lengths of clad flaws because the FAVOR

code can address surface flaws with aspect ratios

other than infinity (i.e., discrete aspect ratios of 2,

6, 10, and infinity).

Tables 8.5 through 8.11 were reproduced from

Schustera to document the data on measured

lengths of clad flaws for the PVRUF and Hope

Creek Unit II vessels. Most of the inspected

cladding was deposited as strip clad to the

PVRUF vessel in a single pass using a welding

machine giving a thickness of 3/16 in. Manual

cladding was deposited over circumferential

welds, over areas that were difficult to weld with

the cladding machine, and for repairs to the clad

surface.

Table 8.5 lists the amount of clad and product

forms, along with a summary of the early

unvalidated inspection results for the PVRUF

vessel (Schuster et al. 1998). Table 8.6 gives

dimensions of 10 of the larger PVRUF cladding

flaws reported in Appendix A of Schuster et al.

(1998). Table 8.7 gives the validated dimensions

of one of the flaws as obtained by sectioning of

the vessel material. Table 8.8 describes the

cladding examined for the Hope Creek Unit II

vessel. In this case the clad was deposited in 1-in.

strips by a multi-wire process. The measured

lengths of the Hope Creek II flaws are given in

Table 8.9. Other measurements of clad flaws for

the PVRUF vessel are indicated by Tables 8.10

and 8.1 1.

The data from the PVRUF and Hope Creek II

vessels were combined into one dataset to

establish a statistical distribution of flaw lengths

(Table 8.12). These evaluations did not include

any uncertainty analyses. It was recognized that

the examined material was from a small sample of

cladding from only two vessels. The flaws

selected for size measurements were clad flaws

with larger flaw depth dimensions. No attempt

was made to normalize the flaw length

dimensions to the thicknesses of the clad layers or

to develop separate distributions for the PVRUF

and Hope Creek II vessels.

Figure 8.3 is a plot of the length data of

Table 8.12 along with exponential fitting of the

data. There were two separate trends in the data.

One trend applied to flaws with lengths less than

about 20 mm, and another trend applied to flaws

with greater lengths. There was no apparent trend

to suggest a separation of the PVRUF data from

the Hope Creek II data. Figure 8.3 shows two

data fits (smaller than 30 mm and greater than

30 mm). The smallest flaw length was 4 mm.

Schuster GJ. 2001. Length of Flaws in Cladding with

Recommendationsfor Treatment of Aspect Ratio, Letter Report

prepared by Pacific Northwest National Laboratory, Richland,

Washington, for U.S. Nuclear Regulatory Commission, JCN W6275,

August 6, 2001.

The two exponential functions forms indicated on

Figure 8.3 are

8.6
Table 8.5. Clad Product Form and Inspection Re sults

Bead Size, # of Clad Volume, or Small # of Large

Product Form mm Passes M3 Area, mi Flaws Flaws

4 in. Strip Clad 6 1 0.016 2.6 180 0

Manual Clad 4 2 0.012 1.4 80 0

I in. Strip Clad 6 1 0.0028 0.46 700 0

Table 8.6. Dimensions of Flaws in Cladding as Reported in Appendix A of Schuster et al. (1998)

Name Product Depth, mm Length, mm . Width, mm

Pi SMAW <1.5 14

P2 Strip, 4 in. <1.5 - 7

P3 SMAW <1.5 _ 8 

P4 SMAW <1.5 .16

VI Strip, 4 in. 3 12 10

V2 SMAW 3 11 12

V3 SMAW 2 6 18

V4 Strip, I in. 2 16 . . . .B

VS SMAW <1.5 12 .11

V6 -Strip, I in. <1.5 20 .

Table 8.7. Validated Dimensions of Flaw in Claddin as Reported in Schuster et al. (2000)

Name I Product I Depth, mm I Length, mm I Width, mm

4-5DBAC-Z5 I Strip, I in. 1 4 _ | .. 80 I 10

0

-j

A

P .E.01

-0Ai D2 " e :

40 60 60

s Length of Clad Flaw, mmn

Figure 83. Lengths of Clad Flaws In PVRUF and Hope Creek II Vessels I , .

8.7
-

Table 8.8. Amount of Multi-Wire

Clad in Specimen HC2A2B

Area of Length of Clad

Clad, cmz) Pass, cm

412 162

Table 8.9. Length of Flaws in

Cridding fnr Sneeimen mC2A2R

Indication Length (mm)

1 7

2 6

3 9

4 17

5 12

6 18

7 6

8 8

9 9

10 14

11 11

12 18

13 5

14 6

15 97

16 19

17 13

18 18

19 48

20 4

21 7

22 12

23 16

24 7

25 6

26 103

27 11

28 31

Table 8.11. Length of Flaws in

Cladding for Specimen 5-1OD

Indication Length, mm

1 15

2 6

3 9

4 53

5 7

6 11

7 9

8 7

9 11

10 6

11 9

12 13

where P(>L) is the probability that the flaw length

is greater than the length L, with P(>L) calculated

from Equation (8.1) that gives the larger

conditional probability. If the calculated value of

P(>L) is greater than 1.0, then P(>L) is set equal

to 1.0.

The flaw distribution algorithm for the FAVOR

code generates a distribution of flaw aspect ratios

rather than a distribution of flaw lengths. Flaw

depths for the clad/surface flaws were set equal to

the clad thickness in accordance with the throughclad surface flaw assumption of the FAVOR

code. The FAVOR code required a distribution of

aspect ratios binned into discrete categories of

four ratios of 2:1, 6:1, 10:1, and infinity. These

aspect ratio bins are assigned the portions of the

probability distributions corresponding to the

aspect ratio ranges of 1 to 3, 3 to 8, 8 to 12, and

12 to 1000.

Table 8.10. Amount of 4 in. Strip

Clad in Specimen 5-1OD

Area of Clad, Length of Clad

cm2r ( Pass, cm

206 20

P(>L) = 1 .8 7 6e~-0 225L

P(>L) = 0.2676e

8.4 Flaw Inputs to Fracture

Mechanics

An estimate of the number and sizes of surfacebreaking and buried flaws in cladding was

(8.1) developed for use in the fracture mechanics

calculations as described below. Figure 8.4

shows a plot of these distributions along with the

data of Figure 8.2 used to support the estimates.

8.8
Table 8.12. Data Used to Develop

Length Distribution for Clad Flaws

Source Table Length, mm

2 14.0

2 8.0

2 12.0

2 11.0

2 6.0

2 16.0

2 12.0

2 20.0

3 80.0

5 7.0

5 6.0

5 9.0

5 17.0

5 12.0

5 18.0

5 6.0

5 8.0

5 9.0

5 14.0

5 11.0

5 18.0

5 5.0

5 6.0

5 97.0

5 19.0

5 13.0

5 18.0

5 .48.0

5 4.0

5 7.0

5 12.0

5 16.0

5 7.0

5 6.0

5 103.0

5 11.0

5 31.0

7 15.0

7 6.0

7 9.0

7 53.0 . 7 7.0

7 11.0

7, 9.0

7 .7.0

7. 11.0

7 6.0 _ 7 _ .__ _9.0.

7 13.0

- - The number of buried flaws per meter of weld

bead is given by the exponential distribution

function (corresponding to a straight line on the

semi log scale of Figure 8.2) as follows

NBURmD (>a) = 1.0 x exp(-5.0 x a) (8.2)

where

NBUM (>a) = number of buried flaws per.

meter of weld bead with depth

greater than a

a = depth of buried flaw as fraction

of weld bead thickness

The best estimate of the number of surface flaws

per meter of weld bead is given by

NSURFACE (>a) = 0.1 x exp(-5.0 x a) (8.3)

NSURFACE (>a) = number of surface flaws per

meter of weld bead with depth

greater than a

a = depth of surface flaw as

fraction of weld bead thickness

Equation (8.2) for buried flaws (as plotted in

Figure 8.4) is intended to describe submerged arc

cladding. The slope of the curve is based on the

PVRUF data for clad flaws, which is consistent

with the slope of the curve from the PRODIGAL

calculations. The selected intercept falls between

the two normalizations of the PVRUF data. This

intercept provides a good correlation with the

PRODIGAL predictions for flaw depths greater

than 50% of the clad thickness.

The curve for surface flaws was assumed to be a

factor of 10 below the corresponding curve for

buried flaws. :This estimate of surface flaw

density may be conservative by perhaps an order

of magnitude. Because no surface-breaking flaws

were observed in the PVRUF examinations, the

approach was to recommend conservative inputs

for fracture mechanics calculations. Refined

inputs can be developed later if surface-breaking

8.9.
-

A

0.

M

M

-6

M

0

0

0

3~0

0

0.

U)

'U

UI.E.02

1.E+01

I.E.00,

I.E-01

I.E-02'

(PVRUF cUlad n Bsjjlfn*~- 3,6O00 Miters Yf IgW Bsad)

:PVRUFWbld Clad

(Norynallzd per BefI~lnet

* PVRL$ WsW!Cla:

--- -- 09oizaprTaip~rTransftou(-----

-PROiGAL'~ % PRODIGAL Clad

...... (SAW4)

for Surd.e Mlaw Ih Claddino

1.E403J

1.E04 i

I.E-06 -

1.E-07-

4 .

FWR| I I l § @ I * I * I -

a acre

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Through-Wall Extent, Fraction of Bead Size

Figure 8.4. Proposed Curves for Estimating Number and Sizes of Flaws in Vessel Cladding

flaws were found to make significant

contributions to calculated vessel failure

probabilities.

The treatment and implementation of clad flaws

for the generation of flaw input files for the

FAVOR code has been based on the following

considerations:

(I) The recommended orientation of the flaws is

circumferential to be consistent with the flaws

observed in the PVRUF and other vessels; the

circumferential orientation is consistent with

information from the expert elicitation and

with the treatment of clad flaws in the

PRODIGAL model.

(2) The number of surface-breaking flaws

accounts for (1) flaws that are truly surfacebreaking and extending into the base metal of

the vessel and (2) a small fraction of buried

clad flaws at the clad-to-base metal interface

that have sufficiently large through-wall

dimensions to contribute to vessel failure.

The fraction of flaws of Type 2 has been

estimated using probabilistic fracture

mechanics calculations.

(3) The flaw input files for surface flaws as

generated by the PNNL algorithm do not

account for statistical uncertainty; the flaw

input file has 1000 datasets that are identical

to maintain a format for the input file to allow

for future work to include a treatment of

statistical uncertainties.

(4) The flaw density for buried clad flaws has

been assigned to be one flaw per meter of

clad weld bead.

(5) The PNNL flaw distribution algorithm

includes inputs for the number of clad layers,

the thickness of each clad layer and the width

of the clad weld bead; this permits

calculations of the total length of weld bead

per unit area of vessel surface and thereby the

number of clad flaws per unit area.

(6) Based on probabilistic fracture mechanics

calculations (described below), the density for

buried surface flaws is reduced by a factor of

8.10
1.OE-3 for a single-layer clad and a factor of

1.OE-6 for clad consisting of two or more

layers.

(7) Flaws from the input file are treated by

FAVOR as surface-breaking flaws with a

depth equal to the clad thickness; the flaws

are assigned to the particular depth bin

(percentage of vessel wall thickness in steps

of 1% of the wall thickness) that includes the

clad-to-base metal interface; the FAVOR

code assigns a flaw depth equal to the

coordinate of the outer extent of the depth

bin.

(8) The PNNL flaw distribution algorithm

assigns a distribution of flaw aspect ratios as

described by the discussion of flaw aspect

ratios as given above.

(9) The PNNL flaw distribution algorithm first

generates the flaw data in terms of flaws per

unit area of vessel surface; these data are then

expressed in terms of flaws per unit volume

following the definitions used in the FAVOR

fracture mechanics model by dividing the

number of flaws per unit area by the vessel

wall thickness.

8.5 Probabilistic Fracture

Mechanics Calculations

Probabilistic fracture mechanics calculations were

performed with the VISA-II computer code

(Simonen et al. 1986) to study the implications to

vessel integrity of the distributions in Figure 8.4.

These calculations had several objectives:

(1) Evaluate the potential contributions of clad

flaws to vessel failure~probabilities relative to

the contributions from flaws in the underlying

seam welds and base metal of the vessel wall.

(2) Evaluate the relative importance of clad flaws

buried in the cladding versus surface-breaking

flaws in the cladding.

-(3) Establish the relative importance of clad flaws

at seam welds compared to flaws in the clad

applied over plate regions of a vessel.

(4) Establish priorities for collecting'data needed

to make refined estimates of clad flaws. The

methodology and results of the calculations

are presented below. More details can be

found in Simonen et al. (2001).

8.5.1 Fracture Mechanics Methodology

The primary objective of the probabilistic fracture

mechanics calculations was to perform sensitivity

calculations to estimate the relative contributions

to failure probabilities from the different' - -'

categories of flaws and the different material

regions of the vessel:

(1) buried clad flaws located such that the outer

flaw tip was at the clad/base metal interface

with the through-wall dimension of this flaw

sampled from the distribution of flaw depths

in Figure 8.4

(2) surface flaws that penetrate the full thickness

- of the clad such that the crack tip is at the '

clad/base metal interface

(3) buried flaws randomly located within the

thickness of the seam welds (or plate

material) with'the flaw depths simulated from

the curve in Figure 8.2 for "PVRUF seam

weld."

Consistent with the FAVOR code (Dickson and

Simonen 1997), the present calculations assumed

that vessel failure does not occur if a clad flaw

has both flaw tips entirely within clad material.

This assumption is consistent with the high

toughness of cladding materials relative to the

embrittled ferritic steels.

Computer calculations were performed for a

single flaw with these failure probabilities

adjusted outside the VISA-Il code to account for

1 the actual number of flaws in the material regions

of interest. Four levels of neutron fluence

8.11
(2.0 x 10'9, 1.0 x 1019, 0.5 x 1019, and 0.25 x 10'9

neutrons/cm2) were evaluated to cover a range of

vessel embrittlement.

The current calculations used the exponential

thermal transient with a constant pressure of

1000 psi that was used in the 1993 benchmarking

study. The copper and nickel compositions were

0.30 and 0.75 wtO/o, respectively, with an initial

value of RTNDT of 20'F.

The probabilistic fracture mechanics model of the

existing VISA-II code could not address the case

of a buried flaw in the cladding. An enhancement

of the code capabilities was therefore required.

The revised model followed the approach

described by Simonen and Johnson (1993) to treat

a buried flaw that has its inner tip located very

close to the inner surface of the vessel. The trend

is that large buried clad flaws can have stress

intensity factors that approach those for surfacebreaking flaws.

Additional inputs and assumptions used for the

calculations were as follows:

(1) Flaw lengths were assumed to be long (twodimensional solutions for stress intensity

factors).

(2) The stress-free temperature for the cladding

was consistent with recent ORNL

publications (4680F).

(3) All buried flaws in the cladding had their

outer crack tip at the clad to base metal

interface, which gave a flaw configuration

that could initiate vessel fracture in

accordance with the toughness for the

embrittled material of the vessel wall.

(4) All flaws in the cladding were assumed to

have a circumferential orientation.

(5) There were no fabrication flaws in the ferritic

steel that linked with the clad flaws, based on

the fact that dye penetrant and/or magnetic

particle examinations of the base metal are

performed prior to cladding of the vessel

surface to ensure a relatively flaw-free

surface.

(6) Flaws in seam welds and base metal were in

random locations through the thickness of the

vessel; inner tips of these flaws could, in the

limit, randomly occur at the clad-base metal

interface but never extend into the clad.

(7) The failures caused by embrittled plate

material were governed by flaws along the

fusion lines along axial welds, with

contributions of flaws within the volume of

the plate material being neglected.

8.5.2 Description of Reference Vessel

All calculations were for the vessel dimensions

used for the joint NRC/industry calculations that

benchmarked probabilistic fracture mechanics

codes (Bishop 1993), as indicated in Table 8.1.

The inner diameter and wall thickness (180.0 and

9.0 in., respectively) were typical for a PWR

vessel. The height of the irradiated/embrittled

beltline region was assumed to be nominally

equal to the vessel inner diameter (4.4 m). Where

additional details were needed to define clad

inputs, the current evaluations based these inputs

on available information from the PVRUF vessel.

The number and sizes of clad flaws were

estimated for the beltline region of the selected

vessel. The surface area of the weld metal at the

inner surface of the vessel and subsequently clad

was estimated from cross sections of welds shown

in Chapman and Simonen (1998). The

evaluations addressed failures of both axial welds

and of base metal regions. These parts of the

vessel surface were assumed to be clad by

submerged arc welding using a strip clad process.

Circumferential welds were assumed to be clad

with a manual metal arc process. The fracture

mechanics calculations, however, indicated that

circumferential welds contribute little to vessel

failure probabilities.

8.12
8.5.3: Results of Probabilistic Fracture

Mechanics Calculations' >`

Figures 8.5 and 8.6 are plots of the calculated

probabilities as a function of the fluence at the

inner surface'of the vessel.' The initiation of flaw

growth from clad flaws for embrittled seam welds

(Figure 8.5) and plate materials (Figure 8.6) are

addressed. In all cases, the crack initiation is due

to a circumferential crack, consistent with the

orientation of the clad flaw. Figure 8.5 shows that

clad flaws make only small contributions to crack'

initiation in axial welds themselves compared to

the contribution of the flaws in the seam welds '

themselves. Surface-breaking flaws make only a

negligible contribution (less than 0.1% of the

total) and buried flaws contribute about 10% of

the total failure probability for seam welds.

In contrast, Figure 8.6 shows that clad flaws make

a dominant contribution to crack initiation for

vessels that have plate material as the limiting

material. Surface flaws again make negligible

contributions. Buried flaws in the clad make a

larger contribution (by a factor of 10 or more) to

vessel failure probability than flaws in the plate

material itself.

These calculations for through-wall crack

probabilities were performed as a sensitivity

study. There appears to be a basis for neglecting

clad flaws if the material of the axial or

circumferential welds governs vessel

embrittlement. The clad for circumferential welds

of a typical vessel is a multi-layer manual weld

type for which the calculations show only small

contributions of clad flaws to vessel failure. The

current study, therefore, focused on axial welds

and base metal regions. In the case of axial

welds, the fracture mechanics calculations

(Figure 8.5) also show small contributions of clad

flaws relative to flaws in the seam welds. Plate

materials appear to be the main concern.

F--hws InAaolWei&..

{ s Bu/l;d F"ows in CW

:2.06 a . -

w1E49

. .

LS g1 1.1 

Figure 8.5. Probability of Flaw Initiation In Vessel

with Axial Welds as Limiting Material

a

I

I

1141 rr w s a

1143 * ub w M lolstJd FwJ /,F' ... .............

11-44 . SwIloceFlows hOCld

MflATXNPROBA8UJTY. PLATE MATERdL4LIS LAWfTfi 1144 1£4T (OneCLad. A, Cld Tom , ha

.3 15 i.J 1J 5. 2.5

Figure 8.6. Probability of Flaw Initiation in Vessel

with Plates as Limiting Material

8.6 Concluding Discussion

In summary, probabilistic fracture mechanics

calculations using the VISA-fl computer code

were performed to explore the implications of the

estimated number and sizes of clad flaws. The

calculations have indicated that clad flaws

contribute only negligibly to the failure of

embrittled axial and circumferential welds in

vessels. In contrast, flaws in cladding over

8.13
embrittled plate material have the potential to be

significant contributors to vessel failure. The

significance of cladding flaws to the failure of

vessels with embrittled plate regions may require

further evaluation if vessel-specific calculations

with the FAVOR code show significant

contributions of such flaws to calculated failure

probabilities. Conservative assumptions were

made in the probabilistic fracture mechanics

calculations. These calculations assumed that

cladding flaws are preferentially located at the

clad-base metal interface, and that these flaws are

crack-like in nature with one crack tip positioned

to grow the crack into the embrittled plate

material. Although examinations of the PVRUF

vessel showed flaws located at the clad-base

metal interface, the morphology of these flaws

(e.g., entrapped slag) had many characteristics of

volumetric rather than crack-like flaws (i.e.,

blunted crack tips). A further assumption was

that the local properties of the ferritic material at

the interface are the same as the bulk properties of

the embrittled plate material. In practice, the

material at the interface is part of a weld fusion

zone, which means that the material will have a

local chemical composition and microstructure

that would give a higher level of fracture

toughness than that for the embrittled properties

of the bulk of the plate material.

8.14
9 ALGORITHM TO GENERATE FLAW INPUT FILES

I FOR FAVOR -

This section describes how PNNL applied the

available data on fabrication flaws in combination

with insights from the expert elicitation and

PRODIGAL flaw simulation model to generate

the computer files that serve as inputs to FAVOR

Details of the algorithm (FORTRAN code) are

described, and sample input and output files of the

algorithm are presented.

9.1 Input Files Required by

FAVOR Code

The flaw model of the FAVOR code requires

three input files to simulate the sizes and locations

of flaws as follows:

(1) flaws in weld regions

(2) flaws in base metal regions

(3) surface-related flaws in the vessel cladding.

The number of flaws per unit volume of vessel

material or per unit area of weld fusion area is

specified to FAVOR using numerical tables of

data. Statistical uncertainties in the flaw-related

parameters are treated by generating 1000 tables

that are based on the estimated uncertainties in the'

parameters of the flaw distributions. The tables

describe the number of flaws per unit volume or

area for defined ranges of depth dimensions

(expressed as a percentage of the vessel wall

thickness), and for defined ranges of aspect ratios

(flaw length divided by flaw depth). Flaw

locations are assumed to be randomly distributed

through the thickness of the vessel wall.

Other inputs to FAVOR include the volume and

areas for the RPV subregions. From the assigned

volumes and areas and from the inputs for the -

number of flaws per unit volume or area of each

size category, the total number of flaws in each

weld region, base metal region, or clad region is

calculated. Flaw locations relative to the vessel

inner surface are assigned randomly. The FAVOR

code also divides the vessel wall thickness into

regions with the first region being the inner oneeighth of the wall thickness, and with second

region being the region from one-eighth to threeeighths of the vessel wall thickness. FAVOR

assumes that flaws located beyond the threeeighths of the wall thickness make negligible

contributions to the vessel failure probabilities.

9.2 Computer Code for Generating

Flaw Input Files

A FORTRAN computer code was written by

PNNL to perform calculations based on the flaw

distribution functions (for flaw densities, flaw

depth dimensions and flaw length or aspect ratios)

as documented in Sections 6 through 8 of this

report. Figure 9.1 describes the parameters and

formats of the input file for the PNNL code. As

indicated, the flaw distribution algorithm typically

requires only five'lines of input data.

The flaw distribution algorithm performs MonteCarlo calculations that simulate or sample from

the uncertainty distributions for the parameters of

the flaw distribution functions. Each application

of flaw distribution algorithm generates a data file

for use as an input to the FAVOR code. Later

'discussions provide several examples of input

files that were supplied to ORNL for calculations

with FAVOR.

The flaw distribution algorithm has three parts to

individually address the three types of vessel

regions (welds, base metal, and cladding). Inputs

are provided in the form of batch input files.

Each run of the algorithm addresses one category

of vessel region. Discussions below describe

details of each of the three parts of the code. The

program logic for simulating flaws in a weld

region is relatively complex and is described first.

The corresponding logic for base metal flaws is a

relatively simple adaptation of the logic for weld

9.1
C

C

C

C

C

C

C

C

C

C

C

C

********************************** ***************************** **

* ********************************* ************************** *** **

INPUT DATA FOR THE COMPUTER CODE VFLAWO3 -FOR

***** ****** ** *** ***************** ********************************

  ** **** *** *** *************************************************

  ** ******* *********************** *************************** **

DATA SET #1 CONTROL PARAMETERS   ** ****** ************* ******** ************************** ******

COL. 1-80 NAME REGION

(A80T

COL. 1-11 N SUBREGIONS

I1O)

NAME OR TITLE FOR REGION

NUMBER OF SUBREGIONS (OR THE NUMBER OF

MATERIAL TYPES MIXED TOGETHER WITHIN

THE REGION)

= 0 BEST ESTIMATE CALCULATION

> 0 UNCERTAINTY CALCULATION WITH

WITH NUMBER OF MONTE CARLO

TRIALS = NSIMULLATIONS

VESSEL TOTAL WALL THICKNESS (MM)

(INCLUDING CLAD)

COL. 11-20

COL. 21-30

COL. 31-40

COL. 41-50

COL. 51-60

COL. 61-65

COL. 66-75

N SIMULATION

(110)

WALL

(F10.4)

IUNITS

(I10)

IVOLAREA

(10)

I BASE METAL

(110) -

IORNL

(I10)

UNIFORMDENSIT

(F10.6)

IY

= 1 METRIC

= 2 ENGLISH

(FLAWS PER MA2 OR Mf3)

(FLAWS PER FTn2 OR FTA3)

UNITS FOR OUTPUT TABLEFS

(FOR WELD AND CLAD FLAWS)

= 1 FLAWS PER UNIT VOLUME

= 2 FLAWS PER UNIT AREA

= 0 NORMALLY

= 1 USE JUNE 20, 2001 ASSUMPTIONS TO

ADDRESS BASEMETAL FLAWS WITH EXPERT

JUDGEMENT DATA AS ADJUSTMENT OF

WELD METAL DISTRIBUTION

= 0 NORMALLY

= 1 USE ORNL FORMAT FOR FLAW OUTPUT

DATA FILE (W/O TWO HEADER LINES)

r FOR UNIFORM FLAW DEPTH DENSITY

= 0.0 NORMALLY

= USER SPECIFID FLAWS

PER UNIT VOLUME OR AREA

FOR EACH CATEGORY OF

ONE PERCENT OF WALL

ASSUMPTIONS 1) DENSITY (INCLUDING UNCERTAINTY) OF SMALL FLAWS

IN BASEMETAL IS 1/10 OF THAT FOR WELD METAL

2) DENSITY (INCLUDING UNCERTAINTY) OF LARGE FLAWS

IN BASEMETAL IS 1/40 OF THAT FOR WELD METAL

Figure 9.1. Input Instructions for Flaw Distribution Algorithm

9.2
C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

. C

C

C

C

C

C

C

C.

DATA SET #2 SUBREGION CHARACTERISTICS

ONE DATA SET FOR EACH SUBREGION

COL. 1-10

COL. 11-15

COL. 16-20

COL. 21-25

COL. 26-35

COL. 36-40

COL. 41-45

COL. 46-50

COL. 51-60

VOLFRAC(N)

(F10.4)

IVESSEL(N)

(I5)

IMATERIAL(N)

('5) -

BEAD(N)

(F5.1)

VOLUME OR AREA FRACTION FOR SUBREGION

a 1 PVRUF VESSEL

. 2 SHOREHAM VESSEL

. 1

= 2

. 3

a 4

- 5

SAW (SUBMERGED METAL ARC WELD)

SMAW(SHIELDED METAL ARC WELD)

REPAIR WELD

CLAD

BASE METAL

BEAD SIZE (MM) FOR SUBREGION

FACTOR(N) FACTOR ON FLAW FREQUENCIES APPLIED

(F10.4) TO HARD WIRED FLAW DENSITIES

CLAD THICK(N) CLAD THICKNESS (MM)

(F5.1) (ONLY IF IMATERIAL ' 4)

CLAD_WIDTH(N) CLAD BEAD WIDTH (MM)

(F5.1) (ONLY IF IMATERIAL * 4)

NLAYERS (N)

(I5)

TRUNC (N)

(F10.3)

NUMBER OF CLAD LAYERS

(ONLY IF IMATERIAL - 4)

TRUNCATION ON FLAW DEPTH

(MM)

FIgure 9.1. Continued

flaws, and requires only a brief explanation. In

the case of surface/clad flaws, the flaw

distributions are treated in a deterministic manner,

and the discussion of the logic for simulating this

category of flaws is again relatively brief.

9.2.1 Input File to PNNL Algorithm

Inputs to the flaw distribution algorithm as

described by Figure 9.1 include:

* title line - A title of up to 80 characters allows

the user to describe the calculation.

* number of subregions - Allows the use of a

rule-of-mixtures if a weld is completed by

more that one weld process (SAW, SMAW

and repair). Other inputs specify the welding

processes in detail and the volume or area

fractions contributed by each of the specified

processes.

* number of Monte Carlo simulations - This

parameter typically has been set to specify

1000 simulations to generate 1000 samples

for the uncertainty analysis. The number of

simulations can be specified to be some

number other than 1000. If the number of

simulations is prescribed to be zero, the

calculation provides one flaw distribution

corresponding to the best-estimate value from

the uncertainty analysis.

9.3
* vessel wall thickness - The wall thickness is

the total thickness including the cladding.

* volume or area - Allows the output file to

give flaw frequencies in terms of flaws per

unit volume or as flaws per unit area of the

vessel inner surface.

* metric or English - Allows the output file to

give flaw frequencies as either flaws per

cubic meter or as flaws per cubic foot. If the

flaw densities are expressed as flaws per unit

area, the units are flaws per square meter or

flaws per square foot.

* base metal option - The current version of the

algorithm does not explicitly treat flaws in

base metal regions but performs simulations

of flaws as if the base metal were weld metal

and then reduces the calculated flaw

frequencies by hardwired factors of 10 for

small flaws and 40 for large flaws.

* header option - The format for the FAVOR

input file of 1000 datasets (for the

uncertainties in flaw distributions) does not

allow for header line to label the columns of

the table. This parameter allows the header

lines to be deleted.

* uniform depth density - This parameter is

normally set to 0.0, which bypasses a logic

that should be used only for sensitivity

studies. Values other than zero cause the

output file to assign flaw frequencies that are

independent of the flaw depth dimensions.

Each of the subregions (as described above)

requires one line of input parameters as follows:

* volume or area fraction - Is the volume

fraction for each weld process (SAW,

SMAW, or repair) for each subregion of the

weld. The sum of the volume fractions for all

subregions should add up to unity.

* vessel - Specifies if the parameters for the

flaw densities and for the conditional flaw

dimensions are to be based on the data from

the PVRUF vessel or from the Shoreham

vessel.

* material - denotes the category of weld

material (SAW, SMAW, or repair weld) for

the subregion of interest. This parameter also

can direct the algorithm to perform

calculations for clad material, in which case

the flaw densities are based on the number of

clad layers and on the specified thickness and

width of the clad weld beads. The flaw

distribution algorithm has an inactive

provision for base metal. The code instead

treats base metal in an approximate manner as

weld metal with the flaw densities reduced

and the depth distributions truncated. The

code currently stops and prints an error

message if the user attempts to address base

metal through this input parameter.

* bead size - This parameter is the estimated

bead size (through-wall dimension) for each

weld material category (SAW, SMAW, and

repair).

* volume or area - Allows the output file to

give flaw frequencies in terms of flaws per

unit volume or flaws per unit area of the

vessel inner surface. This parameter

generally has a default value of 1.0. The

default flaw densities based on the PVRUF

and Shoreham data can be adjusted for each

weld category (SAW, SMAW, and repair) for

sensitivity studies.

* clad thickness - This parameter is the total

clad thickness and accounts for all layers if

the clad consists of more than one layer. This

parameter needs to be specified only if the

material type is clad rather than SAW,

SMAW, and repair.

* clad width - This parameter describes the

bead width or the width of the strip for the

cladding. This parameter needs to be

specified only if the material type is clad

rather than SAW, SMAW, and repair.

9.4
* number of clad layers - This parameter

specifies the number of clad layers, which

will be only one layer for typical 'strip-type

- cladding. This parameter needs to be

specified only if the material type is clad

rather than SAW, SMAW, and repair.

* truncation on flaw depths - This parameter

describes the values of flaw depth, specified

individually for SAW, SMAW, and repair

welding, beyond which the flaw frequencies*

are'set to zero. The truncation would be

typically on the order of 25 nmm for SAW and

SMAW flaws and 50 mm for flaws in repair

welds.

9.2.2 Output File from PNNL Algorithm

An output file from the PNNL algorithm provides

the following information:

* display of input data - The first part of the

output file displays and identifies the input

data that the user has provided to the

algorithm.

* first ten-sample flaw distribution from the

uncertainty'evaluation - The second part of

the output file is a series of 10 tables

corresponding the first 10 (of a typical total of

1000) sample flaw distributions that are also

written on the large file for use as input to

FAVOR.

* largest values from the 1000 simulated flaw

distribution'- the largest values (from a search

through the 1000 simulated flaw

distributions) for each element of the tables

that describe the simulated distributionsThis table does not correspond to any of the

1000 samples but only indicates the

maximum values for the individual elem' ents''

of the flaw distribution table.

* median values from the 1000 simulated flaw

distribution - the median values (from a

search through the 1000 simulated flaw

distributions) for each element of the tables

that describe the simulated distributionsThis table does not correspond to any of the

1000 samples but indicates only the median

values for the individual elements of the flaw

distribution table.

* smallest values from the 1000 simulated flaw

distribution - the smallest values (from a

search through the 1000 simulated flaw

distributions) for each element of the tables

that describe the simulated distributionsThis table does not correspond to any of the

1000 samples but indicates only the smallest

values for the individual elements of the flaw

distribution table.

* 25" percentile values from the 1000 simulated

flaw distribution - the 25" percentile values

-(from a search through the 1000 simulated

flaw distributions) for each element of the

tables that descnlie the simulated

distributions-This table does not correspond

to any of the 1000 samples but indicates only

the 25" percentile values for the individual

elements of the flaw distribution table.

* 75" percentile values from the 1000 simulated

flaw distribution - the 75' percentile values

(from a search through the 1000 simulated

flaw distributions) for each element of the

tables that describe the simulated

distributions-This table does not correspond

to any of the 1000 samples but indicates only

the 75" percentile values for the individual

elements of the flaw distribution table.

* 5" percentile values from the 1000 simulated

flaw distribution - the 5"' percentile values

(from a search through the 1000 simulated

flaw distributions) for each element of the

tables that describe the simulated '_

distributions- This table does not correspond

to any of the 1000 samples but iridicates only

'the'5"' percentile values for the individual

elements of the flaw distribution table.

* 95" percentile values from the 1000 simulated

flaw distribution - the 95"' percentile values

9.5
(from a search through the 1000 simulated

flaw distributions) for each element of the

tables that describe the simulated

distributions-This table does not correspond

to any of the 1000 samples but indicates only

the 95h percentile values for the individual

elements of the flaw distribution table.

9.2.3 Output File from PNNL Algorithm

for Inputs to FAVOR

The second output file from the PNNL algorithm

is generated for use as an input file by FAVOR

This is a relatively large file that is not intended to

be printed as a hard copy. It contains the flaw

distribution tables for all of the samples of flaw

distributions that are calculated by the Monte

Carlo simulation. The output file as described in

Section 9.2.2 can be printed to provide the user

with the first 10 of the large number (e.g., 1000)

of samples.

9.3 Procedure for Weld Regions

Section 6 documents the data and statistical

correlations that were developed to describe the

flaws observed in the welds of the PVRUF and

Shoreham vessels. The following paragraphs

describe the implementation of these statistical

functions into the flaw distribution algorithm.

9.3.1 Treatment of Weld Flaws

Weld regions of concern to RPV integrity are the

axial and circumferential seam welds in the high

neutron fluence region of the vessel beitline.

These welds can be fabricated by the SAW

process or by the SMAW process. Typically, a

given seam weld will have some welding from

both processes, but the largest fraction (e.g.,

>90%) of the weld will have been deposited by

the automatic SAW process. The flaw model

accounts for the differences between densities and

size distributions for these weld processes.

However, the identification of local regions as

produced by specific processes requires

information not generally available from vessel

fabrication records. Therefore, calculations with

FAVOR have assumed a random mixture of SAW

and SMAW materials along with a small fraction

of repair welding. The fractions have been based

on trends observed from the vessels examined by

PNNL.

In practice, some flaws are located randomly

within the volume of weld metal, and some flaws

are located along the fusion line that separates the

weld metal from adjoining base metal. While

many flaws may be within the volume of the

weld, data have shown very few of these flaws to

have significant through-wall dimensions. Thus

most larger weld flaws are located along the weld

fusion line. Only a small fraction of these flaws

has through-wall dimensions approaching or

exceeding the size of a single weld bead.

FAVOR assumes that all weld flaws are located

along fusion lines.

A single flaw input file is used by FAVOR for

both axial and circumferential welds. Flaws for

axial welds are assumed in FAVOR to have axial

orientations, and flaws for circumferential welds

are assumed to have circumferential orientations.

Although repair welding makes up only a few

percentage of the weld metal in a typical vessel,

most of the larger flaws (depth dimensions greater

than a weld bead) have been associated with weld

repairs. Typical repairs are ground-out regions

that have been filled by a manual welding

process. The repairs can be entirely within seam

welds, entirely within base metal, but will most

typically span both weld metal and base metal

because repairs are generally made to defects

along the weld fusion lines. Repairs have been

observed at both the inside and the outside of

vessels. It has not been practical for FAVOR

calculations to identify specific locations of

repairs, such as may be documented by

construction records. The repairs have been

assumed to occur at random locations, such that

the repair flaws are blended into the population of

flaws associated with the normal welding

processes. However, the small amount of

material from repair welding nevertheless makes

9.6
a dominant contribution to the estimated number

of larger flaws.

9.3.2 Flow Chart for Welds

Figure 9.2 is a flow chart for the steps in the

Monte Carlo simulation for flaws in welds.

Details of the calculations are as follows:

* PVRUF versus Shoreham vessel - There is an

option to base simulations of the parameters

of the flaw distributions and the associated

uncertainties in these distributions on the data

from either the PVRUF or the Shoreham

vessel.

* weld type - The weld process can be either

SAW or SMAW, or repair weld, or a mixture

of these processes. An implied assumption is

that a given local region has a random chance

of being of any of the specified weld types.

* bead size - An input to the calculations allows

the user to specify the weld bead size

(through thickness dimension) for each

category of weld. This permits vessel specific

information on welding process to be

accounted for in the estimates of flaw

distributions. If the calculations are based

instead on the observed bead sizes for the

PVRUF or Shoreham vessels, the following

inputs can be used as default inputs:

for small flaws (and likewise for large flaws)

applies to all flaw types (SAW, SMAW and

repair) for each simulated vessel. The length

distributions for repair flaws are assumed to

be the same as for SMAW welds. The Monte

Carlo simulation samples the parameters for

this distribution only once for both weld

types.

large and small flaws - As indicated in

Figure 9.2, there are independent elements of

the model that address the parameters for the

distributions of small and large flaws. Small

flaws are less than one weld bead dimension

in through-wall depth, whereas the large

flaws are greater than one bead dimension.

Results for the two depth categories are

combined in the final step of the calculation.

The resulting tables for use as inputs to

FAVOR do not differentiate between large

and small flaws.

* flaw densities - Six separate simulations

address uncertainties in the densities (flaws

per cubic meter or square meter) of SAW,

SMAW, and repair flaws to address both

small and large flaws. The uncertainties in

the densities for small flaws are relatively

small because the PNNL examinations found

a large number of small flaws. The

uncertainties in the densities of large flaws

are much larger because the vessel

examinations found relatively few large

flaws.

* conditional depth distribution - The

conditional depth distribution was assumed to

be the same for SAW, SMAW, and repair

flaws. Different distribution functions and

parameters are used to describe the depths of

large versus small flaws. Because the small

number of observed large flaws was very

small, the uncertainties in the parameter for

the exponential distribution for the depths of

large flaws were relatively large. The

uncertainties in the depths of small flaws

were relatively small.

Bead Size Bead Size (mm)

(mm) PVRUF Shoreham

Weld Type, Vessel Vessel

Submerged 6.5 5.0

Arc (SAW)

Shielded Metal 3.5 3.5

Arc (SMAW) .

Repair W 3.5 3.5

* vessel simulation - The structure of the Monte

Carlo simulation ensures that uncertainties in

the parameters of the statistical distribution

functions describing flaws are simulated only

once per vessel. For example, in reference to

Figure 9.2, one conditional depth distribution

9.7
Simulate Small

Flaws

Simulate

Large Flaws

Figure 9.2. Flow Chart for Weld Flaws

9.8
* aspect ratio distribution - The database for

validated measurements of aspect ratios for

small and large flaws in the PVRUF vessel

was relatively small, and the uncertainties

were correspondingly large. Data showed

that most SAW flaws in the PVRUF welds

tended to be about 1:1, whereas the aspect

ratios of flaws in SMAW welds were much

larger. A separate data analysis was

performed for aspect ratios for flaws in the

welds of the Shoreham vessel. The Shoreham

vessel (compared to the PVRUF vessel)

showed a trend of larger aspect ratios for the

SAW welds. Differences in aspect ratios for

SMAW and SAW flaws were relatively small

for the Shoreham vessel. It was assumed for

both the PVRUF and Shoreham vessel that

flaws in repair welds and SMAW welds have

the same distribution of aspect ratios.

9.3.3 Sample Input File for Welds

Figures 9.3 through 9.5 present inputs and outputs

for a sample calculation by the PNNL flaw

distribution algorithm. This particular example

was based on the uncertainty distribution obtained

from an analysis of the Shoreham flaw data and

presents the first simulated distribution of a total

of 1000 tables from sampling for the uncertainty

analysis. The Monte Carlo simulation, as

performed by a FORTRAN computer code,

generates a file consisting of a large number of

tables (e.g., 1000) corresponding to Figure 9.5.

The rows of Figure 9.5 come from a binning of

the data from the continuous flaw distributions

into 100 bins. Each bin corresponds to a depth

category definied by 1% increments of the vessel

wall thickness. For example, the bin designated

by the label "1" in Figure 9.5 gives the number of

flaws per square foot that have depth dimensions

between 1% and 2% of the vessel wall thickness.

There are 531.72 flaws per square foot for this

depth category, whereas the number of very large

flaws with depths between 9% and 10% of the

vessel wall thickness is only 0.001 7841 flaw per

cubic foot. There are no flaws with depths greater

than 23% of the vessel wall thickness, consistent

with the specified truncation flaw depth for flaws

in repair welds.

Columns 3-13 of Figure 9.5 give information on

the simulated aspect ratios for each of the flaw

depth categories. In the case of the first row of

the table (the depth category corresponding to

flaws with depths between 0% and 1% of the

vessel wall) it is seen that 2.285% of the flaws in

this category have aspect ratios between 1:1 and

1.25:1. From the final column of Figure 9.5, it is

seen that 27.633% of this category of small flaws

have aspect ratios greater than 15:1. In the case

of relatively deep flaws, it is seen that most flaws

have small aspect ratios.

Figure 9.6 is a sample plot of estimated flaw

frequencies (expressed here in terms of flaws per

cubic foot) as' estimated for a representative

vessel. The flaw depth distributions of Figure 9.6

are truncated to preclude extrapolations of curves

to flaw depths that are significantly larger than the

depth dimensions of flaws that were detected in

the PNNL examinations of vessel materials.

OCONEE-1 OCTOBER 29, 2002 WELD -FLAW/FTA2 SHOREHAM TRUNCATED

3 1000 219.10 2 2 0

0.9700 2 1 4.76 1.0 25.4

0.0100 2 2 5.33 1.0 25.4

0.0200 2 3 3.56 1.0 50.8

1 0.0

Figure 9.3. Sample Flaw Distribution Input File for Weld Region

9.9
GENERATION OF FLAW DISTRIBUTION INPUT FILE FOR THE ORNL FAVOR CODE

NAME OF REGION = OCONEE-1 OCTOBER 29, 2002 WELD FLAW/FT^2 SHOREHAM

TRUNCATED

NUMBER OF SUBREGIONS = 3

UNCERTAINTY CALCULATION

NUMBER OF MONTE CARLO SIMULATIONS = 1000

VESSEL TOTAL WALL THICKNESS (MM) = 219.10

ENGLISH UNITS - FLAWS PER FT^2 OR FLAWS PER FT*3

WELD DENSITY OPTION - FLAWS PER UNIT AREA

BASEMETAL APPROXIMATION NOT USED

OUTPUT FILE REFORMATED FOR INPUT TO ORNL FAVOR CODE

SUBREGION NUMBER 1

VOLUME FRACTION = .9700

SHOREHAM VESSEL PARAMETERS

SAW (SUBMERGED METAL ARC WELD)

BEAD SIZE (MM) = 4.76

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT = 1.0)

CLAD THICKNESS(MM) = .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) = .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) = 25.4000

SUBREGION NUMBER 2

VOLUME FRACTION = .0100

SHOREHAM VESSEL PARAMETERS

SMAW (SHIELDED METAL ARC WELD)

BEAD SIZE (MM) = 5.33

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT = 1.0)

CLAD THICKNESS(MM) = .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) = .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) = 25.4000

SUBREGION NUMBER 3

VOLUME FRACTION = .0200

SHOREHAM VESSEL PARAMETERS

REPAIR WELD

BEAD SIZE (MM) = 3.56

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT = 1.0)

CLAD THICKNESS(MM) = .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) = .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) = 50.8000

Figure 9.4. Sample from Flaw Distribution File for Weld Region

9.10
Lx DiSUTDrtuTtaw 133 smiAIIOst IWlA 1

x VLANS/VT-** 1.0-1.23 1.231.3

1 .404143.02 2.363 2.322

2 .311748.01 o.ee0 0.230

I .lOeo2u.00 11.02S 11.313

4 .941810.01 20.334 16.104

O .24407.401 23.213 19.061

4 .104343-01 34.482 22.371

7 .307223.02 43.742 24.413

* .210433-02 49.201 24.949

3 .290333-02 53.911 24.862

13 .178413.02 06.004 24.304

xi .122433-02 41.693 23.621

12 .801373.03 43.047 22.734

13 .171143.02 40.131 11.714

14 .397033.03 70.017 20.617

is .27313.-03 73.430 13.310

14 .161S23.31 71.761 14.364

17 .123143.03 77.803 17.233

13 .800335.04 73.810 14.110

13 .40033.e04 01.307 13.03

30 .410103.04 13.277 13.393

21 .217312-04 04.447 12.336

22 .197433.04 03.300 12.049

23 .135715.04 17.212 11.113

24 .034303.00 100.o00 .000

3s .00303.30 103.033 .60o

20 .4003o.00 103 .044 .0oe

37 .004003.43 100 .003 .000

a0 .00003.400 100.000 .000

11 .O0000l4d 100.000 .003

30 .000003.00 100.000 .000

31 .0e0033.00 103.000 .600

32 .000003.00 100.000 .000

33 .00003Z300 100.000 .003

24 .000033.00 100.000 .600

23 .000033.04 100.000 .000

30 .0o0ooo.03 100.o00 .e00

37 .6000033.4 100.000 .633

36 .0340033.0 100.000 .000

13 .000003.00 10.040 .0oo

43 .e003.o0oo 100.003 .600

41 .000003.30 108.000 .o00

42 .000031.06 100.000 .0oo

43 .000363.03 103.000 .000

44 .000036.00 100.604 .000

IS .030063.40 100.00 .000

40 .00003.00 100.o00 .ooo

*7 .000003.03 100.000 .006

46 .000003.0 100.000 .400

40 .030003.0 1s44.0eo .e00

s0 .00003.00 100.000 .800

31 .033003.00 100.000 .000

11 .00003.04 100.000 .000

S3 .03333.00 100 .000 .o00

34 .000032.00 100.004 .000

03 .000303.00 100.600 .000

17 .000003.OO 100.600 .000

07 .004003e.0 10.e00 .000

to .00300.00 100.000 .000

3 .000003.00 100.00 ' .*00

go .000003.0e 130.600 .000

01 .600003.04 100.000 .000

42 .4000.002 100 .04o .e00

03 .000001.00 100.000 .603

44 .003032.00 100.000 .300

43 .000003.00 100.603 .000

4u .000003.03 100.000 .000

*7 .000003.03 100.003 .000

Os .00000300 100.000 .600

49 .00036400 100.000 .0°0

70 6 .00000.00 100.000 .000

71 .000003.00 100.600 .000

72 .00e00n.00 113.500 .o00

73 .00000S.00 10.4000 .003

74 .00000S.00 100.003 .o00

7s .00031.o03 100.000 .o00

7e .00000.03 103.e000 .000

77 .000003.00 100.000 .000

76 .000001.00 100.600 .000

7n .000003.00 103.000 .00e

l0 .000003.00 100.000 .000

*1 .000003.30 100.000 .600

02 .000003,00 130.103 .000

83 .60003,003 100.600 .000

04 .000003.00 100.400 .000

Os .000003*43 100.043 .o0o

Is .000003.00 100.000 .000

07 .000003.00 100.000 .003

to .000003.00 100.000 .100

t3 .000003.00 100.000 .000

3o .000003.00 100.000 - .. 00

61 .000003.00 130.030 .000

93 .000013.00 100.000 .000

33 .000003,00 100.000 .000

34 .000003,0 103.00 .000

33 .o03003.44 100.00 .e00

30 .000003.00 100.000 .600

.7 .003000300 100.000 .600

is .000033.03 100.060 .e00

00 .000003.00 106.000 .000

to0 .000003.00 100.000 .600

1.3.3.2 .0 2.00 204. 4.0.3.06 3.0.0.0 -4.0.0.0 0.0.10.0 10.0.11.4 .1I.0

4.310 6.020 7.322 0.071 .0.76 - 10.060 8.701 16.644 27.033

11.230 10.273 13.840 10.304 7.373 10.034 4.233 0.204 2.107

10.043 34.477 13.473 7.486 4.160 2.007 1.310 .646 .040

22.602 33.709 0.749 4.033 1.740 1.077 .204 .047 .031

24.412 19.303 5.130 1.7010 .903 .244 .026 .004 .003

23.016 13.074 2.461 .314 .110 .037 .403 .630 .000

21.467 0.110 1.010 .121 .020 .044 .033 .003 .030

10.003 0.223 .436 .034 .003 .600 .000 .603 .000

15.710 4.322 .200 .010 .001 .000 .003 .003 .033

14.333 3.310 .003 .003 .302 .600 .000 .033 .040

12.321 2.106 .040 .001 .000 .030 .000 .000 .030

10.720 1.470 .022 .030 .000 .330 .000 .600 .000

3.140 1.021 .02.3 .040 .400 .030 .003 ."03 .033

7.737 .712 .003 .030 .033 .000 .000 .6000 .033

0.041 .490 .002 .033 .600 .600 .030 .600 .040

5.334 .345 .601 .003 .030 .030 .030 .600 .6000

4.038 .323 .031 .003 .600 .033 .003 .000 .033

3.013 .164 .000 .000 .030 .033 .003 .600 .030

3.282 .133 .000 .003 .033 .603 .030 .033 .000

2.750 .060 .6000 .000 .033 .030 .000 .003 .030

2.302 .004 .603 .000 .600 .000 .033 .030 .3000

1.020 .033 .000 .000 .030 .603 .000 .633 .600

10) .027 .303 .030 .060 .030 .033 .430 .000

.000 .033 .400 .003 .033 .003 .033 .033 .033

.6000 .000 .000 .003 .030 .003 .000 .000 .000

.030a .000 .000 .4003 .033 .000 .060 .630 .003

.603 .000 .000 .060 .000 .003 .030 .600 .060

.630 .000 .000 .000 .030 .030 .000 .600 .000

.000 .030 .003 .040 .000 .030 .000 .030 .000

.600 .003 .003 .000 .033 .400 .003 .030 .000

.033 .003 .000 .000 .000 .000 .000 .030 .033

.000 .000 .003 .000 .030 .003 .030 .630 .003

.033 .100 .000 .003 .333 .303 .004 .303 .340

.000 .000 .000 .033 .030 .003 .030 .003 .000

.033 .000 .000 .6003 .000 .603 .000 .000 .003

.030 .300 .000 .1000 .440 .003 .000 .000 .000

.603 .000 . -- 000 .000 .000 .000 .000 .000 .030

.600 .600 .000 .000 .033 .003 .600 .000 .000

.033 .000 .000 .000 .003 .003 .000 .000 .000

.000 .000 .033 .000 .600 .000 .000 .603 .010

.033 .600 .303 .000 .400 .030 .000 .000 .000

.600 .J00 .000 .003 .000 .000 .000 .600 .000

.600 .000 .000 .033 .000 .000 .000 .000 .5000

.003 .606 .600 .000 .000 .030 .000 .003 .000

.600 .000 .000 .600 .000 .600 .000 .030 .000

.033 .030 .300 .300 .330 .040 .600 .000 .000

.006 .060 .6000 .000 .030 .033 .00 . 000 M .000

.000 .003 .030 .000 .003 .000 .003 .600 .000

.4040 .004 .003 .044 .030 .033 .000 .000 .000

.030 .000 .800 .003 .000 .030 .000 .000 .000

.030 .000 .600 .003 .003 .000 .030 .000 .000

'.000 .000 .603 .600 .000 .000 .000 .600 .000

.030 .060 .603 .000 .000 .000 .003 .600 .030

.000 .000 .000 .000 .6000 .000 .000 .030 .000

.9000 .000 .000 .003 .000 .603 .003 .033 .000

.000 .030 .630 .030 .333 .300 .000 .030 .043

.000 .003 .630 .000 .033 .003 .000 .600 .600

.630 .000 .8003 .000 .000 .003 .000 .000 .000

.043 to .0 .000 .000 .40 .340 .0 4 .00 0 .000 .0

.800 .000 .000 .003 .000 .003 .000 .030 .000

.000 .000 .000 .000 .000 .000 .030 .000 .000

.000 .000 .000 .000 .000 .006 .000 .000 J010

.600 .000 .600 .000 .000 .000 .003 .600 .000

.000 .030 .600 .600 .600 .600 .000 .003 .000

.000 .000 .030 .000 .000 .003 .000 .003 .060

.030 .003 .000 .000 .003 .800 .000 .000 .300

.030 .003 .003 .000 .000 .800 .030 .000 .600

.030 .000 .003 .000 .000 .003 * _..006 .000 .000

.044 .9003 too .043 .000 .003 .003 .000 .033

.000 .600 :6o0 .600 .000 .000 .000 .040 .000

.000 .000 .606 .000 .040 .000 .000 -. 603 .603

.040 .000 .000 .033 .030 .000 .000 .600 .000

.000 .6000 .003 .000 .000 .6000 .003 .060 .000

.000 .030 .00 .000 .0 30 .600 .000 .040 .00 .000

,400 .30 0 .3 .0.00 .. .0.000 000 .030 .000

.600 .000 .000 .030 .003 .000s .000 .100 .000

.000 .4000 - .600 .033 .000 .030 .034 .000 .000

.100 .600 .000 .630 .000 .000 .000 .003 .030

.000 .040 .4000 .000 .003 .033 .030 .030 .040

.000 .000 .600 .000 .000 .000 .000 .000 .0301

.600 .000 - .000 .060 .000 .000 .000 .000 C.00

.004 .044 .030 .044 .340 .030 .000 .006 .000

.630 .000 .6000 .000 .030 .003 .000 .006 .000

.603 .000 .000 .030 .000 .030 .060 .600 .000

.900 .600 .000 .000 .000 .033 .000 .600 .000

.03 .00 .030 . 003 .000 . 003 .000 . 336.00 .00

.00 60 .0 .0 03 .0 00 .000 .000: .600 .600 .00 a00 .3 .000 .000 06 .00

00 .60.000 .000 .000 .030 .030 .033 .000

.600: :.033 :.00 0000 0 o.030 .03 40 00

::0O0 ::4.O :.00: ::00 00 .000 .000 .600 - .003

00 .00 .300 .3o :.00 .040' :.,:O00 :.00 .000 .04

.60 00 .003 .00 .000 .000 .000 .000 .000

.3 .600 - .000 .000 .003 .030 .000 .000 .000

.600 as000 .000 .000 .000 .000- .000 .4

.6o .60 -. 0 000 .0 .00 00 .03 00

::O,.00 .,0 .00 :.000 .00 000 :.000 .00

.000 0 .00.0 .000 .030 .330030 .00 . .000,

.000 .000 .60 00 00.00:0 ::.00O .0 .030

Figure 9.5. Sample Flaw Data Output File for Weld Region

9.11
1.E+03

A C:%FtLAWATAIORNL COA AG 20 20011 PLOTS OF ORM. NPUTMXLS

A

1.E+02 Wall Thickness = 214 mm

0.

0

C 1.E401 Base Metal Flaws

0

12 I.E+00

Weld Metal Flaws

I.E-01

1.E-02 CL Marshall

3f Distribution I.E-03

o I.E-04 Surface/Clad Flaws

E 1.E-05

z

1.E-06 .

0 5 10 15 20 25 30

a = Flaw Depth, Percent Wall

Figure 9.6. Flaw Distribution for Various Vessel Regions (Median Values from Uncertainty Analyses)

9.4 Procedure for Base Metal

Regions

Section 7 describes the approach for developing

statistical distributions for flaws in base metal

regions. The implementation of the statistical

formulation into the flaw distribution algorithm is

described in the following paragraphs.

9.4.1 Treatment of Base Metal Flaws

Flaws are observed to occur at much lower rates

in base metal (per unit volume of metal) than in

welds. It is also observed that the largest flaws in

plate and forging materials have orientations

parallel to the surface of the vessel. This

orientation is related to the rolling and forming

operations used to fabricate the vessel plates and

forged rings. Although these laminar-type flaws

can be quite large, they have no significance to

vessel integrity. In this discussion, the base metal

flaws of concern are therefore only flaws that

have some through-wall dimension. As discussed

in Section 7, PNNL's examinations of plate

materials show that flaws occur at lower rates per

unit volume (by a factor of 10 or greater) than in

welds.

9.4.2 Flow Chart for Base Metal

Because the flow chart for base metal flaws is

essentially the same as the flow chart for weld

metal (see Figure 9.2), a separate chart is not

needed. The only difference is that the flaw

densities for base metal (flaws per unit volume)

are reduced by a factor of 10 for small flaws and

by a factor of 40 for large flaws relative to values

simulated for weld metal. In accordance with the

questions posed during expert judgment

elicitation, flaw estimates for plate materials are

based on adjustments to distributions derived

from the data from the PVRUF vessel rather than

from the Shoreham vessel. The input file for

FAVOR (1000 datasets) for base metal flaws has

the same treatment of statistical uncertainty as

developed for the PVRUF data for weld flaws.

Truncations for maximum depths of base metal

9.12
flaws (as described in Section 7) are different

from the truncations for weld flaws,'iuch that

recommended truncations for base metal flaws

occur at much smaller sizes than for weld flaws.

9.4.3 Sample Input File for Base Metal

Figures 9.7 through 9.9 present inputs and outputs

for a sample calculation by the PNNL flaw

distribution algorithm. As indicated in Figure 9.8,

this example was based on the flaw distribution

parameters and the uncertainty distribution

obtained from analyses of the PVRUF data.

Figure 9.9 is the first simulated distribution of a

total of 1000 such tables corresponding to

sampling for the uncertainty analysis.

distributions of Figure 9.6 are truncated to

preclude extrapolations of curves to flaw depths

that are much larger than the depth dimensions of

any flaws that were detected in the PNNL

examinations of vessel materials.

9.5 Procedure for Surface/Clad

Flaws

Section 8 describes the approach for developing

statistical distributions for flaws in clad regions.

The implementation of the statistical formulation

' into the flaw distribution algorithm is described in

the following paragraphs.

9.5.1 Treatment of Surface/Clad Flaws

As for the weld flaws, the rows of Figure 9.9

come from a binning of the data from the

continuous flaw distributions into 100 bins. Each

bin corresponds to a depth category defined by

1% increments of the vessel wall thickness. For

example, the bin designated by the label "1" gives

the number of flaws per cubic foot that have depth

dimensions between 1% and 2% of the vessel

wall thickness. There are 17.505 flaws per cubic

foot for this depth category, whereas the number

of very large flaws with depths between 4% and

5% of the vessel wall thickness is only

0.014037 flaw per cubic foot. There are no flaws

with depths greater than 5% of the vessel wall

thickness, consistent with the specified truncation -

flaw depths.

Columns 3 through 13 of Figure 9.9 give

information on the aspect ratios for each of the

flaw depth categories. Considering the first row

of the table (the depth category corresponding to

flaws with depths between 0% and 1% of the

vessel wall), it is seen that 46.753% of the flaws

in this category have aspect ratios between 1:1

and 1.25: 1. From the final column of the table,' it

is seen that only 1.340% of this category of small

flaws have aspect ratios greater than 15: 1.

Figure 9.6 includes a sample plot of estimated

flaw frequencies (flaws per cubic foot) as

estimated for base metal. The flaw depth

As described in Section 8, the number and size of

surface-breaking flaws at the inner surface of a

vessel have been estimated from data on flaws

that have been detected during examinations of

vessel cladding. These flaws can occur randomly

in the cladding applied over both weld and base

metal. Because the vessel inner surface consists

of base metal, all but a small fraction of the clad

(or surface-related) flaws will be adjacent to base

metal rather than at weld metal locations. All of

the surface/clad flaws are assumed to have

circumferential orientations. The flaw depths are

assumed to equal the full thickness of the clad and

are assigned to the depth dimension bin

corresponding to the clad thickness.

9.5.2 Flow Chart for Surface/Clad Flaws

The computational procedure for generating the

distribution tables for surface/clad flaws is

relatively simple compared to the flow chart of

Figure 9.2. Section 8 describes the procedure in

detail. The underlying methodology is designed

to provide flaw distribution tables in terms of

flaws per unit area of vessel inner surface.

However, to be consistent with the FAVOR code,

these distributions are converted to surface flaws

per unit volume or'unit alrea based on the material

for the full thickness of the vessel wall.

'9.13
OCONEE-1 OCTOBER 29, 2002 - BASE METAL FLAWS/FT-3

3 1000 219.10 2 1 1 1 0.0

0.9300 1 1 6.5 1.0 11.00

0.0500 1 2 3.5 1.0 11.00

0.0200 1 3 3.5 1.0 11.00

Figure 9.7. Sample from Flaw Distribution Input File for Base Metal Region

GENERATION OF FLAW DISTRIBUTION INPUT FILE FOR THE ORNL FAVOR CODE

NAME OF REGION = OCONEE-1 OCTOBER 29, 2002 - BASE METAL FLAWS/FT'3

NUMBER OF SUBREGIONS * 3

UNCERTAINTY CALCULATION

NUMBER OF MONTE CARLO SIMULATIONS = 1000

VESSEL TOTAL WALL THICKNESS (MM) - 219.10

ENGLISH UNITS - FLAWS PER FTA2 OR FLAWS PER FT^3

WELD DENSITY OPTION - FLAWS PER UNIT VOLUME

BASE-METAL APPROXIMATION IS USED

OUTPUT FILE REFORMATED FOR INPUT TO ORNL FAVOR CODE

SUBREGION NUMBER 1

VOLUME FRACTION = .9300

PVRUF VESSEL PARAMETERS

SAW (SUBMERGED METAL ARC WELD)

BEAD SIZE (MM) = 6.50

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT * 1.0)

CLAD THICKNESS(MM) = .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) - .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) = 11.0000

SUBREGION NUMBER 2

VOLUME FRACTION = .0500

PVRUF VESSEL PARAMETERS

SMAW (SHIELDED METAL ARC WELD)

BEAD SIZE (MM) 3.50

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT - 1.0)

CLAD THICKNESS(MM) - .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) - .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) = 11.0000

SUBREGION NUMBER 3

VOLUME FRACTION = .0200

PVRUF VESSEL PARAMETERS

REPAIR WELD

BEAD SIZE (MM) = 3.50

FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT = 1.0)

CLAD THICKNESS(MM) = .0000 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) = .0000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS = 0 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) - 11.0000

Figure 9.8. Sample Flaw Distribution Output File for Base Metal Region

9.14
MAX DJStIST2 sunow F 11OTN = I

x ILWIWT-*. 1.0-1.21 1.20.1.0 1.0.2.0

1 .170SX0.02 40.702 21.943 10.41

2 .17462Z.01 80.777 3.000 1.222

J .2042-2.00 31.241 3.413 2.02

4 .222023-01 20.001 13.234 13.420

0 .140273.-1 20.180 10.630 22.648

s .000003.00 1010.60 .0e0 .e0o

7 .000003.00 100.000 -. 000 .00e

I .000003.00 100.000 .e00 .000

I .0ee0000.0 100.000 .e00 .000

0 .000003.00 100.00e ; .000 .000

11 .000003,00 100.000 .000 .000

12 .000403.o0 100.000 .o00 .000

1 .000003.00 100.000 .e00 .000

14 .000003.00 100.000 .000 .o00

1s .000003.00 200.000 .000 .000

10 .000003.00 100.o00 .00o .ee0

17 .000003.00 100.000 .e00 .000

to .000003.00 100.000 .0e0 .e00

is .000003.e0 100.000 .000 .00e

20 .000003.00 100.000 .e00 .006

21 .000003.40 100.000 .0e0 .000

22 .000003.60 100.000 .600 .000

22 .000003.00 100.000 .000 .e00

24 .000003.00 100.000 .600 .000

20 .000003.00 100.000 .000 .000

20 .000003.00 100.000 .000 .000

27 .000003.00 100.000 .000 .000

26 .00000o.00 100.000 .000 .000

20 .000003.00 100.040 .000 .000

20 .000003.00 100.000 .000 .000

31 .000003.00 100.000 .600 .000

1l .000003.00 100.000 .600 .e00

32 .000003.00 100.000 .000 .600

24 .000003.00 100.000 .000 .000

20 .000003.00 100.040 .000 .000

20 .000040.00 100.000 .e00 .000

27 .000003.00 100.000 .e00 .000

26 .000003.00 100.000 .u00 .000

20 .e00000.00 100.000 .000 .000

40 .000003.00 100.000 .600 .000

41 .00000.00 100.000 .000 .000

02 .000003.00 100.000 .0e0 .ee0

43 .600003.00 100.006 .000 .e00

44 .600000.00 100.000 .000 .000

4* .000003.00 100.000 .600 .000

4s .000003.00 100.000 .000 .000

47 .600003.00 100.000 .040 .e00

40 .000003.00 100.000 .000 .000

40 .000003.40 100.000 .000 .000

s0 .e000003.0 160.000 .000 .000

31 .000003.06 100.000 .600 .000

32 .000003.00 100.000 .000 .000

02 .0o0003.00 100.000 .e00 .600

34 .0#0003.00 100.000 .6s0 .600

Ss .0e0000.00 100.600 .040 .000

is .000038.00 100.000 .000 .D00

07 .600003-.0 100.040 .000 .600

30 .000003.06 100.600 .000 .000

it .000003.00 166.040 .600 .000

00 .400003.00 100.000 .000 .000

01 .000003,00 100.000 .000 .600

62 .00e003.00 100.000 .000 .e00

02 .00e000.00 100.000 .ee0 .e00

04 .000003.00 100.000 .000 .000

is .e00003.00 100 .000 .e00 .000

of .000003.00 100.000 .000 .000

07 .000003.60 160.000 .000 .000

It .000003.00 100.000 .000 .000

so .000003.00 100.000 .0e0 .000

70 .0e00003.0 104.000 .044 .000

71 .000003.00 100.600 .000 .000

72 .600o00300 100.000 .o00 .000

73 .600003.00 100.000 .e00 .000

74 .600o00000 100.000 .000 .e00

70 .00003.0o0 100.00o .e00 .0oo

7s .000003.00 100.000 .000 .000

77 .000003.00 100.000 .000 .000

is .000000.00 100.000 .600 .000

70 .o00000.00 100.000 .000 .000

60 .000003.00 100.000 .e00 .o00

01 .e00000.00 100.000 .e00 .000

n2 .000003.00 100.000 .000 .600

62 .0000o0.00 100.000 .e00 .000

u4 .000003.00 100.000 .e40 .000

Is .000003.00 100.000 .000 .000

Is .000003e. 100.000 .0e0 .000

07 .000003.00 100.000 .e00 .000

as .e0oooo." 100.00 .600 .000

es .00000e.06 100.000 .000 .e00

to .e00000.00 100.000 .s00 .e60

I1 .00000e.00 100.040 .s00 .000

02 .00000o.00 100.000 .e00 .000

0n .000003.0o 100.600 .000 .000

00 .00000S.00 100.000 .000 .e00

Ss .e0000e.06 106.000 .000 .e00

I0 .00000s-.0 100.600 .000 .000

n7 .00000e0,0 100.000 .000 .000

ss .e00000.00 100.000 .e00 .0e0

0t .000000.00 100.000 .000 .000

100 .00000.O0 100.004 .440 .000

-1.0..

3.001

.277

2.721

2.10

20.0 0

.000

.000

.000

.000

.000

.000

.000

.000

.000

.600

.000

.000

.000

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.000

.000

.600

.600

.000

.000

.000

.000

.000

.000

.600

.000

.00

.00

oo0

.00

.60

.00

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eoo0

.6o0

.000

.000

.000

.600

.00

.00

.00

.00

.06

ooo0

oo00

eoo0

eee0

.00

eoe0

eoe0

eoo0

.60

eoo0

eoo0

.00

.00

.60

.00

.000

.000

.000

.000

.ooo

.000

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.e000

.§000

.#00

.|000

.@000

.000

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.000

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.000

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.000

.000

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.000

.000

.000

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2.o-.

1.711

.222

2.002

3.12

7.007

.e000

.000

.|000

. 000

.§00

.§000

.§00

.§00

.e00

.000

.400

e0e0

.000

.000

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.000

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.000

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.000

.000

.e0o

.000

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.000

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.000

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.0o0

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.000

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.000

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.000

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.000

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.000

.000

.000

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.0o0

.000

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4.0.0.6. 1.200

.149

2 .411

.@000

,.000

.000

.D000

'.000

',.@00

.g000

.@000

.000

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.000

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.000

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.000

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.000

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.oo0

.000

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.000

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.000

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.eoo

.0o0

.ooo

0.0.0. 0 .0-2.0

1.100 1.717

.000 .101 .011 .121

2.701 1.002 .019 .372 .000 .o00

.000 .000

.000 .000

.000 .000

.000 .000

.000 .000

.000 .000

.o00 .o0o .000 .000

.000 .000

.e4e .000

.00o .o00 .000 .000

.000 .000

.o00 .000 .000 .000

.000 .000

.00o .000 .000 .000

.000 .000

.o00 .000 .000 .600

.00o .000 .000 .000

.000 .000 .000 .000

.000 .o00 .000 .000 .000 .000

.000 .o00 .000 .00e

.000 .o00

.000 .o00

.04o .040 .e00 .e00

.e00 .000

.000 .o00 .000 .000

.000 .000

.000 .000 .000 .e00 .000 .0o

.000 .000 .00e .00e

.000 .0e0 .000 .000 .000 .0o0 .e00 .eoo

.000 .000

.000 .. 000

.000 .000

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.00o .e00 .000 .000 .0o0 .o00

.0ee .000 .000 .000 .000 .o00

.000 .000 .000 .o00

.00o .000

.000 .000

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.000 .000 .000 .000 .00o .00o .000 .000

.000 .000

.000 .000

.000 .000 .000 .000

.000 .000

.000 .000 .000 .000 .000 .00o

.000 .o00

.000 .000

.000 .000 .0e0 .eo0 .000 .600

.000 .000 .000 .000

.000 .000 .000 .000 .000 .o00

.000 .000 .000 .000

.000 .000

.o00 .000 .000 .0e0

.000 .000

.000 .000 .0o0 .000 .000 .000

*.oil* ooXso >l

.a22 1.732 1.240

.00S .021 .000

.100 .003 .002

.100 .040 .001

.042 .000 .000

.0o0 .000 .000

.000 .000 .000

.e0o .000 oo00

.000 .000 .000

.000 .000 .oo0

.000 .e00 .000

eoo0 .000 .000

.000 .000 .o0

.000 ,o0o .000

.000 ,000 .o0o

.000 .000 .000

.000 .00 .000

.000 .000 .o00

.000 .¢00000 .

.000 ,OO .000

.000 .000 .000

.00o .000 .000

.000 .000 .00

.000 .Oo .0o0

.o00 .000 .0o0

.000 000 .000

.000 .0 .000

.0o0 .000 .000

.000 .000 .eo0

.000 .000 .000

.000 .000 .000

.000 .00 .ooo

.000 ---. 000 .000

.000 .000 .000 .000 .000 .0o0

.000 .000 .000

.00 .000 .000 .000 .600 .000

.00 .000 .000

.00 . 000 - . 000

.00 .000 .000

.00 .0O0 .0o0

.00 .600 .000

.000 .000 .000

10 :::.O oo

.000 .000 .0oo

.000 .000 .000

.000 .000 .000

.00 .00 .000

.000 .000 .000

.000 .000 .000

.000 .000 .000

.e00 .000 .eo0

.o00 .000 .000

.000 .oo0 .ooo

.600 .000 .000

.60 .000 .000

.00 .000 .00o

oo0o .000 .600

.00 .00 .000

o000 .0 .000

00o .000 .00

.000 .000 .000 .00 .o00 .00o

eo00 .000 .000

o00 .0o0 .0o0

.000 ,00 .000

o00e .000 .000

.000 .00 .00o

ooo0 .000 .0oo

000 ooo0 .600

.000 .000 .00

e000 .000 .00e

0o0 .000 .000

000 e0o0 .000

000 .000 .000

e000 .000 .00o

e00e .000 .000

ooo0 .00o .000

.0o .000 .ooo

o0o0 .000 .000

ooo0 .000 .000

.00 .000 .00

.0o0 .000 .o0o

o000 .000 .000

o00 .000 .000

.00 .000 .^000

.000 .000 .000

.oe0 .000 .eeo

.00 .00 .000

.000 .60 .o00

.00 .000 .000

.00 .0oo .000

.00 .00 .000

.00 .000 .000

Figure 9.9. Sample Flaw Data from Output File for Base Metal Region

9.15
9.5.3 Sample Input File for Surface/Clad

Flaws

Figures 9.10 through 9.12 present inputs and

outputs for a sample calculation generated by the

PNNL flaw distribution algorithm. This table was

the first of a total of 1000 such tables that make

up the input file for FAVOR. Because there was

no evaluation of statistical uncertainties for the

parameters of the flaw distribution for

surface/clad flaws, all 1000 datasets are identical.

The FAVOR code is, however, structured to

address uncertainties in the distributions, should it

become possible in the future to quantify these

uncertainties.

The rows of Figure 9.12 come from a binning of

the data from the continuous flaw distributions

into 100 bins. Each bin corresponds to a depth

category defined by 1% increments of the vessel

wall thickness. For example, the bin designated

by the label "I" on Figure 9.12 gives the number

of flaws per square foot that have depth

dimensions between 1% and 2% of the vessel

wall thickness. In this case, there are zero flaws

per square foot for this depth category because the

depth of a flaw extending through the full clad

thickness does not correspond to this particular

bin. Rather, the specified clad thickness of

4.77 mm results in flaws having depths within the

bin of 2% to 3% of the vessel wall thickness. In

this case, there are 0.0036589 clad/surface flaw

per square foot of clad surface, and all flaws are

within the bin corresponding to 2% to 3% of the

vessel wall. The value of flaw density of

0.0036589 is relatively small because it accounts

for the factor of 1000 ratio (as discussed in

Section 8) between the total clad flaw density

(including for flaws of all depth dimensions)

versus the small number of flaws that are

sufficiently large to contribute to vessel failure.

It is also seen in Figure 9.12 that 67.45% of the

flaws have aspect ratios equal to 2:1. The final

column of the table indicates that 7.817% of the

flaws have aspect ratios that should be treated as

infinite by FAVOR

Figure 9.6 includes a plot of the clad/surface flaw

distribution. The flaw depth distribution is flat

and is truncated at a flaw depth dimension

corresponding to the thickness of the clad.

9.16
OCONEE-1 CLAD OCTOBER 29, 2002 SINGLE LAYER .FLAWS/FTA2

1 1000 '219.10 2 2 0 1 0.0

1.0000 1 4 4.77 1.0 4.77 25.4 1.. 200.0

Figure 9.10. Sample Flaw Distribution Input File for Surface/Clad Flaws

GENERATION OF FLAW DISTRIBUTION INPUT FILE FOR THE ORNL FAVOR CODE

NAME OF REGION - OCONEE-1 CLAD OCTOBER 29, 2002 SINGLE LAYER FLAWS/FTA2

NUMBER OF SUBREGIONS - 1

UNCERTAINTY CALCULATION

NUMBER OF MONTE CARLO SIMULATIONS - 1000

VESSEL TOTAL WALL THICKNESS (MM) = 219.10

ENGLISH UNITS - FLAWS PER FT 2 OR FLAWS PER FT^3

WELD DENSITY OPTION - FLAWS PER UNIT AREA

BASEMETAL APPROXIMATION NOT USED

OUTPUT FILE REFORMATED FOR INPUT TO ORNL FAVOR CODE

SUBREGION NUMBER 1

VOLUME FRACTION - 1.0000

PVRUF VESSEL PARAMETERS

CLAD

BEAD SIZE (MM) . 4.77

FACTOR ON FLAW FREQUENCIES - 1.0000 (DEFAULT . 1.0)

CLAD THICKNESS(MM) = 4.7700 (USED ONLY FOR CLAD)

CLAD BEAD WIDTH (MM) = 25.4000 (USED ONLY FOR CLAD)

NUMBER OF CLAD LAYERS - 1 (USED ONLY FOR CLAD)

TRUNCATION ON FLAW DEPTH (MM) . 200.0000

Figure 9.11. Sample Flaw Distribution Output File for Surface/Clad Flaws

9.17
FLAK VDSIRU3UTOM 700 SIMOMLT1OI 00033 1

3 ,JM/ro*2 2.0

2. .000003.00 10.0

.oooooI.oo 100.o0o

3 .000303.03 47.400

4 . 000003.00 100.000

5 .000003,00 1OO.00D

0 .000003,00 100.000

7 .000003,00 100.*00

0 .000003,00 100.000

.000003,00 100.000

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Figure 9.12. Sample Flaw Data from Output File for Surface/Clad Flaws

9.18
10 CONCLUSIONS

An improved model for postulating fabrication

flaws in reactor pressure vessels has been

developed that is based on empirical data

representative of fabrication practices in the U.S.

from the late 1960s through early 1980s. This

model addresses three broad categories of flaws:

(1) weld flaws, (2) base metal flaws, and

(3) cladding flaws. A separate set of input data

corresponding to each flaw category is provided

as input to the FAVOR code for PTIS calculations.

The input files describe the number of flaws per

cubic volume, the distribution of flaw depth

dimensions, and the distribution of flaw aspect

ratios. Other key features of the flaw model are

as follows:

(I) The flaw model treats the flaw locations as

uniformly distributed through the thickness of

the vessel wall and does not make the

conservative assumption that the flaws are

inner-surface breaking.

(2) Weld flaws are assumed to lie along the weld

fusion line in a manner to allow them to

potentially grow into either the weld material

or base metal, whichever is more limiting

from the standpoint of fracture toughness.

(3) Clad materials are assumed to have sufficient

fracture toughness to preclude the growth of

flaws within the cladding material, which

implies that the clad flaws are structurally

significant only if they extend up to or

penetrate beyond the clad-to-base metal

interface.

(4) Underclad cracks in base metal are not

addressed, although the model could be

enhanced in the future to evaluate vessels of

concern to PTS for which underclad cracking

is considered a credible mechanism of

cracking.

(5) Flaws of most concern to failure of base metal

regions include flaws associated with weld

fusion line and flaws associated with cladding

in addition to flaws within the base metal

itself.

Data files have been prepared for use by ORNL

for PTS calculations with the FAVOR code.

Calculations will be performed for several

representative vessels that will consider plants

from the major nuclear steam supply system

suppliers. Although most calculations will be for

vessels for which the weld material is the most

limiting from the standpoint of embrittlement, one

vessel will have base metal as the most limiting

material.

10.1
11 REFERENCES

Bishop BA. 1993. .Benchmarking ofProbabilistic

Fracture Mechanics Analyses ofReactor Vessels

Subjected to Pressurized Thermal Shock Loading,

EPRI Research Project 2975-5, Electric Power

Research Institute, Palo Alto, CA.

Chapman OJV. 1993. "Simulation of Defects in

Weld Construction," Reliability and Risk in

Pressure Vessels'and Piping, PVP-Vol. 251,

pp. 81-89, American Society of Mechanical

Engineers, New York.

Chapman OJV, and FA Simonen. 1998.

RR-PRODIGAL - A Modelfor Estimating the

Probabilities of Defects in Reactor Pressure

Vessel Welds, NUREG/CR-5505, U.S. Nuclear

Regulatory Commission, Washington, DC.

Chapman OJV, MA Khaleel, and FA Simonen.

1996. "A Simulation Model for Estimating

Probabilities of Defects in Welds," Fatigue and

Fracture - 1996- Volume 1, PVP Vol. 323,

pp. 375-391, American Society of Mechanical

Engineers, New York.

Crawford SL, GJ Schuster, AF Pardini, and

SR Doctor. 2000. "Initial Studies in Developing

Fabrication Flaw Rates for Base Metal of Pressure

Vessels," presented at the 2"d International

Conference on NDE in Relation to Structural

Integrityfor Nuclear and Pressurized

Components, New Orleans, LA (May 24-26,

2000).

Dickson TL. 1994. FAVOR: A Fracture

Mechanics Analysis Code for Nuclear Reactor

Pressure Vessel, Release 9401,

ORNL/NRC/LTR/94/1, Martin Marietta Energy

Systems, Inc., Oak Ridge National Laboratory,

Oak Ridge, IN.

Dickson TL, and FA Simonen. 1997. "Inclusion

of Embedded Flaws in Pressurized Thermal

Shock Analyses of Nuclear Reactor Pressure

Vessels," Fatigue and Fracture - 1997 -

Volume 2, PVP Vol. 346, pp. 197-205, American

Society of Mechanical Engineers, New York.

Dickson TL, SNM Malik, JW Bryson, and FA

Simonen. 1999. "Revisiting the Integrated

Pressurized Thermal-Shock Studies of an Aging

Pressurized Water," Fracture, Design Analysis of

Pressure Vessels, Heat Exchangers, Piping

Components and Fitnessfor Service - 1999, PVP

Vol. 388, American Society of Mechanical

Engineers, New York.

Halmshaw R, and CA Hunt. 1975. "Can Cracks

Be Found by Radiography?", British Journal of

Nondestructive Testing, May 1975, pp. 71-75.

Jackson DA, and L Abramson. 2000. Report on

the Preliminary Results of the Expert Judgment

Process for the Development of a Methodology

for a Generalized Flaw Size and Density

Distribution for Domestic Reactor Pressure

Vessels, MEB-00-01, PRAB-00-01, U.S. Nuclear

Regulatory Commission, Washington, DC.

Jackson DA, and SR Doctor. 2000. "Developing a

Generic Flaw Distribution for Reactor Pressure

Vessels," 2nd International Conference on NDE in

Relation to Structural Integrityfor'Nuclear and

Pressurized Components,'New Orleans, LA

(May 24-26, 2000).

Jackson DA, L Abramson, SR Doctor, FA

Simonen, and GJ Schuster. 2001. "Developing a

Generalized Flaw Distribution for Reactor

Pressure Vessels," Nuclear Engineering and

Design, Vol. 208, pp. 123-13 1.

11.1
Li YY, and WR Mabe. 1998. "Defect Distribution

in Weld-Deposited Cladding," Fatigue,

Environmental Factors, and New Materials, PVP

Vol. 374, pp. 75-90, American Society of

Mechanical Engineers, New York.

Marshall Committee. 1982. An Assessment of the

Integrity ofPWR Vessels, Second Report by a

Study Group under the Chairmanship of

DW Marshall, published by the U.K. Atomic

Energy Commission.

Pardini AF, GJ Schuster, SL Crawford, and SR

Doctor. 2000. "Validation of Fabrication Flaws in

Weld metal from PVRUF," 2d1u International

Conference on NDE in Relation to Structural

Integrity for Nuclear and Pressurized

Components, New Orleans, LA (May 24-26,

2000).

Schuster GJ, SR Doctor, and PG Heasler. 1998.

Characterization of Flaws in U.S. Reactor

Pressure Vessels: Density and Distribution of

Flaw Indications in PVRUF. NUREG/CR-6471,

Vol. 1, U.S. Nuclear Regulatory Commission,

Washington, DC.

Schuster GJ, SR Doctor, SL Crawford, and AF

Pardini. 1999. Characterization of Flaws in U.S.

Reactor Pressure Vessels: Density and

Distribution ofFlaw Indications in the Shoreham

Vessel, NUREG/CR-6471, Vol. 3, U.S. Nuclear

Regulatory Commission, Washington, DC.

Schuster GJ, SR Doctor, SL Crawford, and AF

Pardini. 2000a. Characterization of Flaws in U.S.

Reactor Pressure Vessels: Validation of Flaw

Density and Distribution in the Weld Metal of the

PVRUF Vessel, NUREG/CR-6471, Vol. 2, U.S.

Nuclear Regulatory Commission, Washington,

DC.

Schuster GJ, AF Pardini, SL Crawford, and SR

Doctor. 2000b. "Overview of Fabrication Flaw

Studies on RPV Material from Four Canceled

Nuclear Power Plants," 2"" International

Conference on NDE in Relation to Structural

Integrity for Nuclear and Pressurized

Components, New Orleans, LA (May 24-26,

2000).

Schuster GJ, and SR Doctor. 200 la. "Fabrication

Flaw Rate Estimates for Base Metal of Pressure

Vessels and Initial Validation Results," 3 rd

International Conference on NDE in Relation to

Structural Integrityfor Nuclear and Pressurized

Components, Seville, Spain.

Schuster GJ, and SR Doctor. 200 lb. "Use of

SAFI-UT in Characterizing Fabrication Flaws in

Nuclear Reactor Pressure Vessels," 3rd

International Conference on NDE in Relation to

Structural Integrity for Nuclear and Pressurized

Components, Seville, Spain.

Simonen FA, KI Johnson, AM Liebetrau,

DW Engel, and EP Simonen. 1986. VISA-Il-A

Computer Code for Predicting the Probability of

Reactor Pressure Vessel Failure, NUREG/CR4486, U.S. Nuclear Regulatory Commission,

Washington, DC.

Simonen FA, and KI Johnson. 1993. "Effects of

Residual Stresses and Underclad Flaws on the

Reliability of Reactor Pressure Vessels,"

Reliability and Risk in Pressure Vessels and

Piping, PVP Vol. 251, pp. 91-100, American

Society of Mechanical Engineers, New York.

Simonen FA, SR Doctor, GJ Schuster, DA

Jackson, and L Abramson. 2001. "Flaws in Vessel

Cladding and Their Potential Contributions to

Vessel Failure Probabilities," Service Experience,

Fabrication, Residual Stresses and Performance,

PVP Vol. 427, pp. 21-32, American Society of

Mechanical Engineers, New York.

11.2
Appendix A

STATISTICAL EQUATIONS FOR

FLAW DISTRIBUTION FUNCTIONS AND UNCERTAINTY

ANALYSES
Appendix A

STATISTICAL EQUATIONS FOR

FLAW DISTRIBUTION FUNCTIONS AND UNCERTAINTY

ANALYSES

This appendix describes the basis of a Monte Carlo methodology to simulate uncertainty in flaw

distribution estimates. This methodology relies on the "generalized flaw distribution model" that NRC

developed (Jackson and Abramnson 2000) to describe flaws in a RPV. The objective is to develop a

methodology for producing a set of flaw distribution functions along with a characterization of the

statistical uncertainties in the parameters of the functions. The FAVOR code performs a random

sampling to incorporate the uncertainty into vessel evaluations. Because such a strategy implicitly views

the flaw density and size distribution functions as random, it is natural to utilize a Bayesian estimation

methodology. Under a Bayesian methodology, the data are summarized in terms of a posterior

distribution, and a Monte Carlo sampling of the posterior will produce a set of results that describe

uncertainty.

A.1 Definitions

The function y(x, a): represents a gamma density function parameterized by the vector a. as defined by

the formula

a1

2 XG2I A

r(a 2 ) exp(-ax) (A.1)

The finction DIR(p: a) is a Dirichlet distribution, which is defined as

DIR(pra)= r(a+) a.-I a2 -1 a.- -1.

r(al)r(a2 ) ... j.(am)PI -Pm"' P2 (A.2)

A.2 Distributional Families Required for Modeling

This section presents three distributional families that are required to model the available flaw data.

These are Poisson, exponential, and multinomial. The Poisson distribution is used to model flaw density

data, while the other two are used to describe the flaw depth and length data. The following describes the

standard posteriors for each distributional family.

A.2.1 Posterior for a Poisson Density Parameter

A flaw density parameter p is to be estimated from count data; a total of N flaws are observed in a volume

Vof material. The count Nis assumed to be Poisson distributed, so the conditional distribution is

A.1
f(Nlp) = exp(- pV) (A.3) N!

The standard conjugate prior employed for such a distribution is a two-parameter gamma distribution.

Assume that the prior distribution is

p(p)=y(p:a) (A.4)

Then the posterior distribution is given by

f(pjN) = y(p: a, + V, a 2 + N) (A.5)

The standard noninfornmative prior assigns a, = 0, and a2 = 0, so that the posterior is the same as the

likelihood. However, if one uses this improper prior, the posterior will not exist when N= 0. We do not

expect to encounter such situations with the current dataset, so we will employ the above prior

distribution for analysis.

This means that the posterior distribution we will employ for the flaw density parameter is

f (PIN)=y(p: V,N) (A.6)

A.2.2 Posterior for an Exponential Distribution Parameter

A set of data, (xi, i = 1, 2, 3, ..., n) is observed from an exponential distribution with rate parameter A. In

other words, the conditional distribution for xi is given by

f(x,1A)=Aexp(-Ix) (A.7)

The standard conjugate prior distribution on A is a gamma of the form

p(2) = yr(: a) (A.8)

and this results in a posterior distribution of

f (21x)=ry(:S+a,,n+ a2) (A.9)

where S = lixi is the sufficient statistic for the data.

A.2.3 Posterior for Multinomial Distribution Parameters

Let Xi, i = 1, 2, 3, ...m represent multinomial variates, with conditional distribution

( X ! X2 !.2 ..Xm! m (A.10)

A.2
The parameter vector, Ai, must sum to one.

The conjugate family for this distribution is the Dirichiet, which is denoted as DIR(p: a). If the prior

distribution is given by

p(fl)=DIR(fi:a) (A.11)

then the posterior is given by

f(fijX)=DIR(f :a +X) (A.12)

The standard noninformative prior is produced by setting acz = 0. With the noninformative assignment,

the posterior will not exist if anyXi is zero. Because we intend to use the multinomial on small flaws

only, which are quite numerous, XI is not expected to be zero, so we will set alpha to zero. The posterior

employed on multinomial data is therefore

f(OJX)=DIR(fl:X) (A.13)

A.3 Reference

Jackson DA, and L Abramson. 2000. Report on the Preliminary Results ofthe Expert Judgment Process

for the Development of a Methodology for a Generalized Flaw Size and Density Distribution for

Domestic Reactor Pressure Vessels, MEB-00-01, PRAB-00-01, U.S. Nuclear Regulatory Commission,

Washington, DC.

A.3
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

(2-9) (Assigned by NRC. Add Vol.. Supp. Rev., NRCM 1102. BIBLIOGRAPHIC DATA SHEET and Addendum Numbers, II any.)

3201.3202 BBIGAHCDT HE

* (See instnrctions on the reverse) a NUREG/CR-681 7

2. TITLE AND SUBTITLE PNNL - 14268

A Generalized Procedure for Generating Flaw-Related Inputs for FAVOR Code

3. DATE REPORT PUBUSHED

MONTH YEAR

March 2004

4. FIN OR GRANT NUMBER

Y6604

5. AUTHOR(S) 6. TYPE OF REPORT

F.A. Simonen, S.R. Doctor, G. J. Schuster, P. G. Heasler Technical

7. PERIOD COVERED (indusive Dates)

8. PERFORMING ORGANIZATION -NAME AND ADDRESS (IfNRC. pmindeo Dn Ofioc orRegior U.S. NudearRegutatoyCommisson. and ,nainv address Vcontactor, provl name and malk', address.)

Pacific Northwest National Laboratory

P.O. Box 999

Richland, WA 99352

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRCa jp 'Same as above'. conracor, provide NnCDvsln. Offreor Region. U.S. NucfearRegulatoryCommission. andmag address.)

Division of Engineering Technology

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555-0001

10. SUPPLEMENTARY NOTES

n A A.Icnken MP(r Prnmiart MAnmnnr _- .' ... - . .- J--.

11. ABSTRACT (200 odsor lss)

The U.S. Nuclear Regulatory Commission (USNRC) has supported research to re-evaluate regulations for pressurized thermal

shock (PTS). A critical factor for a reactor pressure vessel (RPV) Is to fail, In addition to severe overcooling transient and an

embrittled material, Is a crack-like flaw near the Inner vessel surface. This report summarized research on fabrication flaws

performed at Pacific Northwest National Laboratory (PNNL) as part of a larger multi-year program sponsored by the USNRC to

address Issues related to the reliability of ultrasonic testing (UT) and the development of improved programs for Inservice

inspection (ISI). These studies have generated data on flaws In RPVs in terms of flaw densities, flaw locations, and flaw sizes

(through-wall depth dimensions and lengths). The present report describes data from these studies, results from an expert

judgement elicitation on RPV fabrication practices, and probabilistic model that characterize flaws that may exist In vessels. A

procedure Is described for generating flaw parameters for use as inputs to probabilistic fracture mechanics calculations.

12. KEY WORDSIDESCRIPTORS (List ordsorpirsssUt wassist hesh hiatiocalgerepo4) 13. AVAILABILITY STATEMENT

Generalized Flaw Distribution unlimited

PTS Re-evaluation 14. SECURITY CLASSIFICATION

FAVOR Code (is Page)

Inputs for FAVOR Code unclassified

Fabrication Flaws (T Ml Repo"V

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (2-89) This form was electronically produced by Elite Federal Forms, Inc.
I

Federal Recycling Program
NUREG/CR-6817 A GENERALIZED PROCEDURE FOR GENERATING FLAW-RELATED INPUTS

FOR THE FAVOR CODE

MARCH 2004

UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

OFFICIAL BUSINESS