A Generalized Procedure for 

Generating Flaw-Related 

Inputs for the FAVOR Code

Office of Nuclear Regulatory Research

NUREG/CR-6817, Rev. 1

PNNL-14268A
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p 

A Generalized Procedure for

Generating Flaw-Related 

Inputs for the FAVOR Code

Manuscript Completed: March 2013

Date Published: August 2013

Prepared by: 

F. A. Simonen, S. R. Doctor, G. J. Schuster, and P. G. Heasler

Pacific Northwest National Laboratory

P.O. Box 999

Richland, WA 99352

D. Jackson and W. E. Norris, NRC Project Managers 

NRC Job Codes Y6604 and N6398

 

Office of Nuclear Regulatory Research

NUREG/CR-6817, Rev. 1

PNNL-14268A

iii

ABSTRACT

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

technical basis for Title 10 of the Code of Federal Regulations (CFR) 50.61, “Fracture 

toughness requirements for protection against pressurized thermal shock events.” During plant 

operation, the walls of reactor pressure vessels (RPV) are exposed to neutron radiation, 

resulting in a localized embrittlement of the vessel steel and weld materials in the core area. If 

an embrittled RPV had an existing flaw of critical size and certain severe system transients were 

to occur, this flaw could very rapidly propagate through the vessel, resulting in a through-wall 

crack that could challenge the integrity of the RPV. The severe transients of concern, known as 

pressurized thermal shock (PTS), are characterized by a rapid cooling (i.e., thermal shock) of 

the internal reactor pressure vessel surface in combination with re-pressurization of the RPV.

Specifically, the crack-like flaws of concern are those near the inner vessel surface. This report 

documents research performed at Pacific Northwest National Laboratory (PNNL) to assess 

fabrication flaws in RPVs. The research generated data on flaws in RPVs in terms of flaw 

densities, flaw locations, and flaw sizes (through-wall depth dimensions and lengths). This 

report describes data from the research, 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. The report addresses the treatment of welding flaws using the 

flaws per unit area concept and describes additional details of the flaw model used in the 

FAVOR(a) probabilistic fracture mechanics code.

PAPERWORK REDUCTION ACT STATEMENT

This NUREG does not contain information collection requirements and, therefore, is not subject 

to the requirements of the Paperwork Reduction Act of 1995 (44 U.S.C. 3501 et seq.).

PUBLIC PROTECTION NOTIFICATION

The NRC may not conduct or sponsor, and a person is not required to respond to, a request for 

information or an information collection requirement unless the requesting document displays a 

currently valid OMB control number.

 

(a) Fracture Analysis of Vessels – Oak Ridge (FAVOR) computer code developed for the NRC by the 

Heavy Section Steel Technology (HSST) program at Oak Ridge National Laboratory (ORNL). The 

FAVOR computer code is a computational methodology developed through interaction between 

experts in the relevant disciplines of thermal hydraulics, probabilistic risk assessment, materials 

embrittlement, fracture mechanics, and inspection (flaw characterization). This computer code 

represents the baseline NRC-selected applications tool for re-assessing the current PTS regulations 

to ensure that RPVs maintain structural integrity when subjected to transients such as PTS events.

v

FOREWORD

The current regulations to ensure that nuclear reactor pressure vessels (RPVs) maintain 

structural integrity when subjected to transients such as pressurized thermal shock (PTS) 

events were derived from computational models developed in the early-to-mid 1980s. Since 

that time, advancements in the understanding and knowledge of materials behavior, the ability 

to more realistically model plant systems and operational characteristics, and the ability to better 

evaluate PTS transients to estimate loads on vessel walls has led to the realization that the 

earlier analyses contained significant conservatisms. Accordingly, there is an on-going effort by 

the U.S. Nuclear Regulatory Commission (NRC) to re-evaluate the technical basis for Title 10 of 

the Code of Federal Regulations (CFR) 50.61, “Fracture toughness requirements for protection 

against pressurized thermal shock events.”

Updated computational methodologies have evolved through interactions between experts in 

the relevant disciplines of thermal hydraulics, probabilistic risk assessment, materials 

embrittlement, fracture mechanics, and inspection (flaw characterization). Analyses have 

shown that vessel behavior is sensitive to flaw location, type, size, orientation, and other flaw 

characteristics. Accurate estimates of flaw density and distribution are required as input to the 

computer codes that are used in performing structural integrity assessments. The research at 

Pacific Northwest National Laboratory (PNNL) was initiated to determine the relevant properties 

of flaws created during the fabrication of RPVs and develop data on the density and distribution 

of fabrication flaws in the base materials, cladding, and welds. Empirical studies were 

performed on RPV welds obtained from Shoreham, Hope Creek Unit 2, River Bend Unit 2, and 

the Pressure Vessel Research User Facility (PVRUF).

Based on the experimental data from this study in conjunction with calculations and expert 

judgment, it has been concluded that the coincident occurrence of critical size flaws, embrittled 

vessel steel and weld material, and a severe PTS transient is a very low probability event. In 

fact, only a few of the currently operating pressurized water reactors are projected to closely 

approach the current statutory limit on embrittlement level during their planned operational life. 

Thus, the NRC pursued rulemaking activities to revise 10 CFR 50.61.

In April 2008, the NRC published NUREG/CR-6945, Fabrication Flaw Density and Distribution in 

Repairs to Reactor Pressure Vessel and Piping Welds, describing research conducted to 

determine the relevant properties of flaws created during the fabrication of nuclear component 

weldments and the density and distribution of the fabrication flaws. In May 2009, NUREG/CR6989, Methodology for Estimating Fabrication Flaw Density and Distribution – Reactor Pressure 

Vessel Welds, was published describing a generalized flaw density and distribution approach 

that could be used to estimate flaws created during the fabrication of nuclear component 

weldments. The publication of the subject report was held pending re-evaluation of the 

technical basis for 10 CFR 50.61.
vi

It has been determined that no changes are required to the subject report as a result of the reevaluation of the technical basis for 10 CFR 50.61. The report describes the statistical 

distributions used to characterize the number and sizes of flaws in the various regions of RPVs. 

The report also describes how the data was supplemented using insights from an expert 

elicitation and a flaw simulation model. Finally, the statistical treatment of uncertainties in the 

parameters of the flaw distributions, and a presentation of some sample inputs for flaw 

distributions that supported NRC evaluation of the risk of vessel failures caused by PTS events 

are provided.
vii

CONTENTS

ABSTRACT...............................................................................................................................iii

FOREWORD ..............................................................................................................................v

FIGURES...................................................................................................................................xi

TABLES ...................................................................................................................................xv

EXECUTIVE SUMMARY ........................................................................................................xvii

ACKNOWLEDGMENTS..........................................................................................................xix

ACRONYMS AND ABBREVIATIONS.....................................................................................xxi

1 INTRODUCTION..............................................................................................................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 .................................................................................................2-2

2.1.2 Base Metal ...................................................................................................2-3

2.1.3 Repair Welds................................................................................................2-3

2.1.4 Cladding .......................................................................................................2-3

2.1.5 Underclad Cracking ......................................................................................2-4

2.2 Treatment of Flaws by FAVOR Code ........................................................................2-4

2.3 Monte Carlo Simulation .............................................................................................2-5

2.4 Estimation Procedure for Welds ................................................................................2-5

2.5 Estimation Procedure for Base Metal ........................................................................2-6

2.6 Estimation Procedure for Clad/Surface Flaws ...........................................................2-7

2.7 Flaw Locations ..........................................................................................................2-8

2.8 Treatment of Uncertainties ........................................................................................2-9

2.9 Sample Flaw Distributions.........................................................................................2-9

2.10Summary and Conclusions......................................................................................2-10

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.........................................3-9

3.3 Treatment of Large Repair Flaws ............................................................................3-10

3.4 Validated Flaw Densities and Size Distributions ......................................................3-13

3.4.1 Shielded Metal Arc Weld ............................................................................3-14

3.4.2 Submerged Arc Weld..................................................................................3-15

3.4.3 Repair Weld................................................................................................3-15
viii

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 ...........................................................4-2

4.1.3 Elicitation Training ........................................................................................4-2

4.1.4 Preparation of Issue Analyses by the Experts...............................................4-2

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...................................................................4-3

4.3 Flaw Characteristics from Elicitation..........................................................................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..............................................................................5-4

5.6 Calculations and Results...........................................................................................5-4

5.7 Flaw Characterization by PRODIGAL Code ..............................................................5-7

6 WELD FLAWS – DATA AND STATISTICAL CORRELATIONS......................................6-1

6.1 Approach and Assumptions.......................................................................................6-1

6.2 Statistical Functions for Flaw Distributions ................................................................6-5

6.2.1 Flaw Densities ..............................................................................................6-6

6.2.2 Conditional Depth Distribution for Small Flaws .............................................6-9

6.2.3 Conditional Depth Distribution for Large SAW and SMAW Flaws ...............6-12

6.2.4 Length Distribution for Small SAW Flaws in PVRUF Vessel .......................6-16

6.2.5 Length Distribution for Small SMAW and Repair Flaws in PVRUF 

Vessel ........................................................................................................6-18

6.2.6 Length Distribution for Small SAW Flaws in Shoreham Vessel...................6-19

6.2.7 Length Distribution for Small SMAW and Repair Flaws in Shoreham 

Vessel ........................................................................................................6-23

6.2.8 Length Distribution for Large SAW Flaws in PVRUF Vessel .......................6-24

6.2.9 Length Distribution for Large SMAW and Repair Flaws in PVRUF 

Vessel ........................................................................................................6-25

6.2.10 Length Distribution for Large SAW Flaws in Shoreham Vessel...................6-26

6.2.11 Length Distribution for Large SMAW and Repair Flaws in Shoreham 

Vessel ........................................................................................................6-26
ix

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.......................................................7-4

7.4 Flaw Estimation Procedure for Plate Materials ..........................................................7-6

8 CLAD FLAWS – DATA AND STATISTICAL CORRELATIONS ......................................8-1

8.1 Approach and Assumptions.......................................................................................8-1

8.2 Sources of Information Cladding Flaws .....................................................................8-2

8.2.1 PVRUF Data.................................................................................................8-3

8.2.2 Data from Bettis Laboratory..........................................................................8-4

8.2.3 Expert Judgment Elicitation ..........................................................................8-4

8.2.4 PRODIGAL Predictions ................................................................................8-5

8.2.5 Vessel-Specific Considerations ....................................................................8-7

8.3 Flaw Length Distribution for Clad Flaws ....................................................................8-8

8.4 Flaw Inputs to Fracture Mechanics..........................................................................8-11

8.5 Probabilistic Fracture Mechanics Calculations.........................................................8-14

8.5.1 Fracture Mechanics Methodology...............................................................8-14

8.5.2 Description of Reference Vessel.................................................................8-15

8.5.3 Results of Probabilistic Fracture Mechanics Calculations ...........................8-16

8.5.4 Concluding Discussion ...............................................................................8-17

9 ALGORITHM TO GENERATE FLAW INPUT FILES FOR FAVOR..................................9-1

9.1 FAVOR Code Structure and Organization .................................................................9-1

9.1.1 FAVLoad Module..........................................................................................9-1

9.1.2 FAVPFM Module ..........................................................................................9-3

9.1.3 FAVPost Module...........................................................................................9-8

9.2 Required Input Files ..................................................................................................9-8

9.3 Computer Code for Generating Flaw Input Files........................................................9-9

9.3.1 Input File to PNNL Algorithm ......................................................................9-11

9.3.2 Output File from PNNL Algorithm ...............................................................9-13

9.3.3 Output File from PNNL Algorithm for Inputs to FAVOR...............................9-14

9.4 Procedure for Weld Regions ...................................................................................9-14

9.4.1 Treatment of Weld Flaws............................................................................9-14

9.4.2 Flow Chart for Welds ..................................................................................9-15

9.4.3 Sample Input and Output File for Welds .....................................................9-18

9.5 Procedure for Base Metal Regions..........................................................................9-21

9.5.1 Treatment of Base Metal Flaws ..................................................................9-22

9.5.2 Flow Chart for Base Metal ..........................................................................9-22

9.5.3 Sample Input and Output Files for Base Metal............................................9-22
x

9.6 Procedure for Surface/Clad Flaws...........................................................................9-25

9.6.1 Treatment of Surface/Clad Flaws ...............................................................9-25

9.6.2 Flow Chart for Surface/Clad Flaws .............................................................9-25

9.6.3 Sample Input and Output Files for Surface/Clad Flaws...............................9-25

10 CONCLUSIONS.............................................................................................................10-1

11 REFERENCES...............................................................................................................11-1

Appendix A STATISTICAL EQUATIONS FOR FLAW DISTRIBUTION 

FUNCTIONS AND UNCERTAINTY ANALYSES.............................................................A-1

Appendix B LIST OF EXPERTS ON VESSEL FLAWS .........................................................B-1
xi

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 (1 inch = 25.4 mm)..............................2-8

2-4 Sample Flaw Distribution for Use in Probabilistic Fracture Mechanics 

Calculations (1 ft3 = 0.0283 m3

).....................................................................................2-10

3-1 Sequence of Techniques Used To Detect and Size Flaws..............................................3-3

3-2 Techniques Used for Detailed Characterization of Flaws ................................................3-3

3-3 Metallographic Cross Section of a Circumferential Weld from PVRUF Vessel 

Showing Adjacent Regions of Base Metal and Cladding.................................................3-4

3-4 Location of Flaw in the Fusion Zone of a Weld with the Base Metal................................3-4

3-5 Inside View of the PVRUF Vessel During SAFT-UT Clad Surface Inspections ...............3-5

3-6 Weld Normal Inspections ................................................................................................3-5

3-7 Examinations of Plate Specimens...................................................................................3-6

3-8 Image of a Fabrication Flaw Using Conventional Radiology ...........................................3-6

3-9 Micrograph of 25.4-mm (1 in.) Cube Containing a Failed Weld Bead..............................3-8

3-10 Electron Microscope Image of Cracked Weld Bead (100 μm = 0.00394 in.)....................3-8

3-11 Composition of a Complex Flaw ...................................................................................3-10

3-12 Shape and Orientation of 14-mm (0.55 in.) PVRUF Flaw - Relevant to 

Structural Integrity Assessment (1 mm = 0.0394 in.).....................................................3-11

3-13 Shape and Orientation of 32-mm (1.26-in.) Shoreham Repair Flaw with Less 

Conservative Treatment B of Flaw Dimensions (1 mm = 0.0394 in.).............................3-13

3-14 SMAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities 

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.) ..............................................................................3-14

3-15 SAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities (1 m3

= 35.3 ft3

, 1 mm = 0.0394 in.)........................................................................................3-15

3-16 Repair Metal, Through-Wall Size Distribution of Cumulative Flaw Densities 

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.) ..............................................................................3-16

3-17 Comparison of Through-Wall Size Distributions of Cumulative Flaw Densities 

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.) ..............................................................................3-17

4-1 Relative Flaw Densities of Base Metal Compared to Weld Metal as Estimated 

by Expert Judgment Process (from Jackson and Abramson 2000).................................4-5

5-1 Types of Crack-Like Defects...........................................................................................5-2

5-2 Cross Section of Thickness Transition Single V Weld for PVRUF Vessel (1 mm 

= 0.0394 in.)....................................................................................................................5-5
xii

5-3 Model of Thickness Transition Single V Weld for PVRUF Vessel (1 cm = 

0.394 in.).........................................................................................................................5-6

5-4 Calculated Flaw Frequencies for PVRUF Weld Showing Effects of Inspection 

and Repairs (1 mm = 0.0394 in.).....................................................................................5-7

5-5 Distributions of Flaw Aspect Ratio and Flaw Length as Predicted by 

PRODIGAL Weld Simulation (1 mm = 0.0394 in.)...........................................................5-8

6-1 Uncertainty in Flaw Densities for Flaws in PVRUF Vessel (1 ft3 = 0.0283 m3

).................6-8

6-2 Uncertainty in Flaw Densities for Flaws in Shoreham Vessel (1 ft3 = 0.0283 m3

) ............6-9

6-3 PVRUF Weld Metal Specimen Cut into 25.4-mm (1-in.) Plate.........................................6-9

6-4 Depth Distribution for Small Flaws Including Uncertainty Analysis ................................6-12

6-5 Uncertainty Evaluation for Complementary Conditional Depth Distribution for 

Large SAW and SMAW Flaws ......................................................................................6-13

6-6 Uncertainty Evaluation for Complementary Conditional Depth Distribution for 

Large Repair Flaws.......................................................................................................6-16

6-7 Lengths of Small Flaws in SAW and SMAW Welds of PVRUF Vessel..........................6-17

6-8 Lengths of Small Flaws in SAW Welds of PVRUF Vessel Showing Exponential 

Distribution Along with Uncertainties.............................................................................6-18

6-9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel Showing 

Exponential Distribution Along with Uncertainties .........................................................6-19

6-10 Lengths of Small Flaws in SAW and SMAW Welds of Shoreham Vessel......................6-20

6-11 Lengths of Small Flaws in SAW Welds of Shoreham Vessel Showing 

Exponential Distribution Along with Uncertainties .........................................................6-20

6-12 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham 

Vessel Showing Exponential Distribution Along with Uncertainties ...............................6-24

6-13 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel 

Showing Exponential Distribution Along with Uncertainties...........................................6-26

6-14 Lengths of Large Flaws in SAW Welds of Shoreham Vessel Showing 

Exponential Distribution Along with Uncertainties .........................................................6-27

7-1 A Flaw Detected in Plate Material ...................................................................................7-3

7-2 Flaw Frequencies for Plate Materials with Comparisons to Data for Weld Flaws 

(1 mm = 0.0394 in., 1 m3 = 35.3 ft3

) ................................................................................7-5

8-1 Examples of Flaws in Cladding of PVRUF Vessel...........................................................8-1

8-2 Summary of Data on Flaws in Vessel Cladding (1 m = 39.4 in.)......................................8-2

8-3 Lengths of Clad Flaws in PVRUF and Hope Creek II Vessels (1 mm = 

0.0394 in.).....................................................................................................................8-11

8-4 Proposed Curves for Estimating Number and Sizes of Flaws in Vessel 

Cladding (1 m = 39.4 in.)...............................................................................................8-12

8-5 Probability of Flaw Initiation in Vessel with Axial Welds as Limiting Material 

(fluence in units of 1.0 × 1019 neutrons/cm2 [6.45 × 1019 neutrons/in.2

]).........................8-16

8-6 Probability of Flaw Initiation in Vessel with Plates as Limiting Material (fluence 

in units of 1.0 × 1019 neutrons/cm2 [6.45 × 1019 neutrons/in.2

]) ......................................8-17

9-1 Data Streams for FAVOR Code Modules (1) FAVLoad, (2) FAVPFM, and 

(3) FAVPost....................................................................................................................9-2
xiii

9-2 Flaw Models in the FAVOR Code ...................................................................................9-3

9-3 Fabrication Configurations of PWR Vessel Beltline Shells ..............................................9-4

9-4 Input of User-Supplied Data on Flaw Distributions and Embrittlement and 

Output of Data on Vessel Failure Probabilities................................................................9-6

9-5 Weld Fusion Area Definitions for (a) Axial-Weld Subregion Elements and 

(b) Circumferential Subregion Elements .........................................................................9-7

9-6 Input Instructions for Flaw Distribution Algorithm ..........................................................9-10

9-7 Flow Chart for Weld Flaws............................................................................................9-17

9-8 Sample Flaw Distribution Input File for Weld Region ....................................................9-19

9-9 Sample from Flaw Distribution File for Weld Region (1 mm = 0.0394 in.)......................9-19

9-10 Sample Flaw Data Output File for Weld Region (1 ft2 = 0.0929 m2

) ..............................9-20

9-11 Flaw Distribution for Various Vessel Regions (Median Values from Uncertainty 

Analyses) (1 ft3 = 0.0283 m3

) ........................................................................................9-21

9-12 Sample from Flaw Distribution Input File for Base Metal Region...................................9-23

9-13 Sample Flaw Distribution Output File for Base Metal Region (1 mm = 

0.0394 in.).....................................................................................................................9-23

9-14 Sample Flaw Data from Output File for Base Metal Region (1 ft3 = 0.0283 m3

).............9-24

9-15 Sample Flaw Distribution Input File for Surface/Clad Flaws ..........................................9-26

9-16 Output File for Surface/Clad Flaws (1 mm = 0.0394 in.)................................................9-26

9-17 Data from Output File for Surface/Clad Flaw (1 ft2 = 0.0292 m2

) ...................................9-27

xv

TABLES

3-1 Weld Material Evaluated To Generate Data on Flaw Densities .......................................3-1

3-2 Base Metal Material Evaluated To Generate Data on Flaw Densities .............................3-2

3-3 Presence of Metallic and Nonmetallic Oxides in Failed Weld Bead.................................3-9

3-4 Flaw Dimensions, Validated by Use of Multiple Techniques .........................................3-10

6-1 Flaw Density Parameters................................................................................................6-7

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..............................................6-8

6-4 Data from Radiography of 25.4-mm- (1-in.-) Thick Plates from PVRUF Welds..............6-11

6-5 Data and Parameters of the Uncertainty Distribution for Depth Distribution for 

Small Flaws ..................................................................................................................6-12

6-6 Large SAW and SMAW Flaws in PVRUF and Shoreham Vessels ................................6-14

6-7 Large Repair Flaws in PVRUF and Shoreham Vessels.................................................6-15

6-8 Lengths of Small Flaws in SAW Welds of PVRUF Vessel.............................................6-18

6-9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel..........................................6-19

6-10 Lengths of Small Flaws in SAW Welds of Shoreham Vessel.........................................6-21

6-11 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham 

Vessel...........................................................................................................................6-24

6-12 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel .......................6-25

6-13 Lengths of Small Flaws in SAW Welds of Shoreham Vessel.........................................6-27

7-1 Flaws Detected and Sized in PNNL Examinations of Inner 1 Inch of Plate 

Material (from December 2000 monthly report SAFT-UT examination of base 

metal) .............................................................................................................................7-5

8-1 Flaws in Cladding of PVRUF Vessel...............................................................................8-3

8-2 Parameters of Representative PWR Reactor Pressure Vessel for PRODIGAL 

Calculations ....................................................................................................................8-5

8-3 RR-PRODIGAL Predictions for Surface-Breaking Flaws in Cladding by 

Submerged Arc Process (with and without PT)...............................................................8-6

8-4 RR-PRODIGAL Predictions for Buried Flaws in Cladding Applied with Manual 

Metal Arc and Submerged Arc Process ..........................................................................8-6

8-5 Clad Product Form and Inspection Results.....................................................................8-9

8-6 Dimensions of Flaws in Cladding as Reported in Appendix A of Schuster et al. 

(1998).............................................................................................................................8-9

8-7 Validated Dimensions of Flaw in Cladding as Reported in Schuster et al. 

(2000).............................................................................................................................8-9

8-8 Amount of Multi-Wire Clad in Specimen HC2A2B...........................................................8-9

8-9 Length of Flaws in Cladding for Specimen HC2A2B .......................................................8-9

8-10 Amount of 4-in. Strip Clad in Specimen 5-10D..............................................................8-10

8-11 Length of Flaws in Cladding for Specimen 5-10D .........................................................8-10
xvi

8-12 Data Used to Develop Length Distribution for Clad Flaws.............................................8-10

9-1 Applied Flaw Orientations by Major Regions...................................................................9-4
xvii

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 the 

technical basis for Title 10 of the Code of Federal Regulations (CFR) 50.61, “Fracture 

toughness requirements for protection against pressurized thermal shock events.” 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 in RPVs covering vessel fabrication 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. The 

report addresses the treatment of welding flaws using the flaws per unit area concept and 

describes additional details of the flaw model used in the FAVOR probabilistic fracture 

mechanics code.

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 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. 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 and this work is documented in NUREG/CR-6417 

Volumes 1, 2, and 3.

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 
xviii

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 Research User Facility (PVRUF) vessel(a) 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 service 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.
xix

ACKNOWLEDGMENTS

This work was supported by the U.S. Nuclear Regulatory Commission under NRC JCN Y6604

and N6398, Mr. Wallace E. Norris, the current NRC project manager and Deborah Jackson, the 

NRC project manager during the initial years of this work. PNNL wants to thank both of these 

NRC project managers for their support and guidance in conducting this work. The work was 

conducted at Pacific Northwest National Laboratory; Battelle operates this multi-program 

national laboratory for the U.S. Department of Energy under Contract DE-AC05-76RLO1830.

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, and he provided the FAVOR Code documentation that was used in 

writing Section 9.1. 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 report and Ms. Andrea Currie for editorial support.

xxi

ACRONYMS AND ABBREVIATIONS

ASME American Society of Mechanical Engineers

BWR boiling water reactor

CAT computer-assisted tomography

CCDF complementary conditional depth distribution

CPF conditional probability of failure

CPI conditional probability of initiation

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

PT dye penetrant

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

SEM scanning electron microscopy

SMAW shielded metal arc welding
xxii

TWD through-wall dimension

UQ upper quartile

UT ultrasonic testing
1-1

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; Dickson et al. 2004; 

Williams et al. 2004). 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 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 
1-2

Figure 1-1 Elements of Computational Model for Predicting Vessel Failure Probabilities 

and Its Application to Regulations for Pressurized Thermal Shock

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 of an 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.

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.
1-3

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 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. The report 

provides documentation on how welding flaws are treated using the approach of flaws per unit 

area of weld fusion surface. The FAVOR code has adopted this approach, and this report has 

been written to ensure consistency with documentation of the FAVOR code.

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 manufacturers 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 employed 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 
1-4

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 1 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 6.35 mm [0.25 in.] and smaller).

The objective of the recent NRC research on vessel flaws has been to examine RPV materials 

using more sensitive and higher-resolution 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 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 flaw-related 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 
1-5

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. Section 10 provides conclusions.

2-1

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 2-1 Conceptual View of Material Regions of a Vessel and the Categories of 

Flaws That Can Impact Structural Integrity

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 in this report that there are no credible 

mechanisms to cause service-related 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.
2-2

Figure 2-2 Metallographic Cross Section of a Circumferential Weld Showing Adjacent 

Regions of Base Metal and Cladding

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 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 flaws 

for circumferential welds are assumed to have circumferential orientations.
2-3

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 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 
2-4

cladding applied over both weld and base metal. Because the vessel inner surface consists 

mostly of base metal, all but a 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 underclad 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 during the vessel examinations are treated 

by FAVOR as exhibiting ideal crack-like 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 or weld fusion areas for 

each of the RPV subregions. Each of these subregions has its own embrittlement-related 

properties. From the assigned metal volumes and areas 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 
2-5

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. Numerous PFM results 

using FAVOR in support of the proposed PTS rulemaking indicate 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 vessel-specific 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 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 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 or per square 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.
2-6

The second step in the estimation procedure addresses the through-wall depths of simulated 

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). 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., laminations) 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.
2-7

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 [0.24 in.]) and a factor of 40 reduction for large flaws. A truncation of the 

distribution is applied to flaws greater than 11 mm (0.433 in.) in depth dimension, which depth 

corresponds 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 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 available data from 

nondestructive examinations of plate materials. Future work may provide additional validated 

flaw data for plate materials and may 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 low-toughness 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 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 an ASME conference 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 and 

Hope Creek vessels. 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 the circumferential orientation. This trend was 

consistent with expectations because weld-deposited 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 
2-8

been generated for the FAVOR code. Inputs to address both buried clad flaws and surfacebreaking 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 

area of underlying material of the vessel wall.

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 observed flaws from the PNNL 

examinations that were true inner-surface breaking. 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 weld 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.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Flaw Location Relative to Vessel ID, inch

Cumulative Distribution - Fraction of Flaws Located 

Deeper into the Wall

Random Distribution of Flaw Locations

C:\FLAW DATA\SHOREHAM DATA_1.XLS

Figure 2-3 Flaw Locations Relative to Vessel Inner Surface (1 inch = 25.4 mm)
2-9

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 describe 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 prior 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 2-4 presents some sample flaw distributions 

coming from applications of the generalized procedure. Presentation of these results become 

somewhat complicated because the uncertainty analysis provides not one distribution but a 

series of sample distributions, 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. Both the small and large categories of flaws are addressed by the curves of 

Figure 2-4. Large flaws correspond to depth dimensions greater than the weld bead dimensions 

(or about 3 percent of the vessel wall thickness). 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 25.4 mm

(1 in.), which is a depth about two times greater than the measured depth of any flaws detected 

in either the Shoreham or PVRUF vessel. The suggested truncations for plates and welds are 

applicable to other RPVs in the domestic fleet, unless there is plant-specific evidence indicating 

otherwise. The depths for repair flaws were truncated at a depth of 50.8 mm (2 in.), which is a 

factor of two or more greater than any observed flaws in repair welds. The 50.8-mm (2-in.) 

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 clad-related flaws. The maximum possible flaw depth is constrained 

by the thickness of the cladding.
2-10

Figure 2-4 Sample Flaw Distribution for Use in Probabilistic Fracture Mechanics 

Calculations (1 ft3 = 0.0283 m3

)

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 representative 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 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 unit area or unit 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 innersurface breaking.
2-11

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. This is a basic assumption in the 

FAVOR code (Dickson et al. 2004) that is supported by fracture mechanics testing of clad 

materials (Corwin et al. 1984) and by fracture mechanics calculations (Simonen and 

Johnson 1993) for under-clad cracks in embrittled reactor pressure vessels. Clad flaws are 

therefore structurally significant only if they extend up to or penetrate beyond the clad-tobase 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 have 

addressed a vessel that has base metal as the most limiting material.

3-1

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 relatively small samples of weld metal were examined. The sampling of 

plate material was limited to the inner 25.4 mm (1 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; Pardini 

et al. 2000; Jackson et al. 2001; Schuster and Doctor 2001b).

Table 3-1 Weld Material Evaluated To Generate Data on Flaw Densities

Cancelled 

Plant Manufacturer

Reactor 

Type

Years of 

Construction

Total Weld 

Length 

Available for 

Examination,

m (ft)

Volume of 

Weld Metal 

Examined,

m3 (ft3)

Indication 

Density, 

indications/

m3 (ft3)

Shoreham CE BWR 1968 to 1974 25.4 (83.3) 0.15(5.3) 30,000 (849)

Hope Creek II CB&I BWR 1971 to 1975 2.3 (7.5) 0.004 (0.14) 40,000 (1132)

River Bend II CB&I BWR 1974 to 1978 15 (49.2) 0.04 (1.4) 10,000 (283)

PVRUF CE PWR 1976 to 1981 20 (65.6)* 0.17 (6.0) 9,000 (255)

*PNNL inspected 20 m (65.6 ft) at ORNL, then 15 m (49.2 ft) of this inspected weldment was provided to PNNL 

for further study.
3-2

Table 3-2 Base Metal Material Evaluated To Generate Data on Flaw Densities

Cancelled 

Plant

Plate or 

Forging 

Vendor

Year 

Starting 

Vessel 

Fabrication Material

Volume of 

Material 

Available for 

Examination,

m3 (ft3)

Volume of 

Material 

Examined,

m3 (ft3)

Shoreham Lukens 1968 A533B Plate 0.9 (32) 0.016 (0.57)

Hope Creek II Lukens 1971 A533B Plate 6.8 (240) 0.009 (0.32)

River Bend II Lukens 1974 A533B Plate 1.0 (35) 0.024 (0.85)

PVRUF Marrel Freres 1976 A533B Plate 0.6 (21) 0.014 (0.49)

Midland Ladish 1969 A508 Forging 0.4 (14) pending

3.1 Procedures Used to Detect and Size Flaws

PNNL’s methodology for flaw detection and size measurements consisted of four stages of 

increasing refinement. The first two stages form a general category wherein PNNL selected 

material for the later stages for more refined measurements. The final two stages produced the 

validated measurements for best estimates of flaw densities and size distributions.

A combination of techniques was applied as indicated in Figures 3-1 and 3-2. A cross section of 

an examined circumferential weld of the PVRUF 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.

Metallography provided good information on flaw composition. Electron microscopy confirmed 

the metallographic results and provided additional magnification. The X-ray computer-assisted

tomography gave additional shape information for the complex repair flaws. Metallography 

provided information on flaw composition. X-ray spectroscopy provided chemical composition. 

The repair flaws were shown to be a combination of cracks, lack of fusion, porosity, and slag.

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 important,

the material that contained the largest indications was identified for later validation. The sizing 

rules were needed also 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.
3-3

Figure 3-1 Sequence of Techniques Used To Detect and Size Flaws

Figure 3-2 Techniques Used for Detailed Characterization of Flaws
3-4

Figure 3-3 Metallographic Cross Section of a Circumferential Weld from PVRUF Vessel 

Showing Adjacent Regions of Base Metal and Cladding

Figure 3-4 Location of Flaw in the Fusion Zone of a Weld with the Base Metal
3-5

Figure 3-5 Inside View of the PVRUF Vessel During SAFT-UT Clad Surface Inspections

The second stage in developing validated flaw densities for RPVs used weld-normal SAFT-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.

Figure 3-6 Weld Normal Inspections

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 25.4-mm- (1-in.-) thick plates and radiographs
3-6

were taken using film and 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 3-7 Examinations of Plate Specimens

Figure 3-8 Image of a Fabrication Flaw Using Conventional Radiology

Dimensions for the lack-of-fusion flaws were recorded to the nearest 1.0 mm (0.0394 in.). 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 base metal. 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, and computer-assisted tomographic (CAT) scans, as well as metallography 

techniques. In cube form, the measurements by each technique confirmed the measurements 
3-7

by the other techniques. Because of the small variance in measurements from the cubed flaws, 

PNNL was 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 (0.0394 in.), and the images 

were full-volume focused. The scanner’s steps were 0.25.4 mm (1 in.) in both scan and 

increment directions. The majority of the flaws examined were lack 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 (0.2 in.) and recorded 

to the nearest 1.0 mm (0.0394 in.). 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 is capable of imaging complex flaws and giving 

the extent of the flaws as it followed the three-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 μ (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 (0.0394 in.). 

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 3-10 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 

100-μ (0.00394-in.) scale. The crack morphology is shown in the image to be branched and 

filled with segregates.
3-8

Figure 3-9 Micrograph of 25.4-mm (1 in.) Cube Containing a Failed Weld Bead

Figure 3-10 Electron Microscope Image of Cracked Weld Bead (100 μm = 0.00394 in.)

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.
3-9

Table 3-3 Presence of Metallic and Nonmetallic Oxides in Failed Weld Bead

Proportions in Crack

Element Weight % Atomic %

C 3.73 9.30

Mn 1.22 0.66

Fe 55.62 29.83

O 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 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.

Metallography provided the best information for flaw characterization. A 17-mm (0.67 in.) 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 shows the location of a small flaw in the fusion zone of an SAW weld. The weld is to 

the left 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 (through-wall dimension [TWD], length, and width) 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.
3-10

Table 3-4 Flaw Dimensions, Validated by Use of Multiple Techniques

Vol 1 name: HAZ V1

Vol 1 TWD: 7 mm (0.28 in.)

Metallography,

mm (in.)

RT,

mm (in.)

UT of Cubes,

mm (in.)

Depth location 20 (0.79) 19 (0.75) 22 (0.87)

TWD 4 (0.16) 4 (0.16) 5 (0.20)

Length Not Measured 17 (0.67) 16 (0.63)

Width 6 (0.24) 6 (0.24) 6 (0.24)

Figure 3-11 shows the composition of a complex flawed region as measured by metallography. 

The two images shown are from the same region of a vessel but are from different 

micropolished and etched cross sections. The flawed region is shown to be composed of a 

crack, lack of fusion, contamination, and slag.

Figure 3-11 Composition of a Complex Flaw

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 (0.55-in.) Shoreham repair flaw” because of initial examinations 

showing it to have a 14-mm (0.55-in.) 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.
3-11

Figure 3-12 Shape and Orientation of 14-mm (0.55 in.) PVRUF Flaw - Relevant to 

Structural Integrity Assessment (1 mm = 0.0394 in.)

The sketches of Figure 3-12 represent projections of the complex flaw onto a radial plane for 

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. 
3-12

The images used 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 original measurements of the flaw in Figure 3-12 characterized this flaw as approximately 

circular with a maximum through-wall dimension of about 14 mm (0.55 in.). 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 (0.55 in.) to separate flaws with dimensions of 4 mm 

(0.16 in.) and 5 mm (0.20 in.). 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 (0.55 in.) as 

originally estimated.

A very different result was obtained from the detailed characterization for the “32-mm (1.26-in.) 

Shoreham repair flaw,” as shown by Figure 3-13. The original measurements characterized this 

flaw as approximately circular with a maximum through-wall dimension of about 32 mm

(1.26 in.). The more refined SAFT examinations showed a flawed region bounded by 

dimensions of 12 mm (0.47 in.) and 44 mm (1.73 in.). The 32-mm (1.26-in.) maximum throughwall 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 purposes of fracture mechanics calculations of crack tip stress intensity factors was to 

use a smaller flaw with a depth of 12 mm (0.47 in.) and a length of 44 mm (1.73 in.). 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 single flaw with dimensions of 12 mm (0.47 in.) and 44 mm (1.73 in.). 

This characterization removes a large measure of conservatism from the earlier evaluation by 

dealing with the large apparent through-wall dimension of 32 mm (1.26 in.) 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 (1.26-in.) Shoreham repair 

flaws as well as the dimensions of a number of other flaws.
3-13

Figure 3-13 Shape and Orientation of 32-mm (1.26-in.) Shoreham Repair Flaw with Less 

Conservative Treatment B of Flaw Dimensions (1 mm = 0.0394 in.)

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 measurements to determine 

that large flaws are not present in the 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 flawbearing cubes were removed from the welds. The cubes were approximately 25.4 mm (1 in.) on 

a side. This specimen size permitted accurate measurement of flaw characteristics using 

ultrasound, radiography, computed tomography, and metallography.
3-14

The methodology that was developed for estimating fabrication flaw density and distribution for 

RPV welds is documented in Schuster et al. (2009). The “Step 1” in the process was to ensure 

that all flaws were detected and sized to ensure that no large flaws were missed or undersized. 

Succeeding steps were designed to optimize the NDE, to reduce uncertainties, and to include 

destructive tests for validation.

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 (0.24 in.) 

in size or greater. Reasonable agreement is evident between 3 mm (0.12 in.) and 5.4 mm 

Figure 3-14 SMAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.)
3-15

(0.20 in.) in through-wall size. The density of small flaws in SMAW was not selected for 

validation in the cubes, so the 2-mm (0.08-in.) data point for the cubes is artificially low. The 

SMAW data from Jackson and Abramson (2000) is PNNL’s best estimate for the flaw density 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 (0.315 in.) 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 (0.315 in.). For flaws between 

1 mm (0.0394 in.) and 4 mm (0.16 in.) in through-wall size, reasonable agreement can be seen 

in Figure 3-15.

Figure 3-15 SAW Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.)

3.4.3 Repair Weld

Figure 3-16 compares flaw distributions for repair metal. The first distribution uses the throughwall 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 (0.67 in.) were found in 

the vessel. For flaws 12 mm (0.47 in.) to 17 mm (0.67 in.) in through-wall size, the flaw density 

is high for repair metal compared to the unvalidated (Step 1) SAW flaw densities. Smaller flaws 
3-16

in repair metal were not selected for the validation cubes, making the data point at 4 mm 

(0.16 in.) appear artificially low.

Figure 3-16 Repair Metal, Through-Wall Size Distribution of Cumulative Flaw Densities

(1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.)

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.

The results of the selected application of four techniques to the characterization of flaws in 

25.4-mm (1-in.) 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.
3-17

Figure 3-17 Comparison of Through-Wall Size Distributions of Cumulative Flaw 

Densities (1 m3 = 35.3 ft3

, 1 mm = 0.0394 in.)

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 25.4-mm (1-in.) cubes, from weldnormal 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.

4-1

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 expert judgment is a well-documented 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) discussion 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. Appendix B provides the names and qualifications of 

the experts.
4-2

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 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 preservice 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 
4-3

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 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 reelicited 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.
4-4

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 Flaw Characteristics from Elicitation

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

• weld process - 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 [0.24 in.]) 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.
4-5

Figure 4-1 Relative Flaw Densities of Base Metal Compared to Weld Metal as Estimated 

by Expert Judgment Process (from Jackson and Abramson 2000)

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:

• field versus shop fabrication

• weld procedure

• weld materials

• welder skill

• inspection procedure

• inspector skill

• base metal properties

• surface preparation and parameters.
4-6

In summary, 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 was an important input to the generalized flaw distribution 

methodology as described in this report for the fleet of domestic reactor vessels.
5-1

5 PRODIGAL WELD SIMULATION MODEL

This section 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 NRCfunded 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 and 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.
5-2

Figure 5-1 Types of Crack-Like Defects

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 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.
5-3

• 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; that is, 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 Defect Density

The defect occurrence frequencies (per unit length of weld bead) for the resulting set of cracklike 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 
5-4

the weld of interest, with the inspection efficiency being a function of the defect size and it’s

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 inspections. Machining can also expose near-surface buried 

defects and thereby increase the number of surface-breaking defects.

• post-weld heat treatment - The sizes of heat-affect-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 (8.4 in.2

) was used to convert the calculated flaw densities from flaws per meter of 

weld length to flaws per cubic meter.
5-5

Figure 5-2 Cross Section of Thickness Transition Single V Weld for PVRUF Vessel

(1 mm = 0.0394 in.)

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 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 III and XI Codes require repairs of flaws 

between 19 (0.75 in.) and 33 mm (1.30 in.) in measured length. It was recognized, however, 

that there are uncertainties in both the ability of radiographic methods to accurately measure 

flaw lengths and the ability of the PRODIGAL code to predict the distribution of flaw lengths. 

Therefore, the range of the curves from L = 0 mm (0 in.) to 33 mm (1.30 in.) 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.
5-6

Figure 5-3 Model of Thickness Transition Single V Weld for PVRUF Vessel (1 cm = 

0.394 in.)

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 [0.0394- to 

0.08-in.) 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 (0.20 in.), which corresponds to approximately the dimension of the 

weld beads.
5-7

Figure 5-4 Calculated Flaw Frequencies for PVRUF Weld Showing Effects of Inspection 

and Repairs (1 mm = 0.0394 in.)

• If flaws associated with weld repairs are excluded from the PVRUF data, no data remains to 

make comparisons for flaw depths greater than 7 mm (0.28 in.).

• 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-to-weld differences.

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 
5-8

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.

Figure 5-5 Distributions of Flaw Aspect Ratio and Flaw Length as Predicted by 

PRODIGAL Weld Simulation (1 mm = 0.0394 in.)

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.

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 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:
5-9

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 Shoreham 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-tovessel. 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.

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 originate at the 

clad-to-base 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.

6-1

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 surface-breaking 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 and 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 vesselspecific considerations to be addressed:

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 

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 - Past approaches, including that of early 

versions 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-
6-2

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. However, 

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 original reduction of data from the PVRUF and Shoreham vessels was performed to 

estimate flaw densities on a per-unit volume basis. The flaw distribution algorithm makes 

appropriate transformations (based on the average widths of the weld joints) of the PVRUF and 

Shoreham data to go from flaws per unit of volume to flaws per unit area. The transformation 

used weld widths of 40.9 mm (1.61 in.) and 38.6 mm (1.52 in.) for the PVRUF and Shoreham 

vessels, respectively.

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 empirical 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 them 

being smaller or larger than 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 power 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 small 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 

through the thickness 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 from cross-sectioned micrographs of the welds

• flaws in SAW, SMAW and repair-welded material.
6-3

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 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 multinomial 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 Appendix A 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 Shoreham 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 Shoreham 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 
6-4

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 which followed the 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 assumed 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 axial 

coordinates 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.

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. This was done to ensure that no large flaws would be missed. 

Subsequent validation efforts were then 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 therefore 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.
6-5

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 precluded 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 crack

depths 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 × 2 × 3 × 2) as follows:

Variable Values N

Flaw Characteristics Flaw Density

Through-Wall Depth

Flaw Length (Aspect Ratio)

3

Source of Flaw Data PVRUF

Shoreham

2

Weld Process SAW

SMAW

Repair Weld

3

Flaw Depth Category Small

Large

2

In many cases, one function served more than one purpose, which reduced the number of 

independent statistical correlations that were 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. Thus, six conditionals are 

reduced to one (−5).

• One conditional depth distribution described all large repair flaws in the PVRUF and 

Shoreham vessels. Thus, two conditionals are reduced to one (−1).

• One conditional depth distribution described all large SAW and SMAW flaws in both the 

PVRUF and Shoreham vessels. Thus, four conditionals are reduced to one (−3).
6-6

• One length distribution described all large flaws in the PVRUF and Shoreham vessels, 

including all three welding processes. Thus, six conditionals are reduced to one (−5).

• One length distribution described the small SMAW and repair flaws in the PVRUF vessel. 

Thus, two conditionals are reduced to one (−1).

• One length distribution described the small SMAW and repair flaws in the Shoreham vessel. 

Thus, two conditionals are reduced to one (−1).

This commonality reduced the number of independent functions from 36 to 20. This includes 

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 multinomial 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 was 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 used 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. Options with PNNL’s 

algorithm for generating flaw input files for FAVOR convert the output to units of flaws per cubic 

foot and allow flaw densities to be expressed on the basis of flaws per unit area of fusion 

surface. 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. This conversion accounts for two 

fusion surfaces along each seam weld. The weld was assumed to have an average width (or 
6-7

gap) of 40.9 mm (1.61 in.) for the PVRUF vessel and 38.6 mm (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 (see 

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 6-1 Flaw Density Parameters

Vessel

Weld 

Type

Flaw 

Size

Number 

of Flaws

Examined 

Volume, 

m3

Flaw Density, Flaws per Cubic Meter

Mean Median

25th

Quartile

75th

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 Large 8 0.0105 761 “ “ “

Shoreham Repair Large 6 0.0030 2000 “ “ “

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

Note: 1 m3 = 35.3 ft3

Table 6-2 Gamma Distribution Used To Sample for Parameter of Poisson Distribution 

for Flaw Densities

Vessel

Weld 

Type

Flaw 

Size

Number 

of Flaws

Examined 

Volume, 

m3

Parameters for

Gamma Distribution

α2 α2

PVRUF 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 Large 8 0.0105 0.0105 8

Shoreham Repair Large 6 0.0030 0.0030 6

Note: 1 m3 = 35.3 ft3
6-8

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.

Table 6-3 Weld Bead Dimensions for PVRUF and Shoreham Welds

Vessel Weld Type

Weld Bead 

Thickness,

mm (in.)

PVRUF SAW 6.5 (0.26)

PVRUF SMAW 3.5 (0.14)

PVRUF Repair 3.5 (0.14)

Shoreham SAW 5 (0.20)

Shoreham SMAW 3.5 (0.14)

Shoreham Repair 3.5 (0.14)

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.

Figure 6-1 Uncertainty in Flaw Densities for Flaws in PVRUF Vessel (1 ft3 = 0.0283 m3

)
6-9

Figure 6-2 Uncertainty in Flaw Densities for Flaws in Shoreham Vessel (1 ft3 = 0.0283 m3)

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 and Shoreham vessels. The distribution was based on 

sets of flaw size data that were measured by radiography of 25.4-mm (1-in.) 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 (0.08 in.). 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 depth dimensions.

Figure 6-3 PVRUF Weld Metal Specimen Cut into 25.4-mm (1-in.) Plate
6-10

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 (0.02 to 0.28 in.) 

(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 type. The estimated bead size ranged from 3.5 mm (0.14 in.) 

for SMAW welds to 6.0 mm (0.24 in.) 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.

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 distribution of flaw depths. The uncertainties in the 

three parameters of this distribution were described by a Dirichlet distribution. The 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 βi

. The probability density function is defined as

f (a/∆) = βi

/0.3 (6.1)

where a is the flaw through-wall depth dimension and ∆ 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 Ui 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.
6-11

Table 6-4 Data from Radiography of 25.4-mm- (1-in.-) Thick Plates from PVRUF Welds

ID Number Plate

Bead Size, 

mm

Flaw Depth, 

mm

Flaw Depth 

Fraction of Bead Fraction > X

20 5-1C-8 6.50 0.50 0.077 1.000

2 5-1AB-2 6.50 1.00 0.154 0.977

5 5-1AB-5 6.50 1.00 0.154 0.953

10 5-1AB-7 6.50 1.00 0.154 0.930

13 5-1AB-11 6.50 1.00 0.154 0.907

34 5-10B-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 5-1AB-5 6.50 1.20 0.185 0.814

1 5-1AB-2 6.50 1.30 0.200 0.791

27 5-1C-14 6.50 1.30 0.200 0.767

3 5-1AB-3 6.50 1.50 0.231 0.744

14 5-1AB-12 6.50 1.50 0.231 0.721

15 5-1AB-12 6.50 1.50 0.231 0.698

19 5-1C-6 6.50 1.50 0.231 0.674

21 5-1C-8 6.50 1.50 0.231 0.651

22 5-1C-10 6.50 1.50 0.231 0.628

24 5-1C-12 6.50 1.50 0.231 0.605

32 5-10B-7 6.50 1.50 0.231 0.581

33 5-10B-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-11 6.50 1.75 0.269 0.488

4 5-1AB-5 6.50 1.80 0.277 0.465

25 5-1C-13 3.50 1.00 0.286 0.442

8 5-1AB-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 5-10B-4 6.50 2.00 0.308 0.349

39 5-12BA-4 6.50 2.00 0.308 0.326

30 5-10B-5 3.50 1.10 0.314 0.302

31 5-10B-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

18 5-1C-4 3.50 1.50 0.429 0.209

7 5-1AB-6 6.50 3.00 0.462 0.186

12 5-1AB-11 6.50 3.00 0.462 0.163

23 5-1C-11 6.50 3.00 0.462 0.140

38 5-12BA-3 6.50 3.00 0.462 0.116

28 5-10B-2 6.50 3.50 0.538 0.093

40 5-12BA-6 6.50 3.50 0.538 0.070

26 5-1C-13 6.50 4.00 0.615 0.047

16 5-1AB-14 3.50 4.50 1.286 0.023

Note: 1 mm = 0.0394 in.
6-12

Table 6-5 Data and Parameters of the Uncertainty Distribution for Depth Distribution 

for Small Flaws

Index i

Normalized 

Flaw Depth

Number 

of Flaws Ui

βi - Parameters of Multinomial Distribution

Mean βi

25th

Percentile 

βi

50th

Percentile 

βi

75th

Percentile 

βi

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

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

x = Flaw Depth, Fraction of Bead Size

Probability of Flaw > x

Small Flaws

PVRUF Data - RT of Plates 

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

Percentiles Based on 

Flaw Depth of a = 85%t

95%

5%

25%

50%

75%

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 distribution for large SAW and SMAW flaws was 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 

higher-resolution SAFT-UT of small cubes, radiography, and destructive sectioning.

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 
6-13

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 

N(>d/∆) = ρ e-β(d/∆ - 1) (6.2)

where N(>d/∆) is the number of flaws per cubic meter with the normalized depth dimensions 

greater than d/∆ and β 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 Appendix A, a 

gamma distribution function was established to describe the uncertainty in the value of β. The 

parameters of the gamma function are based on the data of Table 6-6. The values were 

established to be α1 = 21.68 and α2 = 52, where (from Table 6-6) the parameter α1 is 

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

0.0 1.0 2.0 3.0 4.0 5.0

Crack Depth, Fraction of Bead Thickness

Probability of Flaw > x

Large Flaws

PVRUF + Shoreham Data

SAW and SMAW Flaws

C:\FLAWDATA\PVRUF-SHOREHAM-JUNE-13.XLS

95%

75%

25%

5%

50%

Exponential Distribution

Figure 6-5 Uncertainty Evaluation for Complementary Conditional Depth Distribution 

for Large SAW and SMAW Flaws
6-14

Table 6-6 Large SAW and SMAW Flaws in PVRUF and Shoreham Vessels

Index ID No.

Bead Size, 

mm

Flaw Depth, 

mm

Depth Frac 

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 1.43

35 31 3.5 5.00 1.43

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 2.29

52 60 3.5 9.00 2.57

Note: 1 mm = 0.0394 in.
6-15

calculated as the sum of the 52 values of the quantity (d/∆ - 1) and α2 corresponds to the 

number of data points in Table 6-6.

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 higher-resolution SAFT-UT of small cubes, radiography, and destructive 

examinations.

Table 6-7 presents the combined 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. 

Table 6-7 Large Repair Flaws in PVRUF and Shoreham Vessels

Index

Bead 

Size, 

mm

Nominal 

Flaw Depth, 

mm

Measured 

Flaw Depth, 

mm

Measured 

Flaw Length, 

mm No. Flaws > 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

Note: 1 mm = 0.0394 in.

Parameters of the gamma function are based on the data of Table 6-7. The values were 

established to be α1 = 17.58 and α2 = 13 where (from Table 6-7) the parameter α1 is calculated 

as the sum of the 17 values of the quantity (d/∆ - 1) and α2 corresponds to the number of data 

points in Table 6-7.
6-16

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

0 2 4 6 8 10

Flaw Depth, Fraction of Bead 

Fraction of Flaws >= x

Large Repair Flaws

PVRUF + Shoreham Data

Treatment A of SAFT Images

Exponential Distribution

With Uncertainty Evaluation

C:\FLAWDATA\PVRUF-SHOREHAM-JUNE-13.XLS

95%

25%

50%

75%

5%

Figure 6-6 Uncertainty Evaluation for Complementary Conditional Depth Distribution 

for Large Repair Flaws

6.2.4 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 the 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 the 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 

comprehensive 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 clad 

surface SAFT-UT 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 
6-17

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[>(l – a)/∆] = e-β(

l – a)/∆ (6.3)

where P[>(l – a)/∆] is the fraction of flaws with the normalized length dimensions greater than 

(l – a)/∆ and β 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 Appendix A, a 

gamma distribution function was established to describe the uncertainty in the value of β. The 

parameters of the gamma function were based on the data of Table 6-8. The values were 

established to be α1 = 0.53846 and α2 = 8, where (from Table 6-8) the parameter α1 is 

calculated as the sum of the eight values of the quantity (l - a)/∆ and α2 corresponds to the 

number of 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 evaluation.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

-1.0 0.0 1.0 2.0 3.0 4.0 5.0

(Length - Depth)/Bead

Probability of Flaw > x

PVRUF

Small Flaws ( < Bead ) 

SAW

(Data Set 9)

Small Flaws ( < Bead )

SMAW

(Data Set 7)

Large Flaws ( > Bead ) 

SMAW and Repair

(Data Set 8)

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

Figure 6-7 Lengths of Small Flaws in SAW and SMAW Welds of PVRUF Vessel
6-18

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-1.0 0.0 1.0 2.0 3.0 4.0 5.0

(Length - Depth)/Bead

Probability of Flaw > x

PVRUF Small Flaws

SAW

C:\FLAWDATA\HEASLER03-REPORT-FIGURES-2.XLS

95%

5%

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

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length Minus 

Depth, mm

Depth 

Frac 

Bead

Length Minus 

Depth Frac 

Bead

Fraction

> x

5-1C-13 SAW 6.50 4.0 3.5 -0.50 0.615 -0.077 1.000

5-10B-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

5-1AB-6 SAW 6.50 3.0 3.5 0.50 0.462 0.077 0.625

5-1AB-11 SAW 6.50 3.0 3.5 0.50 0.462 0.077 0.500

5-1C-11 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 0.462 0.077 0.250

5-12BA-1 SAW 6.50 2.0 3.5 1.50 0.308 0.231 0.125

Note: 1 mm = 0.0394 in.

6.2.5 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 α1 = 

10.857 and α2 = 6, where (from Table 6-9) the parameter α1 is calculated as the sum of the six 

values of the quantity (l - a)/∆ and α2 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.
6-19

Table 6-9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length 

Minus 

Depth, mm

Depth 

Frac 

Bead

Length Minus 

Depth, Frac 

Bead

Fraction

> x

5-7H1iibiic SMAW 3.50 3.0 4.0 1.00 0.857 0.286 1.000

5-4B1iidiie SMAW 3.50 3.0 5.0 2.00 0.857 0.571 0.833

5-10B5ibic SMAW 3.50 3.0 9.0 6.00 0.857 1.714 0.667

5-10EC1iibiic SMAW 3.50 3.0 11.0 8.00 0.857 2.286 0.500

5-10EA1iiibiiic SMAW 3.50 3.0 12.0 9.00 0.857 2.571 0.333

5-10ECiidiie SMAW 3.50 3.0 15.0 12.00 0.857 3.429 0.167

Note: 1 mm = 0.0394 in.

1.E-01

1.E+00

-1.0 0.0 1.0 2.0 3.0 4.0 5.0

(Length - Depth)/Bead

Probability of Flaw > x

PVRUF Small Flaws

SMAW

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

95%

75%

50%

25%

5%

Figure 6-9 Lengths of Small Flaws in SMAW Welds of PVRUF Vessel Showing 

Exponential Distribution Along with Uncertainties

6.2.6 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 

higher-resolution SAFT-UT and destructive evaluations. These less restrictive 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 α1 = 286 and α2 = 105, 

where (from Table 6-10) the parameter α1 is calculated as the sum of the 105 values of the 
6-20

quantity (l - a)/∆ and α2 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 statistical uncertainty in the correlation.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

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 16.0

(Length - Depth)/Bead

Probability of Flaw > x

SHOREHAM

Large Flaws ( > Bead ) 

SMAW

(Data Set 12)

Small Flaws ( < Bead )

 SAW

(Data Set 13)

Large Flaws ( > Bead ) 

SAW

(Data Set 14)

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

Figure 6-10 Lengths of Small Flaws in SAW and SMAW Welds of Shoreham Vessel

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

(Length - Depth)/Bead

Probability of Flaw > x

Shoreham Small Flaws

SAW

Small Flaws ( < Bead )

 SAW

(Data Set 13)

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

95%

5%

25%

50% 75%

Figure 6-11 Lengths of Small Flaws in SAW Welds of Shoreham Vessel Showing 

Exponential Distribution Along with Uncertainties
6-21

Table 6-10 Lengths of Small Flaws in SAW Welds of Shoreham Vessel

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length 

Minus 

Depth, mm

Depth 

Frac 

Bead

Length Minus 

Depth Frac 

Bead

Fraction 

> x

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 1.400 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

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 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

Note: 1 mm = 0.0394 in.
6-22

Table 6-10 Lengths of Small Flaws in SAW Welds of Shoreham Vessel (contd)

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length 

Minus 

Depth, mm

Depth 

Frac 

Bead

Length Minus 

Depth Frac 

Bead

Fraction 

> 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

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

Note: 1 mm = 0.0394 in.
6-23

Table 6-10 Lengths of Small Flaws in SAW Welds of Shoreham Vessel (contd)

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length 

Minus 

Depth, mm

Depth 

Frac 

Bead

Length Minus 

Depth Frac 

Bead

Fraction 

> x

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

Note: 1 mm = 0.0394 in.

6.2.7 Length Distribution for Small SMAW and Repair Flaws in Shoreham 

Vessel

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 high-resolution SAFT-UT and destructive 

evaluation. The 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 6-11. The values were established to be α1 = 46.3 and α2 = 16, where (from 

Table 6-11) the parameter α1 was calculated as the sum of the 16 values of the quantity 

(l - a)/∆ and α2 corresponds to the number of data points in Table 6-11. The resulting 

distribution function is shown in Figure 6-12 along with the data and results of the uncertainty 

evaluation.
6-24

Table 6-11 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham 

Vessel

ID Table Specimen

Total Weld 

Length, mm 

(in.) Figure

TWSize, 

mm

Length, 

mm

LengthTW

Bead 

Size, 

mm

Depth 

Frac 

Bead

LengthTW Frac 

Bead

13 I.1 C0G 1483 (58.4) I.6 7.0 9.0 2.0 3.5 2.0 0.6

14 D.1 B180C-2 1054 (41.5) D.3 7.0 9.0 2.0 3.5 2.0 0.6

47 T.1 C270D 2982 (117.4) T.9 8.0 11.0 3.0 3.5 2.3 0.9

59 D.1 B180C-2 1054 (41.5) D.4 9.0 12.0 3.0 3.5 2.6 0.9

32 G.1 C0E 1401 (55.2) G.1 6.0 10.0 4.0 3.5 1.7 1.1

15 T.1 C270D 2982 (117.4) T.3 4.0 10.0 6.0 3.5 1.1 1.7

36 F.1 C0D 493 (19.4) F.1 4.0 11.0 7.0 3.5 1.1 2.0

37 G.1 C0E 1401 (55.2) G.5 4.0 11.0 7.0 3.5 1.1 2.0

50 G.1 C0E 1401 (55.2) G.4 4.0 12.0 8.0 3.5 1.1 2.3

60 T.1 C270D 2982 (117.4) T.11 4.0 13.0 9.0 3.5 1.1 2.6

80 I.1 C0G 1483 (58.4) I.1 5.0 14.0 9.0 3.5 1.4 2.6

96 T.1 C270D 2982 (117.4) T.8 4.0 16.0 12.0 3.5 1.1 3.4

97 T.1 C270D 2982 (117.4) T.13 4.0 16.0 12.0 3.5 1.1 3.4

98 T.1 C270D 2982 (117.4) T.12 4.0 16.0 12.0 3.5 1.1 3.4

114 M.1 C120E 1361 (53.6) M.9 7.0 20.0 13.0 3.5 2.0 3.7

142 P.1 C180B 1821 (71.7) P.7 4.0 57.0 53.0 3.5 1.1 15.1

Note: 1 mm = 0.0394 in.

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

(Length - Depth)/Bead

Probability of Flaw > x

C:\FLAWDATA\HEASLER03-REPORT-FIGURES MISSING FIG APRIL 2003.XLS

Shoreham Small and Large Flaws

SMAW and Repair

95%

5%

25%

50% 75%

Figure 6-12 Lengths of Small and Large Flaws in SMAW and Repair Welds of Shoreham 

Vessel Showing Exponential Distribution Along with Uncertainties

6.2.8 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 
6-25

selection excluded small flaws that were detected only by the examinations performed with the 

early clad surface 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 α1 = 0.53846 and α2 = 8, where (from Table 6-8) the parameter α1 is 

calculated as the sum of the eight values of the quantity (l - a)/∆ and α2 corresponds to the 

number of data points in Table 6-8.

6.2.9 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 high-resolution SAFT-UT and destructive evaluations after being removed as cube samples. 

The dataset resulted in 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 α1 = 5.428 and α2 = 5, where (from Table 6-12) the parameter α1 is calculated 

as the sum of the five values of the quantity (l - a)/∆ and α2 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.

Table 6-12 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel

Label

Bead 

Size, 

mm

TWSize, 

mm

Length, 

mm

Aspect 

Ratio

L-TW, 

mm

TW 

Frac 

Bead

Large=2

Small=1

L-TW 

Frac 

Bead

Frac > 

L-TW 

Frac 

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

5-1AB14ibic 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

5-10EBiibiic SMAW 3.50 4.0 17.0 4.2500 13.00 1.1429 2 3.7143 0.2000

Note: 1 mm = 0.0394 in.
6-26

1.E-01

1.E+00

-1.0 0.0 1.0 2.0 3.0 4.0 5.0

(Length - Depth)/Bead

Probability of Flaw > x

PVRUF Large Flaws

SMAW and Repair

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

95%

75%

25%

50%

5%

Figure 6-13 Lengths of Large Flaws in SMAW and Repair Welds of PVRUF Vessel 

Showing Exponential Distribution Along with Uncertainties

6.2.10 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 high-resolution SAFT-UT and destructive evaluations. The dataset gave a total of 25 large 

flaws upon which to base a flaw length distribution.

The length distribution 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 α1 = 47.80 and α2 = 25, where (from 

Table 6-13) the parameter α1 is calculated as the sum of the 25 values of the quantity (l - a)/∆

and α2 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.

6.2.11 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.
6-27

Table 6-13 Lengths of Small Flaws in SAW Welds of Shoreham Vessel

Label

Weld 

Type

Bead 

Size, 

mm

Flaw 

Depth, 

mm

Flaw 

Length, 

mm

Length 

Minus Depth, 

mm

Depth 

Frac 

Bead

Length Minus 

Depth Frac 

Bead

Fraction 

> 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

Note: 1 mm = 0.0394 in.

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

(Length - Depth)/Bead

Probability of Flaw > x

C:\FLAWDATA\HEASLER03-REPORT-FIGURES.XLS

Shoreham Large Flaws

SAW

95%

5%

25%

50%

75%

Figure 6-14 Lengths of Large Flaws in SAW Welds of Shoreham Vessel Showing 

Exponential Distribution Along with Uncertainties

7-1

7 BASE METAL FLAWS – DATA AND 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 the material of the surface regions of plates down to a depth of about 

25.4 mm (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 and 

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 under-clad 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 for base metal 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, 
7-2

there was 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 the 

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 which the inputs derived from the expert judgment elicitation could be 

compared.

Vessel-to-Vessel Variability – Examinations of plate material from the four vessels showed 

significant vessel-to-vessel variations in flaw 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 – Flaws in welds were assumed to be 

buried within the thickness of the vessel wall. The locations of the flaw inner tips relative to the 

vessel inner surface were assigned in a random manner. As a limiting case, a weld flaw could 

have its inner tip at the clad-to-base metal interface, a condition that would have a statistically 

zero probability of occurrence.

For base metal, the information from the expert elicitation clearly indicated that the midsections 

of rolled plates consistently have larger flaw densities and larger flaw sizes than near-surface 

regions. The plate flaw distribution was therefore 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 SAFT-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 or blunted 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 
7-3

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 shown to be the most limiting type of flaw to 

the integrity of vessels with an embrittled plate material.

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.

Truncation of Flaw Distributions – Inputs for flaw depth dimensions for use with the FAVOR 

code were truncated to avoid excessive extrapolations of the statistically based 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 (0.43 in.).

Service-Related Flaws – The flaw distribution methodology for base metal flaws 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, all 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

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 manufacture plates and forgings. 
7-4

Other questions related to mechanisms that are most likely to cause flaws in base metal and the 

most likely locations of flaws relative to the inner surface of the vessel.

The experts also were requested to make quantitative estimates of flaw occurrence rates. 

These questions were posed in terms of relative estimates. During the expert elicitation 

process, PNNL described the examination methods 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 were shown earlier in 

Figure 4-1. Large base metal flaws were defined as flaws with through-wall depth dimensions 

greater than a typical bead dimension (6 mm [0.24 in.] for SAW welds).

The chart of Figure 4-1 indicates the rather large range 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 [0.24 in.]) in plate material was a factor of 10 less than the 

flaw density for the PVRUF welds. The density of large flaws (>6 mm [0.24 in.]) 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 II vessels. These examinations detected a total of 

175 flaws in 0.063 m3 (2.2 ft3

) of examined material. Only 9 flaws had through-wall depth 

dimensions as large as 4 mm (0.16 in.). No observed flaws had depth dimensions as large as 

6 mm (0.24 in.).

Figure 7-2 is a plot of the base metal flaw densities as a function of the measured through-wall 

depth dimensions. Also shown are the flaw densities for welds from the examinations of the 

PVRUF and Shoreham vessel. The flaw densities for all the plate materials were less than the 

flaw densities for welds. There was a wide range of flaw densities for the plate materials with a 

factor of 30 difference between the highest density (PVRUF plate material) and the lowest 

density (Shoreham plate material). The average density indicated in Figure 7-2 was obtained 

by combining the data from all four vessels. This density was a factor of about 5 less than the 

flaw density for the PVRUF welds.
7-5

Table 7-1 Flaws Detected and Sized in PNNL Examinations of Inner 1 Inch of Plate 

Material (from December 2000 monthly report SAFT-UT examination of base 

metal)

Flaw Depth, 

mm (in.)

Shoreham 

Cumulative 

Indication 

Rate, per m3

Hope Creek 

Cumulative 

Indication 

Rate, per m3

River Bend 

Cumulative 

Indication 

Rate, per m3

PVRUF 

Cumulative 

Indication 

Rate, per m3

Combined Data 

Cumulative 

Indication Rate, 

per m3

1.0 (0.04) 250 5000 1420 7000 2783

4.0 (0.16) 0.0 222 83 357 142

6.0 (0.24) 0.0 0.0 0.0 0.0 0.0

Volume 

Examined, m3 0.016 0.009 0.024 0.014 0.063

Note: 1 m3 = 35.3 ft3

1

10

100

1,000

10,000

100,000

0 2 4 6 8 10 12 14

Flaw Depth, mm

Flaw Rate- per cubic meter 

Shoreham Weld 

PVRUF Weld

C:\FLAWDATA\ORNL-FLAW-002.XLS

Shoreham

Base Metal River Bend

Base Metal

Hope 

Creek

PVRUF

Base Metal

Average of Base Metal

Figure 7-2 Flaw Frequencies for Plate Materials with Comparisons to Data for Weld 

Flaws (1 mm = 0.0394 in., 1 m3 = 35.3 ft3

)

The average flaw density from the plate examinations is generally consistent with the factor of 

10 ratio of flaw densities 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 densities 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 (0.24 in.) from the PNNL examinations of 

plate material. Extrapolation of the flaw density curves of Figure 7-2 would predict that no flaws 

would be expected from the examination of 0.063 m3 (2.2 ft3

) 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.
7-6

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 densities 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 (0.24 in.), 3.5 mm (0.14 in.), and 3.5 mm (0.14 in.), 

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 density for all flaws with depth dimensions greater than 11 mm 

(0.43 in.) 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 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 aspect ratios for 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 [>0.24 in.]) 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 examinations of base metal 

materials and the validations of the observed flaws are sufficient.
8-1

8 CLAD FLAWS – DATA AND STATISTICAL CORRELATIONS

The flaw distribution model provides three input 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 documented in this section, as are the 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-breaking 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.

Figure 8-1 Examples of Flaws in Cladding of PVRUF Vessel
8-2

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 the PRODIGAL computer code (Chapman and Simonen 1998)

3. examinations of cladding material performed at Bettis Laboratory (Li and Mabe 1998)

4. an NRC expert judgment 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 of the cladding. 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.

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

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

 Flaws per Meter of Weld Bead, Depth > A 

C:\FLAWDATA\PVRUF-CLAD-DEPTH.XLS

PRODIGAL Clad

(SAW)

PRODIGAL Clad

(SMAW)

Li and Mabe (Data) 

(SS - Shielded Metal Arc Clad)

Li and Mabe (Curve Fit)

(Alloy EN82H GTA-HW Clad)

PVRUF Weld Clad

(Normalized per Taper Transition) 

PVRUF Weld Clad

(Normalized per Beltline) 

PVRUF Seam Weld 

PRODIGAL Surf

(SAW No PT)

PRODIGAL Surf

(SAW With PT)

(PVRUF Clad in Beltline ~ 2,690 Meters of Weld Bead)

Figure 8-2 Summary of Data on Flaws in Vessel Cladding (1 m = 39.4 in.)
8-3

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 m3 (0.95 ft3

). 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 (0.08 in.) in depth, for which it was not possible to 

measure flaw sizes with any degree of accuracy by nondestructive methods.

Table 8-1 Flaws in Cladding of PVRUF Vessel

Flaw Depth, 

mm (in.)

Flaw Depth 

Fraction of 

Bead

Number of 

Flaws

Number of 

Flaws with 

Depth > a

Number of Flaws 

Depth > a, per 

Meter of 

Examined Weld 

Bead

Number of Flaws 

Depth > a, per 

Meter of Beltline 

Weld Bead

0.00 (0.00) 0.000 0 1204 5.35 0.447

0.10 (0.004) 0.017 1200 1204 5.35 0.447

3.00 (0.12) 0.500 3 4 0.0177 0.00148

4.00 (0.16) 0.667 1 1 0.0044 0.00037

Data from NUREG/CR-6471 Vol. 3 Length of Examined Clad Bead = 222 m (728.3 ft)

Clad Thickness = 6 mm (0.24 in.) Length of Beltline Clad Bead = 2690 m (8825 ft)

Width of Strip Clad Bead = 20 mm (0.79 in.)

Note: 1 mm = 0.0394 in., 1 m = 39.4 in.

Although a large number 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 

clearly much lower than the frequency for buried clad flaws. It was not possible, 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 bounding 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 (0.08 in.), 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.
8-4

8.2.2 Data from Bettis Laboratory

Li and Mabe (1998) performed tests 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 [0.58 in.3

]). 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 potential 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 

extrapolation of this curve falls between the two curves for the PVRUF cladding. In contrast, the 

data gave a flaw occurrence rate for the shielded metal arc cladding that was more than a factor 

of 10 above the observed flaw density 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 a wide range of 

estimates, a significant subset of the experts provided estimates in a 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.

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 a 

curve 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.
8-5

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 part of building the PRODIGAL code (Chapman and Simonen 1998). 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.

8.2.4.1 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).

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 Beltline 1

Width of Weld at Vessel Inner Surface 5 cm

Total Beltline Surface Area 60.8 m2

Length of Circumferential Welds in Beltline 13.8 m

Surface Area of Circumferential Welds in Beltline 0.69 m2

Length of Axial Welds in Beltline 13.2 m

Surface Area of Axial Welds in Beltline 0.66 m2

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 of Weld (manual clad) 26

Note: 1 m = 39.4 in., 1 mm = 0.0394 in., 1 cm = 0.394 in., 1 m2 = 1550 in.2

All calculations assumed a total clad thickness of 11 mm (0.43 in.), consisting of two weld 

layers. The modeled region of the clad surface was assumed to be 51-mm (2-in.) 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 51 mm (2 in.) 

and length of 1 m (39.4 in.) (surface area of 0.05208 m2 [80.8 in.2

]), giving a total weld bead 

length of 14 m (551 in.).

The number and sizes of weld beads for the PRODIGAL calculations were based on 

dimensions as observed on cross-sectioned welds 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 the weld bead thickness. Flaw 
8-6

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

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.

Table 8-3 RR-PRODIGAL Predictions for Surface-Breaking Flaws in Cladding by 

Submerged Arc Process (with and without PT)

N

Flaw Depth,

mm

Depth,

Fraction of Bead

No PT Inner Surface,

Flaws per Meter of 

Bead with Depth > a

With PT Inner Surface,

Flaws per Meter of 

Bead with Depth > a

1 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 0.000E+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 0.000E+00

9 19.4 3.530 0.000E+00 0.000E+00

10 21.7 3.945 0.000E+00 0.000E+00

Note: 1 mm = 0.0394 in.

Table 8-4 RR-PRODIGAL Predictions for Buried Flaws in Cladding Applied with Manual 

Metal Arc and Submerged Arc Process

N Depth, mm

Depth,

Fraction of Bead

Submerged Arc 

Buried Flaw, 

Flaws per Meter of 

Bead with Depth > a

Shielded Metal Arc 

Buried Flaw, Flaws per 

Meter of Bead 

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 0.000E+00 0.000E+00

7 14.8 2.699 0.000E+00 0.000E+00

8 17.1 3.114 0.000E+00 0.000E+00

9 19.4 3.530 0.000E+00 0.000E+00

10 21.7 3.945 0.000E+00 0.000E+00

Note: 1 mm = 0.0394 in.
8-7

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.

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, even 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 circumferential in orientation. Such 

flaws should have a minimal impact on the integrity of axial welds (and also the plate regions) of 

a vessel. Manual cladding applied 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.
8-8

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 work(a) 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 Schuster(a) 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 as 25.4-mm (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 8-11.

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 (0.79 in.), 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 [1.18 in.] and greater than 30 mm [1.18 in.]). 

The smallest flaw length was 4 mm (0.16 in.).

 

(a) Schuster GJ. 2001. Length of Flaws in Cladding with Recommendations for 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.
8-9

Table 8-5 Clad Product Form and Inspection Results

Product Form

Bead 

Size, 

mm (in.)

No. of

Clad 

Passes

Volume, m3

(ft3)

Area,

m2 (ft2)

No. of 

Small 

Flaws

No. of

Large 

Flaws

101.6 mm (4 in.) Strip Clad 6 (0.24) 1 0.016 (0.565) 2.6 (28) 180 0

Manual Clad 4 (0.16) 2 0.012 (0.424) 1.4 (15.1) 80 0

25.4 mm (1 in.) Strip Clad 6 (0.24) 1 0.0028 (0.099) 0.46 (4.95) 700 0

Table 8-6 Dimensions of Flaws in Cladding as Reported in Appendix A of Schuster 

et al. (1998)

Name Product Depth, mm (in.) Length, mm (in.) Width, mm (in.)

P1 SMAW <1.5 (0.059) 14 (0.55) -

P2 Strip, 101.6 mm (4 in.) <1.5 (0.059) - 7 (0.28)

P3 SMAW <1.5 (0.059) 8 (0.315) -

P4 SMAW <1.5 (0.059) - 16 (0.63)

V1 Strip, 101.6 mm (4 in.) 3 (0.118) 12 (0.47) 10 (0.39)

V2 SMAW 3 (0.118) 11 (0.43) 12 (0.47)

V3 SMAW 2 (0.079) 6 (0.24) 18 (0.71)

V4 Strip, 25.4 mm (1 in.) 2 (0.079) 16 (0.63) 8 (0.315)

V5 SMAW <1.5 (0.059) 12 (0.47) 11 (0.43)

V6 Strip, 25.4 mm (1 in.) <1.5 (0.059) 20 (0.79) -

Table 8-7 Validated Dimensions of Flaw in Cladding as Reported in Schuster et al. (2000)

Name Product Depth, mm (in.) Length, mm (in.) Width, mm (in.)

4-5DBAC-Z5 Strip, 25.4 mm (1 in.) 4 (0.16) 80 (3.15) 10 (0.39)

Table 8-8 Amount of Multi-Wire Clad in Specimen HC2A2B

Area of Clad, cm2 (in.2) Length of Clad Pass, cm (in.)

412 (63.9) 162 (63.8)

Table 8-9 Length of Flaws in Cladding for Specimen HC2A2B

Indication Length, mm (in.) Indication Length, mm (in.)

1 7 (0.28) 15 97 (3.82)

2 6 (0.24) 16 19 (0.75)

3 9 (0.35) 17 13 (0.51)

4 17 (0.67) 18 18 (0.71)

5 12 (0.47) 19 48 (1.9)

6 18 (0.71) 20 4 (0.16)

7 6 (0.24) 21 7 (0.28)

8 8 (0.315) 22 12 (0.47)

9 9 (0.35) 23 16 (0.63)

10 14 (0.55) 24 7 (0.28)

11 11 (0.43) 25 6 (0.24)

12 18 (0.71) 26 103 (4.06)

13 5 (0.2) 27 11 (0.43)

14 6 (0.24) 28 31 (1.22)
8-10

Table 8-10 Amount of 4-in. Strip Clad in Specimen 5-10D

Area of Clad, cm2 (in.2) Length of Clad Pass, cm (in.)

206 (31.9) 20 (7.8)

Table 8-11 Length of Flaws in Cladding for Specimen 5-10D

Indication Length, mm (in.)

1 15 (0.59)

2 6 (0.24)

3 9 (0.35)

4 53 (2.09)

5 7 (0.28)

6 11 (0.43)

7 9 (0.35)

8 7 (0.28)

9 11 (0.43)

10 6 (0.24)

11 9 (0.35)

12 13 (0.51)

Table 8-12 Data Used to Develop Length Distribution for Clad Flaws

Source Table Length, mm (in.) Source Table Length, mm (in.)

2 14 (0.55) 5 13 (0.51)

2 8 (0.315) 5 18 (0.71)

2 12 (0.47) 5 48 (1.89)

2 11 (0.43) 5 4 (0.16)

2 6 (0.24) 5 7 (0.28)

2 16 (0.63) 5 12 (0.47)

2 12 (0.47) 5 16 (0.63)

2 20 (0.79) 5 7 (0.28)

3 80 (3.15) 5 6 (0.24)

5 7 (0.28) 5 103 (4.06)

5 6 (0.24) 5 11 (0.43)

5 9 (0.35) 5 31 (1.22)

5 17 (0.28) 7 15 (0.59)

5 12 (0.47) 7 6 (0.24)

5 18 (0.71) 7 9 (0.35)

5 6 (0.24) 7 53 (2.09)

5 8 (0.315) 7 7 (0.28)

5 9 (0.35) 7 11 (0.43)

5 14 (0.55) 7 9 (0.35)

5 11 (0.43) 7 7 (0.28)

5 18 (0.71) 7 11 (0.43)

5 5 (0.20) 7 6 (0.24)

5 6 (0.24) 7 9 (0.35)

5 97 (3.82) 7 13 (0.51)

5 19 (0.75)

The two exponential functions forms indicated on Figure 8-3 are
8-11

P(>L) = 1.876e-0.1225L

(8.1)

P(>L) = 0.2676e-0.0215L

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.

y = 1.876e-0.1224x

y = 0.2676e-0.0215x

1.E-02

1.E-01

1.E+00

0 20 40 60 80 100 120

Length of Clad Flaw, mm

Probability > Length

Clad Flaws

C:\FLAWDATA\CLAD-FLAW-DATA-JULY 31-2001.XLS

Figure 8-3 Lengths of Clad Flaws in PVRUF and Hope Creek II Vessels (1 mm = 

0.0394 in.)

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 through-clad 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.

8.4 Flaw Inputs to Fracture Mechanics

An estimate of the number and sizes of surface-breaking and buried flaws in cladding was 

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.

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

NBURIED (>a) = 1.0 × exp(-5.0 × a) (8.2)
8-12

where

NBURIED (>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 × exp(-5.0 × 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

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

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

 Flaws per Meter of Weld Bead, Depth > A 

C:\FLAWDATA\PVRUF-CLAD-DEPTH.XLS

PRODIGAL Clad

(SAW)

PVRUF Weld Clad

(Normalized per Taper Transition) 

PVRUF Weld Clad

(Normalized per Beltline) 

PVRUF Seam Weld 

PRODIGAL 

Surf (SAW No PT)

PRODIGAL Surf

(SAW With PT)

(PVRUF Clad in Beltline ~ 2,690 Meters of Weld Bead)

Recommened Distribution 

for Buried Flaws in Cladding

Recommened Distribution 

for Surface Flaws in Cladding

Figure 8-4 Proposed Curves for Estimating Number and Sizes of Flaws in Vessel 

Cladding (1 m = 39.4 in.)

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 
8-13

inputs can be developed later if surface-breaking 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:

1. 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 surface-breaking 

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 1.0E-3 for a single-layer clad and a factor of 

1.0E-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 can then if requested be 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.
8-14

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-II code to account for the actual number of flaws in the material regions of 

interest. Four levels of neutron fluence (2.0 × 1019, 1.0 × 1019, 0.5 × 1019, and 0.25 × 1019

neutrons/cm2 [1 cm2 = 0.155 in.2

]) 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 wt%, respectively, with an initial value of RTNDT of 20°F (–6.7°C).
8-15

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 

surface-breaking flaws.

Additional inputs and assumptions used for the calculations were as follows:

1. Flaw lengths were assumed to be long (two-dimensional solutions for stress intensity 

factors).

2. The stress-free temperature for the cladding was consistent with recent ORNL publications 

(242°C [468°F]).

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 at 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 (4.57 m [180.0 in.] and 229 mm [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 [173 in.]). 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 
8-16

fracture mechanics calculations, however, indicated that circumferential welds contribute little to 

vessel failure probabilities.

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 

compared to the contribution of the flaws in the seam welds. 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.

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0.0 0.5 1.0 1.5 2.0 2.5

Fluence

Probability of Initiation

Buried Flaws in Clad

Surface Flaws in Clad

INITIATION PROBABILITY - AXIAL WELD MATERIAL IS LIMITING

(One Layer Clad - 7 mm Thick)

Flaws in Axial Weld

Vessel Failure Probability

Figure 8-5 Probability of Flaw Initiation in Vessel with Axial Welds as Limiting Material

(fluence in units of 1.0 × 1019 neutrons/cm2 [6.45 × 1019 neutrons/in.2

])
8-17

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0.0 0.5 1.0 1.5 2.0 2.5

Fluence

Probability of Initiation

Buried Flaws in Clad

Surface Flaws in Clad

INITIATION PROBABILITY - PLATE MATERIAL IS LIMITING

(One Layer Clad - 7 mm Thick)

Flaws in Plate/Weld Fusion Line

Vessel Failure Probability

Figure 8-6 Probability of Flaw Initiation in Vessel with Plates as Limiting Material

(fluence in units of 1.0 × 1019 neutrons/cm2 [6.45 × 1019 neutrons/in.2

])

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.

8.5.4 Concluding Discussion

In summary, probabilistic fracture mechanics calculations using the VISA-II 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 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 
8-18

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.
9-1

9 ALGORITHM TO GENERATE FLAW INPUT FILES 

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 develop an 

algorithm that generates computer files to serve as inputs to the ORNL-developed FAVOR 

code. Important details of the FAVOR code are described in Section 9.1; particular attention is 

given to the treatment of fabrication flaws. Details of the PNNL-developed algorithm 

(FORTRAN code) are presented in Section 9.2. Sample input and output files from the 

algorithm are provided in Section 9.3. Implementation of weld region and flaw type statistical 

correlations into the flaw distribution algorithm is described in Sections 9.4 through 9.6.

9.1 FAVOR Code Structure and Organization

As shown by Figure 9-1, FAVOR has three computational modules: (1) a deterministic load 

generator (FAVLoad), (2) a Monte Carlo probabilistic fracture mechanics (PFM) module 

(FAVPFM), and (3) a post-processor (FAVPost). Figure 9-1 also indicates the nature of the 

data streams that flow through these modules. This report concerns the FAVPFM module and 

the element of Figure 9-1 labeled Flaw data. The primary outputs of the module are shown in 

Figure 9-1 as conditional probabilities of flaw initiation (CPI) and of vessel failure (CPF) defined 

as a through-wall crack. The FAVPFM module is described below, based on documentation of 

the FAVOR code made available by ORNL (Dickson et al. 2004; Williams et al. 2004). The 

other two modules of the FAVOR code are described only briefly.

9.1.1 FAVLoad Module

The module FAVLoad uses inputs as generated by thermal-hydraulic calculations for the reactor 

coolant temperatures and pressures at the vessel inner wall. Based on vessel dimensions and 

material properties, FAVLoad calculates temperatures and stresses within the vessel wall, 

which, in turn are used to calculate crack tip stress intensity factors. These results become 

inputs to the probabilistic fracture mechanics calculations performed by the FAVPFM module.

The flaw categories of the FAVLoad module relate to the flaw input files. All flaws can be

oriented in either the axial or circumferential direction. As indicated by Figure 9-2, FAVOR 

addresses three flaw categories:

• Category 1 – surface-breaking flaws:

– infinite length – aspect ratio L/a = ∞

– semi-elliptic – aspect ratio L/a = 2

– semi-elliptic – aspect ratio L/a = 6

– semi-elliptic – aspect ratio L/a = 10

• Category 2 – embedded flaws – fully-elliptic geometry with inner crack tip located between 

the clad/base interface and 1/8 t from the inner surface (t = thickness of the RPV wall)
9-2

• Category 3 – embedded flaws – fully-elliptic geometry with inner crack tip located between 

1/8 t and 3/8 t from the inner surface.

Figure 9-1 Data Streams for FAVOR Code Modules (1) FAVLoad, (2) FAVPFM, and 

(3) FAVPost
9-3

Figure 9-2 Flaw Models in the FAVOR Code

9.1.2 FAVPFM Module

The FAVOR code models the beltline of an RPV that is fabricated using either forged-ring 

segments or rolled plate segments, as shown by Figure 9-3. The vessel wall is lined with an 

internal cladding of austenitic stainless steel. Vessels made with forgings have only 

circumferential welds, while plate-type vessels have both circumferential and axial welds. 

Beltlines of plate-type vessels contain three major region categories to model: (1) axial welds, 

(2) circumferential welds, and (3) plate segments. Only that portion of a weld within the axial 

bounds of the core is addressed because the fast-neutron flux and associated radiation damage 

applied to a weld experience a steep attenuation beyond the fueled region. The potential 

growth of an axially-oriented flaw in a plate segment is limited by the height of the core but not 

by the height of the shell course. Therefore, the lengths of axial flaws in plate segments can 

become greater than those in axial welds. Circumferential flaws in circumferential welds are 

limited only by the full 360-degree arc-length of the weld. Due to the fabrication procedures for 

applying the cladding on the inner vessel surface, FAVOR assumes that all pre-existing surfacebreaking flaws (in plate or weld subregions) are circumferential flaws. Embedded flaws can be 

either oriented axially or circumferentially, depending on the orientation of the weld. Fabrication 

flaws are assigned orientations as described by Table 9-1. Upon the initiation of crack growth, 

the growing cracks retain the original orientation of the fabrication flaws.
9-4

Figure 9-3 Fabrication Configurations of PWR Vessel Beltline Shells

Table 9-1 Applied Flaw Orientations by Major Regions

Major Region Flaw Category 1(a) Flaw Category 2(b) Flaw Category 3(c)

Axial weld Circumferential Axial Axial

Circumferential Weld Circumferential Circumferential Circumferential

Plate/forging Circumferential Axial/circumferential(d) Axial/circumferential(d)

(a) Surface-breaking flaw

(b) Embedded flaw in the base material between the clad/base interface and 1/8 t

(c) Embedded flaw in the base material between 1/8 t and 3/8 t

(d) Flaw Categories 2 and 3 in plates/forgings are divided equally between axial and circumferential 

orientations.
9-5

The FAVPFM probabilistic fracture mechanics model is based on the Monte Carlo technique, 

which performs deterministic fracture analyses for a large number of stochastically generated 

RPV trials or realizations. Each vessel realization can be considered to be a sample of the 

uncertain conditions of the specific RPV of interest. The uncertainties in the vessel include a 

number of the vessel’s material properties along with the flaws in the vessel. Input uncertainties 

to the fracture mechanics analysis are described by statistical distributions. The RPV trials then 

propagate the input uncertainties along with their interactions through the model and thereby 

determine the probabilities of fracture and failure for a set of postulated PTS events at selected 

times during the vessel’s operating history. The PFM model also provides estimates of the 

uncertainties in the estimated probabilities in terms of discrete statistical distributions. By 

repeating the RPV trials a large number of times, the output values constitute a random sample 

of the probability distribution induced by the combined probability distributions over several input 

variables.

The assumed fracture mechanism for the RPV is stress-controlled cleavage fracture in the 

lower-transition temperature region of the vessel material. This mechanism is modeled under 

the assumption of linear-elastic fracture mechanics (LEFM). The predicted failure mechanism is 

of sufficient flaw growth either (1) to produce a net-section plastic collapse of the remaining 

ligament or (2) to advance the crack tip through a user-specified fraction of the wall thickness. 

Flaw growth can be due to either cleavage propagation or stable ductile tearing. 

The Monte Carlo method involves sampling from probability distributions to simulate many 

possible combinations of flaw geometry and RPV material embrittlement. The PFM analysis is 

performed for the beltline of the RPV subjected to transient loading conditions. The RPV 

beltline is divided by FAVOR into major regions such as axial welds, circumferential welds, and 

plates or forgings that each has its own embrittlement-sensitive chemistries. The major regions 

are further discretized into subregions to accommodate detailed neutron fluence maps that 

include significant details regarding azimuthal and axial variations in neutron fluence. The 

general data streams that flow through the FAVPFM module are depicted in Figure 9-4. As 

shown, the FAVPFM module requires, as a key input, user-supplied data on flaw distributions.

The conditional probability of initiation, CPI, was calculated in earlier versions of the FAVOR 

code by simply dividing the number of RPV trials predicted to experience cleavage fracture by 

the total number of trials. Similarly, the conditional probability of failure, CPF, was calculated by 

dividing the number of RPV trials predicted to fail by the total number of failures. The current 

version of FAVOR now addresses the uncertainties in the calculated probabilities by calculating 

discrete distributions of RPV failure probabilities.

Because each RPV trial can be postulated to contain multiple flaws, one of the loops of the 

Monte Carlo simulation is indexed for the number of flaws for the particular trial. Each of the 

simulated flaws is positioned (through sampling) in a specific RPV beltline subregion that has its 

own distinguishing embrittlement parameters. The flaw geometry (depth, length, aspect ratio, 

and location within the RPV wall) is determined by sampling from appropriate distributions, as 

documented in this report. A deterministic fracture mechanics analysis is performed for each 

flaw for each of the PTS transients. The calculated probabilities are conditional probabilities in 

the sense that the transients are assumed to occur.
9-6

Figure 9-4 Input of User-Supplied Data on Flaw Distributions and Embrittlement and 

Output of Data on Vessel Failure Probabilities

The discretization and organization of major regions and subregions of the beltline include a 

special treatment of weld fusion lines. The fusion lines represent the boundaries between the 

weld subregions and the neighboring plate or forging subregions. FAVOR checks for the 

possibility that the plate subregions adjacent to a weld subregion could have a higher degree of 

embrittlement than the weld. The RTNDT values for the weld subregion of interest are compared 

to the corresponding values for the adjacent plate subregions. Each weld subregion will have at 

most two adjacent plate subregions. The embrittlement properties of the most limiting (either 

the weld or the adjacent plate subregion with the highest value of RTNDT) material are used 

when the fracture of the weld subregion is evaluated. 

The method used to quantify the uncertainty in the flaw characterization is to include 1000 flawcharacterization file records in each of the three data files corresponding to the (1) inner 

surface-breaking flaws, (2) embedded flaws in weld metal, and (3) embedded flaws in plate 

material. The flaw-characterization file for inner surface-breaking flaws is applicable to both 

weld and plate material regions. The RPV trials cycle through the flaw-characterization file 

records sequentially up to 1000, and then restart at the first file record.

Inner surface-breaking flaw density data are expressed by FAVOR in flaws per unit of RPV 

inner-surface area. The weld subregion embedded flaws are expressed as flaws per unit area 

of the fusion line between the weld and adjacent plate subregions. These conventions are 

consistent with the physical model used by PNNL to develop the flaw characterization data input 

for FAVOR. Embedded flaws within plate regions are expressed on a volumetric basis. 

Figures 9-5a and 9-5b illustrate how FAVOR defines axial and circumferential weld subregion 

elements. For axial welds, the fusion lines are on the sides of the weld, whereas for 

circumferential welds, the fusion lines are on the top and bottom of the welds. A factor of 2 

accounts for the fact that the input data developed by the PNNL procedure is in terms of the 
9-7

(a)

(b)

Figure 9-5 Weld Fusion Area Definitions for (a) Axial-Weld Subregion Elements and 

(b) Circumferential Subregion Elements
9-8

Figure 9-5 (contd). (c) Plate Subregion Element

area for one side of the fusion line, whereas flaws can occur along fusion lines on both sides of 

the welds. All flaw densities are assumed to be uniform through the vessel wall thickness. The 

numbers of flaws in the plate subregion elements, as illustrated by Figure 9-5c, are calculated in 

a manner similar to that for welds, except that calculations are based on the flaws per unit 

volume of plate material. 

9.1.3 FAVPost Module

The final module of the FAVOR code performs a post-processing of the results of the 

probabilistic fracture mechanics calculations and is not relevant to discussions of input files for 

flaw distributions. Distributions of transient-initiating frequencies obtained from PRA studies and 

the values of conditional probability of vessel failure and fracture (from FAVPFM) are combined 

by the FAVPost module to generate discrete distributions of frequencies of fracture initiation 

(crack growth) and failure (through-wall crack).

9.2 Required Input Files

The flaw model of the FAVOR code requires three input files to simulate the number, sizes, and 

locations of flaws in the beltline of a vessel as follows:

1. flaws in weld regions

2. flaws in base metal regions

3. surface-related flaws in the vessel cladding.
9-9

The number of flaws per unit area of weld fusion area or per unit volume of vessel material is 

specified and input 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 area or volume for defined ranges of flaw depth dimensions (expressed as a 

percentage of the vessel wall thickness) and for defined ranges of flaw aspect ratios (flaw length 

divided by flaw depth). Flaws are assumed to be located randomly through the thickness of the 

vessel wall.

Other inputs to FAVOR include the volumes and areas for the RPV subregions. From the 

assigned volumes and areas and from the inputs for the number of flaws per unit area or 

volume of each size category, the total number of flaws in the weld, base metal, or clad regions 

are calculated. Flaw locations relative to the vessel inner surface are assigned randomly. The 

FAVOR code also divides the vessel wall thickness into regions; the first region consists of the 

inner one-eighth of the wall thickness, and the second consists of the region from one-eighth to 

three-eighths of the vessel wall thickness. FAVOR assumes that flaws located outside the 

region three-eighths of the wall thickness make negligible contributions to vessel failure 

probabilities.

9.3 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. The algorithm performs Monte Carlo 

calculations that simulate or sample from the uncertainty distributions for the parameters of the 

flaw distribution functions. Each application of the flaw distribution algorithm generates a data 

file for use as a possible input to the FAVOR code. Examples of input files that were supplied to 

ORNL for calculations with FAVOR are presented below.

The flaw distribution algorithm has three parts that 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 

each of the three parts of the code. The program logic for simulating flaws in weld regions is 

more complex and is described first. The corresponding logic for base metal flaws is a simple 

adaptation of the logic for weld flaws and requires only a brief explanation. Distributions for 

surface/clad flaws are treated in a deterministic manner, and the discussion of the logic for this 

category of flaws is again relatively brief.

Figure 9-6 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. All input 

parameters are in metric units (mm), whereas output files can be in either metric or English units 

as requested by the user.
9-10

C *****************************************************************

C *****************************************************************

C

C INPUT DATA FOR THE COMPUTER CODE VFLAW03.FOR

C

C *****************************************************************

C *****************************************************************

C

C *****************************************************************

C DATA SET #1 CONTROL PARAMETERS

C *****************************************************************

C

C COL. 1-80 NAME_REGION NAME OR TITLE FOR REGION

C (A80)

C

C

C COL. 1-11 N_SUBREGIONS NUMBER OF TYPES TO BE MIXED TOGETHER

C I10) WITHIN THE REGION

C 

C

C COL. 11-20 N_SIMULATION = 0 BEST ESTIMATE CALCULATION

C (I10) > 0 UNCERTAINTY CALCULATION WITH

C WITH NUMBER OF MONTE CARLO

C TRIALS = N_SIMULLATION

C

C COL. 21-30 WALL VESSEL TOTAL WALL THICKNESS (MM)

C (F10.4) (INCLUDING CLAD)

C

C COL. 31-40 IUNITS UNITS FOR OUTPUT FILES

C = 1 METRIC (FLAWS PER M^2 OR M^3)

C = 2 ENGLISH (FLAWS PER FT^2 OR FT^3)

C

C COL. 41-50 IVOLAREA UNITS FOR OUTPUT TABLES

C (10) (FOR WELD AND CLAD FLAWS)

C = 1 FLAWS PER UNIT VOLUME

C = 2 FLAWS PER UNIT AREA

C

C COL. 51-60 I_BASE_METAL = 0 NORMALLY

C (I10) = 1 JUNE 20, 2001 ASSUMPTIONS USED TO 

C ADDRESS BASEMETAL FLAWS PER EXPERT

C JUDGMENT DATA AS ADJUSTMENT APPLIED 

C TO WELD METAL DISTRIBUTION

C

C COL. 61-65 IORNL = 0 NORMALLY

C (I10) = 1 USE ORNL FORMAT FOR FLAW OUTPUT 

C DATA FILE (W/O TWO HEADER LINES)

C

C COL. 66-75 UNIFORM_DENSITY FOR UNIFORM FLAW DEPTH DENSITY

C (F10.6) = 0.0 NORMALLY

C = USER SPECIFIED FLAWS 

C PER UNIT AREA OR VOLUME

C FOR EACH CATEGORY OF 

C ONE PERCENT OF WALL THICKNESS

C ---------------------------------------------------------------

C 

C BASE METAL 1) DENSITY (INCLUDING UNCERTAINTY) OF SMALL FLAWS

C ASSUMPTIONS IN BASEMETAL IS 1/10 OF THAT FOR WELD METAL

C 2) DENSITY (INCLUDING UNCERTAINTY) OF LARGE FLAWS

C IN BASEMETAL IS 1/40 OF THAT FOR WELD METAL

Figure 9-6 Input Instructions for Flaw Distribution Algorithm
9-11

C *****************************************************************

C DATA SET #2 MATERIAL TYPE CHARACTERISTICS

C (ONE DATA SET FOR EACH MATERIAL TYPE)

C *****************************************************************

C

C COL. 1-10 VOLFRAC(N) VOLUME OR AREA FRACTION FOR MATERIAL TYPE

C (F10.4) 

C

C COL. 11-15 IVESSEL(N) = 1 USE CORRELATIONS FROM PVRUF VESSEL

C (I5) = 2 USE CORRELATIONS FROM SHOREHAM VESSEL

C

C COL. 16-20 IMATERIAL(N) = 1 SAW (SUBMERGED METAL ARC WELD)

C (I5) = 2 SMAW(SHIELDED METAL ARC WELD)

C = 3 REPAIR WELD

C = 4 CLAD

C = 5 BASE METAL

C

C

C COL. 21-25 BEAD(N) BEAD SIZE (MM) FOR MATERIAL TYPE

C (F5.1)

C

C COL. 26-35 FACTOR(N) FACTOR ON FLAW FREQUENCIES APPLIED

C (F10.4) TO HARD WIRED FLAW DENSITIES

C (NORMALLY ASSIGNED AS 1.0)

C

C COL. 36-40 CLAD_THICK(N) CLAD THICKNESS (MM)

C (F5.1) (ONLY IF IMATERIAL(N) = 4)

C

C COL. 41-45 CLAD_WIDTH(N) CLAD BEAD WIDTH (MM)

C (F5.1) (ONLY IF IMATERIAL(N) = 4)

C

C COL. 46-50 N_LAYERS(N) NUMBER OF CLAD LAYERS

C (I5) (ONLY IF IMATERIAL(N) = 4)

C

C

C COL. 51-60 TRUNC(N) TRUNCATION ON FLAW DEPTH

C (F10.3) (MM)

Figure 9-6 (contd)

9.3.1 Input File to PNNL Algorithm

Inputs to the flaw distribution algorithm as described by Figure 9-6 include

• title line - A title of up to 80 characters allows the user to describe the calculation.

• number of material types - Allows the use of a rule-of-mixtures if a weld is made by more 

than one weld process (SAW, SMAW, and repair). Other inputs specify the welding 

processes in detail and the area or volume fractions contributed by each of the specified 

processes.

• number of Monte Carlo simulations - This parameter typically has been set at 1000 

simulations to generate 1000 samples for the uncertainty analysis. The number of 

simulations can be specified to be 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.
9-12

• vessel wall thickness - The wall thickness is the total thickness including the cladding. 

However, in generating flaw data output files for weld and base metal regions, the cladding 

thickness is treated as zero.

• area or volume - Allows the output file to give flaw frequencies in terms of flaws per unit area 

of the weld fusion surface (for welds) or vessel inner surface (for clad/surface-breaking 

flaws). Alternatively, the output for weld regions can be requested in terms of flaws per unit 

volume. Base metal output is always in terms of flaw per unit volume. Clad/surface flaw 

frequencies also can be expressed in terms of flaws per unit volume. In this case, the 

density corresponds to the number of flaws in a given region of clad divided by the total 

volume of metal in the vessel wall beneath the region of the clad. It is noted that the 

FAVOR code made a change from using flaws per unit volume to flaws per unit area (for 

weld and clad/surface flaws). All subsequent applications of the PNNL flaw distribution 

algorithm have used the flaw per unit area approach. The PNNL algorithm has nevertheless 

retained the option of flaws per unit volume for purposes of sensitivity studies and to allow 

output files to be generated for PFM codes other than FAVOR that may be based on the 

flaws per unit volume concept. 

• metric or English - Allows the output file to give flaw frequencies as either flaws per square 

meter or as flaws per square foot. If the flaw densities are expressed as flaws per unit 

volume, the units are flaws per cubic meter or flaws per cubic foot.

• base metal option - The current version of the algorithm does not explicitly treat flaws in 

base metal regions but first performs simulations of flaws as if the base metal were weld 

metal. The calculated flaw frequencies for welds are then reduced by hardwired factors of 

10 for small flaws and 40 for large flaws.

• ORNL header option - The format prescribed by ORNL for the FAVOR input file of 1000 

datasets (for the uncertainties in flaw distributions) does not allow for a header line to label 

the columns of the table. This parameter allows the header lines to be deleted.

• uniform depth density - This parameter normally is set to 0.0. Values other than zero should 

be used only for sensitivity studies. In this case, the output file arbitrarily assigns flaw 

frequencies that are independent of the flaw depth dimensions.

Each of the material types (as described above) requires one line for input parameters as 

follows:

• area or volume fraction - the area (or volume) fraction for each weld process (SAW, SMAW, 

or repair) for each material type of the weld - The sum of the area (or volume) fractions for 

all material types should add up to unity.

• vessel - Specifies if the parameters for the flaw densities and flaw dimensions are to be 

based on the data from the PVRUF vessel or from the Shoreham vessel.

• material type - Denotes the category of weld process (SAW, SMAW, or repair weld) for the 

material type of interest. This parameter also can direct the algorithm to perform 

calculations for clad material. In this 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 
9-13

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 by use of this input parameter.

• bead size - Is the estimated bead size (through-wall dimension) for each weld material type 

(SAW, SMAW, and repair).

• factor - factor (normally set equal to 1.0) that is applied to the hardwired flaw densities -

Values other than 1.0 should be used only for sensitivity studies.

• clad thickness - Is the total clad thickness and accounts for all layers, should the clad 

consist 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 - 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.

• number of clad layers - Specifies the number of clad layers and will specify 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 - Describes the values of flaw depth dimensions, 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 25.4 mm (1 in.) for SAW and 

SMAW flaws and 50.8 mm (2 in.) for flaws in repair welds.

9.3.2 Output File from PNNL Algorithm

Output files from the PNNL algorithm provide the following information:

• display of the input data - The first part of the output file displays and identifies all of the 

input data the user has provided to the algorithm.

• first 10-sample flaw distributions from the uncertainty evaluation - The second part of the 

output file is a series of 10 tables corresponding to the first 10 (of a typical total of 1000) 

sample flaw distributions that are 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 distributions—This table does not correspond to any of the 1000 samples but 

only indicates the maximum values for the individual elements from all of the flaw distribution 

tables.

• 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 distributions—This table does not correspond to any of the 1000 samples but 

indicates only the median values for the individual elements from all of the flaw distribution 

tables.

• 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 
9-14

describe the simulated distributions—This table does not correspond to any of the 

1000 samples but indicates only the smallest values for the individual elements from all of 

the flaw distribution tables.

• 25th percentile values from the 1000 simulated flaw distribution - the 25th 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 25th percentile values for the individual elements from 

all of the flaw distribution tables.

• 75th percentile values from the 1000 simulated flaw distribution - the 75th 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 75th percentile values for the individual elements of the 

flaw distribution table.

• 5th percentile values from the 1000 simulated flaw distribution - the 5th 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 5th percentile values for the individual elements from all 

of the flaw distribution tables.

• 95th percentile values from the 1000 simulated flaw distribution - the 95th 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 95th percentile values for the individual elements from 

all of the flaw distribution tables.

9.3.3 Output File from PNNL Algorithm for Inputs to FAVOR

The second output file from the PNNL algorithm is generated for actual use as an input file by 

FAVOR. This relatively large file 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 9.3.2 provides the user with the 

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

9.4 Procedure for Weld Regions

Section 6 of this report documents the flaw 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 the statistical correlations into the flaw 

distribution algorithm.

9.4.1 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 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 
9-15

both processes, but the largest fraction (e.g., >90%) of the weld will usually be deposited by the 

automatic SAW process. The flaw model accounts for the differences between the flaw 

densities and size distributions for these weld processes. In this regard the identification of local 

regions as produced by specific welding processes requires information not generally available 

from vessel fabrication records. Therefore, calculations with FAVOR have assumed a random 

mixture of SAW and SMAW materials plus 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 other flaws 

are located along the fusion lines that separate the weld metal from the adjoining base metal. 

While many flaws are within the volume of the weld, PNNL data have shown that very few of 

these flaws have significant through-wall dimensions. Most larger weld flaws are located along 

the weld fusion line. FAVOR therefore assumes that all weld flaws are located along fusion 

lines. Only a small fraction of these fusion line flaws has through-wall dimensions approaching 

or exceeding the size of a single weld bead. 

A single flaw input file is used by FAVOR to address 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 small 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 or entirely within base metal, but will 

most typically span both weld metal and base metal because repairs are generally made to the 

defects that reside along the weld fusion lines. Observed repairs have been made from both 

the inside and the outside surfaces of vessels. It has not been considered practical for FAVOR 

calculations to identify specific locations of repairs, although such information can be obtained 

from construction records. The repairs have therefore 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 the dominant contribution to the estimated number of larger flaws.

9.4.2 Flow Chart for Welds

Figure 9-7 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 the simulation 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 composed of any of the specified weld types.
9-16

• bead size - An input to the calculations allows the user to specify the weld bead size 

(through thickness dimension) for each category of weld material. This permits vessel 

specific information on the welding process to be accounted for in the estimates of flaw 

distributions. If the calculations are to be based on the observed bead sizes for the PVRUF 

or Shoreham vessels, the following inputs can be used as default inputs:

Weld Type

Bead Size, mm (in.) 

PVRUF Vessel

Bead Size, mm (in.) 

Shoreham Vessel

Submerged Arc (SAW) 6.5 (0.26) 5.0 (0.20)

Shielded Metal Arc (SMAW) 3.5 (0.14) 3.5 (0.14)

Repair 3.5 (0.14) 3.5 (0.14)

• vessel simulation - The Monte Carlo simulation ensures that uncertainties in the parameters 

of the statistical flaw distribution functions are simulated only once per vessel. For example, 

in reference to Figure 9-7, one conditional depth distribution 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 that 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 9-7, there are independent elements of the 

model that address the parameters for the distributions of small and large flaws. Small flaws 

are those with through-wall depths that are less than one weld bead dimension, 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 

square meter or cubic meter) of SAW, SMAW, and repair flaws for 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.
9-17

Simulate Small 

Flaws

Simulate 

Large Flaws

Read Input for Volume 

Fractions of SAW, SMAW 

and Repair Material 

Sample Parameters for 

Conditional Depth 

Distribution of Small Flaws

Sample Parameters for 

Conditional Depth Distribution 

of Large Flaws

Read Inputs for Bead Sizes 

of SAW, SMAW and Repair 

Flaws

Sample Flaw Density for 

Small Flaws in SAW Material

Sample Flaw Density for 

Large Flaws in SAW Material

Begin Monte Carlo 

Simulation

Sample Flaw Density for 

Small Flaws in SMAW 

Material

Sample Flaw Density for 

Large Flaws in SMAW 

Material

Sample Flaw Density for 

Small Flaws in Repair 

Material

Sample Flaw Density for 

Large Flaws in Repair 

Material

Sample Parameters for 

Length Distribution of Small 

Flaws in SAW Material

Sample Parameters for 

Length Distribution of Large 

Flaws in SAW Material

Sample Parameters for 

Length Distribution of Small 

Flaws in SMAW and Repair 

Material

Sample Parameters for 

Length Distribution of Large 

Flaws in SMAW and Repair 

Material

Generate Table of Small SAW 

Flaw Frequencies for Each 

Flaw Depth/Aspect Ratio 

Category

Generate Table of Large SAW 

Flaw Frequencies for Each 

Flaw Depth/Aspect Ratio 

Category

Generate Table for Small 

SMAW Flaw Frequencies for 

Each Flaw Depth/Aspect 

Ratio Category

Generate Table for Small 

SMAW Flaw Frequencies for 

Each Flaw Depth/Aspect Ratio 

Category

Generate Table for Small 

Repair Flaw Frequencies for 

Each Flaw Depth/Aspect 

Ratio Category

Generate Table for Small 

Repair Flaw Frequencies for 

Each Flaw Depth/Aspect Ratio 

Category

Combine Tables for Small and 

Large Flaw Frequencies

Generate Combined Table for 

Small Flaw Frequencies for 

SAW, SMAW and Repair 

Flaws

Generate Combined Table for 

Small Flaw Frequencies for 

SAW, SMAW and Repair 

Flaws

Write Combined Table for Small 

and Large Flaw Frequencies to 

Interface with Fracture 

Mechanics Model for 

Uncertainities

Figure 9-7 Flow Chart for Weld Flaws
9-18

• conditional depth distribution - The conditional depth distribution (as normalized with respect 

to the weld bead dimension) 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 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.

• 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 these 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 small flaws in 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 and SMAW welds have the same 

distribution of aspect ratios.

9.4.3 Sample Input and Output File for Welds

Figures 9-8 through 9-10 present inputs and outputs for a sample calculation for welds 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 (Figure 9-10) the 

first simulated distribution of a total of 1000 tables from sampling for the uncertainty analysis. 

The Monte Carlo simulation, as performed by the FORTRAN computer code, generates a file 

consisting of a large number of tables (e.g., 1000) corresponding to Figure 9-10. These results 

(along with other results presented below for flaws in plates and for flaws in cladding) are 

intended to be an example rather than a generic basis for probabilistic fracture mechanics 

calculations. Nevertheless, the trends of the data can be viewed as representative of those for 

most PWR vessels. Therefore, the vessel-to-vessel differences in calculated CPI and CPF 

levels coming from inputs for flaw distributions are usually relatively small compared to the 

corresponding differences coming from other factors such as material fracture toughness and 

embrittlement levels. Larger effects of differences in flaw inputs (compared to the values of 

Figure 9-10) will come from significant changes in vessel wall thickness and from use of the 

data trends from the PVRUF vessel rather than the Shoreham data used to generate 

Figure 9-10.

The rows of Figure 9-10 come from a binning into 100 bins of the data from the continuous flaw 

distributions generated by the algorithm. 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” in 

Figure 9-10 gives the number of flaws per square foot of fusion surface that have depth 

dimensions between 0% and 1% of the vessel wall thickness. There are 40.614 flaws per 

square foot (437.18 flaws/m2

) for this depth category, whereas the number of very large flaws 

with depths between 9% and 10% of the vessel wall thickness is only 0.0017841 flaws per 

square foot (0.019 flaws/m2

). There are no flaws with depths greater than 23% of the vessel 

wall thickness, consistent with the specified truncation depth for flaws in repair welds.
9-19

OCONEE-1 OCTOBER 29, 2002 WELD FLAW/FT^2 SHOREHAM TRUNCATED

 3 1000 219.10 2 2 0 1 0.0

 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

Figure 9-8 Sample Flaw Distribution Input File for Weld Region

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 

 BASE_METAL APPROXIMATION NOT USED 

 OUTPUT FILE REFORMATTED 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 9-9 Sample from Flaw Distribution File for Weld Region (1 mm = 0.0394 in.)
9-20

FLAW DISTRIBUTION FOR SIMULATION NUMBER 1

 N FLAWS/FT**2 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0

 1 .40614E+02 2.285 2.232 4.310 8.039 7.322 6.671 6.078 10.588 8.798 16.044 27.633

 2 .31174E+01 6.680 6.230 11.230 18.275 13.849 10.504 7.973 10.654 6.153 6.294 2.157

 3 .29780E+00 13.925 11.939 19.043 24.477 13.479 7.486 4.186 3.687 1.189 .548 .040

 4 .84188E-01 20.384 16.106 22.883 23.709 9.749 4.095 1.746 1.077 .204 .047 .001

 5 .24607E-01 28.213 19.981 24.412 19.303 5.558 1.708 .550 .244 .028 .004 .000

 6 .10494E-01 36.682 22.971 23.618 13.574 2.481 .514 .119 .037 .003 .000 .000

 7 .59722E-02 43.742 24.483 21.487 9.116 1.016 .131 .020 .004 .000 .000 .000

 8 .38645E-02 49.281 24.949 19.069 6.225 .438 .034 .003 .000 .000 .000 .000

 9 .26093E-02 53.918 24.832 16.718 4.322 .200 .010 .001 .000 .000 .000 .000

 10 .17841E-02 58.006 24.354 14.523 3.018 .095 .003 .000 .000 .000 .000 .000

 11 .12243E-02 61.693 23.631 12.521 2.108 .046 .001 .000 .000 .000 .000 .000

 12 .84087E-03 65.047 22.736 10.724 1.470 .022 .000 .000 .000 .000 .000 .000

 13 .57784E-03 68.101 21.724 9.140 1.025 .011 .000 .000 .000 .000 .000 .000

 14 .39709E-03 70.887 20.637 7.757 .713 .005 .000 .000 .000 .000 .000 .000

 15 .27288E-03 73.430 19.510 6.561 .496 .002 .000 .000 .000 .000 .000 .000

 16 .18752E-03 75.751 18.369 5.534 .345 .001 .000 .000 .000 .000 .000 .000

 17 .12886E-03 77.869 17.233 4.658 .239 .001 .000 .000 .000 .000 .000 .000

 18 .88555E-04 79.803 16.118 3.913 .166 .000 .000 .000 .000 .000 .000 .000

 19 .60855E-04 81.567 15.035 3.282 .115 .000 .000 .000 .000 .000 .000 .000

 20 .41819E-04 83.177 13.993 2.750 .080 .000 .000 .000 .000 .000 .000 .000

 21 .28738E-04 84.647 12.996 2.302 .056 .000 .000 .000 .000 .000 .000 .000

 22 .19749E-04 85.988 12.049 1.925 .039 .000 .000 .000 .000 .000 .000 .000

 23 .13571E-04 87.212 11.153 1.609 .027 .000 .000 .000 .000 .000 .000 .000

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

Figure 9-10 Sample Flaw Data Output File for Weld Region (1 ft2 = 0.0929 m2

)
9-21

Columns 3 through 13 of Figure 9-10 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 9-10, it is seen that 27.633% of this category of small flaws have aspect ratios 

greater than 15:1. It is seen in Figure 9-10 that most of the relatively deep flaws have small 

aspect ratios.

Figure 9-11 is a sample plot of estimated flaw frequencies (expressed here in terms of flaws per 

cubic foot) as estimated for a representative vessel. This plot addresses flaws for all categories 

including welds, base metal, and clad/surface flaws. The flaw depth distributions of Figure 9-11 

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.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0 5 10 15 20 25 30

a = Flaw Depth, Percent Wall

Number of Flaws per Cubic Foot, Depth > a

C:\FLAWDATA\ORNL CD AUG 20 2001\ PLOTS OF ORNL INPUTS.XLS

Wall Thickness = 214 mm

Weld Metal Flaws

Base Metal Flaws

Surface/Clad Flaws

Marshall

 Distribution 

Figure 9-11 Flaw Distribution for Various Vessel Regions (Median Values from 

Uncertainty Analyses) (1 ft3 = 0.0283 m3

)

9.5 Procedure for Base Metal Regions

Section 7 of this report 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.
9-22

9.5.1 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 has also been observed that the largest flaws in plate and forging materials have 

orientations parallel to the surfaces 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 those flaws that have some 

through-wall dimension. As discussed above 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.

9.5.2 Flow Chart for Base Metal

Because the flow chart for base metal flaws is essentially the same as the flow chart for weld 

metal flaws (see Figure 9-7), 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 uncertainties as developed for the PVRUF data for weld flaws. 

Truncations for maximum depths of base metal flaws (as described in Section 7) are different 

than the truncations for weld flaws, such that recommended truncations for base metal flaws 

occur at much smaller flaw depths than for weld flaws.

9.5.3 Sample Input and Output Files for Base Metal

Figures 9-12 through 9-14 present inputs and outputs for a sample calculation for base metal by 

the PNNL flaw distribution algorithm. As indicated in Figure 9-13, this example was based on 

the flaw distribution parameters and the uncertainty distributions obtained from analyses of the 

PVRUF data. Figure 9-14 is the first simulated distribution of a total of 1000 such tables 

corresponding to sampling for the uncertainty analysis.

As for the weld flaws, the rows of Figure 9-14 come from a binning into 100 bins of the data 

from the continuous flaw distributions generated by the algorithm. 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 0% and 1% of the vessel wall thickness. There are 17.505 flaws per cubic foot 

(618.55 flaws/m3

) 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 flaws per cubic foot

(0.496 flaws/m3

). 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 9-14 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 
9-23

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.

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 9-12 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 FT^2 OR FLAWS PER FT^3 

 WELD DENSITY OPTION - FLAWS PER UNIT VOLUME 

 BASE_METAL APPROXIMATION IS USED 

 OUTPUT FILE REFORMATTED 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 9-13 Sample Flaw Distribution Output File for Base Metal Region (1 mm = 

0.0394 in.)
9-24

FLAW DISTRIBUTION FOR SIMULATION NUMBER 1

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0

 1 .17505E+02 46.753 21.948 15.541 5.601 1.711 1.308 1.100 1.717 1.229 1.753 1.340

 2 .57462E+01 88.777 8.969 1.222 .377 .233 .149 .095 .101 .043 .029 .005

 3 .25423E+00 85.249 3.578 2.924 3.721 2.042 1.121 .615 .523 .158 .065 .003

 4 .23302E-01 30.069 13.294 19.420 21.146 9.131 3.943 1.703 1.053 .196 .044 .001

 5 .14037E-01 28.880 16.830 22.648 20.893 7.097 2.411 .819 .373 .043 .006 .000

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

Figure 9-14 Sample Flaw Data from Output File for Base Metal Region (1 ft3 = 0.0283 m3

)
9-25

Figure 9-11 includes a sample plot of estimated flaw frequencies (flaws per cubic foot) as 

estimated for base metal. The flaw depth distributions of Figure 9-11 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.

9.6 Procedure for Surface/Clad Flaws

Section 8 of this report 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.

9.6.1 Treatment of Surface/Clad Flaws

As described in Section 8, the numbers and sizes of clad/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 most of 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 consistent with the direction of the weld beads that make up the clad. The flaw 

depths are assumed to be equal to the full thickness of the clad and are assigned to the depth 

dimension bin that approximates the clad thickness.

9.6.2 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 can be converted to surface flaws per unit volume or unit area based on the 

material for the full thickness of the vessel wall.

9.6.3 Sample Input and Output Files for Surface/Clad Flaws

Figures 9-15 through 9-17 present inputs and outputs for a sample calculation for clad/surface 

flaws 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 flaw distribution parameters for surface/clad flaws, all 

1000 datasets are identical. However, the FAVOR code is structured to address uncertainties in 

the distributions, should it become possible in the future to quantify these uncertainties.

The rows of Figure 9-17 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” on Figure 9-17 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 
9-26

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 (0.188 in.) 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 flaws per square foot (0.03939/m2

) 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 clad flaws of all depth dimensions) 

versus the small number of through-clad flaws that are sufficiently large to contribute to vessel 

failure.

OCONEE-1 CLAD OCTOBER 29, 2002 SINGLE LAYER FLAWS/FT^2

 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 9-15 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/FT^2 

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 

 BASE_METAL APPROXIMATION NOT USED 

 OUTPUT FILE REFORMATTED 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 9-16 Output File for Surface/Clad Flaws (1 mm = 0.0394 in.)

It is also seen in Figure 9-17 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 9-11 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.
9-27

FLAW DISTRIBUTION FOR SIMULATION NUMBER 1

 N FLAWS/FT**2 2.0 6.0 10.0 INFINITY

 1 .00000E+00 100.000 .000 .000 .000

 2 .00000E+00 100.000 .000 .000 .000

 3 .36589E-02 67.450 20.769 3.964 7.817

 4 .00000E+00 100.000 .000 .000 .000

 5 .00000E+00 100.000 .000 .000 .000

 6 .00000E+00 100.000 .000 .000 .000

 7 .00000E+00 100.000 .000 .000 .000

 8 .00000E+00 100.000 .000 .000 .000

 9 .00000E+00 100.000 .000 .000 .000

 10 .00000E+00 100.000 .000 .000 .000

 11 .00000E+00 100.000 .000 .000 .000

 12 .00000E+00 100.000 .000 .000 .000

 13 .00000E+00 100.000 .000 .000 .000

 14 .00000E+00 100.000 .000 .000 .000

 15 .00000E+00 100.000 .000 .000 .000

 16 .00000E+00 100.000 .000 .000 .000

 17 .00000E+00 100.000 .000 .000 .000

 18 .00000E+00 100.000 .000 .000 .000

 19 .00000E+00 100.000 .000 .000 .000

 20 .00000E+00 100.000 .000 .000 .000

 21 .00000E+00 100.000 .000 .000 .000

 22 .00000E+00 100.000 .000 .000 .000

 23 .00000E+00 100.000 .000 .000 .000

 24 .00000E+00 100.000 .000 .000 .000

 25 .00000E+00 100.000 .000 .000 .000

 26 .00000E+00 100.000 .000 .000 .000

 27 .00000E+00 100.000 .000 .000 .000

 28 .00000E+00 100.000 .000 .000 .000

 29 .00000E+00 100.000 .000 .000 .000

 30 .00000E+00 100.000 .000 .000 .000

 31 .00000E+00 100.000 .000 .000 .000

 32 .00000E+00 100.000 .000 .000 .000

 33 .00000E+00 100.000 .000 .000 .000

 34 .00000E+00 100.000 .000 .000 .000

 35 .00000E+00 100.000 .000 .000 .000

 36 .00000E+00 100.000 .000 .000 .000

 37 .00000E+00 100.000 .000 .000 .000

 38 .00000E+00 100.000 .000 .000 .000

 39 .00000E+00 100.000 .000 .000 .000

 40 .00000E+00 100.000 .000 .000 .000

 41 .00000E+00 100.000 .000 .000 .000

 42 .00000E+00 100.000 .000 .000 .000

 43 .00000E+00 100.000 .000 .000 .000

 44 .00000E+00 100.000 .000 .000 .000

 45 .00000E+00 100.000 .000 .000 .000

 46 .00000E+00 100.000 .000 .000 .000

 47 .00000E+00 100.000 .000 .000 .000

 48 .00000E+00 100.000 .000 .000 .000

 49 .00000E+00 100.000 .000 .000 .000

 50 .00000E+00 100.000 .000 .000 .000

 51 .00000E+00 100.000 .000 .000 .000

 52 .00000E+00 100.000 .000 .000 .000

 53 .00000E+00 100.000 .000 .000 .000

 54 .00000E+00 100.000 .000 .000 .000

 55 .00000E+00 100.000 .000 .000 .000

 56 .00000E+00 100.000 .000 .000 .000

 57 .00000E+00 100.000 .000 .000 .000

 58 .00000E+00 100.000 .000 .000 .000

 59 .00000E+00 100.000 .000 .000 .000

 60 .00000E+00 100.000 .000 .000 .000

 61 .00000E+00 100.000 .000 .000 .000

 62 .00000E+00 100.000 .000 .000 .000

 63 .00000E+00 100.000 .000 .000 .000

 64 .00000E+00 100.000 .000 .000 .000

 65 .00000E+00 100.000 .000 .000 .000

 66 .00000E+00 100.000 .000 .000 .000

 67 .00000E+00 100.000 .000 .000 .000

 68 .00000E+00 100.000 .000 .000 .000

 69 .00000E+00 100.000 .000 .000 .000

 70 .00000E+00 100.000 .000 .000 .000

 71 .00000E+00 100.000 .000 .000 .000

 72 .00000E+00 100.000 .000 .000 .000

 73 .00000E+00 100.000 .000 .000 .000

 74 .00000E+00 100.000 .000 .000 .000

 75 .00000E+00 100.000 .000 .000 .000

 76 .00000E+00 100.000 .000 .000 .000

 77 .00000E+00 100.000 .000 .000 .000

 78 .00000E+00 100.000 .000 .000 .000

 79 .00000E+00 100.000 .000 .000 .000

 80 .00000E+00 100.000 .000 .000 .000

 81 .00000E+00 100.000 .000 .000 .000

 82 .00000E+00 100.000 .000 .000 .000

 83 .00000E+00 100.000 .000 .000 .000

 84 .00000E+00 100.000 .000 .000 .000

 85 .00000E+00 100.000 .000 .000 .000

 86 .00000E+00 100.000 .000 .000 .000

 87 .00000E+00 100.000 .000 .000 .000

 88 .00000E+00 100.000 .000 .000 .000

 89 .00000E+00 100.000 .000 .000 .000

 90 .00000E+00 100.000 .000 .000 .000

 91 .00000E+00 100.000 .000 .000 .000

 92 .00000E+00 100.000 .000 .000 .000

 93 .00000E+00 100.000 .000 .000 .000

 94 .00000E+00 100.000 .000 .000 .000

 95 .00000E+00 100.000 .000 .000 .000

 96 .00000E+00 100.000 .000 .000 .000

 97 .00000E+00 100.000 .000 .000 .000

 98 .00000E+00 100.000 .000 .000 .000

 99 .00000E+00 100.000 .000 .000 .000

 100 .00000E+00 100.000 .000 .000 .000

Figure 9-17 Data from Output File for Surface/Clad Flaw (1 ft2 = 0.0292 m2

)

10-1

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 United 

States 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 PTS 

calculations. The input files describe the number of flaws per unit of weld fusion surface or per 

cubic volume of metal, 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 make the conservative assumption that the flaws are inner-surface 

breaking.

2. Weld flaws are assumed in the FAVOR code 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 both the flaws associated 

with weld fusion line and the 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 have been performed for several representative vessels of the major nuclear steam 

supply system suppliers. Although most calculations have been for vessels for which the weld 

material is the most limiting from the standpoint of embrittlement, one vessel has had base 

metal as the most limiting material.

The primary objective of this report was to document the flaw distribution model that was used 

to generate key inputs for FAVOR code calculations that supported revisions to the PTS rule. 

Future examinations of vessel material will, however, generate additional data on fabrication 

flaws. The parameters of the model should, therefore, be revised as appropriate to support 

future FAVOR code calculations. For example, a recently published report (Schuster et al. 

2008) includes data on flaws in repair welds in the Hope Creek Unit 2 and River Bend Unit 2 

vessels. Although this additional data confirm the general trends of the model as described in 

the present report, recalculations of model parameters would enhance the accuracy and user 

confidence in vessel integrity calculations.

11-1

11 REFERENCES

Bishop BA. 1993. Benchmarking of Probabilistic Fracture Mechanics Analyses of Reactor 

Vessels Subjected to Pressurized Thermal Shock Loading, EPRI Research Project 2975-5, 

Electric Power Research Institute, Palo Alto, California.

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 Model for Estimating the 

Probabilities of Defects in Reactor Pressure Vessel Welds, NUREG/CR-5505, U.S. Nuclear 

Regulatory Commission, Washington, D.C.

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.

Corwin WR, RG Berggren and RK Nanstad. 1984. Charpy Toughness and Tensile Properties 

in Neutron Irradiated Stainless Steel Submerged-Arc Cladding Overlay. NUREG/CR-3927,

U.S. Nuclear Regulatory Commission, Washington, D.C.

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 2nd International 

Conference on NDE in Relation to Structural Integrity for 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, Tennessee.

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 Fitness for Service - 1999, 

PVP Vol. 388, American Society of Mechanical Engineers, New York.

Dickson TL, PT Williams and S Yin. 2004. Fracture Analysis of Vessels – Oak Ridge, FAVOR, 

v04.1, Computer Code: User’s Guide. NUREG/CR-6855, ORNL/TM-2004/245. Oak Ridge 

National Laboratory, Oak Ridge, Tennessee.

Halmshaw R and CA Hunt. 1975. “Can Cracks Be Found by Radiography?”, British Journal of 

Nondestructive Testing, May 1975, pp. 71–75.
11-2

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, D.C.

Jackson DA, and SR Doctor. 2000. “Developing a Generic Flaw Distribution for Reactor 

Pressure Vessels,” 2nd International Conference on NDE in Relation to Structural Integrity for 

Nuclear and Pressurized Components, New Orleans, Louisiana (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. 123–131.

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 of PWR 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,” 2nd International Conference on NDE in Relation to Structural 

Integrity for Nuclear and Pressurized Components, New Orleans, Louisiana (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, D.C.

Schuster GJ, SR Doctor, SL Crawford and AF Pardini. 1999. Characterization of Flaws in U.S. 

Reactor Pressure Vessels: Density and Distribution of Flaw Indications in the Shoreham 

Vessel, NUREG/CR-6471, Vol. 3, U.S. Nuclear Regulatory Commission, Washington, D.C.

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, D.C.

Schuster GJ, AF Pardini, SL Crawford and SR Doctor. 2000b. “Overview of Fabrication Flaw 

Studies on RPV Material from Four Canceled Nuclear Power Plants,” 2nd 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. 2001a. “Fabrication Flaw Rate Estimates for Base Metal of 

Pressure Vessels and Initial Validation Results,” 3rd International Conference on NDE in 

Relation to Structural Integrity for Nuclear and Pressurized Components, Seville, Spain.

Schuster GJ and SR Doctor. 2001b. “Use of SAFT-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.
11-3

Schuster GJ, FA Simonen and SR Doctor. 2008. Fabrication Flaw Density and Distribution in 

the Repairs to Reactor Pressure Vessel and Piping Welds. NUREG/CR-6945, PNNL-16726. 

U.S. Nuclear Regulatory Commission, Washington, D.C.

Schuster GJ, M Morra and SR Doctor. 2009. Methodology for Estimating Fabrication Flaw 

Density and Distribution - Reactor Pressure Vessel Welds. NUREG/CR-6989, U.S. Nuclear 

Regulatory Commission, Washington, D.C.

Simonen FA, KI Johnson, AM Liebetrau, DW Engel and EP Simonen. 1986. VISA-II-A 

Computer Code for Predicting the Probability of Reactor Pressure Vessel Failure, NUREG/CR4486, U.S. Nuclear Regulatory Commission, Washington, D.C.

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.

Williams PT, TL Dickson and S Yin. 2004. Fracture Analysis of Vessels – Oak Ridge, FAVOR, 

v04.1, Computer Code: Theory and Implementation of Algorithms, Methods, and Correlations. 

NUREG/CR-6854, ORNL/TM-2004/244. Oak Ridge National Laboratory, Oak Ridge, 

Tennessee.

APPENDIX A

STATISTICAL EQUATIONS FOR FLAW DISTRIBUTION 

FUNCTIONS AND UNCERTAINTY ANALYSES

A-1

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 Abramson 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 γ(x, α): represents a gamma density function parameterized by the vector α. as 

defined by the formula

( ) ( ) ( x) x

x 1

2

1

1 : exp

2 2

α

Γ α

α

γ α

α α

= −

−

(A.1)

The function DIR(p : α) is a Dirichlet distribution, which is defined as

( ) ( )

( ) ( ) ( )

1 1

2

1

1

1 2

1 2 : + − − − = m m m

DIR p p p p α α α

Γ α Γ α Γ α

Γ α

α   (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 ρ is to be estimated from count data; a total of N flaws are observed in 

a volume V of material. The count N is assumed to be Poisson distributed, so the conditional 

distribution is
A-2

( ) ( )

( )

! exp N

V f N V

N ρ ρ = − ρ (A.3)

The standard conjugate prior employed for such a distribution is a two-parameter gamma 

distribution. Assume that the prior distribution is

p(ρ) = γ (ρ :α) (A.4)

Then the posterior distribution is given by

f ( N)= ( +V + N) 1 2 ρ γ ρ :α ,α (A.5)

The standard noninformative prior assigns α1 = 0, and α2 = 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 (ρ N)= γ (ρ :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 λ. In other words, the conditional distribution for xi is given by

f (x ) ( x) i λ = λ exp − λ (A.7)

The standard conjugate prior distribution on λ is a gamma of the form

p(λ) = γ (λ :α) (A.8)

and this results in a posterior distribution of

( ) ( ) 1 2 f λ x = γ λ : S +α ,n +α (A.9)

where S = Σi

xi 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

( ) Nm m N N

X X X m

X f X β β β β 

1 2

1 2

1 2 ! ! !

! + = (A.10)
A-3

The parameter vector, β, must sum to one.

The conjugate family for this distribution is the Dirichlet, which is denoted as DIR(p : α). If the 

prior distribution is given by

p(β ) = DIR(β :α) (A.11)

then the posterior is given by

f (β X )= DIR(β :α + X ) (A.12)

The standard noninformative prior is produced by setting αi = 0. With the noninformative 

assignment, the posterior will not exist if any Xi 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 (β X )= DIR(β : X ) (A.13)

A.3 Reference

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, D.C.

APPENDIX B

LIST OF EXPERTS ON VESSEL FLAWS

B-1

APPENDIX B

LIST OF EXPERTS ON VESSEL FLAWS

Name Affiliation Area of Expertise

Frank Ammirato Manager, Electric Power Research 

Institute (EPRI) NDE Center

Non-Destructive Examination

Francis Berry Consulting Engineer

Retired, Chicago Bridge & Iron

Non-Destructive Examination, 

Reactor Vessel Fabrication

Spencer Bush, PhD.

(deceased October 

2005)

President, Review & Synthesis 

Associates 

Retired, Pacific Northwest National 

Laboratory

ASME Code, Non-Destructive 

Examination, Metallurgy

Domenic Canonico, 

PhD.

Industry Consultant ASME Code, Failure Analysis, 

Forgings, Metallurgy, Reactor 

Vessel Fabrication, Welding

O.J. Victor Chapman President, OJVC Consultancy

Retired, Rolls Royce

Expert Elicitation, Failure 

Analysis, Non-Destructive 

Examination, Statistics, Welding

Robert DeNale Naval Surface Warfare Center 

Head, Metals Department

Failure Analysis, Metallurgy, 

Non-Destructive Examination, 

Welding

John Lareau Westinghouse formerly Combustion 

Engineering

ASME Code, Non-Destructive 

Examination, Reactor Vessel 

Fabrication

Carl Lundin, PhD. Professor of Metallurgy, University of 

Tennessee

Consultant

Failure Analysis, Metallurgy, 

Welding

Harry Lunt Consulting Metallurgist

Retired, Burns & Roe

Forgings, Failure Analysis, 

Metallurgy, Non-Destructive 

Examination, Welding

Edward Nisbett Consultant

Retired, National Forge Co.

ASME Code, Failure Analysis, 

Forgings, Metallurgy

Robert B. Pond, PhD President, M-Structures

Adjunct Faculty, Johns Hopkins 

University, American Society of Metals, 

Loyola College

ASME Code, Expert Elicitation 

Process, Failure Analysis, 

Metallurgy, Non-Destructive 

Examination, Welding

Stan Rosinski EPRI NDE Center, Program Manager Metallurgy

James Sims, P.E. Consultant

Retired, Chicago Bridge & Iron

Reactor Vessel Fabrication, 

Welding

Kenneth Stuckey Framatome ASME Code, Reactor Vessel 

Fabrication

Helmut Thielsch, P.E. 

(deceased April 2003)

President, Thielsch Engineering Failure Analysis, Metallurgy, 

Non-Destructive Examination

David Thomas Consultant

Retired, Chairman Arcos Corporation

Welding Materials, Metallurgy, 

Welding.

Robert Warke Senior Research Engineer

Southwest Research Institute

ASME Code, Failure Analysis, 

Forgings, Metallurgy, Welding




UNITED STATES 

NUCLEAR REGULATORY COMMISSION

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OFFICIAL BUSINESS
NUREG/CR

-6817, Rev. 1

Flaw

A Generalized Procedure for Generating -Related Inputs for the FAVOR Code