NUREG-1808

Sensitivity Studies of the 

Probabilistic Fracture 

Mechanics Model Used in 

FAVOR 

Office of Nuclear Regulatory Research 
NUREG-1808 

Sensitivity Studies of the 

Probabilistic Fracture 

Mechanics Model Used in 

FAVOR 

Manuscript Completed: May 2006 

Date Published: March 2010 

Prepared by 

M. EricksonKirk1

, T. Dickson2, T. Mintz3, F. Simonen4 

2

Oak Ridge National Laboratory 

Oak Ridge, TN 37831-6170 

3 Southwest Research Institute 

San Antonio, TX 78227-1301

4

Pacific Northwest National Laboratory 

Richland, WA 99352 

P

1

Office of Nuclear Regulatory Research 
ii
ABSTRACT 

During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron 

radiation, resulting in 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, the flaw could very rapidly propagate through the vessel, resulting in a 

through-wall crack and challenging 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 RPV surface in combination with repressurization of the RPV. 

Advancements in our understanding and knowledge of materials behavior, our ability to 

realistically model plant systems and operational characteristics, and our ability to better 

evaluate PTS transients to estimate loads on vessel walls led the U.S. Nuclear Regulatory 

Commission (NRC) to realize that the earlier analysis, conducted in the course of developing 

the PTS Rule in the 1980s, contained significant conservatisms. 

This report, which describes sensitivity studies performed on the probabilistic fracture 

mechanics model, is one of a series of 21 other documents detailing the results of the NRC 

study. 

PAPERWORK REDUCTION ACT STATEMENT 

The information collections contained in this NUREG are subject to the Paperwork Reduction 

Act of 1995 (44 U.S.C. 3501 et seq.)., which were approved by the Office of Management and 

Budget, approval number 3150-0011. 

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. 

iii
iv
FOREWORD 

The reactor pressure vessel is exposed to neutron radiation during normal operation. Over 

time, the vessel steel becomes progressively more brittle in the region adjacent to the core. If a 

vessel had a preexisting flaw of critical size and certain severe system transients occurred, this 

flaw could propagate rapidly through the vessel, resulting in a through-wall crack. The severe 

transients of concern, known as pressurized thermal shock (PTS), are characterized by rapid 

cooling (i.e., thermal shock) of the internal reactor pressure vessel surface that may be 

combined with repressurization. The simultaneous occurrence of critical-size flaws, embrittled 

vessel, and a severe PTS transient is a very low probability event. The current study shows that 

U.S. pressurized-water reactors do not approach the levels of embrittlement to make them 

susceptible to PTS failure, even during extended operation well beyond the original 40-year 

design life. 

Advancements in our understanding and knowledge of materials behavior, our ability to 

realistically model plant systems and operational characteristics, and our ability to better 

evaluate PTS transients to estimate loads on vessel walls have shown that earlier analyses, 

performed some 20 years ago as part of the development of the PTS rule, were overly 

conservative, based on the tools available at the time. Consistent with the NRC’s Strategic Plan 

to use best-estimate analyses combined with uncertainty assessments to resolve safety-related 

issues, the NRC’s Office of Nuclear Regulatory Research undertook a project in 1999 to 

develop a technical basis to support a risk-informed revision of the existing PTS Rule, set forth 

in Title 10, Section 50.61, of the Code of Federal Regulations [1]. 

Two central features of the current research approach were a focus on the use of realistic input 

values and models and an explicit treatment of uncertainties (using currently available 

uncertainty analysis tools and techniques). This approach improved significantly upon that 

employed in the past to establish the existing 10 CFR 50.61 embrittlement limits. The previous 

approach included unquantified conservatisms in many aspects of the analysis, and 

uncertainties were treated implicitly by incorporating them into the models. 

This report is one of a series of 21 reports that provide the technical basis that the staff will 

consider in a potential revision of 10 CFR 50.61. The risk from PTS was determined from the 

integrated results of the Fifth Version of the Reactor Excursion Leak Analysis Program 

(RELAP5) thermal-hydraulic analyses, fracture mechanics analyses, and probabilistic risk 

assessment. This report documents the sensitivity studies performed on the probabilistic 

fracture mechanics (PFM) model used in the calculations performed to estimate PTS risk to (1) 

provide confidence in the robustness of the PFM model, and (2) to provide confidence that the 

PTS risk results for three specific plants (see NUREG-1806) can be used to develop a 

screening limit applicable to PWRs in general. 

 

_________________________ 

 Brian W. Sheron, Director 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

v
vi
CONTENTS 

Abstract.........................................................................................................................................iii

Foreword....................................................................................................................................... v

Contents.......................................................................................................................................vii

Figures......................................................................................................................................... ix

Tables ........................................................................................................................................... x

Executive Summary ..................................................................................................................... xi

1 . Introduction ..........................................................................................................................1-1

1.1 Description of Pressurized Thermal Shock .....................................................................1-1

1.2 PTS Limits on the Licensable Life of a Commercial Pressurized-Water Reactor ...........1-1

1.3 Technical Factors Suggesting Conservatism of the Current Rule...................................1-3

1.4 PTS Reevaluation Project ...............................................................................................1-3

1.4.1 Restrictions on Model............................................................................................1-3

1.4.2 Overall Structure of Model ....................................................................................1-4

1.4.3 Uncertainty Treatment...........................................................................................1-8

1.4.4 Project Documentation..........................................................................................1-8

2 . Objective, Scope, and Structure of This Report...................................................................2-1

3 . Process for Identifying Sensitivity Studies to Assess the Robustness of the PFM 

Model ....................................................................................................................................3-1

3.1 Ideas Underlying the Process .........................................................................................3-1

3.2 Process for Sensitivity Study Identification......................................................................3-3

4 . Definition of Sensitivity Studies Performed to Assess the Robustness of the PFM 

Model ....................................................................................................................................4-1

4.1 Flaw Model......................................................................................................................4-1

4.2 Crack Initiation Model......................................................................................................4-6

4.2.1 Applied Driving Force to Fracture .........................................................................4-6

4.2.2 Resistance to Crack Initiation................................................................................4-9

4.3 Through-Wall Cracking Model.......................................................................................4-12

4.3.1 Fracture Driving Force Model for Through-Wall Cracking...................................4-13

4.3.2 Fracture Resistance Model for Through-Wall Cracking ......................................4-13

4.4 Summary of Planned Sensitivity Studies.......................................................................4-17

4.5 Sensitivity Study Results...............................................................................................4-22

4.5.1 Residual Stresses ...............................................................................................4-22

4.5.2 Embrittlement Shift Model ...................................................................................4-22

4.5.3 Chemical Composition Resampling for Welds ....................................................4-23

4.5.4 Upper-Shelf Toughness Model ...........................................................................4-23

5 . Sensitivity Studies Performed to Provide Confidence in the Applicability of TWCF 

Results to PWRS in General.................................................................................................5-1

5.1 Simulating Increased Levels of Embrittlement ................................................................5-1

5.2 Applicability to Forged Vessels .......................................................................................5-2

5.2.1 Embedded Forging Flaw Sensitivity Study............................................................5-3

5.2.2 Subclad Crack Sensitivity Study ...........................................................................5-3

vii
5.3 Effect of RPV Wall Thickness on TWCF .........................................................................5-4

6 . Summary and Recommendations........................................................................................6-1

7 . References...........................................................................................................................7-1

Appendix A: Flaw Distribution Correspondence ....................................................................... A-1

Appendix B: Flaw Distributions for Forgings ............................................................................. B-1

viii
FIGURES 

Figure ES-1 Structure of reports documenting the PTS reevaluation effort................................ xi

Figure ES-2 Schematic showing how a probabilistic estimate of through-wall cracking 

frequency (TWCF) is combined with a TWCF acceptance criterion to arrive at a 

proposed revision to the PTS screening limit................................................................. xiv

Figure 1-1 Proximity of currently operating PWRs to the 10 CFR 50.61 screening limit for 

PTS ................................................................................................................................1-2

Figure 1-2 High-level schematic showing how a probabilistic estimate of through-wall 

cracking frequency (TWCF) is combined with a TWCF acceptance criterion to 

arrive at a proposed revision to the PTS screening limit................................................1-4

Figure 1-3 The three plants analyzed in detail in the PTS reevaluation effort ..........................1-6

Figure 1-4 Structure of reports documenting the PTS reevaluation effort ................................1-9

Figure 2-1 Correlation of through-wall cracking frequencies with reference temperature 

metrics for the three study plants (°R = °F + 459.69) reported in NUREG-1806 [20] ....2-2

Figure 3-1 Schematic illustration of overall model used in the PTS reevaluation project .........3-2

Figure 3-2 Illustration of potential outcomes of sensitivity studies ............................................3-4

Figure 4-1 Classification of the submodels and parameter inputs used in the PTS 

reevaluation project according to Table 3-1 criteria .......................................................4-2

Figure 4-2 Flaw dimension and position descriptors adopted in FAVOR..................................4-4

Figure 4-3 Distribution through-wall position of cracks that initiate...........................................4-5

Figure 4-4 Flaw depths that contribute to crack initiation probability in Beaver Valley 

Unit 1 when subjected to medium- and large-diameter pipe break transients at two 

different embrittlement levels .........................................................................................4-5

Figure 4-5 Flaw depths that contribute to crack initiation probability in Beaver Valley 

Unit 1 when subjected to medium stuck-open valve transients at two different 

embrittlement levels .......................................................................................................4-6

Figure 4-6 Schematic illustration of the crack initiation model used in the PTS 

reevaluation project........................................................................................................4-7

Figure 4-7 Through-thickness weld residual stress profile assumed by FAVOR......................4-8

Figure 4-8 Schematic illustration of the model of the applied driving force to fracture used 

in the PTS reevaluation project ......................................................................................4-9

Figure 4-9 Schematic illustration of the model of the crack initiation toughness used in the 

PTS reevaluation project..............................................................................................4-10

Figure 4-10 Model of through-wall cracking adopted by FAVOR............................................4-14

Figure 4-11 Crack driving force model for through-wall cracking............................................4-14

Figure 4-12 Fracture resistance model for through-wall cracking...........................................4-15

Figure 4-13 Identification of transients (shaded boxes) used for Palisades and Beaver 

Valley sensitivity studies ..............................................................................................4-21

Figure 5-1 Effect of different methods to artificially increase embrittlement on the 

predicted TWCF values..................................................................................................5-2

Figure 5-2 Effect of vessel wall thickness on the variation of applied-KI vs. time for a 16-

in. diameter hot-leg break in Beaver Valley. The flaw has the following 

dimensions: L=0.35 in., 2a=0.50 in, 2c=1.5 in................................................................5-5

Figure 5-3 Distribution of RPV wall thicknesses for PWRs currently in service [31].................5-6

Figure 5-4 Effect of vessel wall thickness on the TWCF of various transients in Beaver 

Valley (all analyses at 60 EFPYs)..................................................................................5-6

ix
TABLES 

Table 3-1 Model and Parameter Classification Scheme...........................................................3-3

Table 4-1 Summary of Sources of Experimental Data Sources for the Flaw Distribution.........4-1

Table 4-2 Plant and Embrittlement Conditions Used in Sensitivity Studies ............................4-18

Table 4-3 Transients Used in Sensitivity Studies for Palisades..............................................4-18

Table 4-4 Transients Used in Sensitivity Studies for Beaver Valley Unit 1.............................4-20

Table 4-5 Results of Residual Stress Sensitivity Study ..........................................................4-22

Table 4-6 Results of Embrittlement Shift Model Sensitivity Study ..........................................4-23

Table 4-7 Results of Chemistry Resampling Sensitivity Study ...............................................4-23

Table 4-8 Results of Upper-Shelf Toughness Model Sensitivity Study...................................4-24

Table 5-1 Results of Forging Flaw Sensitivity Study.................................................................5-4

Table 5-2 Results of Subclad Crack Sensitivity Study ..............................................................5-4

x
EXECUTIVE SUMMARY 

This report is one of a series of reports that summarize the results of a 5-year project conducted 

by the U.S. Nuclear Regulatory Commission’s (NRC) Office of Nuclear Regulatory Research. 

The aim of this study was to develop a technical basis to support a revision to the pressurized 

thermal shock (PTS) rule found at Title 10, Section 50.61, of the Code of Federal Regulations 

[1] and the associated PTS screening criteria in a manner consistent with current NRC 

guidelines on risk-informed regulation. Figure ES-1, which highlights this report, also shows all 

of the reports that document this project. 

This executive summary begins with a description of PTS, how it might occur, and what the 

potential consequences are for the vessel. A summary of the current regulatory approach to 

PTS follows, which leads directly to a discussion of the motivations for undertaking this project, 

and concludes with a description of how the project was conducted. This introductory material 

provides a context for the information presented in this report concerning the sensitivity studies 

the NRC performed on the probabilistic fracture mechanics (PFM) model. 

Summary Report – NUREG-1806

• Procedures, Uncertainty, & Experimental 

Validation: EricksonKirk, M.T., et al., 

“Probabilistic Fracture Mechanics: 

Models, Parameters, and Uncertainty 

Treatment Used in FAVOR Version 04.1,”

NUREG-1807.

• FAVOR

• Theory Manual: Williams, P.T., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

Theory and Implementation of 

Algorithms, Methods, and 

Correlations,” NUREG/CR-6854.

• User’s Manual: Dickson, T.L., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

User’s Guide,” NUREG/CR-6855.

• V&V Report: Malik, S.N.M., “FAVOR 

Code Versions 2.4 and 3.1 

Verification and Validation Summary 

Report,” NUREG-1795. 

• Flaw Distribution: Simonen, F.A., et al., 

“A Generalized Procedure for Generating 

Flaw-Related Inputs for the FAVOR 

Code,” NUREG/CR-6817, Rev. 1.

• Baseline: Dickson, T.L. and Yin, S., 

“Electronic Archival of the Results of 

Pressurized Thermal Shock Analyses for 

Beaver Valley, Oconee, and Palisades 

Reactor Pressure Vessels Generated with 

the 04.1 version of FAVOR,”

ORNL/NRC/LTR-04/18.

• Sensitivity Studies: EricksonKirk, M.T., 

et al., “Sensitivity Studies of the 

Probabilistic Fracture Mechanics Model 

Used in FAVOR,” NUREG-1808. 

• TH Model: Bessette, D., “Thermal 

Hydraulic Analysis of Pressurized 

Thermal Shock,” NUREG/1809.

• RELAP Procedures & Experimental 

Validation: Fletcher, C.D., et al., 

“RELAP5/MOD3.2.2 Gamma Assessment 

for Pressurized Thermal Shock 

Applications,” NUREG/CR-6857.

• Experimental Benchmarks: Reyes, J.N., 

et. al., Final Report for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6856.

• Experimental Benchmarks: Reyes, J.N., 

Scaling Analysis for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6731

• Uncertainty: Chang, Y.H., et all., 

“Thermal Hydraulic Uncertainty Analysis 

in Pressurized Thermal Shock Risk 

Assessment,” University of Maryland.

• Baseline: Arcieri, W.C., “RELAP5 

Thermal Hydraulic Analysis to Support 

PTS Evaluations for the Oconee-1, 

Beaver Valley-1, and Palisades Nuclear 

Power Plants,” NUREG/CR-6858.

• Sensitivity Studies: Arcieri, W.C., et al., 

“RELAP5/MOD3.2.2Gamma Results for 

Palisades 1D Downcomer Sensitivity 

Study”

• Consistency Check: Junge, M., “PTS 

Consistency Effort”

• Procedures & Uncertainty: Whitehead, D.W. 

and Kolaczkowski, A.M., “PRA Procedures 

and Uncertainty for PTS Analysis,”

NUREG/CR-6859.

• Uncertainty Analysis Methodology: Siu, N., 

“Uncertainty Analysis and Pressurized 

Thermal Shock, An Opinion,” USNRC, 1999.

• Beaver: Whitehead, D.W., et al., “Beaver 

Valley PTS PRA”

• Oconee: Kolaczkowski, A.M., et al., “Oconee 

PTS PRA”

• Palisades: Whitehead, D.W., et al., 

“Palisades PTS PRA”

• External Events: Kolaczkowski, A.M., et al., 

“Estimate of External Events Contribution 

to Pressurized Thermal Shock Risk”

• Generalization: Whitehead, D.W., et al., 

“Generalization of Plant-Specific PTS Risk 

Results to Additional Plants”

Results Models, Validation, & Procedures

PFM TH PRA

This Report

Figure ES-1 Structure of reports documenting the PTS reevaluation effort

Description of PTS

One potentially significant challenge to the structural integrity of the reactor pressure vessel 

(RPV) in a pressurized-water reactor (PWR) is posed by a PTS event in which rapid cooling of 

the downcomer occurs, possibly followed by repressurization. A number of abnormal events 

xi
and postulated accidents have the potential to thermally shock the vessel (either with or without 

significant internal pressure); some of these include a pipe break in the primary pressure circuit, 

a stuck-open valve in the primary pressure circuit, and the break of the main steamline. During 

these events, the water level drops as a result of the contraction produced by rapid 

depressurization. In events involving a break in the primary pressure circuit, an additional drop 

in the water level occurs because of leakage from the break. Automatic systems and operators 

must provide makeup water in the primary system to prevent overheating of the fuel in the core. 

The makeup water is much colder than that held in the primary system. 

The temperature drop produced by rapid depressurization, coupled with the near-ambient 

temperature of the makeup water, produces significant thermal stresses in the thick-section 

steel wall of the RPV. For embrittled RPVs, these stresses could be high enough to initiate a 

running crack which could propagate all the way through the vessel wall. Through-wall cracking 

of the RPV could precipitate core damage or, in rare cases, a large early release of radioactive 

material to the environment. 

Current PTS Regulations

As required by 10 CFR 50.61, licensees must monitor the embrittlement of their RPVs using a 

surveillance program qualified in accordance with Appendix H to 10 CFR Part 50. Licensees 

use the results of surveillance, together with the formulae and tables in 10 CFR 50.61, to 

estimate the fracture toughness transition temperature (RTNDT) of the steels in the vessel’s 

beltline, as well as how these transition temperatures increase as a result of irradiation damage 

throughout the operational life of the vessel. For licensing purposes, 10 CFR 50.61 provides 

instructions on how to use these estimates of the effect of irradiation damage on RTNDT to 

determine the value of RTNDT that will occur at the end of license (EOL), a value called RTPTS. 

Title 10, Section 50.61, of the Code of Federal Regulations also provides “screening limits,” or 

maximum values of RTNDT, permitted during the operating life of the plant of +270 F (for axial 

welds, plates, and forgings) and +300 F (for circumferential welds). These screening limits 

correspond to a limit of 5x10-6 events/year on the yearly probability of developing a through-wall 

crack [32] Should RTPTS exceed these screening limits, 10 CFR 50.61 requires that the licensee 

either take actions to keep this value below the screening limit (i.e., by implementing 

“reasonably practicable” flux reductions to reduce the embrittlement rate or by de-embrittling the 

vessel by annealing [33]) or perform plant-specific analysis to demonstrate that operating the 

plant beyond the 10 CFR 50.61 screening limit does not pose an undue risk to the public [32]. 

While no currently operating PWR has an RTPTS value that exceeds the 10 CFR 50.61 

screening limit before EOL, several plants are close to the limit (3 are within 2 °F, while 10 are 

within 20 °F). Those plants that are close to the limit are likely to exceed it during the 20-year 

license renewal period that many operators currently seek. Moreover, some plants maintain 

their RTPTS values below the 10 CFR 50.61 screening limits by implementing flux reduction (i.e., 

low-leakage cores, ultra-low leakage cores) and other fuel management strategies that can be 

economically deleterious in a deregulated marketplace. Thus, the 10 CFR 50.61 screening 

limits can restrict the licensable and the economic lifetime of PWRs. 

Motivation for This Project

It is now widely recognized that the state of knowledge and data limitations in the early 1980s 

necessitated a conservative treatment of several key parameters and models used in the 

xii
probabilistic calculations that provided the technical basis of the current PTS rule. The most 

prominent of these conservatisms include the following: 

 the highly simplified treatment of plant transients (i.e., the very coarse grouping of many 

operational sequences (order of 105

) into very few groups (approximately 10)) 

necessitated by limitations in the computational resources needed to perform multiple 

thermal hydraulic (TH) calculations 

 the lack of any significant credit for operator action 

 characterization of fracture toughness using RTNDT, which has an intentional 

conservative bias 

 the use of a flaw distribution that placed all of the flaws on the interior surface of the 

RPV, and, in general, contains larger flaws than those usually detected in service 

 the modeling approach that treated the RPV as if it were made entirely from the most 

brittle of its constituent materials (welds, plates, or forgings) 

 the modeling approach that estimated RPV embrittlement based only on the peak 

fluence occurring anywhere on the entire interior surface of the RPV 

These factors indicate the high likelihood that the current 10 CFR 50.61 PTS screening limits 

are unnecessarily conservative. Consequently, the NRC believes that a reexamination of the 

technical basis for these screening limits, based on a modern understanding of all the factors 

that influence PTS, would most likely provide strong justification for substantial relaxation of 

these limits. For these reasons, the NRC Office of Nuclear Regulatory Research undertook this 

project with the objective of developing the technical basis to support a risk-informed revision of 

the PTS rule and the associated PTS screening limit. 

Approach

As illustrated in Figure ES-2, there are three main models (shown as solid blue squares) that, 

together, permit estimation of the yearly frequency of through-wall cracking in an RPV: 

(1) a probabilistic risk assessment (PRA) event sequence analysis 

(2) a TH analysis 

(3) a PFM analysis 

xiii
PRA Event

Sequence

Analysis

(SAPPHIRE)

Thermal

Hydraulic

Analysis

(RELAP)

Probabilistic

Fracture

Analysis

(FAVOR)

Sequence

Definitions

Sequence

Frequencies

freq

Conditional

Probability of

Thru-Wall

Cracking, CPTWC

P(t), T(t), &

HTC(t)

Yearly

Frequency of

Thru-Wall

Cracking

[CPTWC]

x

[freq]

Probabilistic Estimation of Through-Wall Cracking Frequency

Vessel damage, age, 

or operational metric

Yearly Frequency of

Thru-Wall Cracking

Screening 

Limit

Acceptance Criterion 

for TWC Frequency

Established consistent with

• 1986 Commission safety goal 

policy statement

• June 1990 SRM

• RG1.174

Screening Limit 

Development

Figure ES-2 Schematic showing how a probabilistic estimate of through-wall cracking 

frequency (TWCF) is combined with a TWCF acceptance criterion to arrive at a proposed 

revision to the PTS screening limit

A PRA event sequence analysis is first performed to define the sequences of events that are 

likely to produce a PTS challenge to the RPV integrity, as well as to estimate the frequency with 

which such sequences can be expected to occur. The event sequence definitions are then 

passed to a TH model that estimates the temporal variation of temperature, pressure, and heat 

transfer coefficient in the RPV downcomer characteristic of each of the sequence definitions. 

These pressure, temperature, and heat transfer coefficient histories are passed to a PFM 

model. The PFM model uses the TH output, along with other information concerning plant 

design and materials of construction, to estimate the time-dependent driving force to fracture 

produced by a particular event sequence. The PFM model compares this estimate of fracture 

driving force to the fracture toughness, or fracture resistance, of the RPV steel. This 

comparison allows an estimation of the probability that a particular sequence of events will 

produce a crack all the way through the RPV wall if that sequence of events were actually to 

occur. The final step in the analysis involves a simple matrix multiplication of the probability of 

through-wall cracking (from the PFM analysis) with the frequency at which a particular event 

sequence is expected to occur (as defined by the event-tree analysis). This product establishes 

an estimate of the yearly frequency of through-wall cracking that can be expected for a 

particular plant after a particular period of operation when subjected to a particular sequence of 

events. The yearly frequency of through-wall cracking is then summed for all event sequences 

to estimate the total yearly frequency of through-wall cracking for the vessel due to PTS. 

Performance of such analyses for various operating lifetimes provides an estimate of how the 

yearly through-wall cracking frequency can be expected to vary over the lifetime of the plant. 

The probabilistic calculations just described are performed to establish the technical basis for a 

revised PTS rule within an integrated systems analysis framework. The NRC approach 

considers a broad range of factors that influence the likelihood of vessel failure during a PTS 

event, while accounting for uncertainties in these factors across a breadth of technical 

disciplines. Two central features of this approach are (1) a focus on the use of realistic input 

values and models (whenever possible), and (2) an explicit treatment of uncertainties (using 

currently available uncertainty analysis tools and techniques). Thus, the current approach 

improves upon that used in the development of SECY-82-465 which included, in the many 

xiv
aspects of the analysis, intentional and unquantified conservatisms and which treated 

uncertainties implicitly by incorporating them into the models. 

Key Findings

This report documents sensitivity studies the NRC performed on the FAVOR PFM model (and 

on PFM-related variables) with two goals in mind: 

(1) To provide confidence in the robustness of the PFM model, the NRC assessed the 

effect of the following credible model and input perturbations on TWCF estimates. 

 

— residual stresses assumed to exist in the RPV wall 

— embrittlement shift model 

— resampling of chemical composition variables at the 1/4 T, 1/2 T, and 3/4 T 

 locations for welds 

— upper-shelf toughness model 

(2) To provide confidence that the results of the calculations for three specific plants can be 

 generalized to apply to all PWRs, the NRC performed the following sensitivity studies to 

 assess the influence of factors not fully considered in the baseline TWCF estimates: 

— method for simulating increased levels of embrittlement 

— assessment of the applicability of these results to forged vessels 

— effect of vessel thickness 

In the former category all effects were negligible or small. The small effects included the 

adoption of an embrittlement shift model which differs from that in American Society for Testing 

and Materials (ASTM) Standard E900-02 (which increases TWCF by approximately a factor of 

3). The model also accounts for distinctly different copper contents in different weld layers 

(which reduces TWCF by approximately a factor of 2.5 relative to the assumption that the mean 

value of copper does not vary through the vessel thickness). Neither of these effects is 

significant enough to warrant a change to the baseline model or to recommend a caution 

regarding its robustness. 

Sensitivity studies in the latter category suggest the following minor cautions regarding the 

general applicability of the baseline results for the three study plants reported in NUREG-1806 

to all PWRs: 

 In general, the TWCF of forged PWRs can be assessed using the formulae presented in 

Chapter 11 of NUREG-1806 [20] by ignoring the TWCF contribution of axial welds. 

However, should changes in future operating conditions result in a forged vessel being 

subjected to very high levels of embrittlement, a plant-specific analysis to assess the 

effect of subclad flaws on TWCF would be warranted. 

 For PWRs with a vessel thickness ranging from 7.5 in. to 9.5 in., the TWCF values 

reported in NUREG-1806 [20] are realistic. These results overestimate the TWCF of the 

seven thinner vessels (wall thicknesses below 7 in.) and underestimate the TWCF of 

Palo Verde Units 1, 2, and 3, all of which have wall thicknesses above 11 in. However, 

these thicker vessels have very low embrittlement projected at either EOL or end of 

license extension, suggesting little practical effect of this underestimation. 

xv
xvi
1. INTRODUCTION 

1.1 Description of Pressurized Thermal Shock

One potentially significant challenge to the structural integrity of the reactor pressure vessel 

(RPV) in a pressurized-water reactor (PWR) is posed by a pressurized thermal shock (PTS) 

event in which rapid cooling of the downcomer occurs, possibly followed by repressurization. A 

number of abnormal events and postulated accidents have the potential to thermally shock the 

vessel (either with or without significant internal pressure), including a pipe break in the primary 

pressure circuit, a stuck-open valve in the primary pressure circuit, and the break of the main 

steamline. During these events, the water level drops as a result of the contraction produced by 

rapid depressurization. In events involving a break in the primary pressure circuit system, an 

additional drop in the water level occurs because of leakage from the break. Automatic systems 

and operators must provide makeup water in the primary system to prevent overheating of the 

fuel in the core. The makeup water is much colder than that held in the primary system. 

The temperature drop produced by rapid depressurization, coupled with the near-ambient 

temperature of the makeup water, produces significant thermal stresses in the thick-section 

steel wall of the RPV. For embrittled RPVs, these stresses could be high enough to initiate a 

running crack that could propagate all the way through the vessel wall. Through-wall cracking 

of the RPV could precipitate core damage or, in rare cases, a large early release of radioactive 

material to the environment. 

1.2 PTS Limits on the Licensable Life of a Commercial Pressurized-Water 

Reactor

In the early 1980s, attention focused on the possibility that PTS events could challenge the 

integrity of the RPV wall for two reasons: 

(1) Operational experience suggested that overcooling events, while not common, did 

occur. 

(2) The results of in-reactor materials surveillance programs suggested that the steels used 

in RPV construction were prone to loss of toughness over time as the result of neutron 

irradiation-induced embrittlement. 

The possibility of accident loading, combined with degraded material conditions, motivated 

investigations aimed at assessing the risk of vessel failure posed by PTS for the purpose of 

establishing the operational limits needed to ensure that the likelihood of RPV failures caused 

by PTS transients is kept sufficiently low. These efforts led to the publication of a document [38] 

that provided the technical basis for subsequent development of the PTS rule, found at Title 10, 

Section 50.61, of the Code of Federal Regulations [1]. 

As required by 10 CFR 50.61, licensees must monitor the embrittlement of their RPVs using a 

surveillance program qualified in accordance with Appendix H to 10 CFR Part 50. Licensees 

use the results of surveillance, together with the formulae and tables in 10 CFR 50.61, to 

estimate the fracture toughness transition temperature (RTNDT

†

) of the steels in the vessel’s 

 

†

 The RTNDT index temperature was intended to correlate with the fracture toughness transition temperature of the 

material. Fracture toughness and how it is reduced by neutron irradiation embrittlement are key parameters 

1-1
beltline, as well as how these transition temperatures increase as a result of irradiation damage 

throughout the operational life of the vessel. For licensing purposes, 10 CFR 50.61 provides 

instructions on how to use these estimates of the effect of irradiation damage on RTNDT to 

determine the value of RTNDT that will occur at the end of license (EOL), a value called RTPTS. 

Title 10, Section 50.61, of the Code of Federal Regulations also provides “screening limits,” or 

maximum values of RTNDT, permitted during the operating life of the plant of +270 °F (for axial 

welds, plates, and forgings) and +300 °F (for circumferential welds). These screening limits 

correspond to a limit of 5x10-6 events/year on the yearly probability of developing a through-wall 

crack [32]. Should RTPTS exceed these screening limits, 10 CFR 50.61 requires that the 

licensee either take actions to keep this value below the screening limit (i.e., by implementing 

“reasonably practicable” flux reductions to reduce the embrittlement rate or by de-embrittling the 

vessel by annealing [33]) or perform a plant-specific analysis to demonstrate that operating the 

plant beyond the 10 CFR 50.61 screening limit does not pose an undue risk to the public [32]. 

While no currently operating PWR has an RTPTS value that exceeds the 10 CFR 50.61 

screening limit before EOL, several plants are close to the limit (3 are within 2 °F, while 10 are 

within 20 °F; see Figure 1-1). Those plants that are close to the limit are likely to exceed it 

during the 20-year license renewal period that many operators are currently seeking. Moreover, 

some plants maintain their RTPTS values below the 10 CFR 50.61 screening limits by 

implementing flux reduction (e.g., low-leakage cores, ultra-low leakage cores) and other fuel 

management strategies that can be economically deleterious in a deregulated marketplace. 

Thus, the 10 CFR 50.61 screening limits can restrict the licensable and the economic lifetime of 

PWRs. As detailed in the next section, considerable reason exists to believe that these 

restrictions are not necessary to ensure public safety and, in fact, place an unnecessary burden 

on licensees. 

0

20

40

60

80

0 50 100 150 200 250

o

F from Current 

10CFR50.61 PTS 

Screening Limit

Number of PWRs

Figure 1-1 Proximity of currently operating PWRs to the 10 CFR 50.61 screening limit for 

PTS 

 controlling the resistance of the RPV to any loading challenge. For a more detailed description of RTNDT (in 

specific) and fracture toughness (in general), see [19]. 

1-2
1.3 Technical Factors Suggesting Conservatism of the Current Rule

It is now widely recognized that state of knowledge and data limitations in the early 1980s 

necessitated a conservative treatment of several key parameters and models used in the 

probabilistic calculations that provide the technical basis [38] of the current PTS rule found at 10 

CFR 50.61. The most prominent of these conservatisms include the following: 

 the highly simplified treatment of plant transients (i.e., very coarse grouping of many 

operational sequences (order of 105

) into very few groups (approximately 10)) 

necessitated by limitations in the computational resources needed to perform multiple 

thermal hydraulic (TH) calculations 

 the lack of any significant credit for operator action 

 

 characterization of fracture toughness using RTNDT, which has an intentional 

conservative bias [2] 

 the use of a flaw distribution that placed all of the flaws on the interior surface of the 

RPV, and, in general, contains larger flaws than those usually detected in service 

 the modeling approach that treated the RPV as if it were made entirely from the most 

brittle of its constituent materials (welds, plates, or forgings) 

 the modeling approach that estimated RPV embrittlement based only on the peak 

fluence occurring anywhere on the entire interior surface of the RPV 

These factors indicate the high likelihood that the current 10 CFR 50.61 PTS screening limits 

are unnecessarily conservative. Consequently, the NRC believes that an examination of the 

technical basis for these screening limits, based on a modern understanding of all the factors 

that influence PTS, would most likely provide strong justification for substantial relaxation of 

these limits. For these reasons, the U.S. Nuclear Regulatory Commission’s (NRC) Office of 

Nuclear Regulatory Research undertook this project with the objective of developing the 

technical basis to support a risk-informed revision of the PTS rule and the associated PTS 

screening limit. 

1.4 PTS Reevaluation Project

This section describes the PTS Reevaluation Project, which the NRC Office of Nuclear 

Regulatory Research initiated in 1999. This section discusses restrictions placed on the model 

used to estimate PTS risk, the overall structure of the model, how uncertainties in the model are 

addressed, and how this and other reports document the results of the project. 

1.4.1 Restrictions on Model 

This research effort seeks to establish the technical basis for a new PTS screening limit. To 

enable all operators of commercial PWRs to assess the state of their RPV relative to such a 

new criterion, without making new material property measurements, the fracture toughness 

properties of the RPV steels need to be estimated using only information that is currently 

available (i.e., RTNDT values, upper-shelf energy values, and the chemical composition of the 

1-3
1-4

beltline materials). The NRC Reactor Vessel Integrity Database [31] summarizes all of this 

information. 

1.4.2 Overall Structure of Model 

The overall model involves the following three major components, which are illustrated (along 

with their interactions) in Figure 1-2: 

Component 1—Probabilistic Evaluation of Through-Wall Cracking Frequency. Estimate 

frequency of through-wall cracking as a result of a PTS event given the operating, design, and 

material conditions in a particular plant.

Component 2—Acceptance Criterion for Through-Wall Cracking Frequency. Establish a value 

of reactor vessel failure frequency (RVFF) consistent with current guidance on risk-informed 

decisionmaking. 

Component 3—Screening Limit Development. Compare the results of the two preceding steps 

to determine if some simple, materials-based screening limit for PTS can be established. 

Conceptually, plants falling below the screening limit would be deemed adequately resistant to a 

PTS challenge and would not require further analysis. Conversely, more detailed, plant-specific 

analysis would be needed to demonstrate the safety of plant operation at embrittlement levels 

beyond the screening limit. 

Each of these components is described in the following subsections. 

PRA Event

Sequence

Analysis

(SAPPHIRE)

Thermal

Hydraulic

Analysis

(RELAP)

Probabilistic

Fracture

Analysis

(FAVOR)

Sequence

Definitions

Sequence

Frequencies

freq

Conditional

Probability of

Thru-Wall

Cracking, CPTWC

P(t), T(t), &

HTC(t)

Yearly

Frequency of

Thru-Wall

Cracking

[CPTWC]

x

[freq]

Probabilistic Estimation of Through-Wall Cracking Frequency

Vessel damage, age, 

or operational metric

Yearly Frequency of

Thru-Wall Cracking

Screening 

Limit

Acceptance Criterion 

for TWC Frequency

Established consistent with

• 1986 Commission safety goal 

policy statement

• June 1990 SRM

• RG1.174

Screening Limit 

Development

Figure 1-2 High-level schematic showing how a probabilistic estimate of through-wall 

cracking frequency (TWCF) is combined with a TWCF acceptance criterion to arrive at a 

proposed revision to the PTS screening limit 
1.4.2.1 Component 1—Probabilistic Estimation of Through-Wall Cracking Frequency 

As illustrated in Figure 1-2, there are three main models (shown as solid blue squares) that, 

together, permit estimation of the yearly frequency of through-wall cracking in an RPV: 

(1) a probabilistic risk assessment (PRA) event sequence analysis 

(2) a TH analysis 

(3) a PFM analysis 

The following subsections first describe these three models in general, and then describe their 

sequential execution to provide the reader with an appreciation for the interrelationships and 

interfaces between the different models (Section 1.4.2.1.1). Next, the subsections describe the 

iterative process the NRC undertook, which involved repeated execution of all three models in 

sequence, to arrive at final models for each plant (Section 1.4.2.1.2). Finally, the subsections 

discuss the three specific plants the NRC analyzed in detail (Section 1.4.2.1.3). This section 

concludes with a discussion of the steps taken to ensure that the conclusions based on these 

three analyses apply to domestic PWRs in general (Section 1.4.2.1.4). 

1.4.2.1.1 Sequential Description of How PRA, TH, and PFM Models Are Used to Estimate 

TWCF 

A PRA event sequence analysis is first performed to define the sequences of events that are 

likely to produce a PTS challenge to RPV integrity, as well as to estimate the frequency with 

which such sequences can be expected to occur. The event sequence definitions are then 

passed to a TH model that estimates the temporal variation of temperature, pressure, and heat 

transfer coefficient in the RPV downcomer characteristic of each of the sequence definitions. 

These pressure, temperature, and heat transfer coefficient histories are passed to a PFM 

model. The PFM model uses the TH output, along with other information concerning plant 

design and materials of construction, to estimate the time-dependent driving force to fracture 

produced by a particular event sequence. The PFM model compares this estimate of fracture 

driving force to the fracture toughness, or fracture resistance, of the RPV steel. This 

comparison allows an estimation of the probability that a particular sequence of events will 

produce a crack all the way through the RPV wall if that sequence of events were actually to 

occur. The final step in the analysis involves a simple matrix multiplication of the probability of 

through-wall cracking (from the PFM analysis) with the frequency at which a particular event 

sequence is expected to occur (as defined by the event-tree analysis). This product establishes 

an estimate of the yearly frequency of through-wall cracking that can be expected for a 

particular plant after a particular period of operation when subjected to a particular sequence of 

events. The yearly frequency of through-wall cracking is then summed for all event sequences 

to estimate the total yearly frequency of through-wall cracking for the vessel due to PTS. 

Performance of such analyses for various operating lifetimes provides an estimate of how the 

yearly through-wall cracking frequency can be expected to vary over the lifetime of the plant. 

1.4.2.1.2 Iterative Process Used to Establish Plant-Specific Models 

A PRA event-tree approach was used to identify the set of transients which represent a 

particular plant, wherein many thousands of different initiating event sequences are “binned” 

together into groups of transients believed to produce similar TH outcomes (i.e., similar 

variations of temperature, pressure, and heat transfer coefficient versus time in the 

downcomer). Characteristics, such as similarity of break size, similarity of operator action, etc., 

guide judgments regarding what transients to put into what bin, resulting in “bins” such as 

1-5
1-6

medium break primary system loss-of-coolant accidents (LOCAs), main steamline breaks, etc. 

From each of the tens or hundreds of individual event sequences in each bin, a single sequence 

was then selected and programmed into the TH code RELAP to define the variation of pressure, 

temperature, and heat transfer coefficient versus time. These TH transient definitions were then 

passed to the PFM code FAVOR, which estimated the conditional probability of through-wall 

cracking (CPTWC) for each transient. When multiplied by the initiating event frequency 

estimates from PRA, these CPTWC become through-wall cracking frequency (TWCF) values, 

which, when rank ordered, estimate the degree to which each bin contributes to the total TWCF 

of the vessel. At this stage many bins are found to contribute very little or nothing at all to the 

TWCF, and so receive little further scrutiny. However, some bins invariably dominate the TWCF 

estimate. These bins are then further subdivided by partitioning the initiating event frequency of 

the bin, and by selecting a TH transient to represent each part of the original bin. FAVOR then 

reanalyzes this refined model and the bins that provide significant contributions to TWCF are 

again examined. This process of bin partitioning and selection of a TH transient to represent 

each newly partitioned bin continues until such time as the total estimated TWCF for the plant 

no longer changes significantly. 

1.4.2.1.3 Plant-Specific Analyses Performed 

In this project, the NRC performed detailed calculations for three operating PWRs (Beaver 

Valley 1, Oconee 1, and Palisades; see Figure 1-3. Together, the three plants represent a wide 

range of design and construction methods, and they contain some of the most embrittled RPVs 

in the operating fleet. 

1.4.2.1.4 Generalization to All Domestic PWRs 

Because the objective of this project is to develop a revision to the PTS screening limit 

expressed in 10 CFR 50.61 that applies to PWRs in general, the extent to which these three 

plant-specific analyses adequately address (in either a representative or bounding sense) the 

range of conditions experienced by all domestic PWRs must be understood. To achieve this 

goal, the NRC has taken the following actions: 

Beaver Valley 1

Palisades

• High embrittlement plant

• Westinghouse design

• High embrittlement plant

• Combustion Engineering design

Oconee 1

• Plant used in 1980s PTS study

• Babcox & Wilcox design

Figure 1-3 The three plants analyzed in detail in the PTS reevaluation effort 
 The NRC performed sensitivity studies on both the TH and PFM models to address the 

effect of credible changes to the model and/or its input parameters. The results of these 

studies provide insights regarding how robust the conclusions based on three plants are 

when applied to the entire PWR population. 

 The NRC examined the plant design and operational characteristics of five additional 

plants. The aim of this analysis was to determine whether the design and operational 

features identified as being important in the three plant-specific analyses vary 

significantly enough in the general population to question the generality of the results. 

 In the three plant-specific analyses, the NRC assumed that the only possible causes of 

PTS events have origins that are internal to the plant. However, external events, such 

as fires, floods, earthquakes, can also be PTS precursors. The NRC therefore 

examined the potential for external initiating events to create significant additional risk 

relative to the internal initiating events which have already been modeled in detail. 

1.4.2.2 Component 2—Acceptance Criterion for Through-Wall Cracking Frequency 

Since the issuance of SECY-82-465 and the publication of the original PTS rule, the NRC has 

established a considerable amount of guidance on the use of risk metrics and risk information in 

regulation (e.g., the Safety Goal Policy Statement, the PRA Policy Statement, and RG 1.174). 

To ensure consistency of the PTS reevaluation project with this guidance, the staff identified 

and assessed options for a risk-informed criterion for the RVFF (currently specified in RG 1.154 

in terms of TWCF). 

As described in 39, the options developed involved qualitative concerns (e.g., the definition of 

RPV failure) and quantitative concerns (e.g., a numerical criterion for the RVFF). The options 

reflected uncertainties in the margin between PTS-induced RPV failure, core damage, and large 

early release. The options also incorporated input received from the Advisory Committee on 

Reactor Safeguards (ACRS) [27] regarding concerns about the potential for large-scale 

oxidation of reactor fuel in an air environment. 

The assessment of the options involved identification of technical issues unique to PTS accident 

scenario development, development of an accident progression event tree to structure 

consideration of the issues, performance of a scoping study of the issue of containment 

performance during PTS accidents, and review of the options in light of this information. The 

scoping study involved collection and evaluation of available information, performance of a few 

limited-scope TH and structural calculations, and a semi-quantitative analysis of the likelihood of 

various accident progression scenarios. 

1.4.2.3 Component 3— Screening Limit Development 

As illustrated schematically in Figure 1-2 (lower left corner), a screening limit for PTS can be 

established based on a simple comparison of estimates of the TWCF as a function of an 

appropriate measure of RPV embrittlement with the RVFF acceptance criterion (or RVFF*). 

Beyond the work needed to establish both the TWCF versus embrittlement curve and RVFF* 

values, it is also necessary to establish a suitable vessel damage metric that, ideally, allows 

different conditions in different materials at different plants to be normalized. From a practical 

standpoint, “suitable” implies that the metric needs to be based only on information regarding 

plant operation and materials that is readily available. 

1-7
1.4.3 Uncertainty Treatment 

At the outset of this project in 1999, the NRC staff reviewed the existing approach for PRA 

modeling, focusing on how uncertainties should be treated, how they were propagated through 

the PRA, TH, and PFM models, and how the approach compared with the NRC guidelines on 

work supporting risk-informed regulation [41]. This review established a general framework for 

model development and uncertainty treatment, which is summarized in the following 

paragraphs. 

This project included the performance of probabilistic calculations to establish the technical 

basis for a revised PTS rule within an integrated systems analysis framework [57]. The NRC 

approach considers a broad range of factors that influence the likelihood of vessel failure during 

a PTS event, while accounting for uncertainties in these factors across a breadth of technical 

disciplines [41]. Two central features of this approach are (1) a focus on the use of realistic 

input values and models (whenever possible), and (2) an explicit treatment of uncertainties 

(using currently available uncertainty analysis tools and techniques). Thus, the current 

approach improves upon that used in the development of SECY-82-465 which included, in the 

many aspects of the analysis, intentional and unquantified conservatisms and which treated 

uncertainties implicitly by incorporating them into the models (e.g., RTNDT). 

The probabilistic models distinguish between two types of uncertainties—aleatory and 

epistemic. Aleatory uncertainties arise from the randomness inherent to a physical or human 

process, whereas epistemic uncertainties are caused by a limitation in the current state of 

knowledge (or understanding) of that process. A practical way to distinguish between aleatory 

and epistemic uncertainties is that epistemic uncertainties can, in principle, be reduced by an 

increased state of knowledge. Conversely, because aleatory uncertainties arise from the 

randomness at a level below which a particular process is modeled, they are fundamentally 

irreducible. The distinction between aleatory and epistemic uncertainties is an important part of 

the PTS analysis because different mathematical and/or modeling procedures are used to 

represent these different uncertainty types. 

1.4.4 Project Documentation 

This report is one of a series of reports that summarize the results of a PTS reevaluation 

project. Figure 1-4 illustrates the overall structure of this documentation and highlights this 

report. 

1-8
Summary Report – NUREG-1806

• Procedures, Uncertainty, & Experimental 

Validation: EricksonKirk, M.T., et al., 

“Probabilistic Fracture Mechanics: 

Models, Parameters, and Uncertainty 

Treatment Used in FAVOR Version 04.1,”

NUREG-1807.

• FAVOR

• Theory Manual: Williams, P.T., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

Theory and Implementation of 

Algorithms, Methods, and 

Correlations,” NUREG/CR-6854.

• User’s Manual: Dickson, T.L., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

User’s Guide,” NUREG/CR-6855.

• V&V Report: Malik, S.N.M., “FAVOR 

Code Versions 2.4 and 3.1 

Verification and Validation Summary 

Report,” NUREG-1795. 

• Flaw Distribution: Simonen, F.A., et al., 

“A Generalized Procedure for Generating 

Flaw-Related Inputs for the FAVOR 

Code,” NUREG/CR-6817, Rev. 1.

• Baseline: Dickson, T.L. and Yin, S., 

“Electronic Archival of the Results of 

Pressurized Thermal Shock Analyses for 

Beaver Valley, Oconee, and Palisades 

Reactor Pressure Vessels Generated with 

the 04.1 version of FAVOR,”

ORNL/NRC/LTR-04/18.

• Sensitivity Studies: EricksonKirk, M.T., 

et al., “Sensitivity Studies of the 

Probabilistic Fracture Mechanics Model 

Used in FAVOR,” NUREG-1808. 

• TH Model: Bessette, D., “Thermal 

Hydraulic Analysis of Pressurized 

Thermal Shock,” NUREG/1809.

• RELAP Procedures & Experimental 

Validation: Fletcher, C.D., et al., 

“RELAP5/MOD3.2.2 Gamma Assessment 

for Pressurized Thermal Shock 

Applications,” NUREG/CR-6857.

• Experimental Benchmarks: Reyes, J.N., 

et. al., Final Report for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6856.

• Experimental Benchmarks: Reyes, J.N., 

Scaling Analysis for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6731

• Uncertainty: Chang, Y.H., et all., 

“Thermal Hydraulic Uncertainty Analysis 

in Pressurized Thermal Shock Risk 

Assessment,” University of Maryland.

• Baseline: Arcieri, W.C., “RELAP5 

Thermal Hydraulic Analysis to Support 

PTS Evaluations for the Oconee-1, 

Beaver Valley-1, and Palisades Nuclear 

Power Plants,” NUREG/CR-6858.

• Sensitivity Studies: Arcieri, W.C., et al., 

“RELAP5/MOD3.2.2Gamma Results for 

Palisades 1D Downcomer Sensitivity 

Study”

• Consistency Check: Junge, M., “PTS 

Consistency Effort”

• Procedures & Uncertainty: Whitehead, D.W. 

and Kolaczkowski, A.M., “PRA Procedures 

and Uncertainty for PTS Analysis,”

NUREG/CR-6859.

• Uncertainty Analysis Methodology: Siu, N., 

“Uncertainty Analysis and Pressurized 

Thermal Shock, An Opinion,” USNRC, 1999.

• Beaver: Whitehead, D.W., et al., “Beaver 

Valley PTS PRA”

• Oconee: Kolaczkowski, A.M., et al., “Oconee 

PTS PRA”

• Palisades: Whitehead, D.W., et al., 

“Palisades PTS PRA”

• External Events: Kolaczkowski, A.M., et al., 

“Estimate of External Events Contribution 

to Pressurized Thermal Shock Risk”

• Generalization: Whitehead, D.W., et al., 

“Generalization of Plant-Specific PTS Risk 

Results to Additional Plants”

Results Models, Validation, & Procedures

PFM TH PRA

This Report

Figure 1-4 Structure of reports documenting the PTS reevaluation effort 

1-9
1-10
2. OBJECTIVE, SCOPE, AND STRUCTURE OF THIS REPORT 

Other reports describe the details of the PFM model and its implementation into the FAVOR 

computer code [19, 56]. Additionally, the baseline TWCF results for three of the study plants 

(Oconee, Beaver Valley, and Palisades) have been reported (see Figure 2-1 and References 

20, 15). This report documents sensitivity studies performed on the FAVOR PFM model (and 

on PFM-related variables) with two goals in mind: 

(1) To provide confidence in the robustness of the PFM model, the NRC assessed the effect 

 of credible model and input perturbations on TWCF estimates. 

(2) To provide confidence that the results of the calculations for three specific plants can be 

 generalized to apply to all PWRs, the NRC performed sensitivity studies to assess the 

 influence of factors not fully considered in the baseline TWCF. 

The remainder of this document is structured as follows: 

 Chapter 3 describes a systematic process for identifying which parts of the PFM model 

should be subjected to a sensitivity study (and which parts should not) to provide 

confidence in the robustness of the PFM model. 

 Chapter 4 applies the process developed in Chapter 3 to define the sensitivity studies 

that will be performed. 

 Chapter 5 discusses the sensitivity studies needed to provide confidence that the results 

of the calculations for the three specific study plants apply in general to all PWRs. 

 Chapter 6 presents the study conclusions. 

2-1
y = 4E-26e0.0585x

R2 = 0.9655

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

RT AW [oR]

TWCF Due to Axial Weld flaws

OconeeBeaverPalisadesAllExpon. (All)

y = 9E-27e0.0543x

R2 = 0.9257

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

RTPL [oR]

TWCF Due to Plate Flaw

OconeeBeaverPalisadesAllExpon. (All)

y = 4E-29e0.0561

R2 = 0.7971

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 

R

TWCF Due to Circ Weld Flaw

Figure 2-1 Correlation of through-wall cracking frequencies with reference temperature 

metrics for the three study plants (°R = °F + 459.69) reported in NUREG-1806 [20] 

2-2
3. PROCESS FOR IDENTIFYING SENSITIVITY STUDIES TO ASSESS 

THE ROBUSTNESS OF THE PFM MODEL 

3.1 Ideas Underlying the Process

A detailed depiction (Figure 3-1) of the model used to generate predictions of through-wall 

cracking frequency (TWCF) for the three study plants reveals it to be a complex combination of 

a large number of submodels and parameter inputs. Figure 3-1 illustrates how these submodels 

(blue symbols) and parameter inputs (beige, round-corner rectangles) combine to produce 

intermediate calculated results that, upon passing through yet more submodels, eventually 

become an estimated distribution of TWCF. The existence of each submodel and parameter 

input in the PFM model, and their arrangement with respect to one another, represents a 

decision to structure the overall model in a particular way. Changing any one of these decisions 

can, in principle, change the output of the model (i.e., the distribution of TWCF values). 

Therefore, in this report the NRC investigates the degree to which the selection of credible 

alternative submodels may influence the TWCF estimates. Additionally, many of the input 

parameters to the PFM cannot be known precisely. Therefore, the NRC also investigates the 

degree to which credible variations in the input parameters change the TWCF estimates. 

This approach of basing sensitivity studies on credible alternative submodels and/or on credible 

variations of the input parameters follows directly from two principles of the overall approach to 

model building (see Section 1.4.3): 

 the use of realistic input values and submodels 

 an explicit treatment of uncertainties 

These principles have permitted calculation of TWCF estimates that are systematically biased 

neither high nor low (i.e., values that represent a “best estimate” to the greatest extent 

practicable). By basing sensitivity studies on credible alternative submodels and on credible 

variations of the input parameters, the NRC maintains these principles, thereby allowing the 

TWCF estimates to maintain their “best estimate” label. It can be noted that the model explicitly 

accounts for the sensitivity of the many input variables to credible variations of their values by 

sampling from probability distributions that have been established based on data [19, 56]. 

Finding credible alternative data upon which to justify a sensitivity study can be difficult in this 

situation. 

The focus on motivating sensitivity studies based only on credible perturbations to the baseline 

model deviates from that taken previously [38], wherein sensitivity studies were either focused 

on “important” parameters and submodels (i.e., those to which the TWCF was believed to be 

sensitive), or were performed seemingly without consideration of either the technical justification 

for the baseline submodel nor the credibility of the alternative submodel used to motivate the 

sensitivity study. In most cases, it is important to avoid such ad hoc justifications for performing 

sensitivity studies. Low sensitivity of the output TWCF to a change in a submodel or input 

having an inadequate technical justification does not provide a rational basis for accepting that 

submodel or input as part of the overall model. Similarly, high sensitivity of the output to a welljustified submodel or input provides neither a basis for condemning that submodel/input nor for 

adopting arbitrary margins in an effort to compensate for the high sensitivity. 

3-1
Applied

KI

Elastic Modulus

Vessel Diameter

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

ResistanceKIc

dKI/dt > 0

AND

A-KI > R-KIc

Initiation

Toughness

Transition

Curve

Pressure

vs. time in

Downcomer

CPI>0

Event

Tree

Analysis

(SAPPHIRE)

Simulator Info.

Plant Equipment

Plant Design

Operating

Procedures

Training

Sequence &

Cut Set

Definitions

(1E5)

Fine

Binning

Logic

(SAPPHIRE)

Fine 

Binned

Sequences

(300)

Selection

Criteria

Single

Sequence of

Events that 

Represent Bin

Expert

Judgments

Bin

FrequencyHistogram

Historical

Incidence

of Plant Upsets

Stress

Intensity

Factor

dKI Model /dt

RTNDT(u)Method

RTNDT(u)

(RVID)

YES

Generic?

YES

NO

(u) = 0

+ (u) = S()

Conversion

to Toughness

Transition

Temperature

Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

Physical PlantLayout “inside” the • SG steam outlet• SG feed line• ECCS input

Fluid Static

Equilibrium

Model

Fluid• Viscosity• Density• Enthalpy Sequence • Conductivity

Definition

TH

Nodalization

(1D Model)

Mathematical

Idealization

of Plant

+

CPI=0

NO

Temperature

vs. time in

Downcomer

Control SystemGeometric Loss

Coefficients

(e.g., for elbows)

Conditions ateach node_____• Pressure• Temperature• Fluid velocity• Gas velocity• Void fraction

Flow

Regime

Correlations

Heat

Transfer

Coefficients

Vapor• Viscosity• Density• Enthalpy• Conductivity

STOP

YES

NO

Is

TMIN < 400F 

AND

dT/dt > 100F/hr?

Is

TMIN < 400F 

AND

dT/dt > 100F/hr?

NUREG/CR-5750

Lookup

Tables

Increment

Time

t = t+t

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

time = 0

Initial

Condition

Guess

Equilibrium Conditions ateach node_____• Pressure• Temperature• Fluid velocity• Gas velocity• Void fraction

Plant State

at

t + t

Sequence

Complete?

YES

NO

Coarse

Binning

Logic

Coarse 

Binned

Sequences

(50 - 150)

Risk

Dominant PRA Sequences Judgments

OK?

TWCFSEQUENCE

>

1% TWCFTOTAL?

ANALYSIS

COMPLETE

Refine

PRA

P&T vs. t

T vs. t

to PFM

T vs. t

Metal• Thermal conductivity• Metal surface

roughness

• Metal area

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

Product

Form

Weld

% SMAW

Shoreham

Weld Flaw

Density

Model

Sh. & PVR

Flaw Size

Model

Sh. & PVR

Aspect

Ratio

Model

E.J.

Truncation

Model

(=2-in)

Weld Dir.

Orientation

Model

(Phys + Obs)

Distribution of Embedded

Weld Flaws x

Weld

Fusion

Area

Plate & 

Forging

Sh. Weld

Flaw Density

Model(/10 lg.,

/40 sm.)

(E.J.)

Sh. & PVR

Weld

Flaw Size

Model

Sh. & PVR

Weld

Aspect

Ratio Model

E.J.

Truncation

Model

(0.43-in.)

Coin Toss

Orient. 

Model

(Obser. & 

Phys.)

Distribution of Embedded

Plate Flaws x Plate Volume

Cladding

Obs. Buried

Clad Flaw

Density

in PVRUF/ 10

(E.J.)

E.J. Flaw

DepthModel

(a = tCLAD ALWAYS)

PVR & HC

Aspect

Ratio

Model

E.J.

Truncation

Model (tCLAD)

Circ. Orient.

Model

(Obs.)

Distribution of Surface Flaws

in Plates& Welds x Clad Area

Flaw Location

in Vessel Wall, x’

Flaw Depth, a

Flaw Aspect

Ratio, 2c/a

Flaw Density, 

STOP

NO

YES

Is

Location > 

3/8T from ID?

# of

Layers?

No

Surf.

Flaws

1

>1

Bead Size

Groove Design

Weld Length

Plate Area

Vessel Thickness

Vessel Inner Rad.

Vessel Length

Clad Bead Width

% SAW

Vessel Thickness

P&T vs. t

to PFM

NO YES

YES

Weld residual

CTE Mismatch

residual

CTEWELD

-

% Repair

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEXTEMPERATURE MODEL

FRACTURE DRIVINGFORCE MODEL

Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence

Uncertainty

Sampled

ID Fluence

Local

Fluence

Uncertainty

Fluence

At Flaw

Cu

Uncertainty

Sampled

Cu

Ni

Uncertainty

Sampled

Ni

P

Uncertainty

Sampled

P

MAT=Weld

&

a’ in Next 1⁄4 T

Matrix

Multiply

Yearly Vessel

Failure

Frequency

(TWCF)

Initiation-Arrest

Transition Curve

Separation

Model

RTARREST

Arrest

Toughness

Transition

Curve

NO

YES

Applied

KI

Stress

Intensity

Factor

Model

A-KI

>

R-KI

CPF=

CPI*FAIL/COUNT

YES

Fluence

at Flaw

Thru-Wall

Attenuation

Model

+

1

Irradiated

Toughness Shift

(RTTOUGH)

Irradiated

Arrest

Toughness

Index

Temperature

NO

Extend flaw to Infinite Length

Increment 

Flaw Depth

a’ = a + a

Re-Sample

Cu

Ni

P

Resistance

KIa*

T vs. t

Pf 1=

S{ RAND[0,1] }

MAT=Weld

&

a’ in Next 1⁄4 T

Resistance

KIa@T

No

Pf xT/4=

S{ RAND[0,1] }

Yes

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

a’>1⁄4T

?

YESNO

TUS

Model TUS

Upper Shelf

Toughness

Vs.

Temperature

Curve

T vs. t

Resistance

K{J-R}@T

Resistance

KIa* @T

MIN

Resistance

KI @T

Elastic Modulus

Vessel Diameter

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVINGFORCE MODEL DUCTILE TEARING MODEL

CRACK ARREST MODEL

PROPERTY

GRADIENT

MODEL

Initiation-Arrest

Interaction Model OFF

Unrestricted KIa(MAX)

Weld?

NO

YES

Resistance

KIa@T

A

FAIL = 0 

COUNT = 0

FAIL=FAIL+1

COUNT=COUNT+1

COUNT

=100?

A

NO

YES

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

Flaw Model

PRA

Model

TH

Model

Completion Check

CrackInitiationModel

Thru-WallCrackingModel

Irradiated Initiation

Toughness Index

Temperature

(RTTOUGH(I))

(from initiation model)

Figure 3-1 Schematic illustration of overall model used in the PTS reevaluation project 

3-2
Table 3-1 Model and Parameter Classification Scheme 

Color For Models For Parameters 

M1 A correct and credible representation of 

the underlying physical process 

The value (for deterministic parameters) 

or the mean and distribution (for 

stochastic parameters) accurately 

represent the parameter for the 

conditions of interest. 

M1

The applicability of this model in its 

application to all conditions of interest 

cannot be reliably assessed with the 

current state of knowledge. 

N/A 

M1

Alternatives to the model adopted exist. 

These alternatives have roughly equal 

justification to the model adopted. 

N/A 

M1

A model providing a conservative 

representation of the underlying 

physical process 

The value (for deterministic parameters) 

or the mean and distribution (for 

stochastic parameters) conservatively 

represent the parameter for the 

conditions of interest. 

M1

While it is believed that the model 

provides a correct and credible 

representation of the underlying 

physical process, when uncertainties 

arose in constructing the model 

conservative decisions were made. 

N/A 

3.2 Process for Sensitivity Study Identification 

Table 3-1 provides a set of classifications used to assess the correctness and physical 

credibility of the various submodels, and the accuracy of the various parameter inputs in the 

PFM model depicted in Figure 3-1. These classifications allow one to make systematic and 

consistent decisions in the selection of what sensitivity studies should be performed, as 

described below: 

M1 NO—There is little benefit in subjecting a correct submodel or an accurate parameter 

to a sensitivity study. Instead of performing a sensitivity study, documentation is provided 

describing why a sensitivity study is not warranted. 

M1 USUALLY—Because of limitations on available information, the correctness of these 

submodels is unknown. This state of knowledge limitation also restricts the ability to develop 

credible alternative models that could motivate a sensitivity study. Nevertheless, it may be 

important to conduct sensitivity studies on these submodels to ensure that the engineering 

decisions made in developing the submodel do not have unforeseen significant effects on the 

estimated TWCF values. 

3-3
3-4

M1

USUALLY—Because alternative submodels to that used in the overall model exist, 

and these alternatives models have roughly equal justification, these submodels are usually 

candidates for sensitivity study. 

M1

MAYBE—Conservative submodels and parameter inputs have been adopted as part 

of the overall model either because no more accurate information is available to support a 

better decision or because adopting a conservative submodel or parameter input somehow 

enhances the applicability of the results to all PWRs. In this situation, sensitivity studies are 

generally not useful, however, the merits of each case are discussed and documented 

individually. 

M1 MAYBE—If a quantifiable and credible basis can be developed to support a less 

conservative model, or if independent information becomes available suggesting an 

alternative model, then this information provides the basis of a sensitivity study. 

As suggested by these descriptions, an advanced state of knowledge may motivate very 

specific sensitivity studies to examine the effect of, for example, adopting a particular alternative 

model. In other situations in which the state of knowledge is not so advanced, specifically for 

YELLOW and RED models and parameters, more arbitrary sensitivity studies may be 

conducted simply to examine what effect the changing of an input value or model has on the 

estimated TWCF. 

The results of these sensitivity studies are described according to the terms illustrated in Figure 

3-2: 

 Mitigated—Output changes are smaller than input changes. 

 Proportional—Output changes are of the same order as input changes. 

 Magnified—Output changes are larger than input changes. 

The next chapter uses this classification scheme to identify what sensitivity studies will and will 

not be performed. 

Change of Input

Sub-Model or

Parameter

Resultant Change

In Output (YVFF)

Mitigated

Response

Magnified

Response

Magnified

Response

Mitigated

Response

Proportional

Response

Figure 3-2 Illustration of potential outcomes of sensitivity studies 
4. DEFINITION OF SENSITIVITY STUDIES PERFORMED TO ASSESS 

THE ROBUSTNESS OF THE PFM MODEL 

Figure 4-1 depicts the overall model the NRC used in the PTS reevaluation effort with 

submodels and parameters classified according to the criteria outlined in Table 3-1. While both 

the PRA model and the TH model appear in Figure 4-1, other reports in this series [55 and 6, 

respectively] detail the sensitivity studies performed on these models. This report addresses 

the sensitivity studies performed on the PFM portion of the model. These are discussed in the 

following sections, subdivided by the three major parts of the PFM model: 

 Section 4.1 describes the need for sensitivity studies on the flaw model. 

 Section 4.2 describes the need for sensitivity studies on the crack initiation model. 

 Section 4.3 describes the need for sensitivity studies on the through-wall cracking 

model. 

4.1 Flaw Model

The flaw model provides estimates of the density (flaws per unit area or volume), size, and 

location in the vessel wall of initial fabrication defects‡

. This flaw distribution, reported in detail 

by Simonen, represents a major improvement in realism relative to that adopted in previous 

studies of PTS risk [40]. Indeed, one of the major unknowns/uncertainties identified in the last 

comprehensive evaluation of PTS [38] was the distribution of flaws assumed to exist in the RPV 

wall. SECY-82-465 used flaw models based on the Marshall study, which included data from a 

limited population of nuclear vessels and from many non-nuclear vessels [25]. These flaw 

measurements were part of routine pre-service nondestructive examinations (NDE) performed 

25 or more years ago at vessel fabrication shops. Because of the limitations of the NDE 

technology available at the time, the Marshall flaw distribution only provides a reasonable 

representation for flaws having depth dimensions larger than approximately 1 in. Nevertheless, 

SECY-82-465 and the IPTS studies [28, 29, 30] applied the Marshall distribution by 

extrapolating fits to the data to the much smaller flaws of concern in PTS calculations (less than 

approximately 1/4 in.). Additionally, all flaws in the Marshall distribution were assumed to break 

the inner diameter surface of the RPV despite the fact that the observations rarely, if ever, 

revealed surface-breaking flaws in nuclear-grade construction. 

Table 4-1 Summary of Sources of Experimental Data Sources for the Flaw Distribution 

Vessel Weld Plate Clad 

PVRUF 9150 855 1650 

Shoreham 10375 975 -- 

Hope Creek 245 550 -- 

River Bend 2440 1465 -- 

Table entries represent volume of 

material examined in in3

. 

 

‡

 Growth of initial fabrication defects resulting from subcritical cracking mechanisms does not need to be 

considered; see Chapter 3 of Reference 19. 

4-1
4-2

Applied

KI

Elastic Modulus

Vessel Diameter

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

Resistance

KIc

dKI/dt > 0

AND

A-KI > R-KIc

Initiation

Toughness

Transition

Curve

Pressure

vs. time in

Downcomer

CPI>0

Event

Tree

Analysis

(SAPPHIRE)

Simulator Info.

Plant Equipment

Plant Design

Operating

Procedures

Training

Sequence &

Cut Set

Definitions

(1E5)

Fine

Binning

Logic

(SAPPHIRE)

Fine 

Binned

Sequences

(300)

Selection

Criteria

Single

Sequence of

Events that 

Represent Bin

Expert

Judgments

Bin

Frequency

Histogram

Historical

Incidence

of Plant Upsets

Stress

Intensity

Factor dKI Model /dt

RTNDT(u)

Method

RTNDT(u)

(RVID)

YES

Generic?

YES

NO (u) = 0

+ (u) = S()

Conversion

to Toughness

Transition

Temperature Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

Physical Plant

Layout “inside” the 

• SG steam outlet

• SG feed line

• ECCS input

Fluid Static

Equilibrium

Model

Fluid

• Viscosity

• Density

• Enthalpy

Sequence • Conductivity

Definition

TH

Nodalization

(1D Model)

Mathematical

Idealization

of Plant

+

CPI=0

NO

Temperature

vs. time in

Downcomer

Control System

Geometric Loss

Coefficients

(e.g., for elbows)

Conditions at

each node_____

• Pressure

• Temperature

• Fluid velocity

• Gas velocity

• Void fraction

Flow

Regime

Correlations

Heat

Transfer

Coefficients

Vapor

• Viscosity

• Density

• Enthalpy

• Conductivity

STOP

YES

NO

Is

TMIN < 400F 

AND

dT/dt > 100F/hr?

Is

TMIN < 400F 

AND

dT/dt > 100F/hr?

NUREG/CR-5750

Lookup

Tables

Increment

Time

t = t+t

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

time = 0

Initial

Condition

Guess

Equilibrium 

Conditions at

each node_____

• Pressure

• Temperature

• Fluid velocity

• Gas velocity

• Void fraction

Plant State

at

t + t

Sequence

Complete?

YES

NO

Coarse

Binning

Logic

Coarse 

Binned

Sequences

(50 - 150)

Risk

Dominant PRA Sequences

Judgments

OK?

TWCFSEQUENCE

>

1% TWCFTOTAL?

ANALYSIS

COMPLETE

Refine

PRA

P&T vs. t

T vs. t

to PFM

T vs. t

Metal

• Thermal conductivity

• Metal surface

roughness

• Metal area

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF

 RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

NO

P&T vs. t

to PFM

NO YES

YES

Weld residual

CTE Mismatch

residual

CTEWELD

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEX

TEMPERATURE MODEL

FRACTURE DRIVING

FORCE MODEL Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence

Uncertainty

Sampled

ID Fluence

Local

Fluence

Uncertainty

Fluence

At Flaw

Cu

Uncertainty

Sampled

Cu

Ni

Uncertainty

Sampled

Ni

P

Uncertainty

Sampled

P

MAT=Weld

& a’ in Next 1⁄4 T

Matrix

Multiply

Through Wall

Cracking

Frequency

(TWCF)

Initiation-Arrest

Transition Curve

Separation

Model

RTARREST

Arrest

Toughness

Transition

Curve

NO

YES

Applied

KI

Stress

Intensity

Factor

Model

A-KI

>

R-KI

CPF=

CPI*FAIL/COUNT

YES

Fluence

at Flaw

Thru-Wall

Attenuation

Model

+

1 Irradiated

Toughness Shift

(RTTOUGH)

Irradiated

Arrest

Toughness Index

Temperature

NO

Extend flaw to 

Infinite Length

Increment 

Flaw Depth

a’ = a + a Re-Sample

Cu

Ni

P

Resistance

KIa*

T vs. t

Pf 1= S{ RAND[0,1] }

MAT=Weld

&

a’ in Next 1⁄4 T

Resistance

KIa@T

No

Pf xT/4= S{ RAND[0,1] }

Yes

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

a’>1⁄4T ?

YES

NO

Resistance

K{J-R}@T

Resistance

KIa* @T

MIN

Resistance

KI @T

Elastic Modulus

Vessel Diameter

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVING

FORCE MODEL

CRACK ARREST MODEL

PROPERTY

GRADIENT

MODEL

Initiation-Arrest

Interaction Model OFF

Unrestricted KIa(MAX)

Weld?

NO

YES

Resistance

KIa@T

A

FAIL = 0 

COUNT = 0

FAIL=FAIL+1

COUNT=COUNT+1

COUNT

=100?

A

NO

YES

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

Flaw Model

PRA

Model

TH

Model

Completion Check

Crack

Initiation

Model

Thru-Wall

Cracking

Model

Accurate

Unknown

Other Models

Available

Conservative

Accurate, Conservative

Judgments when Unknown

TUS

Model TUS

Upper Shelf

Toughness

vs.

Temperature

Curve

T vs. t

DUCTILE TEARING MODEL

Irradiated Initiation

Toughness Index

Temperature

(RTTOUGH(I))

(from initiation model)

Product

Form

Weld

% SMAW

Shoreham

Weld Flaw

Density

Model

Sh. & PVR

Flaw Size

Model

Sh. & PVR

Aspect

Ratio

Model

E.J. Truncation

Model

(=2-in)

Weld Dir.

Orientation

Model

(Phys + Obs)

Distribution of Embedded Weld Flaws x Weld

Fusion

Area

Plate & 

Forging

Sh. Weld

Flaw Density

Model(/10 lg.,

/40 sm.)

(E.J.)

Sh. & PVR Weld

Flaw Size

Model

Sh. & PVR Weld

Aspect

Ratio Model

E.J. Truncation

Model

(0.43-in.)

Coin Toss

Orient. 

Model

(Obser. & 

Phys.)

Distribution of Embedded Plate Flaws x Plate

Volume

Cladding

Obs. Buried

Clad Flaw

Density

in PVRUF/ 10

(E.J.)

E.J. Flaw

Depth

Model

(a = tCLAD ALWAYS)

PVR & HC

Aspect

Ratio

Model

E.J.

Truncation

Model (tCLAD)

Circ. Orient.

Model

(Obs.)

Distribution of Surface Flaws in Plates& Welds x Clad

Area

Flaw Location

in Vessel Wall, x’

Flaw Depth, a

Flaw Aspect

Ratio, 2c/a

Flaw Density, 

STOP

NO

YES

Is Location > 

3/8T from ID?

# of

Layers?

No

Surf.

Flaws

1

>1

Bead Size

Groove Design

Weld Length

Plate Area

Vessel Thickness

Vessel Inner Rad.

Vessel Length

Clad Bead Width

% SAW

Vessel Thickness

- % Repair

Figure 4-1 Classification of the submodels and parameter inputs used in the PTS 

reevaluation project according to Table 3-1 criteria 

Table 4-1 summarizes the various sources of experimental data Simonen et al. used to develop 

the flaw distributions employed in FAVOR. While the volume of material represented in Table 

4-1 improves greatly on the Marshall flaw distributions [25], an inescapable conclusion is also 

that the quantity of available data is also quite small compared with the volume of RPV material 

in service. Consequently, it is not possible to ensure on an empirical basis alone that the flaw 

distributions developed based on these data apply to all PWRs in general. However, the flaw 

distributions proposed in Simonen rely on the experimental evidence gained from inspections of 

the materials summarized in Table 4-1 and do not rest solely on this empirical evidence [40]. 

Along with empirical data, Simonen et al. used both physical models and expert opinions when 

developing their recommended flaw distributions. Additionally, where detailed information was 

lacking, Simonen et al. made systematically conservative judgments including the following: 
 All NDE indications used in constructing the flaw models were treated as cracks and, 

 For the larger weld flaws that dominate the estimated failure probabilities, the density of 

other 

 FAVOR imposes truncation limits on the sizes of flaws in plates, and the flaws in welds 

e 

The only cladding flaws that contribute to the conditional probability of vessel failure must 

ic 

r 

laws 

therefore, potentially deleterious to RPV integrity. However, many of these indications 

were in fact volumetric, which lessens significantly the probability of brittle fracture 

initiation. 

flaws found in the Shoreham vessel was adopted because it exceeds the density 

observed in the Pressure Vessel Research Users Facility (PVRUF) weld, the only 

weld that was extensively characterized. 

exceed in size the largest flaw found in either PVRUF or Shoreham by a factor of 2. 

Further increase of these truncation limits has no effect on the calculated vessel failur

probabilities [14]. 

completely penetrate the clad layer (so that a crack tip resides in the potentially brittle ferrit

steel), but no such flaws have been observed. However, owing to the limited amount of 

destructive examination on which this observation was based, the density of full-clad laye

thickness flaws is modeled in FAVOR as 10 percent of the observed density of embedded f

in the clad layer. 

Additionally, the flaw model contains other features known to be accurate. 

 The destructive examinations performed on Shoreham and PVRUF revealed that the 

 fusion 

 The destructive examinations performed revealed that all cladding flaws are a lack of 

ntially in 

his combined use of empirical evidence, physical models, expert opinions, and conservative 

WRs 

overwhelming majority of weld flaws were lack of fusion defects and, so, occurred 

preferentially on the fusion line between the base metal and the weld metal. 

Consequently, in FAVOR, all weld flaws are modeled as occurring on the weld

line, which orients flaws in axial welds axially and flaws in circumferential welds 

circumferentially. 

inter-run fusion defects and, so, occur parallel to the welding direction only. 

Consequently, in FAVOR, all clad flaws are modeled as occurring circumfere

the vessel because the weld cladding was deposited circumferentially. 

T

judgments allowed Simonen et al. to propose flaw distributions for use in FAVOR that are 

believed to be appropriate/conservative representations of the flaw population existing in P

in general (see Appendix A and Reference 40 for details). The overall conservatism associated 

with the Flaw Model led to its classification as red. Consequently, the NRC did not conduct 

sensitivity studies on the details of the flaw model. Nevertheless, it is informative to understan

the characteristics of the flaws drawn from these distributions that contribute most significantly 

to the values of frequency of crack initiation (FCI) and TWCF estimated by FAVOR. Two 

general statements can be made regarding the flaws that contribute most significantly to th

estimated TWCF values: 

d 

e 

(1) They are located close to the inner diameter surface of the vessel. The tensile thermal 

stresses produced by rapid cooling along the vessel inner diameter do not penetrate far 

into the wall thickness of the RPV. A natural consequence of this, which is illustrated in 

4-3
Figure 4-3, is that the great majority of the cracks that are predicted to initiate and 

subsequently propagate through the vessel wall lie very close to the inner diameter

surface. The information in ess 

(2) They have a small through-wall dimension

Figure 4-3 indicates that almost all flaws that initiate lie l

than 1/8 T from the vessel inner diameter. Since they are driven by the thermal stresses

characteristic of cooldown transients, these observations hold true independent of 

embrittlement level. 

. This again occurs as a direct consequence 

er 

nd to not 

e 

 of 

 combination, these observations help to allay concerns that the flaw distributions sampled in 

 this 

al 

of the fact that cooldown transients produce thermal stresses that, together with the 

pressure stresses, are only high enough to initiate cracks at locations close to the inn

diameter of the vessel. Consequently, larger flaws (which would generally be 

considered more deleterious in a fracture evaluation than would small flaws) te

initiate very frequently because their crack tips lie too far away from the inner diameter 

surface and, so, are subjected to low tensile loads or even to compressive loads. Figur

4-4 and Figure 4-5 examine the effects of duration of irradiation exposure, flaw location 

(in plate or weld), and transient type on the flaw sizes that initiated fracture in the 

analyses. This information demonstrates that the combined effects of the duration

irradiation exposure and flaw location are small and entirely as expected because they

correlate well with relative embrittlement levels. Transient type plays a minor role, with 

predominantly thermal transients, such as large pipe breaks, generally initiating fracture 

from smaller flaws, while transients that involve a significant pressure component (such 

as stuck-open valves that may later reclose) tend to initiate fracture from larger flaws. 

Nevertheless, the flaws that contribute to the estimated through-wall cracking frequency

are small, having median depths ranging from 0.1 to 0.3 in. 

In

FAVOR do not simulate enough flaws of large dimensions, or that the postulated future 

discovery of a large (previously undetected) flaw in service could invalidate the results of

study. Neither of these concerns is valid because, as a result of the dominant effects of therm

stresses in controlling crack driving force, large flaws do not play a dominant role in establishing 

the risk of RPV failure caused by PTS. 

ID

tWALL

tCLAD

2a

OD

2c

L

Figure 4-2 Flaw dimension and position descriptors adopted in FAVOR 

4-4
4-5

0

2

4

6

8

0.000 0.125 0.250 0.375

Distance of Inner Crack Tip 

from Clad/Base Interface, 

L/twall

% of Flaws Predicted to Initiate

Beaver Valley at Ext-Bb

Palisades at Ext-Pb

Figure 4-3 Distribution through-wall position of cracks that initiate 

0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

% of Flaws with Non-Zero CPI 

Having Depth < 2a

Weld flaws that initiate from

LOCAs at 60 EFPY

Plate flaws that initiate from

LOCAs at 60 EFPY

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

Weld flaws that initiate from

LOCAs at Ext-Bb

Plate flaws that initiate from

LOCAs at Ext-Bb

Figure 4-4 Flaw depths that contribute to crack initiation probability in Beaver Valley 

Unit 1 when subjected to medium- and large-diameter pipe break transients at two 

different embrittlement levels 
0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

% of Flaws with Non-Zero CPI 

Having Depth < 2a

Weld flaws that initiate from

SO-1s at 60 EFPY

Plate flaws that initiate from

SO-1s at 60 EFPY

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

Weld flaws that initiate from

SO-1s at Ext-Bb

Plate flaws that initiate from

SO-1s Ext-Bb

Figure 4-5 Flaw depths that contribute to crack initiation probability in Beaver Valley 

Unit 1 when subjected to medium stuck-open valve transients at two different 

embrittlement levels 

4.2 Crack Initiation Model

The crack initiation model, detailed in Figure 4-6, is essentially a comparison of the applied 

driving force to fracture (Kapplied) and the material’s resistance to crack initiation (KIc). The model 

KIc is itself made up of three major components—an unirradiated index temperature model, an 

index temperature shift model, and a toughness transition model. Section 4.2.1 describes 

sensitivity studies related to the fracture driving force model, which estimates Kapplied, while 

Section 4.2.2 addresses sensitivity studies related to the model describing the material’s 

resistance to crack initiation. 

4.2.1 Applied Driving Force to Fracture 

As illustrated in Figure 4-8, the model of applied driving force to fracture is a conventional linear 

elastic fracture mechanics model augmented by a warm prestress model. Various parts of the 

model, and the need for sensitivity studies thereon, are discussed below. 

 FAVOR deterministically treats input variables describing the CTEPLATE, CTECLAD , 

Vessel Diameter , Vessel Thickness , Elastic Modulus , and Poisson’s Ratio . In 

all cases, the deterministic input value represents a best estimate. The uncertainty in 

these parameters is very small relative to many other variables in the model that have 

their uncertainties modeled explicitly (e.g., KIc, which exhibits uncertainty on the order of 

the mean value, and the uncertainty in the initiating event frequency can be several 

orders of magnitude). In the face of these much larger uncertainties it is not expected 

that the uncertainties on these input parameters influence the TWCF estimate in any 

significant manner. Consequently, no sensitivity studies are performed of these 

parameters. 

4-6
4-7

Applied

KI

Elastic Modulus

Vessel Diameter

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

Resistance

KIc

dKI/dt > 0

AND

A-KI > R-KIc

Initiation

Toughness

Transition Curve

CPI>0

Stress

Intensity

Factor dKI Model /dt

RTNDT(u)

Method

RTNDT(u)

(RVID)

YES

Generic?

YES

NO (u) = 0

 + (u) = S()

Conversion

to Toughness

Transition

Temperature Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

+

CPI=0

NO

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

T vs. t

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF

 RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

Weld residual

CTE Mismatch

residual

CTEWELD

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEX

TEMPERATURE MODEL

FRACTURE DRIVING

FORCE MODEL Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence Uncertainty

Sampled

ID Fluence

Local

Fluence Uncertainty

Fluence

At Flaw

Cu Uncertainty Sampled

Cu

Ni Uncertainty Sampled

Ni

P Uncertainty Sampled

P

Crack

Initiation

Model Applied

KI

Elastic Modulus

Vessel Diameter

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

Resistance

KIc

dKI/dt > 0

AND

A-KI > R-KIc

Initiation

Toughness

Transition Curve

CPI>0

Stress

Intensity

Factor dKI Model /dt

RTNDT(u)

Method

RTNDT(u)

(RVID)

YES

Generic?

YES

NO (u) = 0

 + (u) = S()

Conversion

to Toughness

Transition

Temperature Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

+

CPI=0

NO

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

T vs. t

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF

 RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

Weld residual

CTE Mismatch

residual

CTEWELD

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEX

TEMPERATURE MODEL

FRACTURE DRIVING

FORCE MODEL Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence Uncertainty

Sampled

ID Fluence

Local

Fluence Uncertainty

Fluence

At Flaw

Cu Uncertainty Sampled

Cu

Ni Uncertainty Sampled

Ni

P Uncertainty Sampled

P

Crack

Initiation

Model

Figure 4-6 Schematic illustration of the crack initiation model used in the PTS 

reevaluation project 

 FAVOR accurately models the effect of the CTE MISMATCH RESIDUAL STRESS on 

the estimated value of Kapplied because the Kapplied solution explicitly accounts for the CTE 

mismatch between the austenitic cladding and the ferritic base material. Therefore, no 

sensitivity study on CTE mismatch is performed. 

 The Weld Residual Stress Model in FAVOR assumes that the stress distribution in 

Figure 4-7 quantifies the residual stresses produced by welding in both axial and 

circumferential welds. These residual stresses were estimated from measurements 

made of how the width of a radial slot cut in the longitudinal weld in a shell segment 

from an RPV changes with cut depth; these measurements were processed through a 

finite element analysis to determine the residual stress profile shown in Figure 4-7 [10]. 

FAVOR also assumes that this residual stress distribution is not relieved by cracking of 

the vessel, (i.e., the residual stresses to the right in the figure are applied equally 

irrespective of a/t). Since residual stresses have to be relieved if a crack were to 

develop through the weld in an RPV, a sensitivity study in which the weld residual 

stresses are retained in the crack initiation calculation, but are removed from the 

through-wall cracking calculation, is performed to assess the effect of this conservative 

assumption.
-6

-4

-2

0

2

4

6

8

02468

Stress (ksi)

Distance From RPV Inner Surface (in.)

Weld residual stress data

Input to FAVOR Code

10

. 

Figure 4-7 Through-thickness weld residual stress profile assumed by FAVOR 

[56] 

 FAVOR adopts a linear elastic Stress Intensity Factor Model. Comparison of FAVOR 

estimates of Kapplied for embedded elliptical flaws and for surface-breaking semi-elliptical 

flaws with closed form solutions and with ABAQUS estimates demonstrate that FAVOR 

estimates are accurate under conditions of predominantly linear elastic loading [9, 11, 

12]. Moreover, an appendix to 19 demonstrates that linear elastic fracture mechanics 

(LEFM) are an accurate and appropriate theoretical framework for use in characterizing 

the resistance of thick-section nuclear RPVs to the structural integrity challenge posed 

by PTS loading. Consequently, sensitivity studies are not performed on the stress 

intensity factor model. 

 FAVOR adopts a Warm Prestress Model (i.e., dKI/dt>0 and KI(APPLIED) > KIc), as part of 

its linear elastic failure criteria. As detailed in Appendix B to 19 and in 23, warm 

prestress (WPS) is a physically understood and empirically demonstrated phenomenon. 

Of particular importance here, WPS has been demonstrated to be active in scale-model 

tests of nuclear RPVs subjected to PTS transients [4, 7]. For these reasons, a 

sensitivity study on the effects of the WPS model is not needed, and WPS is adopted 

as an integral part of the overall model. It should, however, be noted that adopting a 

WPS model can reduce the TWCF estimated for certain classes of transients. For 

example, the TWCF estimated for a primary-side pipe break will be significantly smaller 

when the effects of WPS are considered, while the TWCF estimated for a stuck-open 

valve that recloses later during the transient (thereby repressurizing the primary 

system) may not be affected by WPS at all. In plant analyses based on a complete set 

of transients (i.e., considering the potential for vessel failure from all potential PTS 

precursors), inclusion of WPS in the model reduces the estimated TWCF by between a 

factor of 2.5 and 3 [14]. Similar calculations reported by Meyer et al. indicate that WPS 

reduces TWCF by a factor of between 2 and 100 for individual transients [26]. The 

results reported by Dickson and by Meyer are not consistent because Dickson 

performed the analysis for a complete set of transients with the aim of assessing the 

aggregate PTS risk from all anticipated precursors, while Meyer focused on individual 

transients. The effect of WPS on individual transients reported by Dickson is within the 

range reported by Meyer. 

4-8
4-9

4.2.2 Resistance to Crack Initiation 

As illustrated in Figure 4-9, the model of the resistance of the material to crack initiation is itself 

made up of three major components—an unirradiated index temperature model, an index 

temperature shift model, and a toughness transition model. Sensitivity studies related to these 

three components are discussed, in turn, in each of the following sections. 

Applied

KI

Elastic Modulus

Vessel Diameter

dKI/dt > 0

AND

A-KI > R-KIc CPI>0

Stress

Intensity

Factor dKI Model /dt

YES

CPI=0

NO

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVING

FORCE MODEL

Applied

KI

Elastic Modulus

Vessel Diameter

dKI/dt > 0

AND

A-KI > R-KIc CPI>0

Stress

Intensity

Factor dKI Model /dt

YES

CPI=0

NO

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVING

FORCE MODEL

Figure 4-8 Schematic illustration of the model of the applied driving force to fracture 

used in the PTS reevaluation project 

4.2.2.1 Unirradiated Index Temperature Model 

The model adopted by FAVOR for the unirradiated index temperature recognizes that (1) the 

RTNDT index temperature must be used in the definition of any revised PTS screening criteria so 

that plants can assess their reactors without the need to collect additional material data, and (2) 

the RTNDT index temperature has an intentional conservative bias [2] that needs to be 

considered. In FAVOR, this 

Conversion {of RTNDT} 

to Toughness Transition 

Temperature 

is accomplished using a statistically defined conversion that quantifies the difference, and the 

uncertainty in the difference, between RTNDT and a fracture toughness index temperature. 

While the conversion produces the correct result on average, it introduces a considerable 

nonphysical uncertainty that is an inescapable consequence of the inconsistency in the 

intentional conservative bias that is part of the ASME NB2331 RTNDT definition. The result is 

that the uncertainty in values of the unirradiated toughness index temperature simulated by 

FAVOR greatly exceed those measured experimentally. For this reason, sensitivity studies 

examining alternative characterizations of RTNDT and RTNDT uncertainty are not conducted. 

FAVOR already overestimates RTNDT uncertainty relative to any physically plausible or 

empirically justifiable characterization, and the only way to eliminate this conservatism is to 

eliminate RTNDT from the model (which cannot be done because this project is constrained to 
assess the toughness properties of the RPV based only on information that is available 

currently). 

With reference to Figure 4-9, it can also be noted that the overall Unirradiated TINDEX Model 

has been color coded to indicate that other plausible models exist that have roughly equal 

technical justification to the one adopted by FAVOR. This alternative would involve direct 

measurement of the index temperature using Master Curve technology, as detailed in ASTM 

E1921 and American Society of Mechanical Engineers (ASME) Code Case N-629. Such an 

approach is technically possible and arguably removes the considerable nonphysical 

uncertainty introduced by the statistical conversion between RTNDT and the fracture toughness 

transition temperature. Nevertheless, adoption of this approach would also eliminate RTNDT

from the model and, thereby, would implicitly require licensees to collect additional material data 

on their RPV steels to assess the state of their reactors relative to any new proposed PTS 

screening criteria. Consequently, a sensitivity study on the unirradiated index temperature 

model is not performed. 

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

Resistance

KIc

Initiation

Toughness

Transition Curve

RTNDT(u)

Method

RTNDT(u)

(RVID)

Generic?

YES

NO (u) = 0

 + (u) = S()

Conversion

to Toughness

Transition

Temperature Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

+

T vs. t

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF

 RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEX

TEMPERATURE MODEL

Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence Uncertainty

Sampled

ID Fluence

Local

Fluence Uncertainty

Fluence

At Flaw

Cu Uncertainty Sampled

Cu

Ni Uncertainty Sampled

Ni

P Uncertainty Sampled

P

Un-Irradiated

Index

Temperature

(RTNDT(u)*)

Irradiated

Initiation

Toughness

Index

Temperature

(RTTOUGH(I))

Resistance

KIc

Initiation

Toughness

Transition Curve

RTNDT(u)

Method

RTNDT(u)

(RVID)

Generic?

YES

NO (u) = 0

 + (u) = S()

Conversion

to Toughness

Transition

Temperature Un-Irradiated

Toughness Index

Temperature

(RTTOUGH(U))

Irradiated

Toughness Shift

(RTTOUGH)

1

+

T vs. t

Weld

Flaw?

NO

YES

RTTOUGH(I) =

MAXIMUM OF

 RTTOUGH(I)WELD, &

 RTTOUGH(I)ADJACENT PLATE

INDEX TEMPERATURE SHIFT MODEL

UNIRRADIATED INDEX

TEMPERATURE MODEL

Sampled

Fluence At Flaw

Charpy

Irradiation

Shift

Model

Charpy

Temperature

Shift (T30)

Oper.

Temp.

Cu

(RVID)

Thru-Wall

Attenuation

Model

Best-Estimate

ID Fluence

(Reg-Guide Calcs.)

Ni

(RVID)

P

(RVID)

Oper.

Time

Product

Form

Vessel

Mfg.

Conversion

to Toughness

Shift

Global

Fluence Uncertainty

Sampled

ID Fluence

Local

Fluence Uncertainty

Fluence

At Flaw

Cu Uncertainty Sampled

Cu

Ni Uncertainty Sampled

Ni

P Uncertainty Sampled

P

Figure 4-9 Schematic illustration of the model of the crack initiation toughness used in 

the PTS reevaluation project 

4.2.2.2 Index Temperature Shift Model 

The index temperature shift model includes a number of subcomponents that are discussed 

below in the order of their use in the FAVOR Index Temperature Shift Model: 

 ID Fluence—The variation of fluence over the inner diameter of the vessel is estimated 

using modeling procedures based on the guidance provided in the NRC regulatory 

guide [34, “Calculational and Dosimetry Methods for Determining Pressure Vessel 

Neutron Fluence”]. Fluences calculated in this way are considered best estimates 

4-10
because they are based on the most up-to-date calculational procedures. Sensitivity 

studies involving inner diameter fluence are therefore not performed. 

 Thru-Wall Attenuation Model—FAVOR adopts the RG 1.99, Revision 2, model of 

fluence attenuation through the thickness of the vessel [35]. This model assumes that 

the fluence (and thus the damage caused by irradiation) reduces exponentially as the 

through-wall distance from the inner radius of the RPV increases. The exponential 

coefficient adopted (−0.24) assumes that fluence attenuates at the same rate as 

displacements per atom, which is a conservative assumption. A recent review of 

attenuation models conducted under an EPRI contract [18] concluded that while the RG 

1.99, Revision 2, attenuation model is widely regarded as conservative, no better 

alternative model exists at the current time. For this reason, no sensitivity study 

involving the attenuation model is performed. 

 Cu, Ni, P—The mean values of copper (Cu), nickel (Ni), and phosphorus (P) used by 

FAVOR are the “best-estimate” values docketed by the licensees and recorded in the 

RVID2 database [31]. The statistical distributions assumed to exist around these mean 

values were derived from all data available regarding chemical constituent variability in 

nuclear-grade RPV steels and weldments (see Reference 19 for further explanation). 

Consequently, these distributions overestimate (sometimes significantly so) the degree 

of uncertainty in Cu, Ni, and P relative to what actually exists in a particular plate, weld, 

or forging. While sensitivity studies could be motivated on such a basis, and indeed 

might provide valuable insights about the PTS risk at particular plants, the results of 

such studies would not provide useful information about developing a PTS screening 

criteria applicable to the entire population of operating PWRs. For this reason, 

sensitivity studies on Cu, Ni, and P are not performed. 

 Time, Prod. Form, Mfg.—Each FAVOR analysis is performed at a particular value of 

reactor operating time defined in terms of effective full-power years, or EFPYs. As such, 

the variable time is known without error. Records may also be used to define without 

question the product form (weld, plate, or forging), as well as the company responsible 

for manufacturing each vessel. Sensitivity studies on these variables are therefore not 

needed. 

 Temperature—Since damage of the RPV steels by neutron irradiation exposure is a 

phenomenon that occurs on a time scale of years to decades, transients in the operating 

temperature of the reactor are of no significance to the predictions of this model. The 

temperature value needed is that in the beltline region of the reactor when it is operating 

under full-power conditions. This temperature can be established from operational 

records. For these reasons, sensitivity studies on the operating temperature are not 

needed. 

 Charpy Irradiation Shift Model—This model, also called an embrittlement trend curve, 

relates compositional and exposure variables to the amount by which irradiation shifts 

the Charpy V-notch (CVN) transition temperature curve to higher temperatures. FAVOR 

adopts a model developed by Eason under an NRC research contract [17]. Since that 

time, the American Society for Testing and Materials adopted a similar, but not identical, 

embrittlement trend curve in the E900-02 standard [3]. A sensitivity study will be 

performed to assess the effect of adopting the ASTM embrittlement trend curve rather 

than the model proposed by Eason. 

4-11
 Conversion to Toughness Shift —This model converts the shift in the CVN transition 

temperature into a shift in the fracture toughness transition temperature. The 

relationship between these two transition temperatures has been shown to be consistent 

over a wide range of RPV materials, although it is dependent on product form [42, 22]. 

While there can appear to be considerable uncertainty in this relationship, it has been 

demonstrated that this uncertainty derives principally from an inability of small data sets 

to resolve accurately the transition temperatures [43, 22]. For these reasons no 

sensitivity studies are performed. 

4.2.2.3 Toughness Transition Model 

The toughness transition model adopted by FAVOR (i.e., the variation of KIc with temperature) 

was fit to all available LEFM-valid fracture toughness data for domestic RPV steels [56]. The 

model is not, however, a purely empirical fit since the dispersion coefficient (c) is held fixed at 4, 

a value motivated by a physical understanding of cleavage fracture as expressed by Wallin’s 

Master Curve (see all of the references by Wallin). 

The color-coding of the Toughness Transition Model, signifies that alternative models having 

roughly equal technical justification are available. This alternative model is Wallin’s Master 

Curve. The NRC did not view the adoption of Wallin’s Master Curve for the Toughness 

Transition Model used by FAVOR as appropriate because (1) the Master Curve provides the 

temperature dependency of the elastic-plastic fracture toughness parameter KJc, and (2) the 

Master Curve incorporates explicitly the statistical size dependency of fracture toughness 

values. Both of these features of the Master Curve are inconsistent with the framework of 

FAVOR, which is a linear elastic fracture mechanics code. For these reasons, and because 

adapting FAVOR to include an elastic-plastic fracture toughness model represents a major 

change to the structure of the code, no sensitivity studies are performed. 

4.2.2.4 Other Features 

For weld flaws (which are all fusion line flaws), the FAVOR crack initiation model assumes that 

the fracture toughness transition reference temperature that characterizes the material at the 

crack tip is the maximum of the fracture toughness transition reference temperature of the plate 

material that exists on one side of the flaw and the weld material that exists on the other. This 

model has been classified as Green (i.e., accurate) because a crack, if it propagates, will tend 

to do so through the most brittle material available. For this reason, no sensitivity studies of this 

model are performed. 

4.3 Through-Wall Cracking Model

As illustrated in Figure 4-10, the model of through-wall cracking adopted by FAVOR compares 

the applied driving force to fracture (A-KI) and the material’s resistance to further cracking (R-KI) 

to estimate the conditional probability of through-wall cracking (which is defined as vessel failure 

(CPF)). The through-wall cracking model is executed 100 times by FAVOR for each time step 

in the transient at which the crack initiation model estimates a nonzero conditional probability of 

crack initiation (CPI). Each of these 100 trials constitutes a single, deterministic, crack-arrest 

calculation, and the fraction of these 100 trials for which through-wall cracking is predicted 

provides an estimate of the percentage of CPI that is manifested in CPF. 

4-12
4-13

The through-wall cracking model is composed of the following parts: 

 a fracture-driving-force model 

 a fracture resistance model, which is made up of the following parts: 

— the assumption that upon crack initiation the crack immediately grows along the 

 inner diameter surface of the vessel to a length that greatly exceeds its through-

 wall depth 

— a model that describes the gradient of weld properties through the vessel wall 

 thickness 

— a crack-arrest model 

— a ductile-tearing model 

Section 4.3.1 describes the sensitivity studies related to the fracture-driving-force model, while 

Section 4.2.2 addresses sensitivity studies related to the four different parts of the fracture 

resistance model. 

4.3.1 Fracture Driving Force Model for Through-Wall Cracking 

Similar to the crack initiation model, a conventional linear elastic fracture mechanics approach is 

taken to characterize the applied driving force to fracture (see Figure 4-11). Most details of this 

model are identical to those already discussed in Section 4.2.1 and thus are not repeated. With 

respect to the Stress Intensity Factor Model, comparison of FAVOR estimates of Kapplied for 

axial and circumferential flaws of infinite length with closed form solutions and with the ABAQUS 

estimates demonstrate that FAVOR estimates are accurate under conditions of predominantly 

linear elastic loading [5]. Moreover, an appendix to 19 demonstrates that LEFM is an accurate 

and appropriate theoretical framework for use in characterizing the resistance of thick-section 

nuclear RPVs to the structural integrity challenge posed by PTS loading. 

4.3.2 Fracture Resistance Model for Through-Wall Cracking 

As discussed earlier, the fracture resistance model for through-wall cracking is made up of the 

following parts: 

 the assumption that upon crack initiation the crack immediately grows along the inner 

diameter surface of the vessel to a length that greatly exceeds its through-wall depth 

 a model that describes the gradient of weld properties through the vessel wall thickness 

 a crack arrest model 

 a ductile tearing model 

Sensitivity studies relating to each part of the fracture resistance model for through-wall cracking 

are discussed in the following sections. 
MAT=Weld &

a’ in Next 1⁄4 T

Matrix

Multiply

Through Wall

Cracking

Frequency

(TWCF)

Initiation-Arrest

Transition Curve

Separation

Model

RTARREST

Arrest

Toughness

Transition

Curve

NO

YES

Applied

KI

Stress

Intensity

Factor

Model

A-KI

>

R-KI

CPF=

CPI*FAIL/COUNT

YES

Fluence

at Flaw

Thru-Wall

Attenuation

Model

+

1 Irradiated

Toughness Shift

(RTTOUGH)

Irradiated

Arrest Toughness

Index Temperature

NO

Extend flaw to 

Infinite Length

Increment 

Flaw Depth

a’ = a + a

Re-Sample

Cu

Ni

P

Resistance

KIa*

T vs. t

Pf 1= S{ RAND[0,1] }

MAT=Weld

&

a’ in Next 1⁄4 T

Resistance

KIa@T

No

Pf xT/4= S{ RAND[0,1] }

Yes

Initiation-Arrest

Interaction Model ON KIa(MAX) = KIc

a’>1⁄4T

?

YES

NO

Resistance

K{J-R}@T

Resistance

KIa* @T

MIN

Resistance

KI @T

Elastic Modulus

Vessel Diameter

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVING

FORCE MODEL

CRACK ARREST MODEL

PROPERTY

GRADIENT

MODEL

Initiation-Arrest

Interaction Model OFF

Unrestricted KIa(MAX)

Weld?

NO

YES

Resistance

KIa@T

A

FAIL = 0 

COUNT = 0

FAIL=FAIL+1

COUNT=COUNT+1

COUNT

=100?

A

NO

YES

Initiation-Arrest

Interaction Model ON KIa(MAX) = KIc

Thru-Wall

Cracking

Model

TUS

Model TUS

Upper Shelf

Toughness

vs.

Temperature

Curve

T vs. t

DUCTILE TEARING MODEL

Irradiated Initiation

Toughness Index

Temperature

(RTTOUGH(I))

(from initiation model)

Bin

Frequency

Histogram

(from PRA)

Figure 4-10 Model of through-wall cracking adopted by FAVOR 

Applied

KI

Stress

Intensity

Factor

Model

Elastic Modulus

Vessel Diameter

Vessel Thickness

Clad Thickness

CTEPLATE

Poisson’s Ratio

P&T vs. t

Weld residual

CTE Mismatch

residual

CTEWELD

FRACTURE DRIVING

FORCE MODEL

Figure 4-11 Crack driving force model for through-wall cracking 

4-14
MAT=Weld &

a’ in Next 1⁄4 T

Initiation-Arrest

Transition Curve

Separation

Model

RTARREST

Arrest

Toughness

Transition

Curve

NO

YES

Fluence

at Flaw

Thru-Wall

Attenuation

Model

+

1 Irradiated

Toughness Shift

(RTTOUGH)

Irradiated

Arrest Toughness Index Temperature

Extend flaw to 

Infinite Length

Increment 

Flaw Depth

a’ = a + a Re-Sample

Cu

Ni

P

Resistance

KIa*

T vs. t

Pf 1= S{ RAND[0,1] }

MAT=Weld

& a’ in Next 1⁄4 T

Resistance

KIa@T

No

Pf xT/4= S{ RAND[0,1] }

Yes

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

a’>1⁄4T

?

YES

NO

Resistance

K{J-R}@T

Resistance

KIa* @T

MIN

Resistance

KI @T

CRACK ARREST MODEL

PROPERTY

GRADIENT

MODEL

Initiation-Arrest

Interaction Model OFF

Unrestricted KIa(MAX)

Weld?

NO

YES

Resistance

KIa@T

A

FAIL = 0 

COUNT = 0

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

TUS

Model TUS

Upper Shelf

Toughness

vs.

Temperature

Curve

T vs. t

DUCTILE TEARING MODEL

Irradiated Initiation

Toughness Index

Temperature

(RTTOUGH(I))

(from initiation model)

MAT=Weld &

a’ in Next 1⁄4 T

Initiation-Arrest

Transition Curve

Separation

Model

RTARREST

Arrest

Toughness

Transition

Curve

NO

YES

Fluence

at Flaw

Thru-Wall

Attenuation

Model

+

1 Irradiated

Toughness Shift

(RTTOUGH)

Irradiated

Arrest Toughness Index Temperature

Extend flaw to 

Infinite Length

Increment 

Flaw Depth

a’ = a + a Re-Sample

Cu

Ni

P

Resistance

KIa*

T vs. t

Pf 1= S{ RAND[0,1] }

MAT=Weld

& a’ in Next 1⁄4 T

Resistance

KIa@T

No

Pf xT/4= S{ RAND[0,1] }

Yes

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

a’>1⁄4T

?

YES

NO

Resistance

K{J-R}@T

Resistance

KIa* @T

MIN

Resistance

KI @T

CRACK ARREST MODEL

PROPERTY

GRADIENT

MODEL

Initiation-Arrest

Interaction Model OFF

Unrestricted KIa(MAX)

Weld?

NO

YES

Resistance

KIa@T

A

FAIL = 0 

COUNT = 0

Initiation-Arrest

Interaction Model ON

KIa(MAX) = KIc

TUS

Model TUS

Upper Shelf

Toughness

vs.

Temperature

Curve

T vs. t

DUCTILE TEARING MODEL

Irradiated Initiation

Toughness Index

Temperature

(RTTOUGH(I))

(from initiation model)

Figure 4-12 Fracture resistance model for through-wall cracking 

4.3.2.1 Infinite Length Flaw Assumption 

Whenever the crack initiation model estimates a nonzero conditional probability of crack 

initiation, FAVOR Extends to Infinite Length the surface flaw or buried elliptical flaw that 

caused this initiation. The assumption that flaws extend in length (axially or circumferentially) by 

considerable distances before they extend significantly in depth (through the vessel wall 

thickness) is supported by thermal shock experiments performed on scaled RPVs [7]. However, 

use of this assumption when trying to predict the fracture of a real vessel is believed to be 

conservative for the following reasons: 

 The total propagation length of axial flaws is expected to be limited to a single shell 

course in most cases (slightly over 8 ft long) because at this point the crack would 

propagate first into circumferential welds and, secondly, into a plate or an axial weld. 

These other materials are not likely to be as embrittled as the region where the crack 

started, and so are likely to arrest the crack. In any event, the active core 

(approximately 12 ft in length) is the only region over which significant embrittlement can 

occur, so crack arrest would certainly occur outside of this region. 

 The total propagation length of circumferential flaws is expected to be limited by the 

periodic circumferential variations of fluence that occur because of varying distances 

between the fuel and the vessel wall. At least every 45 degrees (e.g., approximately 

every 5.25 ft in a 13-ft diameter vessel), the fluence in the core region goes through a 

minima, suggesting an increased likelihood of crack arrest at these less embrittled 

locations. 

While the treatment of flaw length adopted by FAVOR is conservative, as detailed above, it is 

not believed to be excessively so because the flaw depth (on the order of 0.01 to 1 in.) is very 

small compared to these flaw lengths (100 to 160 in.). Ample evidence in the fracture 

mechanics literature demonstrates that as the length-to-depth ratio for a flaw becomes large 

(i.e., above 30), the correct Kapplied solution is closely approximated by the infinite length 

assumption. For this reason no sensitivity studies are performed on this topic. 

4-15
4.3.2.2 Weld Property Gradient Model 

In welds, a gradient of properties through the thickness of the RPV is expected to exist because 

of through-wall changes in copper content. These copper content changes arise from the fact 

that, because of the large volume of weld metal needed to fill an RPV weld, oftentimes 

manufacturers needed to use weld wire from multiple spools to completely fill the groove. Lack 

of control of the process used to copperplate the weld wires (a step taken for corrosion control) 

resulted in wide variability in coating thickness from spool to spool, which is manifested in 

measurable variations in reported copper content through the RPV wall thickness. These 

copper variations produce variations in sensitivity to irradiation embrittlement and consequent 

variations in resistance to fracture though the vessel wall. 

Simple calculations involving weld coil weight and weld volume suggest that axial welds are 

likely to have 2–3 layers of different copper content, while circumferential welds (owing to their 

considerably greater length) are likely to have 7–8 layers [19]. However, FAVOR adopts a 

simpler model that All Welds Have 4 Layers and, so, chemical composition (Cu, Ni, P)

§

 is 

resampled when the crack propagates into a new weld layer. A sensitivity study on this model 

is performed in which all weld layers are removed from the model. 

Another feature of the weld property gradient model is the Initiation-Arrest Interaction Model. 

Physical arguments suggest that within the same material the fact that a crack has initiated (at, 

for example, KIc*) suggests that the crack arrest toughness at the temperature of crack initiation 

cannot exceed KIc*, or arrest would have occurred immediately and the initiation event would 

not have been successful [19]. However, no expectations on KIa values exist for a material in 

which crack initiation has not yet occurred. For this reason, once Cu, Ni, and P are resampled, 

all restrictions on KIa based on the KIc observed in the initiating weld layer are relaxed. This 

Initiation-Arrest Interaction Model is premised on a physical understanding of the processes 

responsible for cleavage fracture and, therefore, no sensitivity studies are planned. 

4.3.2.3 Crack Arrest Model 

19 discusses in detail the model of cleavage crack arrest toughness adopted by FAVOR and 

illustrated in Figure 4-12. This model includes an Initiation-Arrest Transition Curve 

Separation Model that varies depending on the crack initiation toughness index temperature, 

and an Arrest Toughness Transition Curve that is indexed based on fracture toughness data 

rather than the correlative index temperature RTNDT. In combination, these treatments model 

available KIa data more realistically than the only available alternative model (i.e., the ASME KIa

curve). Furthermore, the material-dependent separation of the KIa curve from the KIc curve 

conforms to a physical understanding of the mechanics of cleavage fracture in a way that the 

ASME KIa model does not. Thus, while alternatives to the crack arrest model adopted by 

FAVOR exist, it cannot be said that they have “roughly equal technical justification” to the 

FAVOR model. In fact, the alternative model is not as well justified, either empirically or 

physically, as the FAVOR model. For this reason no sensitivity studies based on these models 

are performed. 

 

§

 See Section 4.2.2.2 for a description of sensitivity studies related to chemical composition. 

4-16
4.3.2.4 Ductile Tearing Model 

The model of ductile tearing adopted by FAVOR and illustrated in Figure 4-12 is discussed in 

detail elsewhere (see Reference 21 for model description and Reference 19 and Reference 56

for a discussion of its use in FAVOR). This model includes a TUS Model that estimates an index 

temperature for upper-shelf fracture toughness from the index temperature for transition fracture 

toughness, and is used along with an Upper Shelf Toughness vs. Temperature Curve to 

estimate the resistance to ductile tearing (J-R) at temperatures of interest. The detailed 

discussion of these models (see both Reference 19 and Reference 21) demonstrates that they 

apply, and can be expected to apply, to all material conditions of interest in RPV applications. 

Alternative models of ductile tearing resistance in ferritic steels to that illustrated in Figure 4-12

exist [16, 36, 54], and it is for this reason that the overall Ductile Tearing Model is classified as 

orange in Figure 4-12. These alternatives, which are all based on correlations with CVN uppershelf energy, are much more commonplace than that adopted in FAVOR, which does not rely 

on Charpy correlations in any way and features an explicit treatment of the uncertainty in uppershelf toughness data. The model in FAVOR estimates the upper-shelf toughness properties 

directly from the fracture toughness transition temperature, a relationship motivated by both 

trends in fracture toughness data and by physical considerations. The NRC implemented the 

new model in FAVOR instead of the more conventional approaches based on correlation with 

CVN properties becasue of the notoriously poor correlation coefficients exhibited by these other 

approaches (R2

 < 0.5; see discussion in Chapter 9 of Reference 19). This lack of correlation 

suggests that different physical mechanisms underlie energy absorption in the CVN test versus 

the resistance-to-ductile crack initiation and propagation from a preexisting defect. Additionally, 

these low correlation coefficients engender little confidence in the reliability of calculations made 

on the basis of such relationships. However, because approaches to upper-shelf toughness 

estimation based on correlation with CVN properties are much more commonplace, a sensitivity 

study on the Ductile Tearing Model is planned. 

4.4 Summary of Planned Sensitivity Studies

The following list summarizes the sensitivity studies proposed in the preceding sections: 

 Welding residual stresses are currently assumed to not be affected by through-wall 

crack propagation. A sensitivity study is performed in which the residual stresses are 

set to zero once the crack initiates. 

 FAVOR currently adopts an embrittlement shift model that differs from that 

recommended by ASTM. A sensitivity study is performed in which the ASTM model is 

adopted. 

 FAVOR resamples chemical composition variables at the 1/4 T, 1/2 T, and 3/4 T 

locations for welds in a through-wall propagation analysis to simulate the effect of 

varying copper content on different weld wire spools. A sensitivity study is performed in 

which the chemistry is not resampled. 

 FAVOR adopts a new toughness-based upper-shelf model instead of more conventional 

approaches based on correlation with CVN properties. A sensitivity study is performed 

in which a CVN-based upper-shelf model is adopted. 

4-17
4-18

The material conditions and TH transient sets used for each sensitivity study, and the rationale 

for making these selections, include the following: 

 Material Condition—Results of the baseline PTS analyses [15] and previous results [24] 

all demonstrate that the embrittlement properties of materials that can be associated 

with an axial crack play the dominant role in establishing the risk associated with a PTS 

event. For this reason, the NRC selected a plant in which the axial welds are the most 

embrittled material (Palisades) and a plant in which the plates are the most embrittled 

material (Beaver Valley) for use in sensitivity studies. Two different embrittlement 

conditions are analyzed for each plant, (1) the embrittlement expected to occur at the 

end of the plant’s original 40-year operating license (32 EFPYs), and (2) a much higher 

embrittlement level expected to coincide (approximately) with a yearly through-wall 

cracking frequency of 1x10-6 events/year. Table 4-2 summarizes these different 

embrittlement conditions. Each sensitivity study listed above is analyzed for all four of 

the conditions listed in Table 4-2. 

 Thermal Hydraulic Transient Subset—The subset of transients from the base case 

analyses [24] that contribute the most to the TWCF are used in these analyses. Figure 

4-13 illustrates this subset for the Palisades and Beaver Valley reactors, while Table 4-3

and Table 4-4 provide a detailed description of these transients. 

Table 4-2 Plant and Embrittlement Conditions Used in Sensitivity Studies 

Embrittlement Level 

Plant Type EOL 

Near 

Proposed 

RVFF limit of 

10-6

events/year 

Axial Weld 

Limited 

Palisades at 

32 EFPYs 

Palisades at 

Ext-B 

Plate Limited Beaver at 32 

EFPYs 

Beaver at 

Ext-B 

Table 4-3 Transients Used in Sensitivity Studies for Palisades 

Case Class System Failure Operator Action HZP

19 SO-2 Reactor trip with 1 stuck-open ADV on SG-A. None. Operator does not throttle HPI. Yes

40 LOCA 40.64-cm (16-in.) hot-leg break. Containment sump 

recirculation included in the analysis. None. Operator does not throttle HPI. No

52 SO-2 Reactor trip with 1 stuck-open ADV on SG-A. Failure of 

both MSIVs (SG-A and SG-B) to close. 

Operator does not isolate AFW on 

affected SG. Normal AFW flow assumed 

(200 gpm). Operator does not throttle 

HPI. 

Yes

54 MSLB 

Main steamline break with failure of both MSIVs to close. 

Break assumed to be inside containment causing 

containment spray actuation. 

Operator does not isolate AFW on 

affected SG. Operator does not throttle 

HPI. 

No

55 SO-2 

Turbine/reactor trip with 2 stuck-open ADVs on SG-A 

combined with controller failure resulting in the flow from 

two AFW pumps into affected steam generator. 

Operator starts second AFW pump. No

58 LOCA 

10.16-cm (4-in.) cold-leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40 °F, 

Accumulator temp = 60 °F) 

None. Operator does not throttle HPI. No
Case Class System Failure Operator Action HZP

59 LOCA 

10.16-cm (4-in.) cold-leg break. Summer conditions 

assumed (HPI and LPI injection temp = 100 °F, 

Accumulator temp = 90 °F) 

None. Operator does not throttle HPI. No

60 LOCA 

5.08-cm (2-in.) surge line break. Winter conditions 

assumed (HPI and LPI injection temp = 40 °F, 

Accumulator temp = 60 °F) 

None. Operator does not throttle HPI. No

62 LOCA 

20.32-cm (8-in.) cold-leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40 °F, 

Accumulator temp = 60 °F) 

None. Operator does not throttle HPI. No

63 LOCA 

14.37-cm (5.656-in.) cold-leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40° F, 

Accumulator temp = 60 °F) 

None. Operator does not throttle HPI. No

64 LOCA 

10.16-cm (4-in.) surge line break. Summer conditions 

assumed (HPI and LPI injection temp = 100 °F, 

Accumulator temp = 90 °F) 

None. Operator does not throttle HPI. No

65 SO-1 

One stuck-open pressurizer SRV that recloses at 6000 s 

after initiation. Containment spray is assumed not to 

actuate. 

None. Operator does not throttle HPI. Yes

 

4-19
Table 4-4 Transients Used in Sensitivity Studies for Beaver Valley Unit 1 

Case Class System Failure Operator Action HZP

7 LOCA 2.54-cm (8-in.) surge line break None. No

9 LOCA 2.54-cm (16-in.) hot-leg break None. No

56 LOCA 10.16-cm (4.0-in.) surge line break 

60 SO-1 Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 6000 s. None. No

96 SO-1 Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 6000 s. Operator controls HHSI 10 minutes after allowed. No

97 SO-1 Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 3000 s. None. Yes

101 SO-1 Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 3000 s. Operator controls HHSI 10 minutes after allowed. Yes

102 MSLB Main steamline break with AFW continuing 

to feed affected generator for 30 minutes. 

Operator controls HHSI 30 minutes after allowed. 

Break is assumed to occur inside containment so that 

the operator trips the RCPs as a result of adverse 

containment conditions. 

No

103 MSLB Main steamline break with AFW continuing 

to feed affected generator for 30 minutes. 

Operator controls HHSI 30 minutes after allowed. 

Break is assumed to occur inside containment so that 

the operator trips the RCPs as a result of adverse 

containment conditions. 

Yes

104 MSLB Main steamline break with AFW continuing 

to feed affected generator for 30 minutes. 

Operator controls HHSI 60 minutes after allowed. 

Break is assumed to occur inside containment so that 

the operator trips the RCPs as a result of adverse 

containment conditions. 

No

105 MSLB Main steamline break with AFW continuing 

to feed affected generator for 30 minutes. 

Operator controls HHSI 60 minutes after allowed. 

Break is assumed to occur inside containment so that 

the operator trips the RCPs as a result of adverse 

containment conditions. 

Yes

108 MSLB 

Small steamline break (simulated by sticking 

open all SG-A SRVs) with AFW continuing 

to feed affected generator for 30 minutes. 

Operator controls HHSI 30 minutes after allowed. Yes

4-20
Palisades

0

10

20

30

40

50

F&B, 31F&B, 32

LOCA, 2

LOCA, 40LOCA, 58LOCA, 59LOCA, 60LOCA, 61LOCA, 62LOCA, 63LOCA, 64MSLB, 22MSLB, 24MSLB, 26MSLB, 27MSLB, 29MSLB, 34MSLB, 49MSLB, 50MSLB, 51MSLB, 54

SO-1, 42SO-1, 48SO-1, 53SO-1, 65SO-2, 16SO-2, 18SO-2, 19SO-2, 52SO-2, 55

% Contribution to TWCF

32 EFPY

60 EFPY

200 EFPY

500 EFPY

Beaver

0

20

40

60

80

100

LOCA, 2LOCA, 7

LOCA, 56

LOCA, 114LOCA, 116

MSLB, 74MSLB, 81

M SLB, 103M SLB, 105M SLB, 107M SLB, 109M SLB, 111M SLB, 113

SO-1, 14SO-1, 34SO-1, 60SO-1, 62SO-1, 65SO-1, 67SO-1, 69SO-1, 71SO-1, 73SO-1, 86SO-1, 88SO-1, 90SO-1, 92SO-1, 94SO-1, 96SO-1, 98

SO-1, 100

SO-2, 78

% Contribution to TWCF

32 EFPY

100 EFPY

200 EFPY

Figure 4-13 Identification of transients (shaded boxes) used for Palisades and Beaver 

Valley sensitivity studies 

4-21
4-22

4.5 Sensitivity Study Results

4.5.1 Residual Stresses 

FAVOR assumes that a single distribution quantifies, for both axial and circumferential welds, 

the residual stresses produced by welding [56]. These residual stresses were estimated from 

measurements made of how the width of a radial slot cut in the longitudinal weld in a shell 

segment from an RPV changes with cut depth; these measurements were processed through a 

finite element analysis to determine the residual stress profile used by FAVOR [10]. FAVOR 

also assumes that this residual stress distribution is not relieved by cracking of the vessel (i.e., 

the residual stresses in the figure to the right are applied equally irrespective of the a/t ratio of 

the crack). Since residual stresses would have to be relieved if a crack were to develop through 

the weld in an RPV, the effect of this conservative assumption is assessed by performing a 

sensitivity study in which the weld residual stresses are retained in the crack initiation 

calculation, but are removed from the through-wall cracking calculation. In this sensitivity study, 

the NRC performed analyses of both the Beaver Valley and the Palisades RPVs at two 

embrittlement levels each (32 EFPYs and the Ext-B embrittlement conditions; see Table 4-5). 

The effect of relieving the residual stresses in the through-wall cracking calculations was entirely 

negligible, reducing the TWCF values by less than 1 percent (on average). This limited 

sensitivity of the TWCF values on residual stresses occurs because the crack driving force 

caused by the residual stress is very small relative to that caused by the combination of thermal 

and pressure loading. 

 

Table 4-5 Results of Residual Stress Sensitivity Study

Plant EFPYs Base 

FCI 

Sensitivity 

FCI 

FCI 

Ratio 

Base 

TWCF 

Sensitivity 

TWCF 

TWCF 

Ratio 

BV 32 1.56e-7 1.56e-7 1.00 1.40e-9 1.55e-9 1.10 

BV 200 8.48e-6 8.46e-6 0.99 2.80e-7 2.67e-7 0.95 

Pal 32 9.67e-8 9.75e-8 1.00 9.98e-9 9.56e-9 0.96 

Pal 500 5.83e-6 5.73e-6 0.98 1.85e-6 1.77e-6 0.96 

4.5.2 Embrittlement Shift Model 

The embrittlement shift model relates compositional and neutron exposure variables to the 

amount by which irradiation shifts the CVN transition temperature curve to higher temperatures. 

FAVOR adopts a model developed by Eason under an NRC research contract [17]. Since that 

time ASTM has adopted a similar, but not identical, embrittlement trend curve in the E900-02 

standard [3]. A sensitivity study was therefore performed to assess the effect of adopting the 

ASTM embrittlement trend curve rather than the model proposed by Eason (again analyzing 

Beaver Valley and Palisades at two different embrittlement levels; see Table 4-6). The ASTM 

E900-02 embrittlement shift model produces TWCF estimates that are systematically lower (i.e., 

approximately 1/3 of those estimated using the Eason shift model). Activity is currently 

underway within ASTM Committee E10.02 to revise the E900 model. Representatives of both 

the industry and the NRC are involved in this Code committee work, and it is expected that the 

committee will publish a revised model that incorporates features of both the current Eason and 

ASTM E900-02 relationships. Thus, for the purposes this report, the Agency has continued to 

use the Eason correlation and accepted this approach as conservative relative to the approach 

adopted by an international consensus body. When a consensus emerges from the ASTM 
E10.02 Code committee process it will be a simple matter to assess the effect of the new 

embrittlement shift model on the TWCF values reported in this report. 

4.5.3 Chemical Composition Resampling for Welds 

In welds, a gradient of properties through the thickness of the RPV is expected to exist because 

of through-wall changes in copper content. These copper content changes arise from the fact 

that, because of the large volume of weld metal needed to fill an RPV weld, oftentimes 

manufacturers used weld wire from multiple weld wire spools to completely fill the groove. Lack 

of control of the process used to copperplate the weld wires (a step taken for corrosion control) 

resulted in wide variability in copper coating thickness from spool to spool, which is manifested 

in measurable variations in copper content through the RPV wall thickness. These copper 

variations produce variations in sensitivity to irradiation embrittlement, and consequent 

variations in resistance to fracture though the vessel wall. 

FAVOR adopts a weld composition gradient model in which the copper content is resampled in 

a through-wall cracking calculation every time the crack passes the 1/4 thickness, the 1/2 

thickness, and the 3/4 thickness locations in the vessel wall. A four-weld layer model was 

developed based on considerations of the volume of weld metal needed to fill an RPV weld(see 

Reference 19) To assess the effect of this model on the TWCF, a sensitivity study was 

performed in which the copper resampling feature in FAVOR was deactivated. Again, the 

sensitivity study included analysis of Beaver Valley and Palisades at two different embrittlement 

levels (see Table 4-7). The results of this study show that turning off the FAVOR 4-weld layer 

model increases the estimated TWCF by a small amount (i.e., a factor of 2.5 on average). 

Table 4-6 Results of Embrittlement Shift Model Sensitivity Study 

Plant EFPYs Base 

FCI 

Sensitivity 

FCI 

FCI 

Ratio 

Base 

TWCF 

Sensitivity 

TWCF 

TWCF 

Ratio 

BV 32 1.56e-7 4.26e-8 0.273 1.40e-9 3.68e-10 0.263 

BV 200 8.48e-6 2.75e-6 0.324 2.80e-7 6.05e-8 0.216 

Pal 32 9.67e-8 2.77e-8 0.286 9.98e-9 1.56e-9 0.156 

Pal 500 5.83e-6 4.68e-6 0.803 1.85e-6 1.36e-6 0.735 

Table 4-7 Results of Chemistry Resampling Sensitivity Study 

Plant EFPYs Base 

FCI 

Sensitivity 

FCI 

FCI 

Ratio 

Base 

TWCF 

Sensitivity 

TWCF 

TWCF 

Ratio 

BV 32 1.56e-7 1.56e-7 1.00 1.40e-9 2.09e-9 1.49 

BV 200 8.48e-6 8.48e-6 1.00 2.80e-7 3.65e-7 1.30 

Pal 32 9.67e-8 9.75e-8 1.01 9.98e-9 5.39e-8 5.40 

Pal 500 5.83e-6 5.83e-6 1.00 1.85e-6 2.99E-6 1.62 

4.5.4 Upper-Shelf Toughness Model 

In FAVOR Version 3.1, upper-shelf fracture toughness values (JIc, J-R) were estimated through 

correlations with CVN energy. These empirical relationships had very low correlation 

coefficients and high scatter, reflecting the different underlying physical processes that control 

4-23
Charpy energy and fracture toughness on the upper shelf. Comments from the peer review 

group (see comment #40, Appendix B to Reference 20) questioned the appropriateness of this 

approach. After reviewing the existing FAVOR model and other available alternatives, the staff 

adopted and implemented a new upper-shelf model in FAVOR Version 04.1 to address this 

concern. This new model does not rely on Charpy correlations in any way and features an 

explicit treatment of the uncertainty in upper-shelf toughness (both the ductile initiation 

toughness as measured by JIc and the resistance to further crack extension as measured by JR). Additionally, the new model links transition toughness and upper-shelf toughness 

properties, a relationship motivated by trends in fracture toughness data and physical 

considerations. The FAVOR Version 03.1 models did not have these features. 

As demonstrated by the results in Table 4-8, the new upper-shelf model does not change the 

TWCF values in any substantive way. On average, the TWCF values estimated using the new 

model are approximately 5 percent lower than the values estimated by the correlative 

approaches used in FAVOR Version 03.1. However, the linkage between transition toughness 

and upper-shelf toughness properties in the new model has eliminated FAVOR predictions of 

physically implausible results (e.g., predicting that flaws in a particular axial weld, such as Axial 

Weld A, of the RPV beltline contribute more to the TWCF than do flaws in another axial weld, 

such as Axial Weld B, even though the toughness of Axial Weld A exceeds that of Axial Weld B. 

Table 4-8 Results of Upper-Shelf Toughness Model Sensitivity Study 

Plant EFPYs 

TWCF with CVNBased Upper-- 

Shelf Model 

(FAVOR 3.1) 

TWCF with 

Toughness-Based 

Upper Shelf Model 

(FAVOR 4.1) 

TWCF Ratio 

(Toughness 

Model / CVN 

Model) 

32 2.39E-11 2.30E-11 0.96 

60 8.39E-11 6.47E-11 0.77 

Ext-Oa 2.44E-09 1.30E-09 0.53 

Oconee 

Ext-Ob 1.82E-08 1.16E-08 0.64 

32 5.31E-10 8.89E-10 1.67 

60 5.30E-09 4.84E-09 0.91 

Ext-Ba 2.68E-08 2.02E-08 0.75 

Beaver 

Valley 

Ext-Bb 4.06E-07 3.00E-07 0.74 

32 6.20E-09 4.90E-09 0.79 

60 1.51E-08 1.55E-08 1.03 

Ext-Pa 1.42E-07 1.88E-07 1.32 

Palisades 

Ext-Pb 1.14E-06 1.26E-06 1.11 

Average 0.94 

4-24
5. SENSITIVITY STUDIES PERFORMED TO PROVIDE CONFIDENCE IN 

THE APPLICABILITY OF TWCF RESULTS TO PWRS IN GENERAL 

The NRC performed the following sensitivity studies to assess the applicability of the baseline 

TWCF results to PWRs in general: 

 a sensitivity study assessing the method used to simulate increased levels of 

embrittlement 

 a sensitivity study assessing the applicability of the baseline results on plate welded 

vessels to predict the TWCF of forged vessels 

 the effect of vessel thickness on TWCF 

The following sections summarize the motivation for and results of these sensitivity studies. 

5.1 Simulating Increased Levels of Embrittlement

Use of more realistic models and input values than those used in the calculations that provide 

the technical basis for the current PTS rule produces a considerable reduction in the estimated 

values of TWCF. As detailed in 20, at 60 EFPYs (an operational lifetime beyond that 

anticipated after a single license extension), the TWCF values estimates for the three study 

plants lie between 10-11 and 10-8 events/year. However, the through-wall cracking frequency 

limit consistent with RG 1.174 is 10-6 events/year. Consequently, to develop referencetemperature-based screening limits, it was necessary to increase the level of embrittlement of 

the vessels for the three study plants so that the estimated TWCF values would approach the 

10-6 events/year limit. In the baseline calculations reported in 20, embrittlement was artificially 

increased by increasing EFPY (increasing time) and by extrapolating fluence in linear proportion 

to time. An alternative procedure for artificially increasing embrittlement would be to allow the 

temporal and irradiation exposure parameters to remain within realistic ranges and instead 

increase the unirradiated transition temperature (the RTNDT(u)) of the beltline materials. To 

determine what effect these two procedures have on the estimated TWCF values, the NRC 

performed sensitivity studies using the Beaver Valley and Palisades plants. In these sensitivity 

studies, the 32 EFPY analyses reported in 20 were treated as a baseline above which 

embrittlement was increased. Relative to this baseline, each EFPY/time increase can be 

expressed as an increase in the reference temperature by subtracting the reference 

temperature associated with 32 EFPY from the reference temperature associated with a 

particular EFPY/time increment. In this sensitivity study, the NRC compared the TWCF 

increases produced by these EFPY/time-driven reference temperature increases with TWCF 

increases driven by simply increasing the RTNDT(u) of the beltline materials by different fixed 

amounts. Figure 5-1 shows the result of this analysis, which demonstrates that the EFPY/time 

method of artificially increasing embrittlement results in TWCF estimates that exceed those 

produced by the alternative method of increasing RTNDT(u). 

It must be emphasized that both of these procedures (as well as any other alternative 

procedure) extrapolate outside of the empirical bounds of the database used to establish the 

embrittlement shift model. The staff selected the EFPY/time extrapolation method over the 

RTNDT(u) extrapolation method for the baseline calculations reported in 20 because the 

embrittlement shift model includes explicitly both time and irradiation exposure variables. 

During the development of this model, the staff considered the known physical bases for 

5-1
time/exposure trends, and incorporated this knowledge into the functional form of the model 

[17]. Thus, there is some reason to expect that time and irradiation exposure variables will 

extrapolate better than the fracture toughness before irradiation begins (as quantified by 

RTNDT(u)), which was not considered in the development of the embrittlement shift model. 

0

100

200

300

0 50 100

Increase in Reference Temperature 

from 32 EFPY Analysis [o

F]

Ratio of TWCF to 32 EFPY Analy

s

TWCF Ratio, Beaver, EFPY Increase

TWCF Ratio, Palisades, EFPY Increase

TWCF Ratio, Beaver, RTNDT(u) Increase

TWCF Ratio, Palisades, RTNDT(u) Increase

Figure 5-1 Effect of different methods to artificially increase embrittlement on the 

predicted TWCF values 

5.2 Applicability to Forged Vessels

All three of the study vessels are fabricated by welding together plates that are roll-formed to 

make either 120 or 180 segments. However, 21 of the operating PWRs have beltline regions 

made of ring forgings. As such, these vessels have no axial welds. The lack of the large axially 

oriented axial weld flaws in such vessels indicates that they should, in general, have much lower 

values of TWCF than a comparable plate vessel of equivalent embrittlement. However, forgings 

have a population of embedded flaws that is particular in density and size to their method of 

manufacture. Additionally, under certain conditions, forgings are subject to subclad cracking 

associated with the deposition of the austenitic stainless steel cladding layer. Thus, to 

investigate the applicability of the baseline results reported in 20 to forged vessels, the NRC 

performed a number of analyses on vessels using properties (e.g., RTNDT(u), Cu, Ni, P) and flaw 

populations appropriate to forgings. 

Appendix B details the technical basis for the distributions of flaws used in these sensitivity 

studies. The distribution of embedded forging flaws is based on destructive examination of an 

RPV forging [37]. These flaws are similar in both size and in density to plate flaws. The 

distribution of subclad cracks is based on a review of the literature on subclad flaws, particularly 

a summary article by Dhooge [8]. Subclad cracks occur as dense arrays of shallow cracks 

extending into the vessel wall from the clad-to-base metal interface to depths limited by the 

heat-affected zone (approximately 2 mm). These cracks are oriented normally to the direction 

5-2
of welding for clad deposition, producing axially oriented cracks in the vessel beltline. They are 

clustered where the passes of strip clad contact each other. Subclad flaws are much more 

likely to occur in particular grades of pressure vessel steels that have chemical compositions 

that enhance the likelihood of cracking. Forging grades such as A508 are more susceptible 

than plate materials such as A533. High levels of heat input during the cladding process also 

enhance the likelihood of subclad cracking. 

5.2.1 Embedded Forging Flaw Sensitivity Study 

The NRC used the following three steps to construct this sensitivity study: 

(1) Two sets of forging properties were selected—those of the Sequoyah 1 and Watts Bar 1 

RPVs [31]. These properties were selected because they are among the most 

irradiation sensitive of all the forging materials in RVID. 

(2) Two hypothetical models of forged vessels were constructed based on the existing 

models of the Beaver Valley and Palisades vessels. In each case, the hypothetical 

forged vessels were constructed by removing the axial welds and combining these 

regions with the surrounding plates to make “forgings.” These forgings were assigned 

the material properties from Step 1. 

 

(3) A FAVOR analysis of each vessel/forging combination from Steps 1 and 2 was 

conducted at two embrittlement levels, 32 EFPY and Ext-B. Thus, a total of 23

 = 8 

FAVOR analyses were performed (2 material property definitions x 2 vessel definitions x 

2 embrittlement levels). 

On average, the TWCF of the forging vessels was only 3 percent of the plate welded vessels, 

and at most it was 15 percent. These reductions are consistent with those expected when the 

large axial weld flaws are removed from the analysis. 

5.2.2 Subclad Crack Sensitivity Study 

The NRC used the following three steps to construct this sensitivity study: 

(1) One set of forging properties was selected—that of the Sequoyah 1 [31]. 

. 

(2) One hypothetical model of a forged vessel was constructed based on the existing model 

of the Beaver Valley. The hypothetical forged vessel was constructed by removing the 

axial welds and combining these regions with the surrounding plates to make a forging. 

This forging was assigned the properties from Step 1. 

(3) A FAVOR analysis of each vessel/forging combination from Steps 1 and 2 was 

conducted at three embrittlement levels, 32 EFPY, 60 EFPY, and Ext-B. Thus, a total of 

3 FAVOR analyses was performed (1 material property definition x 1 vessel definition x 

3 embrittlement levels). 

At 32 and 60 EFPY, the TWCF of the forging vessels was approximately 0.2 percent and 18 

percent of the plate welded vessels. However, at the much higher embrittlement level 

represented by the Ext-B condition, the forging vessels had TWCF values 10 times higher than 

that characteristic of plate welded vessels at an equivalent level of embrittlement. While these 

very high embrittlement levels are unlikely to be approached in the foreseeable future, these 

5-3
5-4

results indicate that a more detailed assessment of vessel failure probabilities associated with 

subclad cracks would be warranted should a subclad-cracking-prone forging be subjected to 

very high embrittlement levels in the future. 

Table 5-1 Results of Forging Flaw Sensitivity Study 

Baseline 

Plate 

Welded 

Plant 

Forging 

Property 

Set 

EFPYs Base FCI Sensitivity 

FCI 

FCI 

ratio 

Base 

TWCF 

Sensitivity 

TWCF 

TWCF 

ratio 

1 32 9.67e-8 4.24e-9 0.04 9.98e-9 3.68e-12 0.004 

2 32 9.67e-8 2.08e-8 0.22 9.98e-9 2.31e-12 0.000 

1 Ext-b 5.80e-6 3.67e-6 0.06 2.10e-6 7.02e-8 0.03 Palisades 

2 Ext-b 5.80e-6 6.76e-7 0.12 2.10e-6 9.93e-9 0.005 

1 32 1.56e-7 1.76e-8 0.11 1.40e-9 1.94e-11 0.014 

2 32 1.56e-7 5.67e-9 0.04 1.40e-9 3.91e-12 0.003 

1 Ext-Bb 9.00e-6 2.44e-6 0.27 3.81e-7 5.86e-8 0.15 

Beaver 

Valley 

2 Ext-Bb 9.00e-6 4.59e-7 0.05 3.81e-7 7.98e-9 0.021 

Forging Property Set 1: Cu = 0.13%; Ni = 0.76%; P = 0.020%; RTNDT(u) = 73 F;USE = 72 ft-lbs (Sequoyah) 

Forging Property Set 2: Cu = 0.17%’ Ni = 0.80%; P = 0.012%; RTNDT(u) = 47 F;USE = 50 ft-lbs (Watts Bar) 

Table 5-2 Results of Subclad Crack Sensitivity Study 

EFPYs Base FCI 

Forging 

subclad 

flaws 

FCI 

FCI ratio 

subclad 

/base 

Base 

TWCF 

Forging 

subclad 

flaws 

TWCF 

TWCF 

ratio 

subclad 

/base 

32 1.56e-7 1.60e-8 0.10 1.40e-9 2.57e-12 0.0018 

60 5.66e-7 9.60e-8 0.17 6.15e-9 1.09e-9 0.18 

Ext-Bb 9.00e-6 1.31e-5 1.46 3.81e-7 3.95e-6 10.37 

The baseline for all analyses was Beaver Valley as reported by [EricksonKirk 04b]. The 

sensitivity analyses are based on forging property set 1, as defined in Table 5-1 

5.3 Effect of RPV Wall Thickness on TWCF

20 noted in the FAVOR results for primary-side pipe breaks a potential effect of vessel wall 

thickness on the conditional probability of through-wall cracking. This effect can be expected for 

the following reasons: 

 The magnitude of thermal stress scales in proportion to the thickness, with thicker 

vessels generating higher levels of thermal stress. Figure 5-2 shows the effect of this 

increased thermal stress on the applied driving force to fracture associated with a largediameter pipe break. This effect will tend to increase the probability of through-wall 

cracking for thicker vessels. 

 Because thicker vessels will have a larger volume of plate material and a larger weld 

fusion line area they will also have a larger number of flaws. This effect will also tend to 

increase the probability of through-wall cracking for thicker vessels. 

 There is more distance in a thicker vessel over which an initiated crack can arrest, 

thereby not failing the vessel. Also, thicker vessels would tend to have more weld layers 

with different copper contents. This effect will tend to reduce the probability of throughwall cracking for thicker vessels. 
To investigate the effect of these first two factors (the third could not be investigated without 

modifying the structure of the FAVOR code), the NRC increased the thickness of the Beaver 

Valley vessel from 7 7/8 in. (its actual thickness) in five increments up to 11 in. (characteristic of 

the thickest PWRs in service; see Figure 5-3). For each of these five thicker versions of Beaver 

Valley, the NRC used FAVOR to estimate the CPTWC of the following four transients (all of 

which are dominant contributors to the TWCF of Beaver Valley): 

 BV9—16-in. diameter hot-leg break 

 BV56—4-in. diameter surge line break 

 BV126—stuck-open safety relief valve that recloses after 100 minutes resulting in 

repressurization of the primary system 

 BV102—main steamline break 

Figure 5-4 shows that increasing the vessel wall thickness increases the CPTWC for all four 

transients. Recalling that these CPTWC values would be weighted by their initiating event 

frequencies (and those of other transients) to obtain a TWCF estimate, these results suggest 

that, through a wall thickness of 9.5 in. (thicker than all but three of the in-service PWRs), the 

integrated effect of wall thickness on TWCF should be modest (i.e., a factor of approximately 3 

increase at most) relative to the analyses of the three study plants (one 7 7/8-in. thick vessel 

and two 8.5-in. thick vessels). For vessels of greater wall thicknesses, a plant-specific analysis 

is warranted to properly capture all aspects of increased vessel wall thickness on TWCF. 

However, given that the three plants of 11 in. and greater thickness are Palo Verde Units 1, 2, 

and 3, and that these vessels have very low embrittlement projected at either EOL or end of 

license extension, the practical need for such plant-specific analysis is mitigated. It can also be 

noted that use of the baseline TWCF results from the three study plants will overestimate the 

TWCF of the seven thinner operating PWRs (7 in. thick or less). 

Beaver Valley transient 9 

transient time (minutes) 

0 50 100 150 200 250 300

applied KI (ksi in1/2) 

0

10

20

30

40

50

60

70

80

base (t = 8.036") 

v3 (t = 9.156")

v5 (t = 11.156") 

Figure 5-2 Effect of vessel wall thickness on the variation of applied-KI vs. time for a 16-

in. diameter hot-leg break in Beaver Valley. The flaw has the following dimensions: 

L=0.35 in., 2a=0.50 in, 2c=1.5 in. 

5-5
5-6

0

5

10

15

20

25

30

6.57.07.58.08.59.09.5

10.010.511.011.5

Vessel Wall Thickness [in]

Number of PWR

s

Figure 5-3 Distribution of RPV wall thicknesses for PWRs currently in service [31] 

0

10

20

30

40

50

7 8 9 10 11 12

Vessel Wall Thickness [in]

TWCF / TWCF for 7-7/8-in. Thi

c

Beaver Valley Vessel at 60 EF

P

BV9 - 16" Hot Leg Break

BV56 - 4" Surge Line Break

BV102 - MSLB

BV126 - Stuck open SRV, re-closes after 100 minutes

Figure 5-4 Effect of vessel wall thickness on the TWCF of various transients in Beaver 

Valley (all analyses at 60 EFPYs) 
6. SUMMARY AND RECOMMENDATIONS 

This report documents sensitivity studies performed on the FAVOR PFM model (and on PFMrelated variables) with two goals in mind: 

 To provide confidence in the robustness of the PFM model, the NRC has assessed the 

effect of the following credible model and input perturbations on TWCF estimates: 

 

— residual stresses assumed to exist in the RPV wall 

— embrittlement shift model 

— resampling of chemical composition variables at the 1/4 T, 1/2 T, and 3/4 T 

locations for welds 

— upper-shelf toughness model 

 To provide confidence that the results of the calculations for three specific plants can be 

generalized to apply to all PWRs, the NRC performed the following sensitivity studies to 

assess the influence of factors not fully considered in the baseline TWCF estimates: 

 — method for simulating increased levels of embrittlement 

— assessment of the applicability of these results to forged vessels 

— effect of vessel thickness 

In the former category, all effects were negligible or small. The small effects included the 

adoption of an embrittlement shift model that differs from that in 3 (which increases TWCF by 

approximately a factor of 3). In addition, the NRC model accounts for distinctly different copper 

contents in different weld layers (which reduces TWCF by approximately a factor of 2.5 relative 

to the assumption that the mean value of copper does not vary through the vessel thickness). 

Neither of these effects is significant enough to warrant a change to the baseline model or to 

recommend a caution regarding its robustness. 

Sensitivity studies in the latter category suggest the following minor cautions regarding the 

applicability of the baseline results for the three study plants reported in 20 to PWRs in general: 

 In general, the TWCF of forged PWRs can be assessed using the baseline results (see 

NUREG-1806 [20]) by ignoring the TWCF contribution of axial welds. However, should 

changes in future operating conditions result in a forged vessel being subjected to very 

high levels of embrittlement, a plant-specific analysis to assess the effect of subclad 

flaws on TWCF would be warranted. 

 For PWR vessels ranging in thickness from 7.5 in. to 9.5 in., the baseline TWCF results 

are realistic. The baseline results overestimate the TWCF of the seven thinner vessels 

(i.e., wall thicknesses below 7 in.) and underestimate the TWCF of Palo Verde Units 1, 

2, and 3, all of which have wall thicknesses above 11 in. However, these thicker vessels 

have very low embrittlement projected at either EOL or end of license extension, 

suggesting little practical effect of this underestimation. 

6-1
6-2
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46. Wallin, K., “The Scatter in KIc Results,” Engineering Fracture Mechanics, Vol. 19, No. 6, 

pp. 1085–1093, 1984. 

47. Wallin, K., “The Size Effect in KIc Results,” Engineering Fracture Mechanics, Vol. 22, pp. 

149–163, 1985. 

7-4
48. Wallin, K., “Statistical Modeling of Fracture in the Ductile to Brittle Transition Region,” 

Defect Assessment in Components— Fundamentals and Applications,” ESIS/EGF9, 

J.G. Blauel and K.H. Schwalbe, eds., pp. 415–445, 1991. 

49. Wallin, K., “Irradiation Damage Effects on the Fracture Toughness Transition Curve 

Shape for Reactor Vessel Steels,” Int. J. Pres. Ves. & Piping, Vol. 55, pp. 61–79, 1993. 

 

50. Wallin, K., “Statistical Aspects of Constraint with Emphasis on Testing and Analysis of 

Laboratory Specimens in the Transition Region,” Constraint Effects in Fracture, ASTM 

STP-1171, E.M. Hackett, K.H. Schwalbe, and R.H. Dodds, eds., American Society for 

Testing and Materials, 1993. 

51. Wallin, K., “Loading Rate Effect on the Master Curve To,” Paper IIW- X-1403-97, 1997. 

52. Wallin, K., “Master Curve Analysis of Ductile to Brittle Region Fracture Toughness 

Round Robin Data: The ‘EURO’ Fracture Toughness Curve,” VTT Manufacturing 

Technology, VTT Publication 367, 1998. 

53. Wallin, K., and R. Rintamaa, “Master Curve Based Correlation Between Static Initiation 

Toughness KIc and Crack Arrest Toughness KIa,” Proceedings of the 24th MPA-Seminar, 

October 8 and 9, 1998, Stuttgart. 

54. Wallin, K., “Low-cost J-R curve estimation based on CVN upper shelf energy,” Fatigue 

and Fracture of Engineering Materials and Structures, Vol. 24, pp. 537–549, 2001. 

55. Whitehead, D.W., et al., “Generalization of Plant-Specific Pressurized Thermal Shock 

(PTS) Risk Results to Additional Plants,” ADAMS Accession No. ML042880476. 

56. Williams, P.T. and T.L. Dickson, “Fracture Analysis of Vessels—Oak Ridge, FAVOR 

v04.1, Computer Code: Theory and Implementation of Algorithms, Methods, and 

Correlations,” NUREG/CR-6854. 

57. Woods, R., et al., “Selection of Pressurized Thermal Shock Transients to Include in PTS 

Risk Analysis,” IJPVP, Vol. 78, pp. 179–183, 2001. 

7-5
7-6
APPENDIX A 

FLAW DISTRIBUTION CORRESPONDENCE 

The report authored by F.A. Simonen, S.R. Doctor, G.J. Schuster, and P.G. Heasler entitled, “A 

Generalized Procedure for Generating Flaw Related Inputs for the FAVOR Code,” also known 

as NUREG/CR-6817, Revision 1, published in October 2003, details the flaw distribution 

adopted in FAVOR and used in this investigation (Simonen 10-03). 

This appendix includes the text of a letter sent to the primary author of this report, Dr. Fredric 

Simonen, and Dr. Simonen’s reply. The letter clarifies Dr. Simonen’s views regarding the extent 

to which the flaw distributions reported in NUREG/CR-6817, Revision 1, apply to operating 

PWRs in general. 

Text of Letter Sent to Dr. Simonen 

30th June 2004 

MEMORANDUM 

From: Mark EricksonKirk (mtk@nrc.gov) 

To: Fred Simonen (fredric.simonen@pnl.gov) 

cc: Debbie Jackson 

Allen Hiser 

Subj: NUREG/CR-6817, Rev. 1, “A Generalized Procedure for Generating Flaw-Related 

Inputs for the FAVOR Code,” by F. A. Simonen, et al. 

Motivated by comments received from both the external peer review panel we convened for the 

PTS project and from some members of the industry I have recently re-read the subject 

NUREG/CR report. For the PTS re-evaluation effort it is important to know to what extent the 

flaw distributions reported in NUREG/CR-6817, Rev. 1 apply to operating PWRs in general. 

Neither the executive summary nor the conclusions of this report (which I have attached for your 

reference) speak to this issue. However, I did find the following statements in the body of the 

report that speak to the question of the general applicability of the flaw distribution: 

On p. 5.9 (emphasis added): 

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. 

A-1
On p. 6-2 (emphasis added) 

Use of Data Versus Models and Expert Elicitation - In developing flaw distributions, 

measured data were used to the maximum extent possible. The PRODIGAL flaw simulation 

model and results of the expert judgment elicitation were used only when the data were 

inadequate. In the case of seam welds, there was a relatively large amount of data, and the 

PRODIGAL model and expert elicitation were not used to quantify estimates of flaw 

densities and sizes. The PRODIGAL model did, however, suggest the normalization of flaw 

dimension by the dimensions of weld beads and the separation of data into subsets 

corresponding to small and large flaws (as defined by flaw depth dimensions relative to the 

weld bead dimensions). In addition, the expert elicitation and the PRODIGAL model 

helped to justify the application of data from the PVRUF and Shoreham vessels to the 

larger population of vessels at U.S. nuclear plants. 

The NUREG/CR also includes the following statement: 

On p. 6-3 (emphasis added) 

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. 

The statements from p. 5-9 and 6-2 suggest that the view that the flaw distributions proposed in 

NUREG/CR-6817, Rev. 1 apply to operating PWRs in general. Conversely, the statement 

made on p. 6-3 seems to suggest that you and your co-authors view the flaw distributions as 

being conservative. 

To help me respond to questions I have received regarding use of the flaw distributions 

presented in the NUREG/CR in the PTS re-evaluation project it would be most helpful to me if 

you could respond to the following question: 

What is the view of you and your co-authors? Do you view the flaw distributions published 

in NUREG/CR-6817, Rev. 1 as being applicable to PWRs in general, or do you view them 

as being a conservative representation of the flaw population in the fleet of operating PWRs. 

I greatly appreciate your assistance with this matter. 

A-2
Reply Received from Dr. Simonen 

>>> "Simonen, Fredric A" <fredric.simonen@pnl.gov> 07/01/04 02:23PM >>> 

Mark: 

This is my response to the questions that you posed to me in the attached memo (June 30, 

2004): 

What is the view of you and your co-authors? Do you view the flaw distributions published in 

NUREG/CR-6817, Rev. 1 as being applicable to PWRs in general, or do you view them as 

being a conservative representation of the flaw population in the fleet of operating PWRs? 

Your June 30, 2004 memo accurately reflects my views and those of my co-authors regarding 

the applicability of the flaw distributions in NUREG/CR-6817, Rev1 to PWRs in general as well 

as the conservative nature of the distributions. 

In developing the flaw distribution methodology we were guided by Lee Abramson (statistician 

from NRC staff) in dealing with uncertainties. Because the PNNL flaw data were primarily from 

two vessels (PVRUF and Shoreham) a rigorous statistical treatment of vessel-to-vessel 

differences was not possible. The flaw model was therefore developed with separate 

treatments for the two vessels, along with a recommendation to use the more conservative 

treatment based on the Shoreham vessel when addressing other vessels. Other conservatisms 

can be introduced as appropriate in application of the flaw model to address uncertainties in 

knowledge regarding of a specific vessel. One example of such uncertainties would be the 

amount of repair welding in a particular vessel. 

Fredric A. Simonen 

Laboratory Fellow 

Pacific Northwest National Laboratory 

P.O. Box 999 

2400 Stevens Drive 

Richland, Washington 99352 USA 

phone 509-375-2087 

fax 509-375-6497 

email fredric.simonen@pnl.gov 

 <<d jackson memo 30 jun 04.doc>> 

A-3
A-4
APPENDIX B 

FLAW DISTRIBUTIONS FOR FORGINGS 

This appendix includes two articles prepared by Dr. Frederic Simonen of the Pacific Northwest 

National Laboratory concerning flaw distributions in forgings. The staff used these articles as 

the basis of the forging flaw sensitivity studies reported in Section 5.2. 

Technical Basis for the Input Files to FAVOR Code 

for Flaws in Vessel Forgings 

F.A. Simonen 

Pacific Northwest National Laboratory 

Richland, Washington 

July 28, 2004 

Pacific Northwest National Laboratory (PNNL) has been funded by the U.S. Nuclear Regulatory 

Commission (NRC) to generate data on fabrication flaws that exist in reactor pressure vessels 

(RPV). Work has focused on flaws in welds but with some attention also to flaws in the base 

metal regions. Data from vessel examinations along with insights from an expert judgment 

elicitation (MEB-00-01) and from applications of the PRODIGAL flaw simulation model 

(NUREG/CR-5505, Chapman et. al. 1998) have been used to generate input files (see report 

NUREG/CR-6817, Simonen et. al. 2003) for probabilistic fracture mechanics calculations 

performed with the FAVOR code by Oak Ridge National Laboratory. NUREG/CR-6817 

addresses only flaws in plate materials and provided no guidance for estimating the numbers 

and sizes of flaws in forging materials. More recent studies have examined forging material, 

which has provided a data on flaws that were detected and sized in the examined material. At 

the request of NRC staff PNNL has used these more recent data to supplement insights from 

the expert judgment elicitation to generate FAVOR code input files for forging flaws. The 

discussion below describes the technical basis and results for the forging flaw model. 

Nature of Base Metal Flaws 

PNNL examined material from some forging material from a Midland vessel as described by 

Schuster (2002). The forging was made during 1969 by Ladish. Examined material included 

only part of the forging that had been removed from the top of the forged ring as scrap not 

intended for the vessel. This material was expected to have more than the average flaw 

density, and as such may contribute to the conservatism of any derived flaw distribution. 

Figures 1 and 2 show micrographs of small flaws in plate and forging materials. These flaws are 

inclusions rather than porosity or voids. They are also not are planer cracks. Therefore their 

categorization as simple planar or as volumetric flaws is subject to judgment. The plate flaw of 

Figure 1 has many sharp and crack-like features, whereas such features are not readily 

identified for the particular forging flaw seen in Figure 2. It should, however, be emphasized 

B-1
that the PNNL examined only a limited volume of both plate and forging material and found very 

few flaws in examined material. It is not possible to generalize from such a small sample of 

flaws. Accordingly, the flaw model makes assumptions that may be somewhat conservative, 

due to the limited data on the flaw characteristics. 

Flaw Model for Forging Flaws 

The model for generating distributions of forging flaws for the FAVOR code uses the same 

approach as that for modeling plate flaws as described in NUREG/CR-6817. The quantitative 

results of the expert elicitation are used along with available data from observed forging flaws. 

The flaw data were used as a "sanity check" on the results of the expert elicitation. Figure 3 

summarizes results of the expert elicitation. Each expert was asked to estimate ratios between 

flaw densities in base metal compared to the corresponding flaw densities observed in the weld 

metal of the PVRUF vessel. Separate ratios were requested for plate material and forging 

material. 

As indicated in Figure 3, the parameters for forging flaws are similar to those for plate flaws. 

The forging and plate models used the same factor of 0.1 for the density of “small” flaws (flaws 

with through-wall dimensions less than the weld bead size of the PVRUF vessel). The density 

of “large” flaws in forging material is somewhat greater than the density of flaws in plate 

material. The factor of 0.025 for the flaw density is replaced by a factor of 0.07 for forging flaws. 

A truncation level of 0.11 mm is used for both plate and forging flaws. As described in the next 

section the data from forging examinations show that these factors are consistent with the 

available data. It is noted that the assumption for the 0.07 factor is supported by only a single 

data point corresponding to the largest observed forging flaw (with a depth dimension of 4 mm). 

The factors of 0.1 and 0.07 came from the recommendations from the expert elicitation on 

vessel flaws. As noted below the very limited data from PNNL's examinations of forging 

material show that these factors are consistent with the data, although the 0.07 factor is 

supported by only one data point for an observed forging flaw with a 4-mm depth dimension. 

Comparison with Data on Observed Flaws 

The PNNL examinations of vessel materials included both plate materials and forging materials. 

For plate flaws less than 4-mm in through-wall depth dimension, Figure 4 shows data from 

NUREG/CR-6817 that shows frequencies for plate flaws. Also shown for comparison are the 

flaw frequencies for the welds of the PVRUF and Shoreham vessels. This plot confirmed 

results of the expert judgment elicitation (Figure 4) and indicated: 1) there are fewer flaws in 

plate material than in weld material, and 2) there is about a 10:1 difference in flaw frequencies 

for plates versus welds. 

PNNL generated the data on flaws in forgings after preparation of NUREG/CR-6817. Forging 

data are presented in Figures 5 and 6 along with the previous data for flaws in the PVRUF plate 

material. There is qualitative agreement with the results of the expert judgment elicitation 

(Figure 4), which indicates that 1) plate and forging materials have similar frequencies for small 

(2 mm) flaws, and 2) forging material have higher flaw frequencies for larger (>4 mm) flaws. 

Inputs for FAVOR Code 

Figure 7 compares the flaw frequencies for plates and forgings that were provided to ORNL as 

input files for the FAVOR code. This plot shows mean frequencies from an uncertainty 

distribution as described by the flaw input files. It is seen that the curves for plate and forging 

flaws are identical for small flaws but show differences for the flaws larger than 3 percent of the 

B-2
vessel wall thickness. Also seen is the effect of truncating the flaw distribution at a depth of 11 

mm (about 5 percent of the wall thickness). 

References

Jackson, D.A. 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 Vessel, MED-00-01, PRAB-00-01,U.S. 

Nuclear Regulatory Commission. 

Schuster, G.J., 2002. “Technical Letter Report – JCN-Y6604 – Validated Flaw Density and 

Distribution Within Reactor Pressure Vessel Base Metal Forged Rings,” prepared by Pacific 

Northwest National Laboratory for U.S. Nuclear Regulatory Commission, December 20, 2002. 

Simonen, F.A., S.R. Doctor, G.J. Schuster and P.G. Heasler, 2003. A Generalized Procedure 

for Generating Flaw-Related Inputs for the FAVOR Code, NUREG/CR-6817, Rev. 1, prepared 

by Pacific Northwest National Laboratory for U.S. Nuclear Regulatory Commission. 

Figure 1 Small Flaw in Plate Material 

Figure 2 Small Flaw in Forging Material 

B-3
Figure 3 Relative Flaw Densities of Base Metal Compared to Weld Metal as Estimated by 

Expert Judgment Process (from Jackson and Abramson 2000) 

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 4 Flaw Frequencies for Plate Materials with Comparisons to Data for Weld Flaws 

B-4
1.E+02

1.E+03

1.E+04

01234

Through-wall size (mm)

Cumulative Density 

 (per cubic meter) 

5

PVRUF plate 109-1,2,5 109-1,2

Figure 5 Validated Flaw Density and Size Distribution for Three Forging Specimens. 

Cumulative flaw density is the number of flaws per cubic meter of equal or 

greater size. 

1.E+02

1.E+03

1.E+04

012345

Through-wall size (mm)

Cumulative Density 

(per cubic meter)

6

PVRUF plate 109-5 109-1 109-2

Figure 6 Average of Validated Cumulative Flaw Density for Forging Material, A508 

B-5
1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

0123456

Flaw Depth Dimension, Percent of Wall

Flaws per Cubic Foot

Forging

Plate

Figure 7 Comparison of Flaw Distributions for Forging and Plate 

Basis for Assigning Subclad Flaw Distributions 

F.A. Simonen 

Pacific Northwest National Laboratory 

Richland, Washington 

September 29, 2004 

Pacific Northwest National Laboratory (PNNL) has supported the U.S. Nuclear Regulatory 

Commission (USNRC) in the efforts to revise the Pressurized Thermal Shock (PTS) Rule. In 

this role PNNL has provided Oak Ridge National Laboratory (ORNL) with inputs to describe the 

distributions of fabrication flaws in reactor pressure vessels. These inputs, consisting of 

computer files, have been a key input to the probabilistic fracture mechanics code FAVOR. 

Flaw inputs have addressed seam welds, cladding and base metal materials, but had 

specifically excluded subclad flaws associated with the heat affected zone (HAZ) from the 

process that deposits stainless steel cladding to the inner surface of the vessel. Recently ORNL 

was requested by USNRS to evaluate the potential contribution of these subclad flaws to 

reactor pressure vessel failure for PTS conditions. The present paper describes the technical 

basis for the subclad flaw input files that PNNL provided to ORNL for use with the FAVOR code. 

B-6
PNNL has examined material from vessels welds, basemetal and cladding and has used the 

data on observed flaws in these material types to establish statistical distributions for the 

numbers and sizes of flaws in these categories of materials. None of the examined material 

showed any evidence of the type of subclad flaws of interest. Therefore, the numbers and sizes 

of sub clad flaws for a vessel susceptible to such cracking was estimating from a review of the 

literature. The primary source was a comprehensive paper summarizing European work from 

the 1970's (A. Dhooge, R.E. Dolby, J. Sebille, R. Steinmetz ad A.G. Vinckier, "A Review of Work 

Related to Reheat Cracking in Nuclear Reactor Pressure Vessel Steels", International Journal of 

Pressure Vessels and Piping, Vol. 6, 1978, pp.329-409). This paper was based on experience 

with vessel cracking in Europe and subsequent research programs conducted during the 

1970's. The paper should therefore be relevant to US concerns with older vessels that may 

have been fabricated with European practices. 

The literature shows that subclad cracks 1) are shallow flaws extending into the vessel wall from 

the clad-to-basemetal interface with 4-mm being cited as a bounding through-wall depth 

dimension, 2) have orientations normal to the direction of welding for clad deposition - giving 

axial cracks in a vessel beltline, 3) occur as dense arrays of small cracks extending into the 

vessel wall from the clad to basemetal interface, 4) extend to depths limited by the heat affected 

zone. Pictures in the cited paper show networks of cracks with typical depths estimated from 

micrograph being significantly less than the bounding 4-mm depth. The cracks occur 

perpendicular to the direction of welding and are clustered where the passes of strip clad 

contact each other. Subclad flaws are much more likely to occur in particular grades of 

pressure vessel steels that have chemical compositions that enhance the likelihood of cracking. 

Forging grades such as A508 Class 2 are more susceptible than both A507 Class 3 forgings 

and plate materials such as A533B. High levels of heat input during the cladding process also 

enhance the likelihood of subclad cracking. In addition other details of the cladding process are 

important such as single layer versus two layer cladding. 

The numbers of cracks per unit area of vessel inner surface were estimated from Figure 1 of the 

Dhooge paper. Cracking was shown to occur in bands estimated to have a width of 4 mm. This 

dimension was used to estimate a bounding length of subclad cracks. The longest individual 

cracks in Figure 1 were about 2-mm versus the 4-mm width dimension of the zone of cracking. 

By counting the number of cracks pictured in small region of vessel surface crack density of 

80,512 flaws per square meter was estimated. 

The flaw input files as provide to ORNL were based on the following assumptions: 

1. The crack depth dimensions were described by a uniform statistical distribution from 0 to 

4 mm with no cracks greater than 4 mm in depth. 

2. The crack lengths were also described by a uniform statistical distribution. Like our 

assumption for flaws in seam welds, the amount by which flaw lengths exceed their 

corresponding depth dimension is taken to be a uniform distribution from 0 to 4 mm. 

Thus the extreme length for a flaw with a depth of 4 mm is 8 mm. The 4 mm deep flaws 

can therefore have lengths ranging from 4 to 8 mm (aspect ratios from 1:1 to 2:1). Flaws 

with depths of 1 mm can have lengths ranging from 1 mm to 5 mm (aspect ratios from 

1:1 to 5:1). 

3. The flaw density expressed as flaws per unit area was converted (for purposes of the 

FAVOR code) to flaws per unit volume based on the total volume of the metal in the 

vessel wall. 

B-7
B-8

4. The file prepared for FAVOR assumes that the code simulates flaws for the total vessel 

wall thickness, rather than just the category 1 and 2 regions which address only the 

inner 3/8 of the wall thickness. Terry will need to account for this concern during the 

FAVOR calculations 

The resulting very large number of flaws (> 130,000) per vessel is based on a photograph of 

one small area of a vessel surface, with the implication that this area was representative of the 

entire vessel. It is possible that subclad flaws tend to occur in patches of the vessel surface. 

However it is generally understood that subclad flaws occur in a wide spread manner and that 

there are very large numbers of flaws given the conditions for subclad cracking exist. Based on 

PNNL’s limited review of documents it is difficult to justify reducing the estimated flaw density of 

subclad flaws. However, it would be useful to perform a sensitivity calculation to see if 

refinement of my estimate would have a significant effect on the FAVOR calculations. 

The estimated depths of the subclad flaws is probably conservative. The depth of 4 mm was 

based on statements regarding bounding flaw depths of 4 mm, with no other evidence such as 

micrographs of flaws or data on measured depth dimensions presented. The depth of 4 mm 

could be an estimate for the size of the heat affected zone, which is then taken as a limitation on 

flaw depth. Alternatively the 4 mm depth could be the extreme measured (or reported depth) of 

some observed subclad flaws. A review of available papers showed some examples from 

metallography of subclad flaws, which showed only flaws of much smaller depths (< 2 mm). It is 

therefore suggested that a sensitivity study be based on assumed subclad flaws with a 

bounding depth of 2 mm. In this case the FAVOR code would include only flaws in the "first bin" 

corresponding to sizes 0 to 1% of the vessel wall thickness. 

PNNL’s estimates of subclad flaw distributions have been based on a rather limited review of 

available literature with a particular focus on the Dhooge 1978 paper. It is recommended that 

the scope of the literature review be expanded and that individuals (domestic and overseas) be 

contacted to seek sources of additional information. PNNL will also review notes from past 

sessions with expert elicitation panels that have addressed reactor vessel fabrication and flaw 

distributions for the USNRC. The critical issue is the depth dimensions of typical subclad flaws. 

The depth dimension of 4 mm may be uncharacteristic of most subclad flaws, but rather a 

bounding dimension based on consideration of the depth of heat affected zones. This depth 

has also been used in the literature for deterministic fracture mechanics calculations and could 

therefore reflect the conservative nature of inputs used for such calculations. 
1. REPORT NUMBER 

(Assigned by NRC, Add Vol., Supp., Rev., 

and Addendum Numbers, if any.)

NUREG-1808

3. DATE REPORT PUBLISHED

MONTH YEAR 

2. TITLE AND SUBTITLE 

Sensitivity Studies of the Probabilistic Fracture Mechanics Model Used in FAVOR

4. FIN OR GRANT NUMBER

6. TYPE OF REPORT 

 Technical 

5. AUTHOR(S) 

M.T. EricksonKirk1, T.L. Dickson2, T. Mintz3, F.A. Simonen4

7. PERIOD COVERED (Inclusive Dates)

6-1999 to 6-2006

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor, 

provide name and mailing address.)

1

Division of Fuel, Engineering, and Radiological Research, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission,

Washington, DC 20555-0001, 2Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6075, 3Southwest Research 

Institute, 9503 W Commerce, San Antonio, Texas 78227-1301, 4

Pacific Northwest National Laboratory, P.O. Box 999, 2400 Stevens

NRC FORM 335

(9-2004) 

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION

BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

March 2010

 Drive, Richland, Washington 99352 USA 

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type "Same as above"; if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

and mailing address.)

Division of Fuel, Engineering, and Radiological Research, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 

Washington, DC 20555-0001 

10. SUPPLEMENTARY NOTES

11. ABSTRACT (200 words or less)

During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron radiation, resulting in localized 

embrittlement of the vessel steel and weld materials in the core area. If an embrittled RPV had a flaw of critical size and certain 

severe system transients were to occur, the flaw could very rapidly propagate through the vessel, resulting in a through-wall 

crack and challenging 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 RPV surface in combination with repressurization of the 

RPV. Advancements in our understanding and knowledge of materials behavior, our ability to realistically model plant systems 

and operational characteristics, and our ability to better evaluate PTS transients to estimate loads on vessel walls led the U.S. 

Nuclear Regulatory Commission (NRC) to realize that the earlier analysis, conducted in the course of developing the PTS Rule 

in the 1980s, contained significant conservatisms. 

This report, which describes sensitivity studies performed on the probabilistic fracture mechanics model, is one of a series of

21 other documents detailing the results of the NRC study. 

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

Pressurized thermal shock, reactor pressure vessel, probabilistic fracture mechanics 

13. AVAILABILITY STATEMENT 

unlimited 

14. SECURITY CLASSIFICATION 

(This Page)

unclassified 

(This Report)

unclassified 

15. NUMBER OF PAGES 

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER