NUREG-1874

Recommended Screening 

Limits for Pressurized 

Thermal Shock (PTS) 

Office of Nuclear Regulatory Research 
NUREG-1874 

 

 

Recommended Screening 

Limits for Pressurized 

Thermal Shock (PTS)

Manuscript Completed: March 2007 

Date Published: March 2010 

Prepared by 

M.T. EricksonKirk 1 

T.L. Dickson2 

 

2

Oak Ridge National Laboratory 

Oak Ridge, TN 37831-6170 

 

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 a flaw of critical size and certain severe system transients were to occur, the flaw 

could propagate very rapidly 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) events, 

are characterized by a rapid cooling of the internal RPV surface in combination with repressurization of 

the RPV. Advancements in its understanding and knowledge of materials behavior, its ability to model 

realistically plant systems and operational characteristics, and its ability to better evaluate PTS transients 

to estimate loads on vessel walls led the U.S. Nuclear Regulatory Commission to realize that the analysis 

conducted in the course of developing the PTS Rule in the 1980s contained significant conservatisms. 

This report provides two options for using the updated technical basis described herein to develop PTS 

screening limits. Calculations reported herein show that the risk of through-wall cracking is low in all 

operating pressurized-water reactors, and current PTS regulations include considerable implicit margin. 

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 (RPV) in a nuclear power plant is exposed to neutron radiation during normal 

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

had a preexisting flaw of critical size and certain severe system transients were to occur, this flaw could 

propagate rapidly through the wall of the vessel. The severe transients of concern, known as pressurized 

thermal shock (PTS) events, are characterized by a rapid cooling (i.e., thermal shock) of the internal RPV 

surface that may be combined with repressurization. Advancements in the state of knowledge in the more 

than 20 years since the U.S. Nuclear Regulatory Commission (NRC) promulgated its PTS Rule, (i.e., 

Title 10, Section 50.61, “Fracture Toughness Requirements for Protection against Pressurized Thermal 

Shock Events,” of the Code of Federal Regulations (10 CFR 50.61)) suggest that the embrittlement 

screening limits imposed by 10 CFR 50.61 are overly conservative. Therefore the NRC conducted a study 

to develop the technical basis for revising the PTS Rule in a manner consistent with the NRC’s guidelines 

on risk-informed regulation. In early 2005, the Advisory Committee on Reactor Safeguards (ACRS) 

endorsed the staff’s approach and its proposed technical basis. The staff documented the technical basis 

in an extensive set of reports (Section 4.1 of this report provides a complete list), which were then 

subjected to further internal reviews. Based on these reviews, the staff decided to modify certain aspects 

of the probabilistic calculations to refine and improve the model. This report documents these changes to 

the model and the results of an updated set of probabilistic calculations, which show the following:

 For Plate-Welded Pressurized-Water Reactors (PWRs): Assuming that current operating conditions 

are maintained, the risk of PTS failure of the RPV is very low. Over 80 percent of operating PWRs 

have estimated through-wall cracking frequency (TWCF) values below 1x10-8/ry, even after 60 years 

of operation. After 40 years of operation the highest risk of PTS at any PWR is 2.0x10-7/ry. After 60 

years of operation this risk increases to 4.3x10-7/ry. If the reference temperature screening limits 

proposed herein, which are based on limiting the yearly through wall cracking frequency to below a 

value of 1x10-6, are adopted, and if current operating practices are maintained then no plant will get 

within 30 F of the reference temperature limits within the first 40 years of operation. After 60 years 

of operation, the most embrittled plant will still be 17 F away from the reference temperature limits. 

 For Ring-Forged PWRs: Assuming that current operating conditions are maintained, the risk of PTS 

failure of the RPV is very low. All operating PWRs have estimated TWCF values below 1x10-8/ry, 

even after 60 years of operation. After 40 years of operation the highest risk of PTS at any PWR is 

1.5x10-10/ry. After 60 years of operation this risk increases to 3.0x10-10/ry. If the reference 

temperature screening limits proposed herein, which are based on limiting the yearly through wall 

cracking frequency to below a value of 1x10-6, are adopted, and if current operating practices are 

maintained then no plant will get within 59 F of the reference temperature limits within the first 40 

years of operation. After 60 years of operation, the most embrittled plant will still be 47 F away 

from the reference temperature limits. 

These findings apply to all PWRs currently in operation in the United States. This report describes two 

options by which these findings can be incorporated into a revised version of 10 CFR 50.61. 

 Brian W. Sheron, Director 

 Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

v
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Contents 

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

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

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

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

1 Background and Objective..........................................................................................................1

2 Changes to the PTS Model..........................................................................................................3

2.1 RTNDT Epistemic Uncertainty Data Basis ...................................................................................3

2.1.1 Review Finding .......................................................................................................................3

2.1.2 Model Change .........................................................................................................................3

2.2 FAVOR Sampling Procedures on RTNDT Epistemic Uncertainty...............................................4

2.2.1 Review Finding .......................................................................................................................4

2.2.2 Model Change .........................................................................................................................4

2.3 FAVOR Sampling Procedures on Other Variables.....................................................................4

2.3.1 Review Finding .......................................................................................................................4

2.3.2 Model Change .........................................................................................................................4

2.4 Distribution of Repair Flaws.......................................................................................................4

2.4.1 Review Finding .......................................................................................................................4

2.4.2 Model Change .........................................................................................................................5

2.5 Distribution of Underclad Flaws in Forgings..............................................................................7

2.5.1 Review Finding .......................................................................................................................7

2.5.2 Model Change .........................................................................................................................7

2.6 Embrittlement Trend Curve ........................................................................................................7

2.6.1 Review Finding .......................................................................................................................7

2.6.2 Model Change .........................................................................................................................7

2.7 LOCA Break Frequencies...........................................................................................................7

2.7.1 Review Finding .......................................................................................................................7

2.7.2 Model Change .........................................................................................................................8

2.8 Temperature-Dependent Thermal Elastic Properties ..................................................................8

2.8.1 Review Finding .......................................................................................................................8

2.8.2 Model Change .........................................................................................................................8

2.9 Upper-Shelf Fracture Toughness Model.....................................................................................8

2.9.1 Review Finding .......................................................................................................................8

2.9.2 Model Change .........................................................................................................................8

2.10 Demonstration That the Flaws That Contribute to TWCF are Detectable 

by NDE Performed to ASME SC VIII Supplement 4 Requirements .........................................8

2.10.1 Review Finding...................................................................................................................8

2.10.2 Reply...................................................................................................................................8

3 PTS Screening Limits ...............................................................................................................13

3.1 Overview...................................................................................................................................13

3.2 Use of Plant-Specific Results to Develop Generic RT-Based Screening Limits......................13

3.2.1 Justification of Approach ......................................................................................................13

3.2.2 Use of Reference Temperatures to Correlate TWCF ............................................................15

3.3 Plate-Welded Plants ..................................................................................................................19

3.3.1 FAVOR 06.1 Results ............................................................................................................19

3.3.2 Estimation of TWCF Values and RT-Based Limits for Plate-Welded PWRs ......................25

3.3.3 Modification for Thick-Walled Vessels....................................................................................28

3.4 Ring-Forged Plants ...................................................................................................................28

3.4.1 Embedded Flaw Sensitivity Study ........................................................................................29

vii
3.4.2 Underclad Flaw Sensitivity Study.........................................................................................29

3.4.3 Modification for Thick-Walled Vessels................................................................................31

3.5 Options for Regulatory Implementation of These Results........................................................31

3.5.1 Limitation on TWCF.............................................................................................................32

3.5.2 Limitation on RT...................................................................................................................42

3.6 Need for Margin........................................................................................................................47

3.6.1 Residual Conservatisms ........................................................................................................48

3.6.2 Residual Nonconservatisms ..................................................................................................50

3.7 Summary ...................................................................................................................................52

4 References.................................................................................................................................55

4.1 PTS Technical Basis Citations..................................................................................................55

4.1.1 Summary ...............................................................................................................................55

4.1.2 Probabilistic Risk Assessment ..............................................................................................55

4.1.3 Thermal-Hydraulics ..............................................................................................................55

4.1.4 Probabilistic Fracture Mechanics..........................................................................................56

4.2 Literature Citations ...................................................................................................................58

Appendix A – Changes Requested Between FAVOR Version 05.1 and FAVOR Version 06.1..........A-1 

Appendix B – Review of the Literature on Subclad Flaws and a Technical Basis for Assigning Subclad 

Flaw Distributions..................................................................................B-1 

Appendix C – Sensitivity Study on an Alternative Embrittlement Trend Curve............................C-1 

Appendix D – Technical Basis for the Input Files to the FAVOR Code for Flaws in Vessel Forgings..D-1 

viii
Figures 

Figure 1.1. Structure of documentation summarized by this report and by (EricksonKirk-Sum). 

The citations for these reports in the text appear in italicized boldface to distinguish 

them from literature citations..............................................................................................1 

Figure 2.1. Data on which the RTNDT epistemic uncertainty correction is based..................................3 

Figure 2.2. Distribution of repair flaws in any weld repair cavity ........................................................6 

Figure 2.3. Distribution of weld repair flaws through the vessel wall thickness ..................................6 

Figure 2.4. Flaw dimension and position descriptors adopted in FAVOR ...........................................9 

Figure 2.5. Distribution of through-wall position of cracks that initiate...............................................9 

Figure 2.6. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to (left) medium- and large-diameter pipe break transients and 

(right) stuck-open valve transients at two different embrittlement levels.........................10 

Figure 2.7. Analysis of Palisades transients #65 (repressurization transient) and #62 (largediameter primary-side pipe break transient) to illustrate what combinations of 

flaw size and location lead to non-zero conditional probabilities of crack initiation .......10 

Figure 2.8. Probability of detection curve (Becker 02).......................................................................11

Figure 3.1. TWCF distributions for Beaver Valley Unit 1 estimated for 32 EFPY and for a 

much higher level of embrittlement (Ext-B). At 32 EFPY the height of the “zero” 

bar is 62 percent................................................................................................................20 

Figure 3.2. The percentile of the TWCF distribution corresponding to mean TWCF values at 

various levels of embrittlement.........................................................................................20 

Figure 3.3. Dependence of TWCF due to various transient classes on embrittlement as 

quantified by the parameter RTMAX-AW (curves are hand-drawn to illustrate trends)........23 

Figure 3.4. Relationship between TWCF and RT due to various flaw populations (left: axial 

weld flaws, center: plate flaws, right: circumferential weld flaws). Eq. 3-5 provides 

the mathematical form of the fit curves shown here.........................................................24 

Figure 3.5. Graphical representation of Eqs. 3-5 and 3-6. The TWCF of the surface in both 

diagrams is 1x10-6. The top diagram provides a close-up view of the outermost 

corner shown in the bottom diagram. (These diagrams are provided for visualization 

purposes only; they are not a completely accurate representation of Eqs. 3-5 and 

3-6 particularly in the very steep regions at the edges of the TWCF = 1x10-6 surface.) ..26 

Figure 3.6. Maximum RT-based screening criterion (1E-6 curve) for plate-welded vessels based 

on Eq. 3-6 (left: screening criterion relative to currently operating PWRs after 40 

years of operation; right: screening criterion relative to currently operating PWRs 

after 60 years of operation)...............................................................................................27 

Figure 3.7. Distribution of RPV wall thicknesses for PWRs currently in service (RVID2). This figure 

originally appeared as Figure 9.9 in NUREG-1806.................................................................28 

Figure 3.8. Effect of vessel wall thickness on the TWCF of various transients in Beaver Valley (all 

analyses at 60 EFPY). This figure originally appeared as Figure 9.10 in NUREG-1806............28 

Figure 3.9. Relationship between TWCF and RT for forgings having underclad flaws.....................30 

Figure 3.10. Effect of vessel wall thickness on the TWCF of forgings having underclad flaws 

compared with results for plate-welded vessels (see Figure 3.7)......................................31 

Figure 3.11. Estimated distribution of TWCF for currently operating PWRs using the procedure 

detailed in Section 3.5.1....................................................................................................37

Figure 3.12. Comparison of the distributions (red and blue histograms) of the various RT values 

characteristic of beltline materials in the current operating fleet projected to 48 

EFPY with the TWCF vs. RT relationships (curves) used to define the proposed 

ix
PTS screening limits (see Figure 3.4 and Figure 3.9 for the original presentation 

of these relationships) .......................................................................................................41 

Figure 3.13. Graphical comparison of the RT limits for plate-welded plants developed in 

Section 3.5.2 with RT values for plants at EOLE (from Table 3.3). The top 

graph is for plants having wall thickness of 9.5-in. and less, while the bottom 

graph is for vessels having wall thicknesses between 10.5 and 11.5 in............................47 

Figure 3.14. Graphical comparison of the RT limits for ring-forged plants developed in 

Section 3.5.2 with RT values for plants at EOLE (from Table 3.3) .................................47 

Tables 

Table 3.1. Summary of FAVOR 06.1 Results Reported in (Dickson 07b)........................................22 

Table 3.2. Results of a Sensitivity Study Assessing the Effect of Underclad Flaws 

on the TWCF of Ring-Forged Vessels..............................................................................30 

Table 3.3. RT and TWCF Values for Plate-Welded Plants Estimated Using the 

Procedure Described in Section 3.5.1...............................................................................38 

Table 3.4. RT and TWCF Values for Ring-Forged Plants Estimated Using the 

Procedure Described in Section 3.5.1...............................................................................40 

Table 3.5. RT Limits for PWRs .........................................................................................................46 

Table 3.6. Non-Best-Estimate Aspects of the Models Used to Develop the RT-Based 

Screening Limits for PTS .................................................................................................51 

Table 3.7. RT Limits for PWRs .........................................................................................................53 

x
Executive Summary 

From 1999 through 2007, the U.S. Nuclear Regulatory Commission (NRC) conducted a study to develop 

the technical basis for revising the Pressurized Thermal Shock (PTS) Rule, as set forth in Title 10, Section 

50.61, “Fracture Toughness Requirements for Protection against Pressurized Thermal Shock Events,” 

of the Code of Federal Regulations (10 CFR 50.61) in a manner consistent with the NRC’s guidelines on 

risk-informed regulation. In early 2005, the Advisory Committee on Reactor Safeguards (ACRS) 

endorsed the staff’s approach and its proposed technical basis. The staff documented the technical basis 

in an extensive set of reports (Section 4.1 of this report provides a complete list), which were then 

subjected to further internal reviews. Based on these reviews, the staff decided to modify certain aspects 

of the probabilistic calculations to refine and improve the model. This report documents these changes 

and the results of probabilistic calculations that provide the technical basis for the staff’s development of 

a voluntary alternative to the PTS Rule. 

This executive summary begins with a description of PTS, how it might occur, and its potential consequences 

for the reactor pressure vessel (RPV). This is followed by a summary of the current regulatory approach 

to PTS, which leads directly to a discussion of the motivations for conducting this project. Following this 

introductory information, the executive summary describes the approach used to conduct the study, and 

summarizes key findings and recommendations, which include a proposal for a revision to the PTS screening 

limits. 

To provide a complete perspective on the current understanding of the risk of RPV failure arising from 

PTS, this executive summary draws not only on information presented in this report but also from the 

other technical basis reports listed in Section 4.1 of this report. 

Description of PTS 

During the operation of a nuclear power plant, the RPV walls are exposed to neutron radiation, resulting in 

localized embrittlement of the vessel steel and weld materials in the area adjacent to the reactor core. If an 

embrittled RPV had an existing flaw of critical size and certain severe system transients were to occur, the 

flaw could propagate very rapidly through the vessel, resulting in a through-wall crack and challenging the 

integrity of the RPV. The severe transients of concern, known as PTS events, are characterized by a rapid 

cooling (i.e., thermal shock) of the internal RPV surface and downcomer, which may be followed by 

repressurization of the RPV. Thus, a PTS event poses a potentially significant challenge to the structural 

integrity of the RPV in a pressurized-water reactor (PWR). 

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

(either with or without significant internal pressure). These events include, among others, a pipe break in 

the primary pressure circuit, a stuck-open valve in the primary pressure circuit that later re-closes (causing 

re-pressurization of the primary), or a break of the main steamline. When such events are initiated by a 

break in the primary pressure circuit the water level drops as a result of leakage from the break. Automatic 

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

core. However, the makeup water is much colder than that held in the primary system. As a result, the 

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

makeup water, produces significant thermal stresses in the hotter thick section steel wall of the RPV. For 

embrittled RPVs, these stresses could be sufficient to initiate a running crack, which could propagate all 

the way through the vessel wall. Such through-wall cracking of the RPV could result in core damage or, 

in rare cases, a large early release of radioactive material to the environment. Fortunately, the coincident 

occurrence of critical-size flaws, embrittled vessel steel and weld material, and a severe PTS transient is a 

very low-probability event. In fact, only a few operating PWRs are projected to even come close to the 

xi
current statutory limit (10 CFR 50.61) on the level of embrittlement during the first 40 years of operation 

assuming that current operating practices are maintained. 

Current Regulatory Approach to PTS 

As set forth in 10 CFR 50.61, the PTS Rule requires licensees to monitor the embrittlement of their RPVs 

using a reactor vessel material surveillance program qualified under Appendix H, “Reactor Vessel 

Material Surveillance Program Requirements,” to 10 CFR Part 50, “Domestic Licensing of Production 

and Utilization Facilities.” The surveillance results are then used 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 and how those transition temperatures increase as a result of irradiation damage that 

accumulates over 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 to estimate the value of 

RTNDT that will occur at end of license (EOL), a value called RTPTS. The screening limits provided in 

10 CFR 50.61 restrict the maximum values of RTNDT permitted during the plant’s operational life to 

+270 F (132 C) for axial welds, plates, and forgings, and +300 F (149 C) for circumferential welds. 

These screening limits were selected based upon a limit of 5x10-6 events per year on the annual 

probability of developing a through-wall crack (RG 1.154). Should RTPTS exceed these screening limits, 

10 CFR 50.61 requires the licensee to either take actions to keep RTPTS below the screening limits. These 

actions include implementing “reasonably practicable” flux reductions to reduce the embrittlement rate or 

by deembrittling the vessel by annealing (RG 1.162), or performing plant-specific analyses to demonstrate that 

operating the plant beyond the 10 CFR 50.61 screening limits does not pose an undue risk to the public (RG 

1.154). 

While no currently operating PWR has an RTPTS value that is projected to exceed the 10 CFR 50.61 

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

20 F). Those plants are likely to exceed the screening limits during the 20-year license renewal period 

that many operators are currently seeking or have already received. Moreover, some plants maintain their 

RTPTS values below the 10 CFR 50.61 screening limits by implementing flux reductions (low-leakage 

cores, ultra-low-leakage cores), which are fuel management strategies that can be economically 

deleterious in a deregulated marketplace. Thus, the 10 CFR 50.61 screening limits can restrict both the 

licensable and 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 conservative treatment of several key parameters and models used in the probabilistic 

calculations that provided the technical basis for the current PTS Rule. The most prominent of these 

conservatisms includes the following factors: 

 highly simplified treatment of plant transients (very coarse grouping of many operational sequences 

(on the order of 105

) into very few groups (approximately 10), necessitated by limitations in the 

computational resources needed to perform multiple thermal-hydraulic (TH) calculations) 

 lack of any significant credit for operator action 

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

 use of a flaw distribution that places all flaws on the interior surface of the RPV, and, in general, 

contains larger flaws than those usually detected in service 

xii
 a modeling approach that treated the RPV as if it were made entirely from the most brittle of its 

constituent materials (welds, plates, or forgings) 

 a modeling approach that assessed RPV embrittlement using the peak fluence over 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 staff believes that reexamining 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 substantially relaxing these limits. For these reasons, 

the NRC undertook this study with the objective of developing the technical basis to support a riskinformed revision of the PTS Rule and the associated PTS screening limits. 

Approach 

As illustrated in the following figure, three main models (shown as solid blue squares), taken together, 

permit estimation of the annual frequency of through-wall cracking in an RPV: 

 probabilistic risk assessment (PRA) event sequence analysis 

 TH analysis 

 probabilistic fracture mechanics (PFM) analysis 

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

Schematic showing how a probabilistic estimate of TWCF is combined 

with a TWCF acceptance criterion to arrive at a proposed revision of the 

PTS screening limit 

First, a PRA event sequence analysis is performed to postulate the sequences of events that may cause 

a PTS challenge to RPV integrity and to estimate the frequency with which such sequences might 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, which is characteristic of 

each sequence definition. These temperature, pressure, and heat-transfer coefficient histories are then 

passed to a PFM model that uses the TH output, along with other information concerning RPV design 

and construction materials, to estimate the time-dependent “driving force to fracture” produced by a particular 

event sequence. The PFM model then compares this estimate of fracture-driving force to the fracture toughness, 

or fracture resistance, of the RPV steel. Performing this comparison for many simulated vessels and 

xiii
flaws permits estimation of the probabilities that a crack could grow to sufficient size that it would 

penetrate all the way through the RPV wall (assuming that a particular sequence of events actually occurs). 

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

through-wall cracking (from the PFM analysis) with the distribution of frequencies at which a particular 

event sequence could occur (as defined by the PRA analysis). This product establishes an estimate of 

the distribution of the annual frequency of through-wall cracking that could occur at a particular plant 

after a particular period of operation when subjected to a particular sequence of events. The annual frequency 

distribution of through-wall cracking is then summed for all event sequences to estimate the total annual 

frequency distribution of through-wall cracking for the vessel. Performance of such analyses for various 

operating lifetimes provides an estimate of how the distribution of annual frequency of through-wall 

cracking would vary over the lifetime of the plant. 

Performance of the probabilistic calculations just described establishes the technical basis for a revised 

PTS Rule within an integrated systems analysis framework. The staff’s 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 a focus on the use of realistic input values and models (wherever possible), and an explicit 

treatment of uncertainties (using currently available uncertainty analysis tools and techniques). Thus, the 

current approach improves upon that employed in SECY-82-465, “Pressurized Thermal Shock,” dated 

November 23, 1982, which included intentional and unquantified conservatisms in many aspects of the 

analysis, and treated uncertainties implicitly by incorporating them into the models. 

Key Findings 

The findings from this study are divided into five topical areas—(1) the expected magnitude of the TWCF 

for currently anticipated operational lifetimes, (2) the material factors that dominate PTS risk, (3) the 

transient classes that dominate PTS risk, (4) the applicability of these findings (based on detailed analyses 

of three PWRs) to PWRs in general, and (5) the annual limit on TWCF established consistent with current 

guidelines on risk-informed regulation. In this summary, the conclusions are presented in boldface italic, 

while the supporting information is shown in regular type. 

TWCF Magnitude for Currently Anticipated Operational Lifetimes 

 The degree of PTS challenge is low for currently anticipated lifetimes and operating conditions. 

o For Plate-Welded PWRs: Assuming that current operating conditions are maintained, the risk of 

PTS failure of the RPV is very low. Over 80 percent of operating PWRs have estimated TWCF 

values below 1x10-8/ry, even after 60 years of operation. After 40 years of operation the highest 

risk of PTS at any PWR is 2.0x10-7/ry. After 60 years of operation this risk increases to 4.3x10-

7

/ry. If the RT screening limits proposed herein, which are based on limiting the yearly through 

wall cracking frequency to below a value of 1x10-6, are adopted, and if current operating practices 

are maintained then no plant will get within 30 F of the RT limits within the first 40 years of 

operation. After 60 years of operation, the most embrittled plant will still be 17 F away from the 

RT limits. 

o For Ring-Forged PWRs: Assuming that current operating conditions are maintained, the risk of 

PTS failure of the RPV is very low. All operating PWRs have estimated TWCF values below 

1x10-8/ry, even after 60 years of operation. After 40 years of operation the highest risk of PTS at 

any PWR is 1.5x10-10/ry. After 60 years of operation this risk increases to 3.0x10-10/ry. If the RT 

screening limits proposed herein, which are based on limiting the yearly through wall cracking 

xiv
frequency to below a value of 1x10-6, are adopted, and if current operating practices are 

maintained then no plant will get within 59 F of the RT limits within the first 40 years of 

operation. After 60 years of operation, the most embrittled plant will still be 47 F away from the 

RT limits. 

Material Factors and Their Contributions to PTS Risk 

 Axial flaws, and the toughness properties that can be associated with such flaws, control nearly all 

of the TWCF. 

o Plate-Welded Vessels 

 Axial flaws are much more likely than circumferential flaws to propagate through the RPV 

wall because the applied fracture-driving force increases continuously with increasing crack 

depth for an axial flaw. Conversely, circumferentially oriented flaws experience a drivingforce peak mid-wall, providing a natural crack arrest mechanism. It should be noted that 

crack initiation from circumferentially oriented flaws is likely; only their through-wall 

propagation is much less likely (relative to axially oriented flaws). 

 The toughness properties that can be associated with axial flaws control nearly all of the 

TWCF. These include the toughness properties of plates and axial welds at the flaw locations. 

Conversely, the toughness properties of both circumferential welds and forgings have little 

effect on the TWCF of plate-welded PWRs because these can be associated only with 

circumferentially oriented flaws. 

o Ring-Forged Vessels 

 As with plate-welded PWRs, axial flaws are again much more likely than circumferential 

flaws to propagate through the RPV wall. However, because there are no axial welds in ringforged vessels, the axial flaws that can be associated with these welds are absent. However, 

for particular combinations of forging chemistry and cladding heat input, underclad cracks 

can form in the forging. As implied by the name, these cracks form in the forging just below 

the cladding layer, and they form perpendicular to the direction in which the clad weld layer 

was deposited (i.e., axially). Therefore, the toughness properties that can be associated with 

these axial flaws (i.e., that of the forging) control nearly all of the TWCF in ring-forged vessels. 

Transients and Their Contributions to PTS Risk 

 Transients involving primary-side faults are the dominant contributors to TWCF, while transients 

involving secondary-side faults play a much smaller role. 

o The severity of a transient is controlled by a combination of three factors: 

 initial cooling rate, which controls the thermal stress in the RPV wall 

 minimum temperature of the transient, which controls the resistance of the vessel to fracture 

 pressure retained in the primary system, which controls the pressure stress in the RPV wall 

o The significance of a transient (i.e., how much it contributes to PTS risk) depends on these three 

factors and the likelihood that the transient will occur. 

o The analysis considered transients in the following classes: 

 primary-side pipe breaks 

 stuck-open valves on the primary side 

 main steamline breaks 

xv
 stuck-open valves on the secondary side 

 feed-and-bleed 

 steam generator tube rupture 

 mixed primary and secondary initiators 

o Of these, transients in the first two categories were responsible for 90 percent or more of the PTS 

risk, while transients in the third category were responsible for nearly all of the remainder. 

 For medium- to large-diameter primary-side pipe breaks, the fast-to-moderate cooling rates 

and low downcomer temperatures (generated by rapid depressurization and emergency injection 

of low-temperature makeup water directly to the primary system) combine to produce a highseverity transient. Despite the moderate-to-low likelihood that these transients will occur, their 

severity (if they do occur) makes them significant contributors to the total TWCF. 

 For stuck-open primary-side valves that later reclose, the repressurization associated with 

valve reclosure coupled with low temperatures in the primary system combine to produce a 

high-severity transient. This, coupled with a high likelihood of transient occurrence, makes 

stuck-open primary-side valves that may later reclose significant contributors to the total 

TWCF. 

 The small or negligible contribution of all secondary-side transients (main steamline break, 

stuck-open secondary valves) results directly from the lack of low temperatures in the primary 

system. For these transients, the minimum temperature of the primary system for times of 

relevance is controlled by the boiling point of water in the secondary system (212 F (100 C) 

or above). At these temperatures, the fracture toughness of the embrittled RPV steel is still 

sufficiently high to resist vessel failure in most cases. 

Applicability of These Findings to PWRs in General 

 Credits for operator action, while included in the analysis, do not influence these findings in any 

significant way. Operator action credits can influence dramatically the risk-significance of individual 

transients. Therefore, a “best estimate” analysis needs to include appropriate credits for operator action 

because it is not possible to establish a priori if a particular transient will make a large contribution to the 

total risk. Nonetheless, the results of the analyses demonstrate that these operator action credits have a 

small overall effect on a plant’s total TWCF, for reasons detailed below.

o Medium- and Large-Diameter Primary-Side Pipe Breaks: No operator actions are modeled 

for any break diameter because, for these events, the safety injection systems do not fully refill 

the upper regions of the reactor coolant system. Consequently, operators would never take action 

to shut off the pumps. 

o Stuck-Open Primary-Side Valves That May Later Reclose: The PRA model includes reasonable 

and appropriate credit for operator actions, such as throttling of the high-pressure injection (HPI) 

system. However, these credits have a small influence on the estimated values of vessel failure 

probability attributable to transients caused by a stuck-open valve in the primary pressure circuit 

(SO-1 transients) because the credited operator actions only prevent repressurization when SO-1 

transients initiate from hot zero power (HZP) conditions and the operators act promptly (within 1 

minute) to throttle the HPI. Complete removal of operator action credits from the model only 

increases slightly the total risk associated with SO-1 transients. 

o Main Steamline Breaks: For the overwhelming majority of transients caused by a main steamline 

break, vessel failure is predicted to occur between 10 and 15 minutes after transient initiation because 

the thermal stresses associated with the rapid cooldown reach their maximum within this 

xvi
timeframe. Thus, all of the long-term effects (isolation of feedwater flow, timing of the highpressure safety injection control) that can be influenced by operator actions have no effect on 

vessel failure probability because such factors influence the progression of the transient after 

failure has occurred (if it occurs at all). Only factors affecting the initial cooling rate (i.e., plant 

power level at time of transient initiation, break location inside or outside of containment) can 

influence the conditional probability of through-wall cracking (CPTWC), and operator actions do 

not influence these factors in any way. 

 Because the severity of the most significant transients in the dominant transient classes is controlled 

by factors that are common to PWRs in general, the TWCF results presented herein can be used 

with confidence to develop revised PTS screening criteria that apply to the entire fleet of operating 

PWRs. 

o Medium- and Large-Diameter Primary-Side Pipe Breaks: For these break diameters, the fluid 

in the primary system cools faster than the wall of the RPV. In this situation, only the thermal 

conductivity of the steel and the thickness of the RPV wall control the thermal stresses and, thus, 

the severity of the fracture challenge. Perturbations in the fluid cooldown rate controlled by 

break diameter, break location, and season of the year do not play a significant role. Thermal 

conductivity is a physical property, so it is very consistent for all RPV steels, and the thicknesses of 

the three RPVs analyzed are typical of most PWRs. Consequently, the TWCF contribution of 

medium- to large-diameter primary-side pipe breaks is expected to be consistent from plant-to-plant 

and can be well represented for all PWRs by the analyses reported herein. 

o Stuck-Open Primary-Side Valves That May Later Reclose: A major contributor to the risk-significance 

of SO-1 transients is the return to full system pressure once the valve recloses. The operating 

and safety relief valve pressures of all PWRs are similar. Additionally, as previously noted, 

operator action credits affect only slightly the total TWCF associated with this transient class. 

o Main Steamline Breaks: Since main steamline breaks fail early (within 10–15 minutes after 

transient initiation), only factors affecting the initial cooling rate can have any influence on the 

CPTWC values. Operator actions do not influence these factors, which include the plant power 

level at event initiation and the location of the break (inside or outside of containment), in any 

way. 

 Sensitivity studies performed on the TH and PFM models to investigate the effect of credible model 

variations on the predicted TWCF values revealed that only vessel wall thickness was a factor so 

significant as to require modification of the baseline results for the three detailed study plants. 

This finding resulted in the revised PTS screening limits being expressed as a function of RPV wall 

thickness. 

 An investigation of design and operational characteristics for five additional PWRs revealed 

no differences in sequence progression, sequence frequency, or plant TH response significant 

enough to call into question the applicability of the TWCF results from the three detailed plant 

analyses to PWRs in general. 

 An investigation of potential external initiating events (e.g., fires, earthquakes, floods) revealed 

that the contribution of those events to the total TWCF can be regarded as negligible. 

xvii
Annual Limit on TWCF

 The current guidance provided by Regulatory Guide 1.174 for large early release is conservatively 

applied to setting an acceptable annual TWCF limit of 1x10-6 events/year. 

o While many post-PTS accident progressions led only to core damage (which suggests a TWCF limit 

of 1x10-5 events/year in accordance with Regulatory Guide 1.174, Revision 1, “An Approach for 

Using Probabilistic Risk Assessment in Risk-Informed Decisions on Plant-Specific Changes to 

the Licensing Basis,” issued November 2002), uncertainties in the accident progression analysis 

led to the recommendation to adopt the more conservative limit of 1x10-6 events/year based on 

the large early release frequency. 

Recommended Revision of the PTS Screening Limits 

The NRC staff recommends using different RT-metrics to characterize the resistance of an RPV 

to fractures initiating from different flaws at different locations in the vessel. Specifically, the staff 

recommends an RT for flaws occurring along axial weld fusion lines (RTMAX-AW), another for the 

embedded flaws occurring in plates (RTMAX-PL), a third for flaws occurring along circumferential weld 

fusion lines (RTMAX-CW), and a fourth for embedded and/or underclad cracks in forgings (RTMAX-FO). 

These values can be estimated based mostly on the information in the NRC’s Reactor Vessel Integrity 

Database (RVID). The staff also recommends using these different RT values together to characterize the 

fracture resistance of the vessel’s beltline region, recognizing that the probability of a vessel fracture 

initiating from different flaw populations varies 

considerably in response to factors that are both 

understood and predictable. Correlations between 

these RT values and the TWCF attributable to 

different flaw populations show little plant-to-plant 

variability because of the general similarity of PTS 

challenges among plants. 

This report proposes a formula to estimate the total 

TWCF for a vessel based only on these RT values 

and on the vessel wall thickness, and uses this 

formula to estimate the TWCF values for all 

operating PWRs. Currently none of these estimates 

exceeds the 1x10-6/ry limit during either current or 

extended (through 60 years) operations. One 

option that may be considered when implementing 

these results in a revised version of 10 CFR 50.61 

is to simply require licensees to ensure that these 

TWCF estimates remain below the 1x10-6/ry limit. 

An alternative implementation option is to use the 

equation presented herein that relates TWCF to the 

various RT-metrics to transform the 1x10-6/ry limit 

into limits on the various RT values. The staff has 

established candidate RT-based screening limits by 

setting the total TWCF equal to 1x10-6/ry. The figure 

to the right graphically represents one set of these 

screening limits along with an assessment of all 

operating plate-welded PWRs relative to the 

proposed limits at the end of license extension (the 

projected plant RT-values for EOLE reported in this figure are premised on the assumption that current 

Plate Welded Plants 

at 48 EFPY (EOLE)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1x10-6/ry TWCF limit

Simplified Implementation

RTMAX-AW ≤ 269F, and

RTMAX-PL ≤ 356F, and

RTMAX-AW + RTMAX-PL ≤ 538F.

Comparison of RT-based screening limits 

(curves or dashed lines) with assessment 

points for operating plate-welded PWRs at 

EOLE. Limits are shown for vessels 

having wall thicknesses of 9.5 inches or 

less. This report provides similarly defined 

limits for thicker vessels and for ringforged vessels. 

xviii
operating practices are maintained). In this figure, the region of the graphs between the red locus and the 

origin has TWCF values below the 1x106

/ry acceptance criterion, so the staff would consider these 

combinations of RTs to be acceptable and require no further analysis. By contrast, the region of the graph 

outside of either the red locus has TWCF values above the 1x10-6/yr acceptance criterion, indicating the 

need for additional analysis or other measures to justify continued plant operation. Clearly, operating 

PWRs will not exceed the 1x10 6/ry limit, even after 60 years of operation. This separation of operating 

plants from the screening limits contrasts markedly with the current regulatory situation in which several 

plants are within 1 F (0.5 C) of the screening limits set forth in 10 CFR 50.61 after only 40 years of 

operation. 

Aside from relying on RT-metrics that differ from those currently used in 10 CFR 50.61, these proposed 

implementation options also differ from the current approach in terms of the absence of a margin term. Use of 

a margin term is appropriate to account for (at least approximately) factors that occur in application, but that 

were not considered in the analysis upon which the screening limits are based. For example, the current 

10 CFR 50.61 margin term accounts for uncertainty in copper, nickel, and initial RTNDT values. However, 

the model adopted in this study explicitly considers uncertainty in all of these variables and models these 

uncertainties as being larger (a conservative representation) than would be appropriate in any plantspecific application. Consequently, use of the 10 CFR 50.61 margin term with the new screening limits 

proposed herein is inappropriate. In general, the following three reasons suggest that use of any margin 

term with the proposed screening limits is inappropriate: 

(1) The TWCF values used to establish the screening limits are 95th percentile values. 

(2) The results from the staff’s three plant-specific analyses apply to PWRs in general. 

(3) While certain aspects of the modeling cannot reasonably be represented as “best estimates,” there is, 

on balance, a conservative bias to these non-best-estimate aspects of the analysis because residual 

conservatisms in the model far outweigh residual nonconservatisms. 

Assessing the Continued Appropriateness of the Recommended PTS 

Screening Limits 

As described in this and in companion reports, the screening limits the staff has recommended for PTS are 

premised on the view that the mathematical model of PTS we have described is an appropriate 

representation of PTS events, both in terms of the likelihood of their occurance as well and in terms of 

their effect on the RPV were they to occur. Because the appropriatness of the staff’s model of PTS may 

change in the future due to changes in operating practice, changes in initiating event frequencies, changes 

in radiation damage mechanisms, and potential changes in other factors, the staff should periodically 

evaluate the PTS model described here for appropriateness. Should these evaluations reveal a significant 

departure between this model and physical reality then appropriate actions, if any, could be taken. 

xix
xx
Chapter 1 - Background and Objective 

In early 2005, the U.S. Nuclear Regulatory 

Commission (NRC) staff completed a series of 

reports detailing the technical basis for a riskinformed revision of the pressurized thermal 

shock (PTS) Rule (Title 10, Section 50.61, 

“Fracture Toughness Requirements for 

Protection against Pressurized Thermal Shock 

Events,” of the Code of Federal Regulations

(10 CFR 50.61)). Figure 1.1 depicts these 

reports; Section 4.1 includes the full references. 

Both an external peer review panel and the 

Advisory Committee for Reactor Safeguards 

(ACRS) (ACRS 05) critiqued and approved the 

reports (see Appendix B to NUREG-1806 

(EricksonKirk-Sum) for details). Following 

ACRS review, these reports were then subjected 

to further internal reviews. Based on these 

reviews, the staff decided to modify certain 

aspects of the probabilistic calculations to refine 

and improve the model. The purpose of this 

report is threefold—(1) to document the changes 

made to the PTS models based on the postACRS reviews, (2) to report the results of the 

new computations, and (3) to make 

recommendations on the use of these results to 

revise screening limits for PTS. Chapter 2 of 

this report details changes to the model since 

publication of NUREG-1806 (EricksonKirkSum) while Chapter 3 describes the results of 

the calculations and recommendations on 

revised screening limits for PTS. This report 

does not provide a comprehensive summary of 

NRC activities undertaken over the last 7 years 

to develop the technical basis for a risk-informed 

revision to 10 CFR 50.61 (see (EricksonKirk–

Sum) for these details). 

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., et al., 

“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 Version 03.1,” NUREG1808. 

• 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 APEXCE Integral Test Facility,” NUREG/CR6856.

• Experimental Benchmarks: Reyes, J.N., 

“Scaling Analysis for the OSU APEX-CE 

Integral Test Facility,” NUREG/CR-6731.

• Uncertainty: Chang, Y.H., et al., “Thermal 

Hydraulic Uncertainty Analysis in 

Pressurized Thermal Shock Risk 

Assessment,” NUREG/CR-6899.

• Baseline: Arcieri, W.C., et al., “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/MOD3.2.2 Gamma Results for 

Palisades 1D Downcomer Sensitivity 

Study”

• Consistency Check: Junge, M., “PTS 

Consistency Effort”

• Procedures & Uncertainty: Whitehead, 

D.W., et al., “PRA Procedures and 

Uncertainty for PTS Analysis,” NUREG/CR6859.

• Uncertainty Analysis Methodology: Siu, N., 

“Uncertainty Analysis and Pressurized 

Thermal Shock, An Opinion.”

• 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

Figure 1.1. Structure of documentation summarized by this report and by (EricksonKirk-Sum). The 

citations for these reports in the text appear in italicized boldface to distinguish them from 

literature citations. 

1
2
Chapter 2 - Changes to the PTS Model 

Following ACRS review and acceptance of the 2.1.1 Review Finding 

staff’s methodology for developing probabilistic 

estimates of the risk of through-wall cracking of 

a pressurized-water reactor (PWR) vessel caused 

by PTS (see the reports detailed in Section 4.1 of 

this report), these reports were subjected to 

further internal reviews and quality control 

checks. On the basis of these reviews, the NRC 

staff decided that certain aspects of the 

probabilistic calculations should be refined or 

improved. These aspects, which are listed 

below, are described in both the remainder of 

this chapter and in Appendix A to this report. 

From the descriptions of the parameters RTLB

(lower bound reference temperature) and To

(fracture toughness reference temperature) 

provided in the documentation, it seems that 

these two parameters should have a more 

systematic relationship and, in particular, that 

RTLB should always be greater than or equal to 

To. Nevertheless, Figure 2.1, which displays the 

data on which the RTNDT epistemic uncertainty 

correction is based, shows that RTLB can be 

considerably less than To. Is there a problem 

with our understanding of how RTLB and To

relate to one another, or is there some 

inconsistency in the data shown in Figure 2.1? 

 Section 2.1: Data basis for the reference 

temperature nil ductility (RTNDT) epistemic 

uncertainty correction 

-250

-200

-150

-100

-50

0

50

-200 -150 -100 -50 0 50

To [oF]

RTLB [oF]

 Data

 RTLB = To

 Section 2.2: RTNDT epistemic uncertainty 

correction: sampling procedures 

 Section 2.3: Fracture Analysis of Vessels: 

Oak Ridge (FAVOR) computer code 

sampling procedures on other variables 

 Section 2.4: The distribution of flaws in 

repair welds 

 Section 2.5: The distribution of subclad 

flaws in forgings 

 Section 2.6: The relationship used to predict 

embrittlement based on exposure and on 

composition variables Figure 2.1. Data on which the RTNDT epistemic 

uncertainty correction is based  Section 2.7: The upper-shelf fracture 

toughness model 

 Section 2.8: The temperature dependence of 

thermal-elastic properties 2.1.2 Model Change 

 Section 2.9: Loss-of coolant accident 

(LOCA) break frequencies 

The review correctly identifies that the data in 

Figure 2.1 for which RTLB falls below To are 

erroneous. The change specification for the 

Fracture Analysis of Vessels—Oak Ridge 

(FAVOR) Code detailed in Appendix A 

provides a detailed explanation of the origins of 

these erroneous data and develops a revised 

epistemic uncertainty correction for RTNDT that 

does not rely on these data. 

Additionally, while not resulting in a model 

change, discussion is included in Section 2.10 

discusses the ability of nondestructive 

examination (NDE) techniques to detect and size 

the flaws found to be risk-significant for PTS. 

2.1 RTNDT Epistemic Uncertainty Data 

Basis 

3
2.2 FAVOR Sampling Procedures on 

RTNDT Epistemic Uncertainty 

2.2.1 Review Finding 

The FAVOR code uses an RTNDT fracture 

toughness indexing parameter and a Master 

Curve Approach fracture toughness indexing 

parameter (To) to estimate material toughness 

properties. The sampling of the RTNDT-To

correction parameter in the Monte Carlo process 

(used in the FAVOR code), may affect the 

variation that is seen in the results for the 

example plants. Currently the correction is 

sampled inside the flaw loop so that each flaw is 

potentially assigned a different correction. It 

may be more appropriate to sample the 

correction outside of the flaw loop so that the 

correction is sampled once for each material for 

each vessel simulation. 

2.2.2 Model Change 

The review finding correctly identifies that it is 

more appropriate to sample the uncertainty in 

the RTNDT-To correction parameter outside of the 

flaw loop (but still inside the vessel loop). The 

previous sampling procedure simulated a degree 

of uncertainty in the unirradiated fracture 

toughness transition temperature that is 

unrealistic, a deficiency reconciled by the new 

sampling procedure. The FAVOR change 

specification details both the rationale 

supporting this change and how it is 

implemented in FAVOR Version 06.1.

2.3 FAVOR Sampling Procedures on 

Other Variables 

2.3.1 Review Finding 

Similar to the comment made in Section 2.2.1 

regarding the location in FAVOR at which the 

RTNDT epistemic uncertainty correction is 

sampled, the location of other sampled 

parameters (e.g., copper, copper variability, 

nickel) may not be most appropriately placed 

within the flaw loop. 

2.3.2 Model Change 

The NRC performed a comprehensive review of 

the FAVOR uncertainty sampling strategy. On 

the basis of this review, the staff decided that, in 

addition to the RTNDT epistemic uncertainty 

discussed in Section 2.2, the uncertainty on the 

following variables is more appropriately 

sampled outside of the flaw loop, requiring a 

modification of FAVOR 04.1: 

 the unirradiated value of RTNDT

 standard deviation on copper 

 standard deviation on nickel 

The FAVOR change specification details both 

the rationale supporting these changes and how 

they are implemented in FAVOR Version 06.1.

2.4 Distribution of Repair Flaws 

2.4.1 Review Finding 

To develop the sample flaw distributions as 

input to the FAVOR code, Pacific Northwest 

National Laboratory (PNNL) assumed that 

2 percent of the volume of weld seams consisted 

of repair welds. The repair welds were assumed 

to be uniformly distributed through the 

submerged metal arc weld (SMAW) thickness. 

Since repairs typically intersect the surface, it is 

possible that flaws associated with repairs would 

be preferentially located adjacent to the outside 

diameter (OD) or inside diameter (ID) surfaces 

of the RPV. The extra flaws associated with 

repairs are typically located at the deepest point 

of the repair. Examination of the repairs detailed 

in Section 5.7 of NUREG/CR-6471, Volume 2, 

“Characterization Of Flaws in U.S. Reactor 

Pressure Vessels: Density and Distribution of 

Flaw Indications in PVRUF,” indicates the 

deepest part of the excavation cavity would be 

more often associated with the surface (or within 

2 inches of the surface) than with the interior 

regions of the plate or weld (Schuster 98). 

Accordingly, it seems reasonable to increase the 

proportion of the flaw distribution that should be 

attributed to weld repairs from the current 

2 percent to some higher value. The higher 

value should be associated with the typical area 

4
density of weld repair along weld seams. The 

current approach uses a 2-percent contribution, 

which was chosen so that it would be a bound to 

the observed 1.5-percent proportion of weld 

repair in the Pressure Vessel Research Users 

Facility (PVRUF) vessel. The 1.5-percent value 

seems to have been calculated on a volume 

basis. 

(1) What is the proportion of weld repair 

associated with the weld seams on the 

PVRUF vessel near the ID surface of the 

vessel on an area rather than a volume basis? 

(2) What is the expected or calculated effect of 

this change in the assumptions regarding 

repair flaw distributions on the TWCFs? 

2.4.2 Model Change 

Regarding the first question in Section 2.4.1, it 

is correctly noted that the judgment to include 2-

percent repair flaws in the flaw distribution used 

in the baseline PTS analysis was made on the 

basis that a 2-percent repair weld volume 

exceeded the proportional volume of weld 

repairs to original fabrication welds observed in 

any of the PNNL work (the largest volume of 

weld repairs relative to original fabrication 

welds was 1.5 percent). However, flaws in 

welds are almost always fusion-line flaws, 

which suggests that their number scales in 

proportion to weld fusion line area and not in 

proportion to weld volume. To address this 

issue, PNNL reexamined the relative proportion 

of repair welds that occur on an area rather than 

on a volume basis. PNNL determined that the 

ratio of weld repair fusion area to original 

fabrication fusion area is 1.8 percent for the 

PVRUF vessel. Thus, the input value of 2 

percent used in the FAVOR calculations can still 

be regarded as bounding. 

Regarding the second question in Section 2.4.1, 

FAVOR does assumes that a simulated flaw is 

equally likely to occur at any location through 

the vessel wall thickness. Upon further 

consideration the staff has determined that this 

model is incorrect for flaws occurring in repair 

welds. Figure 2.2 shows that if a flaw forms in a 

weld repair it is equally likely to occur anywhere 

with respect to the depth of the excavation 

cavity. However, Figure 2.3 shows that weld 

repair areas occur with much higher frequency 

close to the surfaces of the vessel than they do at 

mid-wall thickness, as noted in Section 2.4.1. 

Taken together, this information indicates that a 

flaw from a weld repair is more likely to be 

encountered close to the ID or OD surface than 

it is at the mid-wall thickness, a fact not well 

modeled by the approach adopted in FAVOR 

Version 04.1. 

FAVOR currently uses as input a “blended” flaw 

distribution for welds. The flaws placed in the 

blended distribution are scaled in proportion to 

the fusion area of the different welding 

processes used to fabricate the vessel. Because 

of this approach, it is not possible, without 

significant recoding, to specify a through 

thickness distribution of repair weld flaws that is 

biased toward the surfaces while maintaining a 

random through-thickness distribution 

appropriate for submerged are weld (SAW) and 

SMAW flaws. Therefore, to account for the 

nonlinear through-thickness distribution of weld 

flaws the 2-percent blending factor currently 

used for repair welds will be modified on the 

following bases: 

 Only flaws within 3/8T of the inner diameter 

can contribute to the vessel failure 

probability. Because PTS transients are 

dominated by thermal stresses, flaws buried 

in the vessel wall more deeply than 3/8T do 

not have a high enough driving force/low 

enough fracture toughness to initiate. 

 In Figure 2.3, 3/8T corresponds to 3 inches 

on the x-axis. The curve fit to the data 

indicates that 79 percent of all repair flaws 

occur from 0 to 3/8T of the outer surfaces of 

the vessel. Figure 2.3 also indicates that 

7 percent of all repair flaws occur between 

5/8T and 1T from the outer surfaces of the 

vessel. Therefore 43 percent 

(i.e., (79%+7%)/2) of all repair flaws occur 

between the ID and the 3/8T position in the 

vessel wall.

5
 FAVOR’s current assumption of a random 

through-wall distribution of repair flaws 

generates 37.5 percent of all repair flaws 

between the ID and 3/8T. Thus, FAVOR 

underestimates the 43-percent value based 

on the data given above. 

 To account for this underestimation, the 2-

percent blend factor for repair welds will be 

increased in future analyses to 2.3 percent 

(i.e., 2%43/37.5) (see Appendix A). 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80 1.00

Depth of Flaw from Cavity Surface (fraction)

Cummulative distribution ( faction)

Random distribution 

of flaw locations

 Weld Repair Mouth Weld Repair Root 

Figure 2.2. Distribution of repair flaws in any weld repair cavity 

NUREG/CR-6471, Vol.2

6

y = 1.1066e-0.558x

R2 = 0.9773

0%

20%

40%

60%

80%

100%

012345678

Depth of Repair Excavation [inches]

Percent of Repair 

Excavations Extending to 

this Depth or Greater

Repair made from ID (26 observations)

Repair made from OD (26 observations)

Combined (52 Observations)

Expon. (Combined (52 Observations))

Figure 2.3. Distribution of weld repair flaws through the vessel wall thickness 
2.5 Distribution of Underclad Flaws in 

Forgings 

2.5.1 Review Finding 

Very shallow flaws were created on some forged 

vessels by underclad cracking that occurred 

during or following the cladding process. What 

is the effect of underclad flaws on TWCF, and 

how does this affect RT-based PTS screening 

limits for ring-forged vessels? 

2.5.2 Model Change 

Dr. Fredric Simonen of PNNL performed a 

literature review to establish a distribution for 

underclad flaws suitable for use within the 

probabilistic fracture mechanics code FAVOR. 

Appendix B is a report summarizing 

Dr. Simonen’s findings. When unfavorable 

welding conditions (high-heat inputs) and 

material conditions (chemistries having high 

proportions of impurity elements) coincide, 

underclad cracks can appear in forgings. When 

underclad cracks appear they do so as dense 

arrays (typical intercrack spacing is 1 or 2 

millimeters). They will have depths on the order 

of 1 millimeter, but in rare cases can extend into 

the ferritic steel of the RPV wall by as much as 

6 millimeters. Underclad cracks are oriented 

perpendicular to the direction in which the weld 

cladding was deposited, which is to say axially 

in the vessel. While the conditions under which 

underclad cracks form are not believed to typify 

those characteristic of most or all of the 21 

forged PWRs now in service, the staff was not 

able to establish a criteria that could 

differentiate, with a high degree of confidence, 

those vessels that are believed to be prone to 

underclad cracking from those that are not. For 

this reason, the staff decided to perform 

sensitivity studies at different levels of 

embrittlement using FAVOR, along with 

Dr. Simonen’s underclad flaw distribution on 

forged vessels. In these analyses the staff 

assumed that underclad cracks exist. Section 3.4 

of this report summarizes the results of these 

sensitivity studies and uses these results to 

develop RT-based screening limits for forged 

vessels. 

2.6 Embrittlement Trend Curve 

2.6.1 Review Finding 

FAVOR uses an embrittlement trend curve to 

estimate how transition temperature shift 

depends on both composition (copper, nickel, 

phosphorus) and exposure (flux, fluence, time) 

variables for the steels used in the beltline region 

of operating PWRs. Version 04.1 of FAVOR 

uses an embrittlement trend curve (Kirk 03) that 

differs from both the trend curve recommended 

by the American Society for Testing and 

Materials (ASTM) (ASTM E900) as well as 

from the trend curve most recently 

recommended by NRC contractors (Eason 07). 

Should the staff consider any revisions to the 

trend curve adopted by FAVOR? 

2.6.2 Model Change 

Both the embrittlement trend curve adopted in 

FAVOR Version 04.1 (Kirk 03) and the ASTM 

E900 trend curve (ASTM E900) are based on an 

analysis of surveillance data available through 

approximately 2001, whereas the trend curve 

detailed in (Eason 07) features an analysis of all 

surveillance data available through 

approximately 2004. For this reason, FAVOR 

Version 06.1 will be based on the trend curve in 

(Eason 07), as detailed in the change 

specification (see Appendix A). A description 

of the basis for this relationship is available 

elsewhere (Eason 07). 

Subsequent to the development of FAVOR 06.1, 

in accordance with the change specification in 

Appendix A, Eason developed an alternative 

embrittlement trend curve of a slightly 

simplified form (Eason 07). The results reported 

in Appendix C demonstrate that the effect of this 

alternative trend curve on the TWCF values 

estimated by FAVOR is insignificant. 

2.7 LOCA Break Frequencies 

2.7.1 Review Finding 

Recently the NRC staff conducted an expert 

elicitation to update the LOCA break 

7
frequencies needed as part of a risk-informed 

revision to 10 CFR 50.46, “Acceptance Criteria 

for Emergency Core Cooling Systems for LightWater Nuclear Power Reactors.” These 

frequencies were documented in NUREG-1829 

(Tregoning 05). Have the calculations 

documented by the various reports listed in 

Section 4.1 used these most recent estimates of 

LOCA break frequencies? 

2.7.2 Model Change 

The FAVOR 04.1 results used values for LOCA 

break frequencies that pre-dated the (Tregoning 

05) document. The FAVOR 06.1 results, which 

are detailed in Chapter 3, make use of the LOCA 

break frequencies from the (Tregoning 05) 

document. 

2.8 Temperature-Dependent Thermal 

Elastic Properties 

2.8.1 Review Finding 

FAVOR 04.1 adopts temperature-invariant 

thermal elastic properties despite welldocumented evidence, as reflected by American 

Society of Mechanical Engineers (ASME) 

codes, that these properties depend on 

temperature. Is the FAVOR 04.1 model 

appropriate? 

2.8.2 Model Change 

The NRC staff does not believe that the 

FAVOR 04.1 model is appropriate. 

Temperature-dependent thermal elastic 

properties have been adopted in FAVOR 06.1, 

as detailed in Appendix A and in (Williams 07). 

2.9 Upper-Shelf Fracture Toughness 

Model 

2.9.1 Review Finding 

Since FAVOR 04.1 was finalized, further work 

has been published on an upper-shelf fracture 

toughness model for ferritic steels (EricksonKirk 

06a; EricksonKirk 06b). Should the FAVOR 

06.1 model incorporate these new results? 

2.9.2 Model Change 

The NRC staff believes that the FAVOR 06.1 

model should incorporate these new results. As 

detailed in Appendix A, FAVOR 06.1 adopts the 

latest findings on the upper-shelf fracture 

toughness model described in (EricksonKirk 

06a) and (EricksonKirk 06b). 

2.10 Demonstration That the Flaws 

That Contribute to TWCF are 

Detectable by NDE Performed 

to ASME SC VIII Supplement 4 

Requirements 

2.10.1 Review Finding 

NUREG-1806 (EricksonKirk-Sum) indicates 

that a low density of flaws is one major factor in 

keeping the total risk associated with PTS low. 

The state of knowledge of the flaw densities in 

the 70 individual PWR plants now in service is 

based primarily on detailed destructive 

examinations of a small number of welds and 

plates from four vessels (but mostly from two 

vessels), coupled with expert elicitation and 

physical modeling. Another potential source of 

information on flaw density is the in-service 

inspections performed at 10-year intervals on 

each operating vessel. It would be very helpful 

if those inspections could provide evidence to 

support the assumptions in the current analysis. 

Specifically, it is important to know the 

significance of a flaw to the FAVOR analysis 

(based on its size and through-wall location) as 

well as the probability of detection for those 

flaws found, based on the FAVOR analysis, to 

be risk significant. 

2.10.2 Reply 

Flaw Depths Important for PTS 

Figure 2.4, Figure 2.5, and Figure 2.6 originally 

appeared in NUREG-1808 (EricksonKirk-SS)

as Figures 4-3, 4-4, and 4-5, respectively. 

Collectively these figures demonstrate that the 

flaws that contribute to PTS risk are (1) all 

8
located within approximately 1 inch of the 

vessel inner diameter and (2) almost invariably 

have a 2a (or through-wall extent) dimension of 

0.5 inch or less. 

To examine the flaw size/location combinations 

that contribute to PTS risk in further detail, the 

staff performed a series of deterministic analyses 

by locating flaws of various sizes axially in the 

Palisades RPV. Analyses were performed of 

both a repressurization transient (#65) and of a 

large-diameter primary-side pipe break transient 

(#62) to address the two types of loadings that 

collectively are responsible for more than 90 

percent of the PTS risk. Additionally, the staff 

performed analyses for embrittlement conditions 

ranging from those characteristic of current 

service to those that would be needed to produce 

a TWCF equal to the 1x10-6/ry limit. The results 

of these analyses at 60 effective full-power years 

(EFPY) and at an embrittlement level 

characteristic of the 1x10-6/ry limit appear in 

Figure 2.7. Consistent with the conclusions 

based on the probabilistic analyses, these results 

also indicate that small flaws located close to the 

ID will dominate PTS risk. 

9

Probability of Detection 

Historically, the inspection of PWR vessels has 

been conducted from the ID. Before 1986, the 

inspections were conducted with ultrasonic 

testing that was quite unreliable for flaw sizes 

and locations important to PTS. Thus, these 

examinations would be of little value when 

assessing the risk of vessel failure resulting from 

PTS. 

In 1986, the ASME Code, Section XI, began to 

require that the inspection of the vessel must be 

conducted using a technique that was effective 

for the ID near-surface zone of the vessel. This 

new requirement was based on results from the 

Program for Inspection of Steel Components 

(PISC). PISC II showed that inspection 

sensitivity needed to be increased from 50-

percent distance amplitude correction (DAC) to 

20-percent DAC and a special technique is 

required for this ID near-surface zone using the 

increased sensitivity. PISC II showed that a 

technique using 70 dual-L wave probes would 

accomplish this. Subsequently, the NRC has 

required the implementation of Appendix VIII, 

leading to the availability of improved data to 

document the effectiveness of the NDE for the 

flaws important to PTS. Supplement 4 of 

Appendix VIII covers the clad-to-base metal 

region up to a depth of 1 inch or 10 percent of 

the vessel wall thickness, whichever is larger. 

Thus, Supplement 4 or Appendix VIII of the 

ASME Code addresses the flaw locations and 

sizes of interest for PTS. 

tWALL

tCLAD

2a

ID OD

L

2c

Figure 2.4. Flaw dimension and position 

descriptors adopted in FAVOR 

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 2.5. Distribution of through-wall position 

of cracks that initiate 
Figure 2.6. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to (left) medium- and large-diameter pipe break transients and (right) stuckopen valve transients at two different embrittlement levels 

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0

2a [inches]

(note: c=6a)

L [inches]

In a probabilistic analysis, 

almost all of the TWCF comes 

from this shaded region.

Re-pressurization 

transient

at 10-6/ry TWCF limit

at 60 EFPY

Large diameter 

pipe break 

transient

CPI  0

CPI > 0

tWALL

tCLAD

2a

ID OD

L

2c

at 60 EFPY

at 10-6/ry TWCF limit

Note: Each curve in the figure above divides the graph into two regions: 

 The region above each curve represents combinations of flaw location (L) and flaw size (2a) that 

cannot produce crack initiation for the embrittlement and loading conditions represented by the curve. 

 The region below each curve represents combinations of flaw location (L) and flaw size (2a) that 

produce some finite probability of crack initiation for the embrittlement and loading conditions 

represented by the curve. 

Figure 2.7. Analysis of Palisades transients #65 (repressurization transient) and #62 (large-diameter 

primary-side pipe break transient) to illustrate what combinations of flaw size and location 

lead to non-zero conditional probabilities of crack initiation 

10
In 2002, Becker documented the performance of 

inspectors that have gone through the 

Supplement 4 qualification process (Becker 02). 

Becker’s paper describes the findings of the U.S. 

Performance Demonstration Initiative (PDI), 

which has manufactured 20 RPV mockups that, 

in total, contain in excess of 300 flaws. Since its 

inception in 1994, the PDI has performed over 

10 separate automated demonstrations as well as 

numerous manual qualifications. The welds 

examined include both shell welds and the more 

difficult to examine nozzle-to-shell and nozzleinner-radius welds. Figure 2.8, digitized from 

Figure 2 of Becker’s paper, shows the 

probability of detection as a function of crack 

depth (here called through-wall extent) 

considering pooled data from both manual and 

automated inspection processes. This 

probability of detection (POD) curve is based on 

results of passed plus failed candidates, which is 

standard industry practice. Inclusion of passed 

candidates only when deriving a POD curve is 

regarded as being overly optimistic; the 

inclusion of passed plus failed candidates is 

taken to provide a lower-bound estimate of 

expected inspection performance. 

Summary 

Combining the information on POD from Figure 

2.8 with the information on the flaw sizes that 

are needed to produce non-zero crack initiation 

probabilities (Figure 2.5 through Figure 2.7) 

leads to the following conclusions: 

 For the foreseeable future (i.e., out to 60 

years of operation) if an inspection were to 

be performed that inspection should focus 

on detection of flaws having a through-wall 

extent of 0.3–0.4 inches and larger because 

these are the flaws that make the greatest 

contribution to the non-zero probability of 

crack initiation from PTS loading. 

Performing RPV inspections in accordance 

with ASME Code, Appendix VIII, 

Supplement 4 requirements results in a 99-

percent or greater probability that such flaws 

can be detected. 

 If a vessel were to be embrittled to the point 

that it challenged the 1x10-6/ry limit on 

TWCF and if an inspection were to be 

performed that inspection should focus on 

detection of flaws having a through-wall 

extent of approximately 0.1 inch and larger 

because these are the flaws that make the 

greatest contribution to the non-zero 

probability of crack initiation from PTS 

loading. Performing RPV inspections in 

accordance with ASME Code, Appendix 

VIII, Supplement 4 requirements results in 

an 80-percent or greater probability that 

such flaws can be detected. 

Based on the information presented in this 

section it seems highly likely that the flaw sizes 

of importance to PTS can be detected if 

inspections are performed in accordance with 

ASME Code, Appendix VIII, Supplement 4 

requirements. 

No samples had flaws 

with TWE < 0.1-in. POD curve is 

extrapolated below 0.1-in.

[Becker 2002]

0%

20%

40%

60%

80%

100%

0.0 0.2 0.4 0.6 0.8 1.0

Through-Wall Extent [in]

Probability of 

Detection for ID Exam

Figure 2.8. Probability of detection curve (Becker 02)

11
12
Chapter 3 - PTS Screening Limits 

3.1 Overview 

On the basis of the findings of the internal 

reviews that Chapter 2 detailed, the NRC 

developed a change specification for FAVOR 

(see Appendix A). FAVOR Version 04.1, which 

was used to develop the TWCF estimates 

reported in NUREG-1806 (EricksonKirk-Sum), 

was revised in accordance with this specification 

to produce FAVOR Version 06.1 (Williams 07; 

Dickson 07a). Additionally, a special version of 

FAVOR 06.1 was developed to run on the Oak 

Ridge National Laboratory super-computer 

cluster to facilitate efficient simulation of large 

populations of underclad cracks. Detailed 

results from the FAVOR Version 06.1 analyses 

of plate-welded and ring-forged vessels can be 

found in (Dickson 07b). 

Information in this chapter is organized as 

follows: 

 Section 3.2 reviews the rationale first put 

forward in NUREG-1806 for using plantspecific TWCF versus RT results to develop 

RT-based screening limits useful for 

assessing the PTS risk of any PWR currently 

operating in the United States. 

 Section 3.3 examines the FAVOR 06.1 

results for Beaver Valley Unit 1, Oconee 

Unit 1, and Palisades (Dickson 07b). 

Similarity to the FAVOR 04.1 results 

reported in NUREG-1806 is assessed, and 

the FAVOR 06.1 results are used to 

establish relationships between TWCF and 

RT-metrics for plate-welded PWRs 

currently in operation. 

 Section 3.4 examines the FAVOR results for 

ring-forged vessels (Dickson 07b). These 

results are used to establish relationships 

between TWCF and RT-metrics for ringforged PWRs currently in operation. 

 Section 3.5 combines the information in 

Sections 3.3 and 3.4 to produce two options 

for regulatory implementation of these 

results. The first option places a limit on the 

estimated TWCF value while the second 

option places limits on the RT values 

associated with the various steels from 

which the reactor beltline is constructed. 

These options are completely equivalent, as 

they both derive directly from the results 

presented in Sections 3.3 and 3.4. 

3.2 Use of Plant-Specific Results to 

Develop Generic RT-Based 

Screening Limits 

This section first justifies the approach of using 

the results of plant-specific probabilistic 

analyses to develop RT-based screening limits 

applicable to all U.S. PWRs. The section then 

discusses the use of an RT approach to 

correlating the TWCF that occurs as a result of 

various flaw populations. The section concludes 

with a discussion of the need for margin when 

using the proposed approach. 

3.2.1 Justification of Approach 

Chapter 8 of NUREG-1806 (EricksonKirkSum) estimates the variation of TWCF with 

embrittlement level in the three study plants 

(Oconee Unit 1, Beaver Valley Unit 1, and 

Palisades). NUREG-1806 reported the 

following major findings: 

 Only the most severe primary-side transients 

(medium- to large-diameter pipe breaks and 

stuck-open valves that later reclose) 

contribute in any significant manner to the 

risk of vessel failure from PTS. At lower 

embrittlement levels stuck-open valves are 

the dominant risk contributors. However, at 

the embrittlement levels needed to produce 

an estimated TWCF equal to the 10-6/ry 

limit, medium- to large-diameter pipe breaks 

dominate. 

 Severe secondary-side transients (e.g., a 

break of the main steamline) do not 

contribute significantly to the risk of vessel 

failure from PTS. These transients have 

13
extremely rapid initial cooling rates, which 

generate high thermal stresses close to the 

vessel inner diameter. Nevertheless, the 

minimum temperature in the primary system 

that occurs during these transients, the 

boiling point of water, is not low enough to 

produce a significant risk of brittle fracture 

in the RPV steel. Additionally, a 

conservatism of the TH models adopted for 

the main steamline break (MSLB) (i.e., not 

accounting for the fact that pressurization of 

containment caused by the break will raise 

the boiling point of water by 30–40 F 

above that assumed, 212 F, in the TH 

analysis) suggests strongly that reported 

TWCF values for this transient class 

overestimate those that can actually occur. 

Collectively, these findings demonstrate that 

only the most severe transients contribute 

significantly to the estimated risk of RPV failure 

caused by PTS. Information presented in 

NUREG-1806 demonstrates that the nature of 

these transient classes is not expected to vary 

greatly among the population of currently 

operating PWRs. This information is 

summarized below: 

 Medium- to Large-Diameter Primary-Side 

Pipe Breaks: To be risk significant the 

break diameter needs to exceed 

approximately 5 inches. The similarity of 

PWR vessel sizes in the operating U.S. 

reactor fleet suggests that different plants 

will have nominally equivalent reactor 

coolant system (RCS) cooling rates for these 

large break diameters. Additionally, the 

cooling rate of the RCS inventory for these 

large breaks exceeds that achievable by the 

RPV steel, which is limited by its thermal 

conductivity of the vessel steel and does not 

vary from vessel to vessel because it is a 

physical property of the material. 

Consequently, any small plant-to-plant 

variability that may exist in RCS inventory 

cooling rate cannot be transmitted to the 

cooling rate of the RPV steel, which controls 

the thermal stresses in the RPV wall. The 

only possible operator action in response to 

such a large break is to maximize injection 

flow to keep the core covered, so no plantto-plant differences arising from different 

human responses is expected. (See 

NUREG-1806, Section 8.5.2 for details.) 

 Stuck-Open Primary-Side Valves: For this 

class of transients to be risk significant two 

criteria must be met—(1) the valve must 

remain stuck open long enough that the 

temperature of the RCS inventory 

approaches that of the injection water and 

(2) once the valve recloses the primary 

system must repressurize to the safety valve 

setpoint. Both of these parameters (injection 

water temperature and safety valve setpoint 

pressure) are input to the RELAP analysis 

and so are not influenced significantly by 

RELAP modeling uncertainties. Moreover, 

neither parameter varies much within the 

population of currently operating PWRs. 

The modeling of this transient class reflects 

credible operator actions. These actions do 

alter some details of the predicted pressure 

and temperature transients and do vary 

somewhat based on the RPV vendor because 

training programs are vendor specific. 

Nevertheless, the analysis demonstrated that 

most differences caused by operator actions 

do not appreciably influence the risk 

significance of the transient. Operator 

actions only matter if repressurization of the 

primary system can be prevented after valve 

reclosure. If the operator throttles injection 

within 1 minute of being allowed, and if the 

transient was initiated under HZP conditions 

then repressurization can be prevented. 

Because HZP accounts for only a small 

percentage of the plant’s operating time, the 

total effect of the modeled operator actions 

on the estimated risk significance of these 

transients is small. (See NUREG-1806, 

Section 8.5.3 for details.) 

 Main Steamline Breaks: As discussed 

earlier, even though these transients produce 

an extremely rapid initial cooling rate of the 

RCS inventory (as a result of the large break 

area) the minimum temperature of the RCS 

(the boiling point of water) is generally high 

enough to ensure a high level of fracture 

toughness in the vessel wall, thereby 

preventing MSLB transients from 

14
As discussed in Section 8.4 of NUREG-1806, to 

correlate and/or predict resistance of an RPV to 

fracture, information concerning the fracture 

resistance of the materials in the vessel at the 

location of the flaws in the vessel is needed. RT 

values characterize the resistance of a ferritic 

steel to cleavage crack initiation and arrest and 

to ductile crack initiation (EricksonKirk-PFM). 

NUREG-1806 proposed both weighted and 

maximum RT metrics. Weighted RT metrics 

accounted for differences in weld length and 

plate volume between different plants, while 

maximum RT metrics did not. However, 

because of the similarities in the size of all 

domestic PWRs, the weighted RT metrics did 

not provide significantly better correlations with 

the TWCF data than did the maximum RT 

metrics. Furthermore, maximum RT metrics can 

be estimated for all operating PWRs based 

mostly on information currently contained 

within the NRC’s RVID database (RVID2) 

while weighted RT metrics require additional 

information from plant construction drawings. 

While this information is available, it is not 

currently compiled for all plants in a single 

location. For these reasons, this report restricts 

its attention to maximum RT metrics. 

contributing significantly to the total TWCF 

estimated for a plant. The size of the main 

steamline is sufficiently large that the 

cooling rate of the RPV wall is limited by 

the thermal conductivity of the vessel steel, 

which does not vary from plant to plant. In 

the rare instance that through-wall cracking 

does arise from an MSLB transient, it will 

occur within 10–15 minutes after transient 

initiation, long before any operator actions 

can credibly be expected to occur, so plantspecific operator action differences cannot 

be expected to alter the TWCF associated 

with this transient class. (See NUREG1806, Section 8.5.4 for details.) 

With one small exception, the “generalization 

study,” in which the plant characteristics that 

can influence PTS severity of five additional 

high embrittlement plants were investigated, 

validated these expectations. (See (WhiteheadGen) and Section 9.1 of NUREG-1806 for 

details.) The recommended PTS screening 

limits presented in Section 3.5 account for this 

exception. 

In summary, the NRC’s study demonstrates that 

risk-significant PTS transients do not have any 

appreciable plant-specific differences within the 

population of PWRs currently operating in the 

United States. These findings motivate the 

development of generic screening limits that can 

be applied to all operating PWRs. 

Formulae for the three maximum RT metrics 

proposed in NUREG-1806 (RTMAX-AW, RTMAXPL, and RTMAX-CW) are repeated below (the 

algebraic expression of these formulae have 

been modified slightly from the form reported in 

NUREG-1806 to improve clarity): 

3.2.2 Use of Reference Temperatures to 

Correlate TWCF 

RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found along the 

axial weld fusion lines. It is evaluated using the following formula for each axial weld 

fusion line within the beltline region of the vessel (the part of the formula inside the 

{...}). The value of RTMAX-AW assigned to the vessel is the highest of the reference 

temperature values associated with any individual axial weld fusion line. In evaluating 

the T30 values in this formula the composition properties reported in the RVID 

database are used for copper, nickel, and phosphorus. An independent estimate of the 

manganese content of each weld and plate evaluated is also needed. 

Eq. 3-1   

    

































   

 





FL

ipladj ipladj

uNDT

FL

iawadj iawadj

uNDT

RT tT

RT tT





)(

30

)(

)(

)(

30

)(

)(

AWFL(i)

n

1i

AWMAX

, RT MAX MAX AWFL

 where 

15
 nAWFL is the number of axial weld fusion lines in the beltline region of the 

vessel, 

 i is a counter that ranges from 1 to nAWFL, 

tFL is the maximum fluence occurring on the vessel ID along a particular 

axial weld fusion line, 

is the unirradiated RTNDT of the weld adjacent to the ith axial weld 

fusion line, 

)(

)(

iawadj RT uNDT

is the unirradiated RTNDT of the plate adjacent to the ith axial weld 

fusion line, 

)(

)(

ipladj RT uNDT

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the weld 

adjacent to the ith axial weld fusion line, and 

)(

30

iawadj T  

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the plate 

adjacent to the ith axial weld fusion line. 

)(

30

ipladj T  

RTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in plates that are 

not associated with welds. It is evaluated using the following formula for each plate 

within the beltline region of the vessel. The value of RTMAX-PL assigned to the vessel is 

the highest of the reference temperature values associated with any individual plate. In 

evaluating the T30 values in this formula the composition properties reported in the 

RVID database are used for copper, nickel, and phosphorus. An independent estimate of 

the manganese content of each weld and plate evaluated is also needed. 

Eq. 3-2    )()(

30

)(

)(

n

1i

PLMAX MAXPL

RT iPL

MAX

iPL iPL

uNDT  RT  tT 



 where 

 nPL is the number of plates in the beltline region of the vessel, 

i is a counter that ranges from 1 to nPL, 

 is the maximum fluence occurring over the vessel ID occupied by a 

particular plate, 

iPL )(

MAX t

is the unirradiated RTNDT of a particular plate, and )(

)(

iPL RT uNDT

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to of a 

particular plate. 

)(

30

iPL T

iPL )(

MAX t

RTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along the 

circumferential weld fusion lines. It is evaluated using the following formula for each 

circumferential weld fusion line within the beltline region of the vessel (the part of the 

formula inside the {...}). Then the value of RTMAX-CW assigned to the vessel is the 

highest of the reference temperature values associated with any individual 

circumferential weld fusion line. In evaluating the T30 values in this formula the 

composition properties reported in the RVID database are used for copper, nickel, and 

phosphorus. An independent estimate of the manganese content of each weld, plate, and 

forging evaluated is also needed. 

16
Eq. 3-3 

  

   

    















































 

 

 





FL

ifoadj ifoadj

uNDT

FL

ipladj ipladj

uNDT

FL

icwadj icwadj

uNDT

RT tT

RT tT

RT tT







)(

30

)(

)(

)(

30

)(

)(

)(

30

)(

)(

CWFL(i)

n

1i

CWMAX ,

,

RT MAX MAX CWFL

 where 

 nCWFL is the number of circumferential weld fusion lines in the beltline 

region of the vessel, 

 i is a counter that ranges from 1 to nCWFL, 

tFL is the maximum fluence occurring on the vessel ID along a particular 

circumferential weld fusion line, 

is the unirradiated RTNDT of the weld adjacent to the ith

circumferential weld fusion line, 

)(

)(

icwadj RT uNDT

is the unirradiated RTNDT of the plate adjacent to the ith

circumferential weld fusion line (if there is no adjacent plate this 

term is ignored), 

)(

)(

ipladj RT uNDT

is the unirradiated RTNDT of the forging adjacent to the ith

circumferential weld fusion line (if there is no adjacent forging this 

term is ignored), 

)(

)(

ifoadj RT uNDT

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the weld 

adjacent to the ith circumferential weld fusion line, 

)(

30

icwadj T  

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the plate 

adjacent to the ith axial weld fusion line(if there is no adjacent plate 

this term is ignored), and 

)(

30

ipladj T  

is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

forging adjacent to the ith axial weld fusion line(if there is no 

adjacent forging this term is ignored). 

)(

30

ifoadj T  

The T30 values in Eq. 3-1 to Eq. 3-3 are determined as follows:†

Eq. 3-4 30  CRPMDT

   e RCS AMD T PMn t 471.2  001718.01  130.61

    e e e

RCS tNiCugPCuf T BCRP Ni ,,,  1.543

769.31

100.1

191.1 



 



  

 

†

 The results reported in Appendix C demonstrate that the alternative form of this relationship presented in 

Chapter 7 of (Eason 07) has no significant effect on the TWCF values estimated by FAVOR. 

17




























for welds 10x417.1

platesfor 10x561.1

forgingsfor 10x140.1

7

7

7

A































for welds 0.155

manufactur CEin platesfor 2.135 vesselsed

manufactur CE-nonin platesfor 5.102 vesselsed

 forgingsfor 3.102

B





















 













 



 10

2595.0 10

10

103925.4for 103925.4

103925.4for 

  



 t

t

te

Note: Flux () is estimated by dividing fluence (t) by the time (in seconds) that 

the reactor has been in operation. 

    



 



    

6287.0

12025.184483.01390.1log tanh

2

1

2

1 ,, 10 t Cu Ni tNiCug e e

e e

 

   

  



















  

  





072.0for 0.008)-(359.1072.0 008.0

072.0for 072.0 008.0

072.0for 0

, 0.6679

0.6679

Cu P Cu Pand

Cu Cu Pand

Cu

PCuf

e

e e















  wt%072.0for 

 wt%072.0for 0

CuCu

Cu

Cue





























flux) L1092 with welds(all wt%0.75 Nifor 301.0

 wt%0.75 Ni 0.5for 2435.0

 wt%0.5 Nifor 370.0

)(CuMax e

NUREG-1806 proposes the use of these three 

different RTs in recognition of the fact that the 

probability of vessel fracture initiating from 

different flaw populations varies considerably 

as a result of the following known factors: 

 The degree of irradiation damage suffered 

by the material at the flaw tips varies with 

location in the vessel because of differences 

in chemistry and fluence. 

These differences indicate that it is impossible 

for a single RT value to represent accurately the 

resistance of the RPV to fracture in the general 

case. Indeed, this is precisely the liability 

associated with the RT value currently adopted 

by 10 CFR 50.61, the RTPTS. The RTPTS, as 

defined in 10 CFR 50.61, is the maximum 

RTNDT of any region in the vessel (a region is an 

axial weld, a circumferential weld, a plate, or a 

forging) evaluated at the peak fluence occurring 

in that region. Consequently, the RTPTS value 

currently assigned to a vessel may only 

coincidentally correspond to the toughness 

 Different regions of the vessel have flaw 

populations that differ in size (weld flaws 

are considerably larger than plate flaws), 

density (weld flaws are more numerous than 

plate flaws), and orientation (axial and 

circumferential welds have flaws of 

corresponding orientations, whereas 

plate flaws may be either axial or 

circumferential). The driving force to 

fracture depends both on flaw size and 

orientation, so different vessel regions 

experience different fracture-driving forces. 

18
properties of the material region responsible for 

the bulk of the TWCF, as illustrated by the 

following examples: 

 Out of 71 operating PWRs, 14 have their 

RTPTS values established based on 

circumferential weld properties (RVID2). 

However, the results in NUREG-1806 show 

that the probability of a vessel failing as a 

consequence of a crack in a circumferential 

weld is extremely remote because of the 

lack of through-wall fracture driving force 

associated with circumferentially oriented 

cracks. For these 14 vessels, the RTPTS

value is unrelated to any material that has 

any significant chance of causing vessel 

failure. 

 Out of 71 operating PWRs, 32 have their 

RTPTS values established based on plate 

properties (RVID2). Certainly, plate 

properties influence vessel failure 

probability; however, the 10 CFR 50.61 

practice of evaluating RTPTS at the peak 

fluence occurring in the plate is likely to 

estimate a toughness value that cannot be 

associated with any large flaws because the 

location of the peak fluence may not 

correspond to an axial weld fusion line. 

While the RTPTS value for these 32 vessels is 

based on a material that significantly 

contributes to the vessel failure probability, 

it is likely that RTPTS has been overestimated 

(perhaps significantly so) because the 

fluence assumed in the RTPTS calculation 

does not correspond to the fluence at a likely 

flaw location. 

 Out of 71 operating PWRs, 15 have their 

RTPTS values established based on axial 

weld properties (RVID2). It is only for 

these vessels that the RTPTS value is clearly 

associated with a material region that 

contributes significantly to the vessel failure 

probability and is evaluated at a fluence that 

is clearly associated with a potential location 

of large flaws. 

For these reasons, the use of the three RTmetrics proposed here (RTMAX-AW, RTMAX-PL, and 

RTMAX-CW) is expected to increase the accuracy 

with which the TWCF in a vessel can be 

estimated relative to the current 10 CFR 50.61 

procedure, which uses a single RT-metric 

(RTPTS). 

3.3 Plate-Welded Plants 

3.3.1 FAVOR 06.1 Results 

Detailed results from the FAVOR 06.1 analyses 

of Oconee Unit 1, Beaver Valley Unit 1, and 

Palisades can be found in a separate report by 

(Dickson 07b). Table 3.1 includes a summary of 

these results, which have been reviewed and 

found to be consistent in most respects with the 

findings presented in NUREG-1806. This 

section highlights two key findings that support 

the use of these results to develop RT-based 

screening limits applicable to all plate-welded 

plants. 

Characteristics of TWCF Distributions 

Section 8.3.2 of NUREG-1806 reported that the 

TWCF distributions calculated previously by 

FAVOR Version 04.1 were heavily skewed 

towards zero or very low values, and that this 

skewness occurs as a natural consequence of (1) 

the rarity of multiple unfavorable factors 

combining to produce a high failure probability 

and (2) the fact that the distributions of both 

cleavage crack initiation and cleavage crack 

arrest fracture toughness have finite lower 

bounds. Figure 3.1 demonstrates that the 

changes made to the FAVOR code (see 

Appendix A) have not qualitatively altered this 

situation. However, as illustrated in Figure 3.2, 

the percentile of the TWCF distribution 

corresponding to the mean TWCF value is lower 

for the FAVOR 06.1 results than it was for the 

FAVOR 04.1 results. The mean TWCF values 

estimated using FAVOR 04.1 corresponded to 

between the 90th and 99th percentile, depending 

on the level of embrittlement. Conversely, the 

mean TWCF values estimated using FAVOR 

06.1 corresponded to between the 80th and 99th 

percentile. The percentile associated with the 

mean TWCF has been reduced in FAVOR 06.1 

results for the following two reasons: 

19
(1) The change in the data basis for the RTNDT

epistemic uncertainty correction (see Task 

1.1 in the FAVOR change specification in 

Appendix A) and the change in the 

embrittlement trend curve (see Task 1.5 in 

the FAVOR change specification in 

Appendix A) have increased the 

embrittlement level associated with each 

EFPY analyzed. This increase in 

embrittlement reduces the TWCF percentile 

associated with the mean along the same 

trend line established by the FAVOR 04.1 

analyses (see Figure 3.2). Indeed, the 

percentile associated with the mean should 

reduce with increased embrittlement 

because, for more embrittled materials, 

fewer zero failure probability vessels are 

simulated, leading to a less skewed 

distribution of TWCF. 

(2) The change in the RTNDT epistemic 

uncertainty sampling procedure (in FAVOR 

04.1, the RTNDT epistemic uncertainty was 

sampled inside the flaw loop; in FAVOR 

06.1, this sampling was moved outside of 

the flaw loop—see Task 1.3 in the FAVOR 

change specification in Appendix A) has 

pushed more of the density of the TWCF 

distributions to occur in their upper tails, 

thereby broadening them. This change was 

motivated by the observation that the 

FAVOR 04.1 procedure simulated an 

uncertainty in RTNDT for an individual 

major-region of a simulated vessel (a majorregion is an individual weld, plate, or 

forging) having a total range in excess of 

150 F. This range is much larger than that 

measured in laboratory tests, so FAVOR 

was modified to bring its simulations into 

better accord with observations. 

NUREG-1806 uses mean TWCF values in the 

TWCF versus RT regressions because the 

percentile associated with the mean exceeded 90 

percent in all cases (see Figure 3.2). As 

explained earlier, this is no longer the case, and 

it is not appropriate to use 80th percentile 

TWCF values in the TWCF versus RT 

regressions because doing so would create too 

high a chance (1 chance out of 5) that the TWCF 

associated with a particular RT value is 

underestimated. Consequently, the following 

sections of this report use 95th percentile TWCF 

values in the TWCF versus RT regressions. Use 

of 95th percentile values makes the probability 

that the TWCF is underestimated acceptably 

small (1 chance out of 20). 

 

0%

5%

10%

15%

20%

25%

30%

35%

zero

<= E-16

E-15E-14E-13E-12E-11E-10

E-9E-8E-7E-6E-5E-4

TWCF Value

Percent of Simulated Vessels

32 EFPY

Ext-B

Figure 3.1. TWCF distributions for Beaver 

Valley Unit 1 estimated for 32 

EFPY and for a much higher level 

of embrittlement (Ext-B). At 32 

EFPY the height of the “zero” bar 

is 62 percent. 

0

10

20

30

40

50

60

70

80

90

100

100 200 300 400

Maximum RTNDT Along Axial Weld 

Fusion Line [o

F]

Percentile of Mean TWCF Value

Oconee

Beaver Valley

Palisades

Shaded Symbols: FAVOR 04.1

(NUREG-1806)

Solid Symbols: FAVOR 06.1

(This Report)

0

10

20

30

40

50

60

70

80

90

100

100 200 300 400

Maximum RTNDT Along Axial Weld 

Fusion Line [o

F]

Percentile of Mean TWCF Value

Oconee

Beaver Valley

Palisades

Shaded Symbols: FAVOR 04.1

(NUREG-1806)

Solid Symbols: FAVOR 06.1

(This Report)

Figure 3.2. The percentile of the TWCF 

distribution corresponding to mean 

TWCF values at various levels of 

embrittlement 

20
Dominant Transients 

As reported in Section 8.5 of NUREG-1806 and 

summarized in Section 3.2.1 of this report, only 

the most severe transients make any significant 

contribution to the total estimated risk of 

through-wall cracking from PTS. Examination 

of the results in (Dickson 07b) shows that the 

risk-dominant transients listed in Tables 8.7, 8.8, 

and 8.9 of NUREG-1806 also dominate the risk 

in the current (i.e., FAVOR 06.1) analyses. 

21

Figure 3.3 shows the dependence of the TWCF 

resulting from the two dominant transient 

classes (medium- to large-diameter primary-side 

pipe breaks, and stuck-open primary valves that 

may later reclose) and of MSLBs on 

embrittlement level (as quantified by RTMAXAW). The trends in these figures agree well with 

those reported previously in Section 8.5 of 

NUREG-1806, i.e.: 

 Stuck-open primary-side valves dominate 

the TWCF at lower embrittlement levels. 

As embrittlement increases, medium- to 

large-diameter primary-side pipe breaks 

become the dominant transients. In 

combination these transient classes 

constitute 90 percent or more of the total 

TWCF irrespective of embrittlement level. 

 MSLBs are responsible for virtually all of 

the remaining risk of through-wall cracking. 

It should, however, be remembered that the 

models of MSLBs are intentionally 

conservative. More accurate modeling of 

MSLB transients is therefore expected to 

further reduce their perceived risk 

significance. 

 None of the other transient classes (smalldiameter primary-side breaks, stuck-open 

secondary valves, feed and bleed, steam 

generator tube rupture) are severe enough to 

significantly contribute to the total TWCF. 

Dominant Material Features 

Figure 3.4 shows the relationship between the 

three RT metrics described in Section 3.2.2 (i.e., 

RTMAX-AW, RTMAX-PL, and RTMAX-CW) and the 

TWCF resulting from their three respective flaw 

populations—axial fusion line flaws in axial 

welds, axial and circumferential flaws in plates, 

and circumferential flaws in circumferential 

welds. The following trends, demonstrated by 

the data in this figure agree well with those 

reported previously in Section 11.3.2 of 

NUREG-1806: 

 The TWCF produced by axial weld flaws 

dominates the PTS risk of plate-welded 

PWRs. 

 The TWCF produced by plate flaws makes a 

more limited contribution to PTS risk than 

do axial weld flaws. This is because the 

plate flaws, while more numerous than axial 

weld flaws, are considerably smaller. 

Additionally, half of the plate flaws are 

oriented circumferentially and half are 

oriented axially. 

 The TWCF produced by circumferential 

flaws is essentially negligible. At the 

highest RTMAX-CW currently expected for any 

PWR after 60 years of operation (258 F or 

718R), circumferential weld flaws are 

responsible for approximately 0.04 percent 

of the 1x10-6/ry TWCF limit proposed in 

Chapter 10 of NUREG-1806. 

The equations of the curves in Figure 3.4 all 

share the same form, which is as follows: 

Eq. 3-5

TWCF95xx    lnexp   RTm xxMAX  xxTH  bRT 

In Eq. 3-5, the 95 subscript denotes the 95th 

percentile; while the “xx” subscript indicates the 

flaw population (xx is AW for axial weld flaws, 

CW for circumferential weld flaws, and PL for 

plate flaws). The value RTTH-xx is a fitting 

coefficient that permits Eq. 3-5 to have a lower 

vertical asymptote on a semi-log plot. Values of 

temperature are expressed in absolute degrees 

(Rankine = Fahrenheit + 459.69) to prevent a 

logarithm from being taken of a negative 

number. Values of the best-fit coefficients for 
Table 3.1. Summary of FAVOR 06.1 Results Reported in (Dickson 07b)

TWCF Partitioned by 

Flaw Population (% of 

total TWCF) 

TWCF Partitioned b

95 tota

th

%ile 

TWCF 

(/ry) 

Plant EFPY RTMAX- AW

[

oF] 

RTMAXCW

[

oF] 

RTMAXPL

[

oF] 

MEAN 

FCI 

(/ry) 

Mean 

TWCF 

(/ry) 

%ile of 

Mean 

TWCF Primary StuckOpen 

Valves 

Axial 

Welds 

Circ. 

Welds Plates 

Primary 

Pipe 

Breaks 

32 187 224 224 1.10E- 07 1.69E- 09 97.4 3.54E- 10 93.29 0.59 6.12 7.66 92.21 60 204 253 253 5.64E- 07 6.84E- 09 93.7 1.03E- 08 68.15 3.32 28.52 34.45 64.67 

Ext-A 221 284 284 2.31E- 06 4.08E- 08 87.2 1.52E- 07 

Beaver 53.88 5.30 40.83 49.25 47.63 

Ext-B 252 339 339 1.44E- 05 5.73E- 07 80.5 2.45E- 06 21.53 15.05 63.42 70.41 19.58 

32 163 183 75 1.25E- 09 1.13E- 09 98.8 1.16E- 13 100.00 0.00 0.00 0.01 99.99 60 179 198 87 2.84E- 09 2.15E- 09 98.2 5.35E- 11 100.00 0.00 0.00 0.11 99.88 

Ext-A 253 277 158 3.19E- 07 2.84E- 08 93.1 4.63E- 08 

Oconee 99.91 0.07 0.03 9.10 90.89 

Ext-B 298 326 206 2.77E- 06 1.40E- 07 86.7 4.39E- 07 98.96 0.68 0.36 35.65 64.36 

32 222 208 184 1.46E- 07 1.59E- 08 93.2 2.50E- 08 99.99 0.00 0.00 49.64 47.61 60 247 231 209 4.64E- 07 7.85E- 08 90.0 1.96E- 07 100.01 0.00 0.00 59.70 28.52 

Ext-A 322 302 286 5.21E- 06 1.74E- 06 81.5 6.12E- 06 99.84 0.02 0.14 80.60 10.02 

Palisades 

Ext-B 416 393 389 4.70E- 05 2.49E- 05 76.9 8.37E- 05 97.53 0.17 2.33 77.91 4.77 

22
August 2006

FAVOR 06.1

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-04

550 650 750 850

Max. RT AW [R]

95th Percentile TWCF Due to 

Primary Side Pipe Breaks Beaver

OconeePalisades

August 2006

FAVOR 06.1

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-04

550 650 750 850

Max. RT AW [R]

95th Percentile TWCF Due to 

Primary Side Pipe Breaks Beaver

OconeePalisades

August 2006

FAVOR 06.1

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-04

550 650 750 850

Max. RT AW [R]

95th Percentile TWCF Due to Stuck-

Open Primary Valves

BeaverOconeePalisades

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-04

550 65

Ma

95th Percentile TWCF Due to Main 

Steam Line Breaks

Figure 3.3. Dependence of TWCF due to various transient classes on embrittlement as quantified by the parameter RTMAX-A

drawn to illustrate trends) 

23
August 2006

FAVOR 06.1

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 650 750 850

Max. RT AW [R]

95th %ile TWCF - Axial Weld Flaws Beaver Oconee Palisades

Fit

August 2006

FAVOR 06.1

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 650 750 850

Max. RT PL [R]

95th %ile TWCF - Plate Flaws Beaver Oconee

PalisadesFit

August 2

FAVOR 

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 65

M

95th %ile TWCF - Circ Weld Flaws 

Figure 3.4. Relationship between TWCF and RT due to various flaw populations (left: axial weld flaws, center: plate flaws

weld flaws). Eq. 3-5 provides the mathematical form of the fit curves shown here. 

24
each flaw population, established by leastsquares analysis of the data in Figure 3.4, are as 

follows:

Regressor Variable m b RTTH [R]

RTMAX-AW 5.5198 -40.542 616 

RTMAX-PL 23.737 -162.36 300 

RTMAX-CW 9.1363 -65.066 616 

Below the value of RTTH-xx the value of 

TWCF95-xx is undefined and should be taken as 

zero.

3.3.2 Estimation of TWCF Values and

RT-Based Limits for Plate-Welded 

PWRs 

Similar to the procedure described in NUREG1806, the fits to the TWCF95-xx versus RTMAX-xx

relationships shown in Figure 3.4 and quantified 

by Eq. 3-5 are combined to develop the 

following formula that can be used to estimate 

the TWCF of any currently operating platewelded PWR in the United States: 

Eq. 3-6 























 

 











CW CW

PL PL

AW AW

TOTAL

TWCF

TWCF

TWCF

TWCF

95

95

95

95







Here the values of TWCF95-xx are estimated 

using Eq. 3-5. The  factors are introduced to 

prevent underestimation of TWCF95 at low 

embrittlement levels from stuck-open valves on 

the primary side that may later reclose (see 

Chapter 9 of NUREG-1806). Values of  are 

defined as follows: 

 If RTMAX-xx ≤ 625R, then  = 2.5 

 If RTMAX-xx ≥ 875R, then  = 1 

 If 625R < RTMAX-xx < 875R then 

  625

250

5.1

 5.2  RT xxMAX 

Reduction of  as embrittlement (RT) increases 

is justified because the generalization study only 

revealed the potential for the severity of stuckopen valve transients to be slightly 

underrepresented, and stuck-open valves make 

only small contributions to the total TWCF95 at 

high embrittlement levels. 

 

Eqs. 3-5 and 3-6 define a relationship between 

RTMAX-AW, RTMAX-PL, and RTMAX-CW and the 

resultant value of TWCF95. Eqs. 3-5 and 3-6 

may be represented graphically as illustrated in 

Figure 3.5; the TWCF of the surface shown is 

1x10-6. Combinations of RTMAX-AW, RTMAX-PL, 

and RTMAX-CW that lie inside the surface 

therefore have TWCF95 values below 1x10-6. 

Eqs. 3-5 and 3-6 can be used, together with 

values of RTMAX-AW, RTMAX-PL, and RTMAX-CW

determined from information in the RVID 

database, to estimate the TWCF of any platewelded PWR currently operating in the United 

States. (See Section 3.3.3 for a necessary 

modification to these formulae for RPVs having 

wall thicknesses above 9.5 inches.) These 

calculations (see Section 3.5.1 for details) show 

that no operating PWRs are expected to exceed 

or approach a TWCF of 1x10-6/ry after either 40 

or 60 years of operation. 

The two-dimensional version of the threedimensional graphical representation of Eq. 3-6 

provided inFigure 3.5 can be used to develop 

RT-based screening limits for plate-welded 

plants. As was done in NUREG-1806, RT limits 

can be established by setting the total TWCF in 

Eq. 3-6 equal to the reactor vessel failure 

frequency acceptance criterion of 1x10-6

events/year proposed in Chapter 10 of that 

document. Plate vessels are made up of axial 

welds, plates, and circumferential welds, so in 

principle, flaws in all of these regions will 

contribute to the total TWCF. However, as 

revealed by the RT values reported in Table 3.3, 

the contribution of flaws in circumferential 

welds to TWCF is negligible. The highest 

RTMAX-CW anticipated for any currently operating 

PWR after 60 years of operation (assuming 

current operating conditions are maintained) is 

258 F. At this embrittlement level flaws in 

circumferential welds would contribute 

approximately 0.04 percent of the 1x10-6/ry 

limit. In view of this very minor contribution of 

flaws in circumferential welds to the overall 

risk, RT-based screening limits for plate-welded 

plants are developed as follows: 

25
(2) Set TWCFTOTAL to the 1x10-6/ry limit 

(1) Set TWCF95-CW to 1x10 proposed in Chapter 10 of NUREG-1806. -8/ry (this 

corresponds to an RTMAX-CW value of 

312 F, which far exceeds the highest value 

expected for any currently operating PWR 

after 60 years of operation. 

(3) Solve Eq. 3-6 to establish (RTMAX-AW, 

RTMAX-PL) pairs that satisfy equality. 

Figure 3.5. Graphical representation of Eqs. 3-5 and 3-6. The TWCF of the surface in both diagrams is 

1x10-6. The top diagram provides a close-up view of the outermost corner shown in the bottom 

diagram. (These diagrams are provided for visualization purposes only; they are not a 

completely accurate representation of Eqs. 3-5 and 3-6 particularly in the very steep regions at 

the edges of the TWCF = 1x10-6 surface.) 

26
As illustrated in Figure 3.6, this procedure 

establishes the locus of (RTMAX-AW, RTMAX-PL) 

pairs that define the horizontal cross-section of 

the three-dimensional surface depicted in Figure 

3.5 at an RTMAX-CW value of 312 F. In the 

region of the graph between the red loci and the 

origin, the TWCF is below the 1x10-6 acceptance 

criterion, so these combinations of RTMAX-AW

and RTMAX-PL would satisfy the 1x10 6/ry limit 

on TWCF. In the region of the graph outside of 

the red loci, the estimated TWCF exceeds the 

1x10-6/ry limit, indicating the need for additional 

analysis or other measures to justify continued 

plant operation. For reference, Figure 3.6 shows 

loci corresponding to other TWCF values. Of 

particular interest is the 5x10-6 locus, which 

appears in dark green. A 5x10-6 TWCF limit 

corresponds to that viewed as being acceptable 

according to the current version of Regulatory 

Guide 1.154, “Format and Content of PlantSpecific Pressurized Thermal Shock Safety 

Analysis Reports for Pressurized Water 

Reactors,” issued January 1987. 

Figure 3.6 also shows assessment points (blue 

circles and blue triangles), one representing each 

plate-welded PWR after 40 and 60 years of 

operation. The coordinates (RTMAX-AW, RTMAXPL) for each plant were estimated from 

information in the RVID database (see Table 

3.3). Comparison of the assessment points for 

the individual plants to the (proposed) 1x10-6

and (current) 5x10-6 limits in Figure 3.6 supports 

the following conclusions: 

 The risk of PTS failure is low. Over 80 

percent of operating PWRs have estimated 

TWCF values below 1x10-8/ry, even after 60 

years of operation. 

 After 40 years of operation the highest risk 

of PTS at any PWR is 2.0x10-7/ry. After 60 

years of operation this risk increases to 

4.3x10-7/ry. 

 The current regulations assume that plants 

have a TWCF risk of approximately 

5x10 6/ry when they are at the 10 CFR 50.61 

RTPTS screening limits. Contrary to the 

current situation in which several plants are 

thought to be within fractional degrees 

Fahrenheit of these limits, the staff’s 

calculations show that when realistic models 

are adopted no plant is closer than 53 F at 

EOL (40 F at end-of-license extension 

(EOLE)) from exceeding the 5x10-6/ry limit 

implicit in RG 1.154. 

 

Plate Welded Plants 

at 32 EFPY (EOL)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1E-8

1E-7

1E-6

5E-6

30oF

53oF

 

Plate Welded Plants 

at 48 EFPY (EOLE)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1E-8

1E-7

1E-6

5E-6

17oF

40oF

Figure 3.6. Maximum RT-based screening criterion (1E-6 curve) for plate-welded vessels based on Eq. 3-6 

(left: screening criterion relative to currently operating PWRs after 40 years of operation; 

right: screening criterion relative to currently operating PWRs after 60 years of operation). 

27
3.3.3 Modification for Thick-Walled Vessels 

Figure 3.7 shows that the vast majority of PWRs 

currently in service have wall thicknesses between 8 

and 9.5 inches. The three vessels analyzed in detail 

in this study are all in this range and thus represent 

the vast majority of the operating fleet. As discussed 

in Section 9.2.2.3 of NUREG-1806, the few PWRs 

having thicker walls can be expected to experience 

higher TWCF than the thinner vessels analyzed here 

(at equivalent embrittlement levels) because of the 

higher thermal stresses that occur in the thicker vessel 

walls. Figure 3.8 reproduces the results of a 

sensitivity study on wall thickness reported in 

NUREG-1806. These results show that for PTSdominant transients (the 16-inch hot leg break and 

the stuck-open safety/relief valve) the TWCF in a 

thick (11 to 11.5 inch) wall vessel will increase by 

approximately a factor of 16 over the values 

presented in this report for vessels having wall 

thicknesses between 8 and 9.5 inches. To account for 

this increased driving force to fracture in thick-walled 

vessels the staff recommends that the TWCF 

estimated by Eq. 3-6 be increased by a factor of 8 for 

each inch of thickness by which the vessel wall 

exceeds 9.5 inches. Section 3.5 provides a formula 

that formally implements this recommendation. 

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 3.7. Distribution of RPV wall thicknesses for 

PWRs currently in service (RVID2). 

This figure originally appeared as 

Figure 9.9 in NUREG-1806. 

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 3.8. Effect of vessel wall thickness 

on the TWCF of various transients in 

Beaver Valley (all analyses at 60 EFPY). 

This figure originally appeared as Figure 

9.10 in NUREG-1806. 

3.4 Ring-Forged Plants 

All three of the detailed study plants are platewelded vessels. However, 21 of the currently 

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 flaws from such vessels indicates 

that they may 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 rare 

conditions forgings may contain underclad 

cracks that are produced by the deposition of the 

austenitic stainless steel cladding layer. Thus, to 

investigate the applicability of the results 

reported in Section 3.3 to forged vessels, the 

staff performed a number of analyses on vessels 

using properties (RTNDT(u), copper, nickel, 

phosphorus, manganese) and flaw populations 

appropriate to forgings. Appendices B and D 

detail the technical basis for the distributions of 

flaws used in these sensitivity studies. 

28
3.4.1 Embedded Flaw Sensitivity Study 

Appendix D describes the distribution of 

embedded forging flaws based on destructive 

examination of an RPV forging (Schuster 02). 

These flaws are similar in both size and density 

to plate flaws. A sensitivity study based on the 

embedded forging flaw distribution described in 

Appendix D was described previously in 

NUREG-1808 (EricksonKirk-SS) and will not 

be repeated here. This study showed that the 

similarities in flaw size and density between 

forgings and plates allow the relationship 

between RTMAX-PL and TWCF95 (Eq. 3-6) to be 

used for forgings containing embedded flaws. 

For forgings the RT metric is defined as follows: 

RTMAX-FO characterizes the resistance of the 

RPV to fracture initiating from flaws in 

forgings that are not associated with welds. It 

is evaluated using the following formula for 

each forging within the beltline region of the 

vessel. The value of RTMAX-FO assigned to the 

vessel is the highest of the reference 

temperature values associated with any 

individual plate. In evaluating the T30 values 

in this formula the composition properties 

reported in the RVID database are used for 

copper, nickel, and phosphorus. An 

independent estimate of the manganese 

content of each weld and plate evaluated is 

also needed. 

Eq. 3-7 

  )()(

30

)(

)(

n

1i

FOMAX MAXFO

RT iFO

MAX

iFO iFO

uNDT  RT  tT 

 

where 

 nFO is the number of forgings in the 

beltline region of the vessel, 

 i is a counter that ranges from 1 to 

nFO, 

 is the maximum fluence occurring 

over the vessel ID occupied by a 

particular forging, 

iFO )(

MAX t

 is the unirradiated RTNDT of a 

particular forging, and 

)(

)(

iFO RT uNDT

 is the shift in the Charpy V-Notch 

30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced 

by irradiation to of a 

particular forging. 

)(

30

iFO T

iFO )(

MAX t

3.4.2 Underclad Flaw Sensitivity Study 

By May 1973 the causes of underclad cracking 

were sufficiently well understood for the NRC to 

issue Regulatory Guide 1.43, “Control of 

Stainless Steel Weld Cladding of Low Alloy 

Steel Components” (RG 1.43). Vessels 

fabricated after this date would have had to 

comply with the provisions of Regulatory Guide 

1.43 and, therefore, should not be susceptible to 

underclad cracking. Vessels fabricated before 

1973 may have been compliant as well because 

the causes of and remediation for underclad 

cracking were widely known before the issuance 

of the regulatory guide. Nevertheless, to provide 

the information needed to support a 

comprehensive revision of the PTS Rule the 

NRC staff considered it necessary to establish 

PTS screening limits for vessels containing 

underclad cracking for those situations in which 

compliance with Regulatory Guide 1.43 cannot 

be demonstrated. 

As discussed in detail in Appendix B, underclad 

cracks occur as dense arrays of shallow cracks 

extending into the vessel wall from the clad-tobasemetal interface to depths that are limited by 

the extent of the heat-affected zone 

(approximately 0.08 inch (approximately 

2 millimeters)). These cracks are oriented 

normal to the direction 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. 

Underclad 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 enhance the likelihood of 

underclad cracking. 

The NRC staff could find only limited 

information in the literature concerning 

underclad crack size and density. This lack of 

information on which to base the probabilistic 

29
calculations exists because when underclad 

cracking was discovered in the late 1960s and 

early 1970s the understandable focus of the 

investigations performed at that time was to 

prevent the phenomena from occurring 

altogether, not to characterize the size and 

density of the resulting defects. Because of this 

lack of information, the flaw distribution 

detailed in Appendix B reflects conservative 

judgments. 

Hypothetical models of forged vessels were 

constructed based on the existing models of the 

Beaver Valley Unit 1 and Palisades vessels. In 

these hypothetical forged vessels both the axial 

welds and the plates in the beltline region were 

combined and assigned the following properties, 

which are characteristic of the forging in 

Sequoyah Unit 1 (RVID2)—copper = 0.13 

percent, nickel = 0.76 percent, phosphorus = 

0.020 percent, manganese = 0.70 percent, 

RTNDT(u) = 73 F, upper-shelf energy = 72 ft-lbs 

(this forging was selected because it has among 

the most embrittlement sensitive properties of 

any forging in the current operating fleet). 

Using these properties along with the underclad 

flaw distribution described in Appendix B, 

FAVOR analyses were conducted at a number of 

different EFPY values to investigate the 

variation of TWCF with embrittlement level. 

Because of the extremely high density of 

underclad flaws assumed by the Appendix B 

flaw distribution, a super-computer cluster was 

used to perform these FAVOR analyses (see 

(Dickson 07b) for a full description of the 

underclad flaw analysis). Table 3.2 and Figure 

3.9 summarize the results of these analyses. The 

rate of increase of TWCF with increasing 

embrittlement (as quantified by RTMAX-FO) 

shown in Figure 3.9 for underclad cracks is 

much more rapid than shown previously (see 

Figure 3.4) for plate and weld flaws. The 

steepness of this slope occurs as a direct 

consequence of the very high density of 

underclad cracks assumed in the analysis (the 

mean crack-to-crack spacing is on the order of 

millimeters). Because of this high density, it is a 

virtual certainty that an underclad crack will be 

simulated to occur in locations of high fluence 

and high stress. Thus, once the level of 

embrittlement has increased to the point that the 

underclad cracks can initiate, their failure is 

almost certain, and additional small increases in 

embrittlement will lead to large increases in 

TWCF. Because of the steepness of the TWCF 

versus RTMAX-FO relationship, the staff made no 

attempt to develop a “best fit” to the results. 

Instead, the following bounding relationship 

(which also appears on Figure 3.9) is proposed: 

Eq. 3-8 RT FOMAX TWCF FO   

  137 185.095 10103.1

Table 3.2. Results of a Sensitivity Study Assessing 

the Effect of Underclad Flaws on the TWCF of 

Ring-Forged Vessels 

Analysis 

ID 

RTMAX-FO 

[

o

F] 

TWCF95 from Underclad 

Flaws 

BV 32 187.2 0 (see Note 1) 

BV 60 205.8 0 (see Note 1) 

BV 100 225.4 5.67E-11 

BV 200 261.2 2.35E-04 

Pal 32 193.0 0 (see Note 1) 

Pal 60 209.9 0 (see Note 1) 

Pal200 263.2 3.92E-05 

Pal 500 332.8 2.08E-04 

Note 1: All TWCF was from circumferential weld 

flaws in these analyses 

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

550 650 750 850

Max RT FO [R]

95th %ile TWCF for Underclad Flaws

 FAVOR Results

Bound

RT FOMAX TWCF FO   

  137 185.095 10103.1

Figure 3.9. Relationship between TWCF and RT 

for forgings having underclad flaws 

30
3.4.3 Modification for Thick-Walled 

Vessels 

As was the case for plate-welded vessels, the 

effect of increased vessel wall thickness on the 

TWCF in ring-forged vessels must also be 

quantified. The sensitivity study presented 

previously for plate-welded vessels (see Figure 

3.8) can be used to correct for thickness effects 

in forgings that have only embedded flaws (no 

underclad cracking) because of the similarity in 

both flaw density and flaw size between 

embedded flaws in forgings and plates. To 

investigate the magnitude of an appropriate 

thickness correction for forgings containing 

underclad cracks, the thickness of the 

hypothetical forging based on the Beaver Valley 

vessel was increased to 11 inches and the 

analysis was rerun using subclad cracks. Figure 

3.10 presents the results of these analyses and 

compares them with the results presented 

previously for plate-welded vessels (see Figure 

3.7) as well as to the thickness correction 

recommended in Section 3.3.3. This comparison 

demonstrates that the thickness correction 

recommended in Section 3.3.3 for plate-welded 

vessels can also be applied to ring-forged vessels 

that have underclad cracks. 

31

3.5 Options for Regulatory 

Implementation of These 

Results 

Any future revision of 10 CFR 50.61 must 

include a procedure by which licensees can 

demonstrate compliance with the 1x10-6/ry 

TWCF limit based on information that 

characterizes a particular plant. Sections 3.5.1 

and 3.5.2 describe two completely equivalent 

approaches to achieving this goal, both based on 

the information presented so far in this chapter. 

The first approach places a limit on TWCF of 

1x10-6/ry, whereas the second approach places a 

limit on the maxima of the various RT values, or 

combinations thereof, which would produce a 

TWCF value at the limit of 1x10-6/ry. Equations 

presented elsewhere in this report are repeated in 

these sections for clarity. Adoption of either 

approach in regulations would be fully 

consistent with the technical basis information 

presented in this report, in NUREG-1806, and in 

the other companion documents listed in 

Section 4.1. 

It should be noted that Steps 1 and 2 are 

identical in both approaches. Additionally, 

Step 2 uses the embrittlement trend curve from 

the FAVOR 06.1 change specification 

(Appendix A). Eason has developed an 

alternative embrittlement trend curve of a 

slightly simplified form (Eason 07). The results 

reported in Appendix C demonstrate that the 

effect of this alternative trend curve on the 

TWCF values estimated by FAVOR is 

insignificant. Thus, the equations in 

Appendix C could be adopted instead of the 

equations presented in Step 2 of Sections 3.5.1 

and 3.5.2 without the need to change any other 

part of the procedure. 

F

F

Results from analyses of forged 

vessels having subclad cracks.

Thickness 

correction 

recommended in 

Section 3.3.3

Figure 3.10. Effect of vessel wall thickness on the 

TWCF of forgings having underclad 

flaws compared with results for 

plate-welded vessels (see Figure 3.7) 
3.5.1 Limitation on TWCF 

Step 1. Establish the plant characterization parameters, which include the following: 

RTNDT(u) [ F] The unirradiated value of RTNDT. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Cu [weight percent] Copper content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Ni [weight percent] Nickel content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

P [weight percent] Phosphorus content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Mn [weight percent] Manganese content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

t [seconds] The amount of time the RPV has been in operation. 

TRCS [ F] The average temperature of the RCS inventory in the beltline 

region under normal operating conditions. 

tMAX [n/cm2] The maximum fluence on the vessel ID for each plate and 

forging in the beltline region of the RPV. 

tFL [n/cm2/sec.] The maximum fluence occurring along each axial weld and 

circumferential weld fusion line. This value is needed for each axial 

weld and circumferential weld fusion line in the beltline region of the 

RPV. 

Twall [inches] The thickness of the RPV wall, including the cladding. 

Step 2. Estimate values of RTMAX-AW, RTMAX-PL, RTMAX-FO, and RTMAX-CW using the following 

formulae and the values of the characterization parameters from Step 1: 

RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found 

along the axial weld fusion lines. It is evaluated using the following formula 

for each axial weld fusion line within the beltline region of the vessel (the 

part of the formula inside the {...}). The value of RTMAX-AW assigned to the 

vessel is the highest of the reference temperature values associated with any 

individual axial weld fusion line. In evaluating the T30 values in this 

formula the composition properties reported in the RVID database are used 

for copper, nickel, and phosphorus. An independent estimate of the 

manganese content of each weld and plate evaluated is also needed. 

  

    

































   

 





FL

ipladj ipladj

uNDT

FL

iawadj iawadj

uNDT

RT tT

RT tT





)(

30

)(

)(

)(

30

)(

)(

AWFL(i)

n

1i

AWMAX

, RT MAX MAX AWFL

 where 

 nAWFL is the number of axial weld fusion lines in the beltline region 

of the vessel, 

 i is a counter that ranges from 1 to nAWFL, 

tFL is the maximum fluence occurring on the vessel ID along a 

particular axial weld fusion line, 

 is the unirradiated RTNDT of the weld adjacent to the ith axial 

weld fusion line, 

)(

)(

iawadj RT uNDT

32
 is the unirradiated RTNDT of the plate adjacent to the ith axial 

weld fusion line, 

)(

)(

ipladj RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

weld adjacent to the ith axial weld fusion line, and 

)(

30

iawadj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

plate adjacent to the ith axial weld fusion line. 

)(

30

ipladj T  

RTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in 

plates that are not associated with welds. It is evaluated using the following 

formula for each plate within the beltline region of the vessel. The value of 

RTMAX-PL assigned to the vessel is the highest of the reference temperature 

values associated with any individual plate. In evaluating the T30 values in 

this formula the composition properties reported in the RVID database are 

used for copper, nickel, and phosphorus. An independent estimate of the 

manganese content of each weld and plate evaluated is also needed. 

   )()(

30

)(

)(

n

1i

PLMAX MAXPL

RT iPL

MAX

iPL iPL

uNDT  RT  tT 



 where 

 nPL is the number of plates in the beltline region of the vessel, 

 i is a counter that ranges from 1 to nPL, 

 is the maximum fluence occurring over the vessel ID occupied 

by a particular plate, 

iPL )(

MAX t

 is the unirradiated RTNDT of a particular plate, and )(

)(

iPL RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to of 

a particular plate. 

)(

30

iPL T

iPL )(

MAX t

RTMAX-FO characterizes the resistance of the RPV to fracture initiating from flaws in 

forgings that are not associated with welds. It is evaluated using the 

following formula for each forging within the beltline region of the vessel. 

The value of RTMAX-FO assigned to the vessel is the highest of the reference 

temperature values associated with any individual plate. In evaluating the 

T30 values in this formula the composition properties reported in the RVID 

database are used for copper, nickel, and phosphorus. An independent 

estimate of the manganese content of each weld and plate evaluated is also 

needed. 

   )()(

30

)(

)(

n

1i

FOMAX MAXFO

RT iFO

MAX

iFO iFO

uNDT  RT  tT 



 where 

 nFO is the number of forgings in the beltline region of the vessel, 

 i is a counter that ranges from 1 to nFO, 

 is the maximum fluence occurring over the vessel ID occupied 

by a particular forging, 

iFO )(

MAX t

 is the unirradiated RTNDT of a particular forging, and )(

)(

iFO RT uNDT

33
 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to of 

a particular forging. 

)(

30

iFO T

iFO )(

MAX t

RTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found 

along the circumferential weld fusion lines. It is evaluated using the 

following formula for each circumferential weld fusion line within the 

beltline region of the vessel (the part of the formula inside the {...}). Then 

the value of RTMAX-CW assigned to the vessel is the highest of the reference 

temperature values associated with any individual circumferential weld 

fusion line. In evaluating the T30 values in this formula the composition 

properties reported in the RVID database are used for copper, nickel, and 

phosphorus. An independent estimate of the manganese content of each 

weld, plate, and forging evaluated is also needed. 

  

   

    















































 

 

 





FL

ifoadj ifoadj

uNDT

FL

ipladj ipladj

uNDT

FL

icwadj icwadj

uNDT

RT tT

RT tT

RT tT







)(

30

)(

)(

)(

30

)(

)(

)(

30

)(

)(

CWFL(i)

n

1i

CWMAX ,

,

RT MAX MAX CWFL

 where 

 nCWFL is the number of circumferential weld fusion lines in the 

beltline region of the vessel, 

 i is a counter that ranges from 1 to nCWFL, 

tFL is the maximum fluence occurring on the vessel ID along a 

particular circumferential weld fusion line, 

 is the unirradiated RTNDT of the weld adjacent to the ith

circumferential weld fusion line, 

)(

)(

icwadj RT uNDT

 is the unirradiated RTNDT of the plate adjacent to the ith

circumferential weld fusion line (if there is no adjacent plate 

this term is ignored), 

)(

)(

ipladj RT uNDT

 is the unirradiated RTNDT of the forging adjacent to the ith

circumferential weld fusion line (if there is no adjacent forging 

this term is ignored), 

)(

)(

ifoadj RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

weld adjacent to the ith circumferential weld fusion line, 

)(

30

icwadj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

plate adjacent to the ith axial weld fusion line(if there is no 

adjacent plate this term is ignored), and 

)(

30

ipladj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

forging adjacent to the ith axial weld fusion line(if there is no 

adjacent forging this term is ignored). 

)(

30

ifoadj T  

34
The T30 values in the preceding equations are determined as follows‡

: 

 30  CRPMDT

   e RCS AMD T PMn t 471.2  001718.01  130.61

    e e e

RCS tNiCugPCuf T

BCRP Ni ,,,  1.543769.31

100.1

191.1 



 



  





























for welds 10x417.1

platesfor 10x561.1

forgingsfor 10x140.1

7

7

7

A































for welds 0.155

manufactur CEin platesfor 2.135 vesselsed

manufactur CE-nonin platesfor 5.102 vesselsed

 forgingsfor 3.102

B





















 













 



 10

2595.0 10

10

103925.4for 103925.4

103925.4for 

  



 t

t

te

Note: Flux () is estimated by dividing fluence (t) by the time (in seconds) that 

the reactor has been in operation. 

    



 



    

6287.0

12025.184483.01390.1log tanh

2

1

2

1 ,, 10 t Cu Ni tNiCug e e

e e

 

   

  



















  

  





072.0for 0.008)-(359.1072.0 008.0

072.0for 072.0 008.0

072.0for 0

, 0.6679

0.6679

Cu P Cu Pand

Cu Cu Pand

Cu

PCuf

e

e e















  wt%072.0for 

 wt%072.0for 0

CuCu

Cu

Cue





























flux) L1092 with welds(all wt%0.75 Nifor 301.0

 wt%0.75 Ni 0.5for 2435.0

 wt%0.5 Nifor 370.0

)(CuMax e

Step 3. Estimate the 95th percentile TWCF value for each of the axial weld flaw, plate flaw, 

circumferential weld flaw, and forging flaw populations using the RTs from Step 2 and 

the following formulae. RT must be expressed in degrees Rankine. The TWCF 

 

‡

 The results reported in Appendix C demonstrate that the alternative form of this relationship presented in 

Chapter 7 of (Eason 07) has no significant effect on the TWCF values estimated by FAVOR. Thus, the equations 

in Appendix C could be used instead of the equations presented in Step 2 without the need to change any other 

part of the procedure. 

35
contribution of a particular axial weld, plate flaw, circumferential weld, or forging is zero 

if either of the following conditions are met: (a) if the result of the subtraction from 

which the natural logarithm is taken is negative, or (b)if the beltline of the RPV being 

evaluated does not contain the product form in question. 

 TWCF95AW    ln5198.5exp RT AWMAX   542.40616  

 TWCF95PL   ln737.23exp RT PLMAX    38.162300  

 TWCF95CW   ln1363.9exp RT CWMAX   066.65616  

 TWCF95FO    ln737.23exp RT FOMAX    38.162300  

        137 185.0 RT FOMAX 1 10103.

The factor  = 0 if the forging is compliant with Regulatory Guide 1.43; otherwise  = 1. 

The factor  is determined as follows: 

 If TWALL  91⁄2 -in, then  = 1. 

 If 91⁄2 < TWALL < 111⁄2 -in, then  = 1+ 8(TWALL - 91⁄2) 

 If TWALL  111⁄2 -in, then  = 17. 

Step 4. Estimate the total 95th percentile TWCF for the vessel using the following formulae 

(note that depending on the type of vessel in question certain terms in the following 

formula will be zero). TWCF95-TOTAL must be less than or equal to 1x10-6. 



























 

 

 













FO FO

CW CW

PL PL

AW AW

TOTAL

TWCF

TWCF

TWCF

TWCF

TWCF

95

95

95

95

95









 is determined as follows: 

If RTMAX-xx ≤ 625R, then  = 2.5 

If 625R < RTMAX-xx < 875R then   625

250

5.1

 5.2  RT xxMAX 

If RTMAX-xx ≥ 875R, then  = 1 

Table 3.3 and Table 3.4 provide the RTs and 

TWCF95 values estimated by this procedure for 

every currently operating PWR. In Table 3.4 

TWCF95 values are reported for all ring-forged 

vessels based on both the assumption that 

underclad cracking can occur and on the 

assumption that underclad cracking cannot 

occur. No judgment regarding the incidence (or 

not) of underclad cracking in any operating ringforged PWR is made in presenting these values. 

However, these calculations do demonstrate that 

for the embrittlement levels currently expected 

through EOLE the contribution of underclad 

cracks to the total TWCF of ring-forged plants is 

estimated to be vanishingly small because, even 

at EOLE, the embrittlement levels expected of 

the ring forgings is low (at EOLE the highest 

RTMAX-FO of any ring-forged plant is 199 F). 

The graphs in Figure 3.11 summarize the TWCF 

values provided in these tables for all currently 

operating PWRs. Eighty-one percent of platewelded PWRs (100 percent of ring-forged 

PWRs) have estimated TWCF95 values that are 

36
two orders of magnitude or more below the 

1x10-6/ry regulatory limit (i.e., below 1x10-8/ry), 

even after 60 years of operation. After 40 years 

of operation the highest risk of PTS producing a 

through-wall crack in any plate-welded PWR is 

2.0x10-7/ry (for ring-forged PWRs this value is 

1.5x10-10/ry). After 60 years of operation this 

risk increases to 4.3x10-7/ry (3.0x10-10/ry for 

ring-forged PWRs). Figure 3.12 provides a 

perspective on the relative contributions to the 

total TWCF made by the various components 

(axial welds, circumferential welds, plates, and 

forgings) from which the beltline regions of the 

operating nuclear RPV fleet are constructed. 

This figure compares the histograms depicting 

the distributions of the various RT values 

characteristic of beltline materials in the current 

operating fleet (projected to EOLE) to the 

TWCF versus RT relationships used to define 

the proposed PTS screening limits (see Figure 

3.4 and Figure 3.9). These comparisons show 

that the level of embrittlement in most plants is 

so low, even when projected to EOLE, that the 

estimated TWCF resulting from PTS is very, 

very small. 

0

2

4

6

8

10

12

14

Below E-13

E-13 to E-12

E-12 to E-11

E-11 to E-10

E-10 to E-9

E-9 to E-8

E-8 to E-7

E-7 to E-6

Number of Currently Operating 

Power Reactors

Plate Welded Plants at 48 EFPY

Ring Forged Plants at 48 EFPY

0

2

4

6

8

10

12

14

Below E-13

E-13 to E-12

E-12 to E-11

E-11 to E-10

E-10 to E-9

E-9 to E-8

E-8 to E-7

E-7 to E-6

Number of Currently Operating 

Power Reactors

Plate Welded Plants at 32 EFPY

Ring Forged Plants at 32 EFPY

Estimated Yearly Through Wall Cracking Frequency All 

 2E-7

2E-7 to 4E-7

Figure 3.11. Estimated distribution of TWCF for currently operating PWRs using the procedure detailed 

in Section 3.5.1 

37
Table 3.3. RT and TWCF Values for Plate-Welded Plants Estimated Using the Procedure Described in Sect

Values at 32 EFPY (EOL) Values at 48 EFP

RTMAX-AW 

[oF] RTMAX-PL [oF] RTMAX-CW [oF] 95th Percentile TWCF (/ry) RTMAX-AW [oF] Plant Name RTMAX-PL [oF] R

ARKANSAS NUCLEAR 1 121.0 84.0 184.6 3.7E-14 128.7 92.0 ARKANSAS NUCLEAR 2 97.9 97.9 97.9 1.3E-13 112.3 112.3 BEAVER VALLEY 1 183.3 214.8 214.8 1.3E-09 194.0 230.1 BEAVER VALLEY 2 95.4 114.4 114.4 5.7E-13 103.4 126.6 CALLAWAY 1 84.7 84.9 84.9 3.8E-14 92.6 92.8 CALVERT CLIFFS 1 196.6 149.8 149.8 4.2E-09 213.5 168.1 CALVERT CLIFFS 2 174.1 174.1 174.1 1.1E-10 192.4 192.4 CATAWBA 2 82.9 82.9 82.9 3.1E-14 90.2 90.2 COMANCHE PEAK 1 60.3 60.3 60.3 3.1E-15 69.3 69.3 COMANCHE PEAK 2 44.3 44.3 44.3 5.1E-16 52.0 52.0 COOK 1 159.1 161.1 204.8 2.4E-11 174.2 175.1 COOK 2 160.2 174.1 174.1 6.0E-11 171.9 188.1 CRYSTAL RIVER 3 135.4 122.5 193.0 1.2E-12 143.8 130.4 DIABLO CANYON 1 191.3 130.5 130.5 1.9E-09 207.6 144.1 DIABLO CANYON 2 181.4 191.5 191.5 5.1E-10 193.6 205.0 FARLEY 1 134.8 164.7 164.7 3.1E-11 147.5 183.1 FARLEY 2 153.5 184.4 184.4 1.2E-10 167.1 203.6 FORT CALHOUN 204.1 131.1 169.9 1.0E-08 221.6 149.3 INDIAN POINT 2 199.3 208.4 208.4 6.5E-09 219.4 225.0 INDIAN POINT 3 236.8 236.8 236.8 1.7E-07 249.9 249.9 MCGUIRE 1 166.0 119.9 119.9 2.6E-12 176.0 128.7 MILLSTONE 2 128.1 132.2 132.2 2.5E-12 139.4 144.2 MILLSTONE 3 116.1 116.1 116.1 6.6E-13 128.8 128.8 OCONEE 1 164.5 77.0 182.8 6.9E-13 174.4 84.3 PALISADES 217.2 181.6 207.7 3.8E-08 237.2 200.4 PALO VERDE 1 90.6 90.6 90.6 1.1E-12 101.9 101.9 PALO VERDE 2 60.6 60.6 60.6 5.4E-14 71.9 71.9 PALO VERDE 3 50.6 50.6 50.6 1.8E-14 61.9 61.9 POINT BEACH 1 172.5 117.5 222.4 3.4E-11 185.7 125.6 ROBINSON 2 136.8 141.8 199.8 5.6E-12 146.4 152.3 SALEM 1 212.8 218.2 218.2 2.7E-08 225.9 232.0 

38
Values at 32 EFPY (EOL) Values at 48 EFP

Plant Name RTMAX-AW 

[oF] RTMAX-PL [oF] 

95th RTMAX-CW RTMAX-AW RTMAX-PL [o Percentile F] [oF] [oF] TWCF (/ry) R

SALEM 2 171.2 153.0 153.0 3.1E-11 185.7 166.7 SEABROOK 79.4 79.4 79.4 2.2E-14 88.2 88.2 SHEARON HARRIS 143.0 158.7 158.7 2.0E-11 150.8 169.8 SONGS-2 133.8 133.8 133.8 2.9E-12 149.2 149.2 SONGS-3 104.1 104.1 104.1 2.3E-13 118.5 118.5 SOUTH TEXAS 1 42.4 47.6 47.6 7.5E-16 49.7 56.0 SOUTH TEXAS 2 21.3 26.2 26.2 5.7E-17 28.3 34.4 ST. LUCIE 1 158.2 143.4 143.4 6.2E-12 169.2 155.2 ST. LUCIE 2 124.8 124.8 124.8 1.4E-12 136.0 136.0 SUMMER 107.7 107.7 107.7 3.2E-13 119.4 119.4 SURRY 1 239.2 138.7 198.7 2.0E-07 252.2 158.0 SURRY 2 157.8 114.7 189.2 5.9E-13 169.8 133.3 TMI-1 238.3 67.1 240.2 1.9E-07 247.7 74.3 VOGTLE 1 72.5 72.5 72.5 1.1E-14 79.9 79.9 VOGTLE 2 97.7 97.7 97.7 1.3E-13 108.4 108.4 WATERFORD 3 73.6 73.6 73.6 1.2E-14 85.2 85.2 WOLF CREEK 72.7 72.7 72.7 1.1E-14 80.0 80.0 At 32 EFPY the fluence is the value reported in (RVID2) at EOL for the vessel ID. The 48 EFPY fluence is estimated as 1.5 times the 32 Chemistry values are from (RVID2), except that manganese of 0.70 and 1.35 weight percent were used, respectively, for forgings and fo

These defaults represent the approximate averages of the data used to establish the uncertainty distributions for FAVOR 06.1 (see Appe

39
Table 3.4. RT and TWCF Values for Ring-Forged Plants Estimated Using the Procedure Described in Sect

32 EFPY (EOL) 48 EFPY (EOLE

95th Percentile TWCF (/ry) 95th P

RTMAX-FO 

[oF] 

RTMAX-CW 

[oF] 

Plant Name without 

Underclad 

Cracking 

RTMAX-FO 

[oF] 

RTMAX-CW 

[oF] with Underclad Cracking witho

Under

Crack

BRAIDWOOD 1 28.4 85.1 7.5E-17 7.5E-17 32.5 95.3 1BRAIDWOOD 2 43.5 74.7 4.6E-16 4.6E-16 46.5 82.6 6BYRON 1 70.7 70.7 9.2E-15 9.2E-15 77.5 77.5 1BYRON 2 28.7 68.1 7.8E-17 7.8E-17 33.0 81.3 1CATAWBA 1 41.1 41.1 3.5E-16 3.5E-16 46.2 46.2 6DAVIS-BESSE 70.6 184.5 1.1E-14 1.1E-14 75.3 193.3 4GINNA 187.2 196.6 1.4E-10 1.4E-10 195.4 209.8 2KEWAUNEE 120.3 237.5 3.3E-11 3.3E-11 133.8 258.3 2MCGUIRE 2 96.6 96.6 1.1E-13 1.1E-13 103.0 103.0 2NORTH ANNA 1 159.1 159.1 2.0E-11 2.0E-11 168.4 168.4 4NORTH ANNA 2 164.2 164.2 3.0E-11 3.0E-11 173.4 173.4 5OCONEE 2 75.6 242.0 5.2E-11 5.2E-11 81.5 251.2 1OCONEE 3 84.6 186.8 4.2E-14 4.2E-14 91.4 196.0 1POINT BEACH 2 112.4 219.5 3.9E-12 3.9E-12 123.1 234.9 2PRAIRIE ISLAND 1 85.1 125.4 3.9E-14 3.9E-14 101.1 148.4 1PRAIRIE ISLAND 2 91.3 109.6 7.0E-14 7.0E-14 107.6 129.6 3SEQUOYAH 1 187.3 187.3 1.5E-10 1.5E-10 198.6 198.6 3SEQUOYAH 2 107.0 107.0 3.0E-13 3.0E-13 115.9 115.9 6TURKEY POINT 3 102.2 215.8 2.2E-12 2.2E-12 108.9 230.1 1TURKEY POINT 4 92.9 215.8 2.0E-12 2.0E-12 99.7 230.1 1WATTS BAR 1 172.2 172.2 5.2E-11 5.2E-11 181.4 181.4 9At 32 EFPY the fluence is the value reported in (RVID2) at EOL for the vessel ID. The 48 EFPY fluence is estimated as 1.5 times the 32 Chemistry values are from (RVID2), except that manganese of 0.70 and 1.35 weight percent were used, respectively, for forgings and fo

These defaults represent the approximate averages of the data used to establish the uncertainty distributions for FAVOR 06.1 (see Appe

40
0

246810

475-500

525-550

575-600

625-650

675-700

Max. RT CW [R]

# of Ring

Forged PWRs

0246810

475-500

525-550

575-600

625-650

675-700

Max. RTFO [R]

# of Ring

Forged PWRs

1.E-231.E-211.E-191.E-171.E-151.E-131.E-111.E-091.E-071.E-051.E-03

450 550 650 750 850

Max RT AW [R]

95th %ile TWCF - Axial Weld Flaws

BeaverOconeePalisadesFit

1.E-231.E-211.E-191.E-171.E-151.E-131.E-111.E-091.E-071.E-051.E-03

450 550 650 750 850

Max RT PL or RT FO [R]

95th %ile TWCF - Plate Flaws

BeaverOconeePalisadesFit

0246810

# of Plate

Welded PWRs

0246810

# of Plate

Welded PWRs

0246810

# of Plate

Welded PWRs

1.E-231.E-211.E-191.E-171.E-151.E-131.E-111.E-091.E-071.E-051.E-03

450 550 650 750 850

Max RT CW [R]

95th %ile TWCF - Circ Weld Flaws

BeaverOconeePalisadesFit

Histograms depict current estimates of RTvalues at EOLE (48 EFPY)

1.E-231.E-211.E-191.E-171.E-151.E-131.E-111.E-091.E-071.E-051.E-03

450 

95th %ile TWCF for Underclad Flaws

Figure 3.12. Comparison of the distributions (red and blue histograms) of the various RT values characteristic of beltline ma

operating fleet projected to 48 EFPY with the TWCF vs. RT relationships (curves) used to define the proposed P

Figure 3.4 and Figure 3.9 for the original presentation of these relationships) 

41
3.5.2 Limitation on RT 

Step 1. Establish the plant characterization parameters, which include the following: 

RTNDT(u) [ F] The unirradiated value of RTNDT. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Cu [weight percent] Copper content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Ni [weight percent] Nickel content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

P [weight percent] Phosphorus content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

Mn [weight percent] Manganese content. Needed for each weld, plate, and 

forging in the beltline region of the RPV. 

t [seconds] The amount of time the RPV has been in operation. 

TRCS [ F] The average temperature of the RCS inventory in the beltline 

region under normal operating conditions. 

tMAX [n/cm2] The maximum fluence on the vessel ID for each plate and 

forging in the beltline region of the RPV. 

tFL [n/cm2/sec.] The maximum fluence occurring along each axial weld and 

circumferential weld fusion line. This value is needed for each axial 

weld and circumferential weld fusion line in the beltline region of the 

RPV. 

Twall [inches] The thickness of the RPV wall, including the cladding. 

Step 2. Estimate values of RTMAX-AW, RTMAX-PL, RTMAX-FO, and RTMAX-CW using the following 

formulae and the values of the characterization parameters from Step 1: 

RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found 

along the axial weld fusion lines. It is evaluated using the following formula 

for each axial weld fusion line within the beltline region of the vessel (the 

part of the formula inside the {...}). The value of RTMAX-AW assigned to the 

vessel is the highest of the reference temperature values associated with any 

individual axial weld fusion line. In evaluating the T30 values in this 

formula the composition properties reported in the RVID database are used 

for copper, nickel, and phosphorus. An independent estimate of the 

manganese content of each weld and plate evaluated is also needed. 

  

    

































   

 





FL

ipladj ipladj

uNDT

FL

iawadj iawadj

uNDT

RT tT

RT tT





)(

30

)(

)(

)(

30

)(

)(

AWFL(i)

n

1i

AWMAX

, RT MAX MAX AWFL

 where 

 nAWFL is the number of axial weld fusion lines in the beltline region 

of the vessel, 

 i is a counter that ranges from 1 to nAWFL, 

tFL is the maximum fluence occurring on the vessel ID along a 

particular axial weld fusion line, 

 is the unirradiated RTNDT of the weld adjacent to the ith axial 

weld fusion line, 

)(

)(

iawadj RT uNDT

42
 is the unirradiated RTNDT of the plate adjacent to the ith axial 

weld fusion line, 

)(

)(

ipladj RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

weld adjacent to the ith axial weld fusion line, and 

)(

30

iawadj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

plate adjacent to the ith axial weld fusion line. 

)(

30

ipladj T  

RTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in 

plates that are not associated with welds. It is evaluated using the following 

formula for each plate within the beltline region of the vessel. The value of 

RTMAX-PL assigned to the vessel is the highest of the reference temperature 

values associated with any individual plate. In evaluating the T30 values in 

this formula the composition properties reported in the RVID database are 

used for copper, nickel, and phosphorus. An independent estimate of the 

manganese content of each weld and plate evaluated is also needed. 

   )()(

30

)(

)(

n

1i

PLMAX MAXPL

RT iPL

MAX

iPL iPL

uNDT  RT  tT 



 where 

 nPL is the number of plates in the beltline region of the vessel, 

 i is a counter that ranges from 1 to nPL, 

 is the maximum fluence occurring over the vessel ID occupied 

by a particular plate, 

iPL )(

MAX t

 is the unirradiated RTNDT of a particular plate, and )(

)(

iPL RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to of 

a particular plate. 

)(

30

iPL T

iPL )(

MAX t

RTMAX-FO characterizes the resistance of the RPV to fracture initiating from flaws in 

forgings that are not associated with welds. It is evaluated using the 

following formula for each forging within the beltline region of the vessel. 

The value of RTMAX-FO assigned to the vessel is the highest of the reference 

temperature values associated with any individual plate. In evaluating the 

T30 values in this formula the composition properties reported in the RVID 

database are used for copper, nickel, and phosphorus. An independent 

estimate of the manganese content of each weld and plate evaluated is also 

needed. 

   )()(

30

)(

)(

n

1i

FOMAX MAXFO

RT iFO

MAX

iFO iFO

uNDT  RT  tT 



 where 

 nFO is the number of forgings in the beltline region of the vessel, 

 i is a counter that ranges from 1 to nFO, 

 is the maximum fluence occurring over the vessel ID occupied 

by a particular forging, 

iFO )(

MAX t

 is the unirradiated RTNDT of a particular forging, and )(

)(

iFO RT uNDT

43
 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to of 

a particular forging. 

)(

30

iFO T

iFO )(

MAX t

RTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found 

along the circumferential weld fusion lines. It is evaluated using the 

following formula for each circumferential weld fusion line within the 

beltline region of the vessel (the part of the formula inside the {...}). Then 

the value of RTMAX-CW assigned to the vessel is the highest of the reference 

temperature values associated with any individual circumferential weld 

fusion line. In evaluating the T30 values in this formula the composition 

properties reported in the RVID database are used for copper, nickel, and 

phosphorus. An independent estimate of the manganese content of each 

weld, plate, and forging evaluated is also needed. 

  

   

    















































 

 

 





FL

ifoadj ifoadj

uNDT

FL

ipladj ipladj

uNDT

FL

icwadj icwadj

uNDT

RT tT

RT tT

RT tT







)(

30

)(

)(

)(

30

)(

)(

)(

30

)(

)(

CWFL(i)

n

1i

CWMAX ,

,

RT MAX MAX CWFL

 where 

 nCWFL is the number of circumferential weld fusion lines in the 

beltline region of the vessel, 

 i is a counter that ranges from 1 to nCWFL, 

tFL is the maximum fluence occurring on the vessel ID along a 

particular circumferential weld fusion line, 

 is the unirradiated RTNDT of the weld adjacent to the ith

circumferential weld fusion line, 

)(

)(

icwadj RT uNDT

 is the unirradiated RTNDT of the plate adjacent to the ith

circumferential weld fusion line (if there is no adjacent plate 

this term is ignored), 

)(

)(

ipladj RT uNDT

 is the unirradiated RTNDT of the forging adjacent to the ith

circumferential weld fusion line (if there is no adjacent forging 

this term is ignored), 

)(

)(

ifoadj RT uNDT

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

weld adjacent to the ith circumferential weld fusion line, 

)(

30

icwadj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

plate adjacent to the ith axial weld fusion line(if there is no 

adjacent plate this term is ignored), and 

)(

30

ipladj T  

 is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energy 

(estimated using Eq. 3-4) produced by irradiation to tFL of the 

forging adjacent to the ith axial weld fusion line(if there is no 

adjacent forging this term is ignored). 

)(

30

ifoadj T  

44
The T30 values in the preceding equations are determined as follows§

: 

 30  CRPMDT

   e RCS AMD T PMn t 471.2  001718.01  130.61

    e e e

RCS tNiCugPCuf T

BCRP Ni ,,,  1.543769.31

100.1

191.1 



 



  





























for welds 10x417.1

platesfor 10x561.1

forgingsfor 10x140.1

7

7

7

A































for welds 0.155

manufactur CEin platesfor 2.135 vesselsed

manufactur CE-nonin platesfor 5.102 vesselsed

 forgingsfor 3.102

B





















 













 



 10

2595.0 10

10

103925.4for 103925.4

103925.4for 

  



 t

t

te

Note: Flux () is estimated by dividing fluence (t) by the time (in seconds) that 

the reactor has been in operation. 

    



 



    

6287.0

12025.184483.01390.1log tanh

2

1

2

1 ,, 10 t Cu Ni tNiCug e e

e e

 

   

  



















  

  





072.0for 0.008)-(359.1072.0 008.0

072.0for 072.0 008.0

072.0for 0

, 0.6679

0.6679

Cu P Cu Pand

Cu Cu Pand

Cu

PCuf

e

e e















  wt%072.0for 

 wt%072.0for 0

CuCu

Cu

Cue





























flux) L1092 with welds(all wt%0.75 Nifor 301.0

 wt%0.75 Ni 0.5for 2435.0

 wt%0.5 Nifor 370.0

)(CuMax e

Step 3. Compare the RTs from Step 2 to the limits in Table 3.5. The limits on RTMAX-CW given in 

this table correspond to a TWCF95 limit of 1x10-8/ry, not 1x10-6/ry. This more restrictive 

limit was imposed to enable a simple two-dimensional representation of the 

 

§

 The results reported in Appendix C demonstrate that the alternative form of this relationship presented in 

Chapter 7 of (Eason 07) has no significant effect on the TWCF values estimated by FAVOR. Thus, the equations 

in Appendix C could be used instead of the equations presented in Step 2 without the need to change any other 

part of the procedure. 

45
46

multidimensional relationship between the various RT values and TWCF95 illustrated 

inFigure 3.5 while not unduly diminishing the resulting 1x10-6/ry limits placed on RTMAXAW and RTMAX-PL. Adoption of this lower limit for the TWCF produced by 

circumferential welds is not expected to have any practical impact because the highest 

projected values RTMAX-CW at EOLE are 250 F and 258 F for plate-welded and ringforged plants (respectively), both of which are well below the limits on RTMAX-CW that 

appear in Table 3.5. Should changes in operations or other unforeseen changes that 

develop in the future increase a value of RTMAX-CW above the Table 3.5 limits, the 

licensee could always assess its plant using the approach that places a limit on TWCF 

described in Section 3.5.1. 

Table 3.5. RT Limits for PWRs 

Limit on RT value for different values of TWALL [F] 

RT Value 

9.5 in. >9.5 in., 

10.5 in. 

>10.5 in., 

11.5 in. 

RTMAX-AW 269 230 222 

RTMAX-PL 356 305 293 

RTMAX-AW + RTMAX-PL 538 476 445 

RTMAX-CW (see note below) 312 277 269 

For RPVs complying with RG 1.43 356 305 293 

RTMAX-FO For RPVs not complying with RG 

1.43 246 241 239 

Note: The limit on RTMAX-CW corresponds to a TWCF value of 10-8/ry. Should these limits on RTMAX-CW

be exceeded, the RTMAX-AW, RTMAX-PL, RTMAX-FO, and RTMAX CW values should be used, along with 

Eq. 3-6, to estimate the total TWCF value. This total TWCF should be limited to 1x10-6. 

Figure 3.13 and Figure 3.14 provide a graphical 

comparison of (1) the RT limits expressed in 

Table 3.5, (2) the RT limits derived from 

Eqs. 3-6 and 3-8, and (3) the RT values for 

operating PWRs at EOLE taken from Table 3.3 

and Table 3.4. These graphs show that 85 

percent of all plate-welded plants and 90 percent 

of all ring-forged plants are 50 F or more away 

from the proposed RT screening limits at EOLE 

(these numbers increase to 94 percent for platewelded plants and 100 percent for ring-forged 

plants at EOL). At EOLE, 17 F separates the 

most embrittled plate-welded plant from these 

screening limits (this number increases to 30 F 

at EOL). For ring-forged plants at EOLE, 47 F 

separates the most embrittled plant from the 

most restrictive screening limit (the number 

increases to 59 F at EOL). 
Plate Welded Plants 

at 48 EFPY (EOLE)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1x10-6/ry TWCF limit

Simplified Implementation

RTMAX-AW ≤ 269F, and

RTMAX-PL ≤ 356F, and

RTMAX-AW + RTMAX-PL ≤ 538F.

Palo Verde 1, 2, and 3

at 48 EFPY (EOLE)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1x10-6/ry TWCF limit

Simplified Implementation

RTMAX-AW ≤ 222F, and

RTMAX-PL ≤ 293F, and

RTMAX-AW + RTMAX-PL ≤ 445F.

Figure 3.13. Graphical comparison of the RT limits for plate-welded plants developed in Section 3.5.2 with

RT values for plants at EOLE (from Table 3.3). The top graph is for plants having wall 

thickness of 9.5-in. and less, while the bottom graph is for vessels having wall thicknesses 

between 10.5 and 11.5 in. 

Ring Forged Plants 

at 48 EFPY (EOLE)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300

RTMAX-CW [oF]

RTMAX-FO [oF]

TWCF = 1x10-6/ry

limit if not in compliance with Reg. Guide 1.43

TWCF = 1x10-8/ry limit

TWCF = 1x10-6/ry

limit if in compliance with Reg. Guide 1.43

Figure 3.14. Graphical comparison of the RT 

limits for ring-forged plants 

developed in Section 3.5.2 with RT 

values for plants at EOLE (from 

Table 3.3) 

3.6 Need for Margin 

Aside from relying on different RT-metrics, the 

PTS screening limits proposed in Section 3.5 

differ from the current 10 CFR 50.61 RTPTS

screening limits by the absence of a “margin 

term.” Use of a margin term is appropriate to 

account (at least approximately) for factors that 

occur in application that were not considered in 

the analyses upon which these proposed 

screening limits are based. For example, the 

10 CFR 50.61 margin term accounts for 

uncertainty in copper, nickel, and initial RTNDT. 

However, as discussed in detail by 

(EricksonKirk-PFM), the NRC model explicitly 

considers uncertainty in all of these variables 

and represents these uncertainties as being larger 

(a conservative representation) than would be 

characteristic of any plant-specific assessment 

application. Consequently, use of the 

10 CFR 50.61 margin term with the screening 

limits proposed in this report would be 

inappropriate. 

The following additional reasons suggest that 

use of any margin term with the proposed 

screening limits is inappropriate: 

47
(1) The TWCF values used to establish the 

screening limits represent 95th percentile 

values. 

(2) Information presented in Chapter 9 of 

NUREG-1806 (EricksonKirk-Sum) and 

summarized in Section 3.2.1 herein 

demonstrates that the results from the three 

plant-specific analyses apply to PWRs in 

general. 

It is correct that certain aspects of the models 

used to establish the proposed PTS limits cannot 

be considered as “best estimates.” On balance, 

there is a conservative bias to these non-bestestimate aspects of the analysis, as discussed in 

the following section. 

Throughout this project, every effort has been 

made to perform a “best estimate” analysis. 

Nonetheless, comparison of the analytical 

models used to assess risk with the actual 

situation being assessed reveals that certain 

features of that situation have not been 

represented as realistically as possible. These 

parts of the model may be judged as providing 

either a conservative representation (i.e., tending 

to increase the estimated TWCF) or a 

nonconservative representation (i.e., tending to 

decrease the estimated TWCF) relative to the 

actual situation in service. Table 3.6 

summarizes these conservatisms and 

nonconservatisms, which are discussed in 

greater detail in Section 3.6.1 and Section 3.6.2, 

respectively. This discussion does not include 

factors that the models do not accurately 

represent when these inaccuracies have been 

demonstrated to not significantly influence the 

TWCF results. This information demonstrates 

that, on balance, more conservatisms than 

nonconservatisms remain in the model, 

suggesting the appropriateness of applying the 

proposed screening limits without an additional 

margin term. 

3.6.1 Residual Conservatisms 

In the reactor vessel failure frequency limit— 

 The reactor vessel failure frequency limit of 

1x10-6 events/reactor year was established 

based on the assumption that through-wall 

cracking of the RPV will produce a large 

early release in all circumstances. As 

discussed in Chapter 10 of NUREG-1806 

through-wall cracking of the RPV is likely 

to lead to core damage, but large early 

release is unlikely for two reasons: (1) 

because of reactor safety systems and the 

multiple barriers that block radioactive 

release to the environment 

(e.g., containment), and (2) because if a 

through wall crack were to develop it would 

happen when the temperature and pressure 

in the primary circuit are low, both of which 

produce a low system energy. Current 

guidelines on core damage frequency 

provided by Regulatory Guide 1.174 and the 

Option 3 framework for risk-informing 

10 CFR Part 50 suggest a reactor vessel 

failure frequency limit of 1x10-5

events/reactor year (RG1.174). Changing 

from a 1x10-6 to a 1x10-5 limit would 

increase all of the proposed RT limits 

by between 50 and 60 F (between 28 and 

33 C). 

In the PRA model— 

 In the PRA binning process, if there was a 

question about what bin to place a particular 

scenario in, the scenario was intentionally 

binned in a conservative manner. Thus, the 

loading severity has a tendency toward 

being overestimated. 

In the PRA model— 

 External initiating events. As detailed in 

Section 9.4 of NUREG-1806 and in 

(Kolaczkowski-Ext), the NRC’s analysis has 

not considered the potential for a PTS 

transient to be started by an initiating event 

external to the plant (e.g., fire, earthquake). 

The bounding analyses performed 

demonstrate that this would increase the 

TWCF values reported herein by at most a 

factor of 2. However, the bounding nature 

of the NRC’s external events analysis 

suggests strongly that the actual effect of 

ignoring the contribution of external 

initiating events is much smaller than 2 

times. 

 The temperature of water held in the safety 

injection accumulators was assumed to be 

60 F (15.6 C). These accumulators are 

48
inside containment and so exist at 

temperatures of 80–90 F (26.7–32.2 C) 

in the winter and above 110 F (43.3 C) 

in the summer. This conservative estimate 

of injection water temperature increases the 

magnitude of the thermal stresses that occur 

during of pipe breaks and reduces the 

fracture resistance of the vessel steel. 

 When a main steamline breaks inside of 

containment, the release of steam from the 

break pressurizes the containment structure 

to approximately 50 pounds per square inch 

(psi) (335 kilopascals (kPa). Consequently, 

the minimum temperature for MSLBs is 

bounded by the boiling point of water at 

approximately 50 psi (335 kPa), or 

approximately 260 F (126.7 C). However, 

the NRC’s secondary-side breaks do not 

account for pressurization of containment, 

so the minimum temperature calculated by 

RELAP for these transients is 212 F (100 

C), or approximately 50 F (28 C) too 

cold. This conservative estimate of the 

minimum temperature associated with an 

MSLB increases the magnitude of the 

thermal stresses and reduces the fracture 

resistance of the vessel steel. 

In the fracture model— 

 Once a circumferential crack initiates, it is 

assumed to instantly propagate 360 around 

the vessel wall. However, full 

circumferential propagation is highly 

unlikely because of the azimuthal variation 

in fluence, which causes alternating regions 

of more embrittled and less embrittled 

material to exist circumferentially around 

the vessel wall. Thus, the NRC model tends 

to overestimate the extent of cracking 

initiated from circumferentially oriented 

defects because it ignores this natural crack 

arrest mechanism. 

 Once an axial flaw initiates, it is assumed to 

instantly become infinitely long. In reality, 

it only propagates to the length of an axial 

shell course (approximately 8 to 12 feet 

(approximately 2.4 to 3.7 meters)), at which 

point, it encounters tougher material and 

arrests. Even though a shell course is very 

long, flaws of finite length tend to arrest 

more readily than do flaws of infinite length 

because of systematic differences in the 

through-wall variation of crack-driving 

force. Because of this approximation, the 

NRC model tends to overestimate the 

likelihood of through-wall cracking. 

 As detailed in Section 4.2.3.1.3 of 

(EricksonKirk-PFM) and in (English 02), 

the adopted FAVOR model of how fluence 

attenuates through the RPV wall is 

conservative relative to experimental data 

 As detailed in Section 4.2.2.2 of 

(EricksonKirk-SS) and in Appendix E 

to (EricksonKirk-PFM), the statistical 

distributions of copper, nickel, phosphorus, 

and RTNDT sampled by FAVOR 

overestimate the degree of uncertainty in 

these variables relative to what can actually 

exist in any particular weld, plate, or 

forging. 

 While the FAVOR model corrects (on 

average) for the systematic conservative bias 

in RTNDT, the model overestimates the 

uncertainty associated with the fracture 

toughness transition temperature metric. 

In the flaw model— 

 In the experimental data upon which the 

flaw distribution is based, all detected 

defects were modeled as being crack-like 

and, therefore, potentially deleterious to the 

fracture integrity of the vessel. However, 

many of these defects are actually 

volumetric rather than planar, making them 

either benign or, at a minimum, much less of 

a challenge to the fracture integrity of the 

vessel. Thus, the NRC model overestimates 

the seriousness of the defect population in 

RPV materials, which leads to overly 

pessimistic assessments of the fracture 

resistance of the vessel. 

49
50

 FAVOR incorporates an interdependence 

between initiation and arrest fracture 

toughness values premised on physical 

arguments (see Sections 5.3.1.1 and 5.3.1.2 

of (EricksonKirk-PFM)). While the staff 

believes these models are appropriate, this 

view is not universally held (see reviewer 

comment 40D in Appendix B of NUREG1806). The alternative model, with no 

interdependence between initiation and 

arrest fracture toughness values, would 

reduce the estimated values of TWCF. 

 As detailed in Section 9.2.2.1 of NUREG1806, the NRC has simulated levels of 

irradiation damage beyond those occurring 

over currently anticipated lifetimes using the 

most conservative available techniques. 

3.6.2 Residual Nonconservatisms 

In the reactor vessel failure frequency limit— 

Air oxidation. The large early release 

frequency (LERF) criterion provided in 

Regulatory Guide 1.174, which was used to 

establish the 1x10-6/ry TWCF limit, assumes 

source terms that do not reflect scenarios 

where fuel cooling has been lost, exposing 

the fuel rods to air (rather than steam). 

Should such a situation arise, some portion 

of the reactor fuel would eventually be 

oxidized in an air environment, which would 

result in release fractions for key fission 

products (ruthenium being of primary 

concern) that may be significantly (e.g., a 

factor of 20) larger than those associated 

with fuel oxidation in steam environments. 

These larger release fractions could lead to 

larger numbers of prompt fatalities than 

predicted for non-PTS risk-significant 

scenarios. Nonetheless, the accident 

progression event tree (APET) developed in 

Chapter 10 of NUREG-1806 demonstrates 

that the number of scenarios in which air 

oxidation is possible is extremely small, 

certainly far smaller than the number of 

scenarios in which only core damage (not 

LERF) is the only plausible outcome. Thus, 

the nonconservatism introduced by not 

explicitly considering the potential for air 

oxidation is more than compensated for by 

the conservatism of establishing a TWCF 

limit based on LERF when many accident 

sequences can only plausibly result in core 

damage. 

In the PRA model— 

 External initiating events. As detailed in 

Section 9.4 of NUREG-1806 and in 

(Kolaczkowski-Ext), the NRC’s analysis has 

not considered the potential for a PTS 

transient to be started by an initiating event 

external to the plant (e.g., fire, earthquake). 

The bounding analyses performed 

demonstrate that this would increase the 

TWCF values reported herein by at most a 

factor of 2. However, the bounding nature 

of the NRC’s external events analysis 

suggests strongly that the actual effect of 

ignoring the contribution of external 

initiating events is much smaller than 2 

times. 

In the fracture model— 

 Through-wall chemistry layering. 

As detailed in (EricksonKirk-PFM), 

FAVOR models the existence of a gradient 

of properties through the thickness of the 

RPV because of through-wall changes in 

copper content. These copper content 

changes arise from the fact that, given the 

large volume of weld metal needed to fill an 

RPV weld, manufacturers used weld wire 

from multiple weld wire spools (having 

different amounts of copper coating) to 

completely fill the groove. The model 

adopted in FAVOR resamples the mean 

copper content of the weld at the 1⁄4T, 1⁄2T, 

and 3⁄4T locations through the thickness. 

This resampling increases the probability of 

crack arrest because it allows the simulation 

of less irradiation-sensitive materials, which 

could arrest the running crack before it fails 

the vessel. If these weld layers did not occur 

in a real vessel, the TWCF would increase 

relative to those reported herein by a small 

factor (approximately 2.5 based on the 

limited sensitivity studies performed). 
Table 3.6. Non-Best-Estimate Aspects of the Models Used to Develop the RT-Based Screening Limits 

for PTS 

Situation Potential Conservatism in the Analytical Model 

The model assumes that all failures produce a large early release; 

however, in the accident progression event tree (APET) (Ch. 10, NUREG1806), most sequences lead only to core damage. 

An initiated axial crack is assumed to instantly propagate to infinite length. 

In reality, the crack length will be finite and limited to the length of a single 

shell course because the cracks will most likely arrest when they 

encounter higher toughness materials in either the adjacent 

circumferential welds or plates. 

If the vessel fails, what happens next? 

An initiated circumferential crack is assumed to instantly propagate 360o

around the vessel ID. In reality, the crack length is limited because the 

azimuthal fluence variation places strips of tougher material in the path of 

the extending crack. 

How the many possible PTS initiators 

are binned, and how TH transients are 

selected to represent each bin to the 

PFM analysis 

When uncertainty of how to bin existed, consistently conservative 

decisions were made. 

The minimum temperature of an MSLB inside containment is modeled as 

approximately 50 o

F (28 C) colder than it can actually be because Characterization of secondary-side containment pressurizes as a result of the steam escaping from the break. failures Stuck-open valves on the secondary side are conservatively modeled in 

Palisades. 

Through-wall attenuation of neutron 

damage 

Attenuation is assumed to be more significant than measured in 

experiments. 

Model of material unirradiated 

toughness and chemical composition 

variability 

The statistical distributions sampled produce more uncertainty than could 

ever occur in a specific weld, plate, or forging. 

Correction for systematic conservative 

bias in RTNDT

Model corrects for mean bias, but overrepresents uncertainty in RTNDT. 

All defects found were assumed to be planar. 

Flaw model Systematically conservative judgments were made when developing 

the flaw distribution model. 

Interdependency of between initiation 

toughness and arrest toughness 

Model employed allows all initiated flaws a chance to propagate into the 

vessel. 

Most conservative approach taken (increasing time vs. increasing 

unirradiated RTNDT). Extrapolation of irradiation damage 

Situation Potential Nonconservatism in the Analytical Model 

If the vessel fails, what 

happens next? The potential for air oxidation has been ignored. 

External PTS initiators 

The potential for external events (e.g., fires, earthquakes) initiating PTS transients has 

not been modeled explicitly. A conservative bounding analysis estimates the effect of 

external events to be at most a factor of 2 increase in TWCF, but the likely increase is 

expected to be much less than 2 times. 

Through-wall chemistry 

layering 

Model assumes that the mean level of copper can change 4 times through the vessel 

wall thickness. If copper layering is not present, the TWCF would increase. 

51
3.7 Summary 

This report presents the results of FAVOR 06.1 

calculations, compares them to the FAVOR 04.1 

results presented in NUREG-1806, and uses the 

new results to propose two options for 

implementing these findings in a revision of the 

PTS Rule (10 CFR 50.61). Changes made in 

FAVOR 06.1 have placed a greater density in 

the upper tails of the TWCF distributions, 

resulting in the agency’s adoption of the 95th 

percentile of the TWCF distribution for use in 

the analyses that produced the recommended 

implementation options. Nevertheless, as was 

reported previously in NUREG-1806, the NRC 

again finds that only the most severe transient 

classes (i.e., medium- to large-diameter primaryside pipe breaks, valves on the primary side that 

stick open and may suddenly reclose later) 

contribute significantly to the TWCF. The 

minor plant-to-plant variation of the thermal 

hydraulic characteristics of such transients 

cannot significantly alter the stresses borne by 

the vessel wall, and thus cannot significantly 

alter the TWCF. Thus, the results presented 

herein can be regarded as being generally 

applicable to all PWRs currently operating in the 

United States. Also, the current results reinforce 

the finding from NUREG-1806 that it is the 

material properties associated with axially 

oriented flaws that dominate PTS risk. Thus, the 

embrittlement properties of axial welds and 

plates in plate-welded vessels and of forgings in 

ring-forged vessels are the most important 

indicators of PTS risk. Conversely, the much 

lower probability that cracks initiated from 

circumferentially oriented flaws will propagate 

through wall makes the embrittlement properties 

of circumferential welds much less important 

contributors to the total PTS risk. 

The two recommended implementation options 

include either (1) limiting the TWCF estimated 

for an operating plant to a total value no greater 

than 1x10-6/ry or (2) limiting RT values of the 

various materials in the RPV beltline so that 

their total TWCF is not permitted to exceed 

1x10-6/ry. These options are completely 

equivalent and interchangeable because they are 

both based on the same formula, provided 

herein, that estimates the total TWCF from the 

RT values for the materials in the RPV 

beltline—RT values that can be determined from 

information in the NRC’s RVID database, and 

surveillance program information (to develop an 

estimate for manganese content). Table 3.7 

provides the recommended RT limits (i.e., 

implementation option 2. Assuming that current 

operating practices are maintained, the status of 

currently operating PWRs relative to these limits 

is as follows: 

For plate-welded PWRs—

 The risk of PTS failure of the RPV is very 

low. Over 80 percent of operating PWRs 

have estimated TWCF values below 1x10-

8

/ry at EOLE. 

 At EOL the highest risk of PTS at any PWR 

is 2.0x10-7/ry. At EOLE this risk increases 

to 4.3x10-7/ry. 

 Eighty-five percent of all plants are 50 F or 

more away from the proposed RT screening 

limits at EOLE (this number increases to 94 

percent at EOL). 

 At EOLE, 17 F separates the most 

embrittled plant from these screening limits 

(this number increases to 30 F at EOL). 

For ring-forged PWRs—

 The risk of PTS failure of the RPV is very 

low. All operating PWRs have estimated 

TWCF values below 1x10-8/ry at EOLE. 

 At EOL the highest risk of PTS at any PWR 

is 1.5x10-10/ry. At EOLE this risk increases 

to 3.0x10-10/ry. 

 Ninety percent of all plants are 50 F or 

more away from the most restrictive of the 

proposed RT screening limits at EOLE (this 

number increases to 100 percent at EOL). 

 At EOLE 47 F separates the most 

embrittled plant from these screening limits 

(this number increases to 59 F at EOL). 

52
Table 3.7. RT Limits for PWRs 

Limit on RT value for different values of TWALL [F] RT Value 

9.5 in. >9.5 in., 10.5 in. >10.5 in., 11.5 in. 

RTMAX-AW 269 230 222 

RTMAX-PL 356 305 293 

RTMAX-AW + RTMAX-PL 538 476 445 

RTMAX-CW (see note below) 312 277 269 

RTMAX- For RPVs complying with RG 1.43 356 305 293 

FO For RPVs not complying with RG 1.43 246 241 239 

Note: The limit on RTMAX-CW corresponds to a TWCF value of 10-8/ry. Should these limits on RTMAX-CW

be exceeded the RTMAX-AW, RTMAX-PL, RTMAX-FO, and RTMAX-CW values should be used, along with 

Eq. 3-6, to estimate the total TWCF value. This total TWCF should be limited to 1x10-6. 

53
54
Chapter 4 - References 

4.1 PTS Technical Basis Citations 

The following three sections provide the citations that, together with this report, comprise the 

technical basis for risk-informed revision of the PTS Rule. When these reports are cited in 

the text, the citations appear in italicized boldface to distinguish them from the related 

literature citations. 

4.1.1 Summary 

EricksonKirk-Sum EricksonKirk, M.T., et al., “Technical Basis for Revision of the 

Pressurized Thermal Shock (PTS) Screening Limits in the PTS Rule 

(10 CFR 50.61): Summary Report,” NUREG-1806, U.S. Nuclear 

Regulatory Commission. 

4.1.2 Probabilistic Risk Assessment 

Kolaczkowski-Oco Kolaczkowski, A.M., et al., “Oconee Pressurized Thermal Shock 

(PTS) Probabilistic Risk Assessment (PRA),” September 28, 2004, 

available in the NRC’s Agencywide Documents Access and 

Management System (ADAMS) under Accession #ML042880452. 

Kolaczkowski-Ext Kolaczkowski, A. et al., “Estimate of External Events Contribution 

to Pressurized Thermal Shock (PTS) Risk,” Letter Report, October 1, 

2004, available in ADAMS under Accession #ML042880476. 

Siu 99 Siu, N., “Uncertainty Analysis and Pressurized Thermal Shock: An 

Opinion,” U.S. Nuclear Regulatory Commission, 1999, available in 

ADAMS under Accession #ML992710066. 

Whitehead-PRA Whitehead, D.L. and A.M. Kolaczkowski, “PRA Procedures and 

Uncertainty for PTS Analysis,” NUREG/CR-6859, U.S. Nuclear 

Regulatory Commission, December 31, 2004. 

Whitehead-BV Whitehead, D.L., et al., “Beaver Valley Pressurized Thermal Shock 

(PTS) Probabilistic Risk Assessment (PRA),”September 28, 2004, 

available in ADAMS under Accession #ML042880454. 

Whitehead-Gen Whitehead, D.W., et al., “Generalization of Plant-Specific 

Pressurized Thermal Shock (PTS) Risk Results to Additional 

Plants,” October 14, 2004, available in ADAMS under Accession 

#ML042880482. 

Whitehead-Pal Whitehead, D.L., et al., “Palisades Pressurized Thermal Shock (PTS) 

Probabilistic Risk Assessment (PRA),” October 6, 2004, available in 

ADAMS under Accession #ML042880473. 

4.1.3 Thermal-Hydraulics 

Arcieri-Base Arcieri, W.C., R.M. Beaton, C.D. Fletcher, and D.E. Bessette, 

“RELAP5 Thermal-Hydraulic Analysis to Support PTS Evaluations 

for the Oconee-1, Beaver Valley-1, and Palisades Nuclear Power 

55
Plants,” NUREG/CR-6858, U.S. Nuclear Regulatory Commission, 

September 30, 2004. 

Arcieri-SS Arcieri, W.C., et al., “RELAP5/MOD3.2.2 Gamma Results for 

Palisades 1D Downcomer Sensitivity Study,” August 31, 2004, 

available in ADAMS under Accession #ML061170401.

Bessette Bessette, D.E., “Thermal-Hydraulic Evaluations of Pressurized 

Thermal Shock,” NUREG-1809, U.S. Nuclear Regulatory 

Commission, May 30, 2005.

Chang Chang, Y.H., K. Almenas, A. Mosleh, and M. Pour-Gol, “ThermalHydraulic Uncertainty Analysis in Pressurized Thermal Shock Risk 

Assessment: Methodology and Implementation on Oconee-1, Beaver 

Valley, and Palisades Nuclear Power Plants,” NUREG/CR-6899, 

U.S. Nuclear Regulatory Commission.

Fletcher Fletcher, C.D., D.A. Prelewicz, and W.C., Arcieri, 

“RELAP5/MOD3.2.2γ Assessment for Pressurized Thermal Shock 

Applications,” NUREG/CR-6857, U.S. Nuclear Regulatory 

Commission, September 30, 2004.

Junge “PTS Consistency Effort,” Staff Letter Report to file, October 1, 

2004, available in ADAMS under Accession #ML042880480. 

Reyes-APEX Reyes, J.N., et al., “Final Report for the OSU APEX-CE Integral 

Test Facility,” NUREG/CR-6856, U.S. Nuclear Regulatory 

Commission, December 16, 2004.

Reyes-Scale Reyes, J.N., et al., “Scaling Analysis for the OSU APEX-CE Integral 

Test Facility,” NUREG/CR-6731, U.S. Nuclear Regulatory 

Commission, November 30, 2004.

4.1.4 Probabilistic Fracture Mechanics 

Dickson-Base Dickson, T.L., and S. Yin, “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, October 15, 2004, 

available in ADAMS under Accession #ML042960391 

Dickson-UG Dickson, T.L., and P.T. Williams, “Fracture Analysis of Vessels Oak 

Ridge, FAVOR v04.1, Computer Code: User’s Guide,” NUREG/CR6855, U.S. Nuclear Regulatory Commission, October 21, 2004. 

EricksonKirk-PFM EricksonKirk, M.T., “Probabilistic Fracture Mechanics: Models, 

Parameters, and Uncertainty Treatment Used in FAVOR Version 

04.1,” NUREG-1807, U.S. Nuclear Regulatory Commission, January 

26, 2005. 

EricksonKirk-SS EricksonKirk, M.T., et al., “Sensitivity Studies of the Probabilistic 

Fracture Mechanics Model Used in FAVOR Version 03.1,” 

NUREG-1808, U.S. Nuclear Regulatory Commission, November 30, 

2004. 

56
Kirk 12-02 EricksonKirk, M.T., “Technical Basis for Revision of the 

Pressurized Thermal Shock (PTS) Screening Limits in the PTS Rule 

(10 CFR 50.61),” December 2002, available in ADAMS under 

Accession #ML030090626. 

Malik Malik, S.N.M., “FAVOR Code Versions 2.4 and 3.1: Verification 

and Validation Summary Report,” NUREG-1795, U.S. Nuclear 

Regulatory Commission, October 31, 2004. 

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

Generalized Procedure for Generating Flaw Related Inputs for the 

FAVOR Code,” NUREG/CR-6817, Rev. 1, U.S. Nuclear Regulatory 

Commission, October 2003, available in ADAMS under Accession 

#ML051790410. 

Williams 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, U.S. 

Nuclear Regulatory Commission, October 21, 2004. 

57
4.2 Literature Citations 

10 CFR 50.61 Title 10, Section 50.61, “Fracture Toughness Requirements for 

Protection against Pressurized Thermal Shock Events,” of the Code 

of Federal Regulations, promulgated June 26, 1984. 

10 CFR 50 App. H Appendix H to Part 50, “Reactor Vessel Material Surveillance 

Program Requirements,” of the Code of Federal Regulations, 

promulgated December 31, 2003. 

ACRS 05 ACRSR-2116, Letter from Graham Wallis to Luis Reyes entitled 

“Pressurized Thermal Shock (PTS) Reevaluation Project: Technical 

Basis for Revision of the PTS Screening Criterion in the PTS Rule,” 

available in ADAMS under Accession # ML050730177. 

ASME S4 AVIII ASME Boiler and Pressure Vessel Code, Section XI, Division I, 

1989 Edition, 1989 Addenda, Appendix VIII, Supplement 4. 

ASTM E900 ASTM E900-02, “Standard Guide for Predicting Radiation-Induced 

Transition Temperature Shift in Reactor Vessel Materials,” 

American Society for Testing and Materials, Philadelphia, 

Pennsylvania, 2002. 

Becker 02 Becker, L., “Reactor Pressure Vessel Inspection Reliability,” 

Proceedings of the Joint EC-IAEA Technical Meeting on 

Improvements in In-Service Inspection Effectiveness, Petten, 

Netherlands, November 2002. 

Dickson 07a Dickson, T.L., P. T. Williams, and S. Yin, “Fracture Analysis of 

Vessels—Oak Ridge FAVOR, v06.1, Computer Code: User’s 

Guide,” ORNL/TM-2007/0031, Oak Ridge Natinoal Laboratory, 

2007. 

Dickson 07b Dickson, T.L., and S. Yin, “Electronic Archival of the Results of 

Pressurized Thermal Shock Analyses for Beaver Valley, Oconee, 

and Palisades Reactor Pressure Vessels Generated with the 06.1 

Version of FAVOR,” ORNL/NRC/LTR-07/04. 

Eason 07 Eason, E.D., G.R. Odette, R.K. Nanstad, and T. Yamamoto, “A 

Physically Based Correlation of Irradiation-Induced Transition 

Temperature Shifts for RPV Steels,” Oak Ridge National 

Laboratory, ORNL/TM-2006/530. 

English 02 English, C., and W. Server, “Attenuation in US RPV Steels—MRP56,” Electric Power Research Institute, June 2002. 

EricksonKirk 06a EricksonKirk, Mark and Marjorie EricksonKirk, “An Upper-Shelf 

Fracture Toughness Master Curve for Ferritic Steels,” International 

Journal of Pressure Vessels and Piping 83 (2006) 571–583. 

EricksonKirk 06b EricksonKirk, Marjorie and Mark EricksonKirk, “The Relationship 

between the Transition and Upper-Shelf Fracture Toughness of 

Ferritic Steels,” Fatigue Fract Engng Mater Struct 29 (2006) 672–

684. 

Kirk 03 Kirk, Mark, Cayetano Santos, Ernest Eason, Joyce Wright, and G. 

Robert Odette, “Updated Embrittlement Trend Curve for Reactor 

Pressure Vessel Steels,” Transactions of the 17th International 

58
Conference on Structural Mechanics in Reactor Technology (SMiRT 

17), Prague, Czech Republic, August 17–22, 2003. 

RG 1.43 Regulatory Guide 1.43, “Control of Stainless Steel Weld Cladding of 

Low Alloy Steel Components,” May 1973, ADAMS Accession No. 

ML 003740095. 

RG 1.162 Regulatory Guide 1.162, “Thermal Annealing of Reactor Pressure 

Vessel Steels,” U.S. Nuclear Regulatory Commission, February 

1996. 

RG 1.154 Regulatory Guide 1.154, “Format and Content of Plant-Specific 

Pressurized Thermal Shock Safety Analysis Reports for PressurizedWater Reactors,” U.S. Nuclear Regulatory Commission, November 

2002. 

RG 1.174 Rev 1 Regulatory Guide 1.174, Rev. 1, “An Approach for Using 

Probabilistic Risk Assessment in Risk-Informed Decisions on PlantSpecific Changes to the Licensing Basis,” U.S. Nuclear Regulatory 

Commission, January 1987. 

RVID2 Reactor Vessel Integrity Database, Version 2.1.1, U.S. Nuclear 

Regulatory Commission, July 6, 2000. 

Schuster 02 Schuster, G.J., “Technical Letter Report—JCN-Y6604—Validated 

Flaw Density and Distribution within Reactor Pressure Vessel Base 

Metal Forged Rings,” Pacific Northwest National Laboratory, for 

U.S. Nuclear Regulatory Commission, December 20, 2002. 

Schuster 98 Schuster, G.J., S.R. Doctor, S.L. Crawford, and A.F. Pardini, 1998, 

“Characterization of Flaws in U.S. Reactor Pressure Vessels: 

Density and Distribution of Flaw Indications in PVRUF,” 

NUREG/CR-6471, Vol. 2, U.S. Nuclear Regulatory Commission, 

Washington, D.C. 

Tregoning 05 Tregoning, R., and P. Scott, “Estimating Loss-of-Coolant Accident 

(LOCA) Frequencies through the Elicitation Process,” NUREG1829, U.S. Nuclear Regulatory Commission, June 2005. 

Williams 07 Williams, P.T., T.L. Dickson, and S. Yin, “Fracture Analysis of 

Vessels—Oak Ridge FAVOR, v06.1, Computer Code: Theory and 

Implementation of Algorithms, Methods, and Correlations,” 

ORNL/TM-2007/0030, Oak Ridge Natinoal Laboratory, 2007. 

59
60
APPENDIX A 

CHANGES REQUESTED BETWEEN 

FAVOR VERSION 05.1 AND FAVOR VERSION 06.1 
 

24 March 2006 

MEMORANDUM 

From: Mark EricksonKirk, NRC/RES 

To: Terry Dickson, ORNL 

Concurrence: Jennifer Uhle, NRC/RES 

 Shah Malik, NRC/RES 

 Bob Hardies, NRC/NRR 

 Steve Long, NRC/NRR 

 Barry Elliott, NRC/NRR 

 Lambros Lois, NRC/NRR 

cc: B. Richard Bass, ORNL 

 

Subj: Changes requested between FAVOR Version 05.1 and FAVOR Version 06.1 

Dear Terry: 

As you are aware, over the past eight months staff from the NRC’s Office of Nuclear Reactor Regulation 

(NRR) have reviewed the technical basis RES has proposed for a risk-informed revision of the 

pressurized thermal shock (PTS) rule (10 CFR 50.61). As a consequence of this review, I am requesting 

that ORNL take the following actions: 

1. Make certain changes to FAVOR 05.1. 

2. Issue a new version of FAVOR, Version 06.1, including revisions to both the Theory and the 

Users manuals. 

3. Re-analyze the base-case for the three study plants (Oconee Unit 1, Beaver Valley Unit 1, and 

Palisades) using certain new input data and issue the results to the NRC. 

4. Perform sensitivity studies to assess the effects of subclad cracking on the through wall cracking 

frequency associated with forged vessels and issue the results to the NRC. 

The purpose of this memorandum is to document in detail the particular tasks you are requested to take 

within each of these actions, and (in the case of changes made to the FAVOR code) document the 

technical basis for the requested changes. 

Should you have any questions or require clarification of any of the points made herein, please do not 

hesitate to contact me by email addressed to both mtk@nrc.gov and to markericksonkirk@verizon.net, or 

by telephone to 301-415-6015. 

Many thanks, 

 

Mark T EricksonKirk

A-1
 

Action 1: Change FAVOR 05.1 

Note: Information provided at the beginning of each of the following tasks establishes the technical 

basis/motivation for the requested change to FAVOR. At the end of each task writeup, the 

specific requested change can be found in a box highlighted, as is this one, in pink. 

Task 1.1 Change in the data basis for RTEPISTEMIC

Question 1: Tables 4.1 and 4.2 in NUREG-1807 provide information on materials for which both 

RTNDT and To are known. It is only the information in Table 4.2 that is eventually 

used in FAVOR because it is only for this subset of materials for which enough KIc

data are available to establish a RTLB value. There is a discrepancy between the To

value given in these tables for HSST Plate 03 (shaded in gold in the tables). Table 

4.1 gives a value of -21 F, while Table 4.2 gives a value of +31 F. What is the 

reason for the discrepancy? 

Answer 1: The values were calculated from different sets of KJc data, which is the reason they are 

different. However, the +31 F value in Table 4.2 is not considered valid per ASTM 

E1921 procedures because all of the KJc values were measured at a temperature that is 

more than 90 F below To. The value of -21 F, which is valid per ASTM E1921, should 

therefore be used. 

Action: In the FAVOR Theory manual (Table 10), change the value of To for HSST Plate 03 to -21 F, 

and change the resultant RTNDT-To value to +41 F. 

A-2
 

Table 4.1 Summary of Unirradiated RPV Materials 

Having Both RTNDT and To Values Available 

Author Year Product 

Form Spec Material Designation To [°F] RTNDT [°F] 

RTNDT - To

[°F] 

Iwadate, T. 1983 A508 Cl. 3 -54 -13 41 

Marston, T.U. 1978 A508 Cl. 2 -6 65 71 

Marston, T.U. 1978 A508 Cl. 2 -60 51 111 

VanDerSluys, W.A. 1994 A508 Cl. 3 -154 -22 132 

Marston, T.U. 1978 

Forging 

A508 Cl. 2 -124 50 174 

McGowan, J.J. 1988 A533B Cl. 1 HSST 02 -8 0 8 

Marston, T.U. 1978 A533B Cl. 1 HSST 02 -17 0 17 

Marston, T.U. 1978 A533B Cl. 1 HSST 01 -2 20 22 

Ahlf, Jurgen 1989 A533B Cl. 1 HSST 03 -21 20 41 

Onizawa, Kunio 1999 A533B Cl. 1 -99 -31 68 

Ishino, S. 1988 Generic Plate -81 -13 68 

CEOG 1998 A533B Cl. 1 -85 -15 70 

Link, Richard 1997 A533B Cl. 1 HSST 14A -70 10 80 

McCabe, D.E. 1992 A533B Cl. 1 HSST 13A -110 -9.4 100 

Onizawa, Kunio 1999 A533B Cl. 1 -152 -49 103 

Ishino, S. 1988 Generic Plate -131 -22 109 

CEOG 1998 A533B Cl. 1 -133 5 138 

Marston, T.U. 1978 A533B Cl. 1 -74 65 139 

Morland, E 1990 A533B Cl. 1 -142 5 147 

Ingham, T. 1989 

Plate 

A533B Cl. 1 -154 5 159 

Ishino, S. 1988 -39 -58 -19 

Ishino, S. 1988 -98 -76 22 

CEOG 1998 -126 -80 46 

Ramstad, R.K. 1992 HSST 73W -78 -29.2 48 

McCabe, D.E. 1994 Midland Nozzle -32 27 59 

Ramstad, R.K. 1992 HSST 72W -70 -9.4 60 

CEOG 1998 -138 -60 78 

CEOG 1998 -136 -50 86 

Williams. 1998 Kewaunee 1P3571 -144 -50 94 

McCabe, D.E. 1994 Midland Beltline -70 27 97 

Marston, T.U. 1978 -105 0 105 

CEOG 1998 -139 -20 119 

CEOG 1998 -157 -30 127 

CEOG 1998 -186 -50 136 

CEOG 1998 -189 -50 139 

Williams, J. 1998 

Weld 

-203 -50 153 

Table 4.2 Three Reference Transition Temperatures Defined 

Using the ORNL 99/27 KIc Database 

A-3
 

Property Reference Temperatures Uncert. Terms 

Set ID 

Material 

Description 

Product 

Form 

Sample 

Size RTNDT(u) T0 RTLB RTNDT(u) - 

T0 

ΔRTLB

N (°F) (°F) (°F) (°F) (°F) 

1 HSST 01 Weld 8 0 -105 -64.3 105 64.3 

2 A533 Cl. 1 Weld 8 0 -57 10.9 57 -10.9 

3 HSST 01 Plate 17 20 -1 -77.8 21 97.8 

4 HSST 03 Plate 9 20 31 -71.5 -11 91.5 

5 A533 Cl. 1 Plate 13 65 -74 -121.4 139 186.4 

6 HSST 02 Plate 69 0 -17 -2.1 17 2.1 

7 A533B Weld 10 -45 -151 -187.2 106 142.2 

8 A533B Weld/HA

Z 

6 0 -132 -162.4 132 162.4 

9 A508 Cl. 2 Forging 12 50 -124 -97.6 174 147.6 

10 A508 Cl. 2 Forging 9 51 -60 0.9 111 50.1 

11 A508 Cl. 2 Forging 10 65 -55 10.4 120 54.6 

12 HSSI 72W Weld 12 -9.4 -70 -15.4 60.6 6 

13 HSSI 73W Weld 10 -29.2 -78 -67.6 48.8 38.4 

14 HSST 13A Plate 43 -9.4 -109 -42.6 99.6 33.2 

15 A508 Cl. 3 Forging 6 -13 -46 -11.3 33 -1.7 

16 Midland Nozzle Weld 6 52 -34 from 

other 

sources 

-37.4 86 89.4 

17 Midland 

Beltline 

Weld 2 23 -71 from 

other 

sources 

-58.9 94 81.9 

18 Plate 02 4th Irr. Plate 4 0 -8 from 

other 

sources 

-62.3 8 62.3 

A-4
 

Question 2: When the RTLB data in Table 4.2 are plotted versus To (using the corrected value of To

identified in Question 1), the plot shown below results. (Note that three To values 

have been added to the original table for materials 16–18; these values are backed in 

blue.) Is there a reason why 7 of the data points have RTLB values that are lower 

than To (these data are indicated in red print in Table 4.2 above), while 11 of the 

values have RTLB values higher than To? 

-250

-200

-150

-100

-50

0

50

-200 -150 -100 -50 0 50

To [oF]

RTLB [oF]

 Data

 RTLB = To

Answer 2: The figure at the top of the next page, which is taken from the FAVOR 04.1 Theory 

Manual, indicates that RTLB is established for a particular data set using the following 

procedure: 

1. Identify a set of ASTM E399 valid KIc data for which you want to identify RTLB and 

for which RTNDT is known. 

2. Plot the KIc data, and also plot the ASME KIc curve located using RTNDT. 

3. Shift the ASME KIc curve downward by 9.5 ksiin. and call this curve the Adjusted 

Lower Bound ASME KIc Curve. 

4. Shift the Adjusted Lower Bound ASME KIc Curve leftward until it intersects the first 

measured KIc value. Call the amount by which the curve has been translated RTLB. 

5. RTLB is now defined as RTLB = RTNDT - RTLB. 

A-5
 

For data sets such as those shown in the figure above (i.e., those having KIc values measured over a range 

of temperatures), the RTLB value will always exceed the To value. This is illustrated in the figure at the 

top of the next page, where 100 KJc values are randomly simulated over the temperature range of -150 C 

 T-To  +75 C. The 11 actual sets of data for which RTLB exceeds To all have KIc values measured over 

a wide range of temperatures and so can be expected to have RTLB > To. We used the Master Curve to 

simulate 100 data sets of 100 KJc values over the temperature range of -150 C  T-To  +75 C (-270 F 

 T-To  +135 F). The 100 simulated RTLB values estimated from these simulated data exceeded To by, 

on average, 38 F (with a standard deviation of 19 F). This simulated amount by which RTLB exceeds To

is in good agreement with the 11 actual data sets for which RTLB exceeds To by 41 F (on average). From 

this analysis, we draw the following conclusions: 

 RTLB should exceed To. 

 For well-populated data sets where KIc or KJc values are measured in transition, RTLB will be 

estimated to exceed To. 

 The average amount by which RTLB exceeds To for the 11 data sets shown in black type in Table 

4.2 is in good agreement with our simulation based on the Master Curve. 

A-6
 

0

50

100

150

200

250

-200 -150 -100 -50 0 50 100

T-To [o

C]

KJc [MPa*m0.5]

KJc simulated based on MC

 2.5% MC Bound

 Median MC

 97.5% MC Bound

RTLB Curve, RTLB = To + 25C

The seven data sets shown in red type in Table 4.2 do not have measured KIc values distributed over a 

wide range of temperatures. In general, the measured KIc values for all five data sets fall in a range of 

temperatures between -111 C  T-To  -83 C (-200 F  T-To  -150 F). As illustrated by the 

simulation shown below, this places all of the measured KIc data very close to the lower shelf and causes 

the estimated value of RTLB to fall below To. To investigate the degree to which RTLB can be expected to 

fall below To for data sets of this type, we used the Master Curve to simulate 100 data sets of 20 KJc

values over the temperature range of -111 C  T-To  -83 C (-200 F  T-To  -150 F). The 100 

simulated RTLB values estimated from these simulated data fell below To by, on average, 77 F (with a 

standard deviation of 49 F). This simulated amount by which RTLB falls below To is well within one 

standard deviation of the seven actual data sets that have only KIc values on the lower shelf. These data 

sets, shown in red type in Figure 4.2, have RTLB values that fall below To by 43 F (on average). From 

this analysis, we draw the following conclusions: 

0

50

100

150

200

250

-200 -150 -100 -50 0 50 100

T-To [o

C]

KJc [MPa*m0.5]

KJc simulated based on MC

 2.5% MC Bound

 Median MC

 97.5% MC Bound

RTLB Curve, RTLB = To -45C

 RTLB will fall below To if the only KIc data available for analysis lie on or near the lower shelf. 

A-7
 

 The result RTLB < To is anomalous. It arises as a consequence of a limited amount of data that lie 

only on the lower shelf and, therefore, does not capture the temperature dependence inherent to 

transition fracture. RTLB < To does not reflect anything intrinsic about the material that should be 

simulated in FAVOR. Moreover, the KIc values estimated when RTLB falls below To become 

nonconservative at higher temperatures. 

 The data sets shown in red type in Table 4.2 should therefore not be used in the estimation of the 

RTEPISTEMIC value sampled in FAVOR to represent the difference between a known value of 

RTNDT and a simulated value of RTLB. 

The plot below shows the relationship (or lack thereof) between RTLB and RTNDT for the 11 data sets in 

black type shown in Table 4.2. For purposes of illustration only, a nonparametric CDF derived from 

these data is also shown on the next page. 

Action: Modify the data basis for the RTEPISTEMIC distribution used by FAVOR. The data used to 

establish the RTEPISTEMIC distribution should include only those data sets from Table 4.2 (see 

pages 4 and 5 of this memorandum) for which RTLB > To. Also, include the three new To

values given for materials 16, 17, and 18 in the FAVOR Theory manual. The analysis 

methodology used to establish the RTEPISTEMIC distribution from these data should be the same 

as that used currently. 

-150

-100

-50

0

50

-100 -50 0 50 100

RTNDT [oF]

RTLB [oF]

A-8
 

0.00

0.25

0.50

0.75

1.00

-50 0 50 100 150 200

RTEPISTEMIC = RTNDT - RTLB [o

F]

Cumulative Probability

Task 1.2 Change in where the uncertainty in RTNDT(u) is sampled in the FAVOR looping 

structure

The uncertainty assigned to a value of RTNDT(u) is a variable input to FAVOR. In practice, RTNDT(u)

uncertainty is only assigned a nonzero value when the input value of RTNDT(u) is determined by the socalled generic method. In FAVOR Version 05.1, RTNDT(u) uncertainty is sampled inside of both the flaw 

and the vessel loops. Because FAVOR simulates the existence of hundreds of thousands of flaws in a 

particular major region in a particular vessel, the current sampling strategy implies that RTNDT(u) can vary 

point-wise throughout any one weld, plate, or forging. This simulation is inconsistent with the ASME 

definition of RTNDT(u). Per ASME, the value of RTNDT(u) assigned to a particular weld, plate, or forging 

must be the highest of any value calculated from all of the Charpy V-notch and nil-ductility temperature 

measurements made for the weld, plate, or forging in question. Per ASME, RTNDT(u) should therefore be 

single-valued for each major region in each simulated vessel. 

Action: To reconcile this problem, ORNL is requested to modify the location where the RTNDT(u)

uncertainty is sampled in FAVOR. RTNDT(u) uncertainty should be sampled inside of the vessel 

loop, but outside of the flaw loop. 

Task 1.3 Change in where RTEPISTEMIC is sampled in the FAVOR looping structure

The FAVOR program includes a series of nested FORTRAN DO-loops that are used to perform a Monte 

Carlo simulation. Of these, the outermost loop is called the vessel loop. Immediately inside the vessel 

loop is the flaw loop. In FAVOR Version 05.1, a new value of RTEPISTEMIC is sampled from the 

RTEPISTEMIC distribution for each new flaw simulated. The sampled RTEPISTEMIC value is used to 

estimate the reference temperature for the fracture toughness transition curve in the following way: 

RTIrradiated RT uNDT )(  RTEPISTEMIC  SHIFT  ,,, tPNiCuRT 

For any particular simulated vessel, hundreds of thousands of individual flaws may be simulated to exist 

within a particular weld, plate, or forging (i.e., within what FAVOR refers to as a major region). Thus, 

A-9
 

the uncertainty simulated by FAVOR Version 05.1 in the RTIrradiated value will be as large as the 

uncertainty in RTEPISTEMIC, which, as shown by the graph at the top of the preceding page, can have a 

total range exceeding 150 F. This range is much larger than that measured in laboratory tests when 

fracture toughness samples were removed from different areas of a weld, plate, or forging. 

Action: To reconcile this problem (i.e., that FAVOR 05.1 simulates an uncertainty on RTIrradiated that 

exceeds that measured in laboratory experiments), ORNL is requested to modify the location 

where the RTEPISTEMIC distribution is sampled in FAVOR. RTEPISTEMIC should be sampled 

inside of the vessel loop, but outside of the flaw loop. 

No changes to the FAVOR code should be made inside the flaw loop to simulate the uncertainty 

associated with RTIrradiated. Once the actions requested in Tasks 1.2 and 1.3 are taken, there will be no 

uncertainty simulated within the flaw loop in either of the following variables, RTNDT(u) and RTEPISTEMIC. 

However, there is uncertainty within the flaw loop in the RTShift value. This uncertainty arises as a 

consequence of uncertainties simulated in the Cu, Ni, P, and fluence values. The graph below shows the 

effect of these simulated uncertainties on the resultant uncertainty in RTShift and, consequently, the 

resultant uncertainty in RTIrradiated. It can be observed that, except at low mean copper values, FAVOR 

simulates more uncertainty in RTShift (and, consequently, in RTIrradiated) than is reflected in either the data 

from which Eason derived the embrittlement shift model or than is characteristic of uncertainty in the To

reference temperature (ASTM E1921). If FAVOR simulates a negative RTShift value, it instead sets the 

RTShift used in the calculation to zero, which is why the simulated uncertainty in the low copper shift 

values is so small. The general overestimation by FAVOR of the uncertainty in RTShift occurs because 

information on chemical composition 

uncertainty from many sources had to be 

combined to obtain enough data to 

establish a distribution (see discussion in 

Appendix D of NUREG-1807). This 

procedure tends to overestimate the 

variability in chemical composition that 

would characteriz

0

10

20

30

40

50

60

012345

Fluence / 1019 [n/cm2]

Standard Deviation of 1000 Simulated 

Shift Values [oF]

Mean Cu = 0.05

Mean Cu = 0.10

Mean Cu = 0.20

Mean Cu = 0.30

Standard deviation of Eason model for welds

e any individual weld. 

Because of these factors, there is no need to 

add logic inside the flaw loop to simulate 

the uncertainty associated with RTIrradiated; 

this uncertainty is already accounted for in 

FAVOR by simulating uncertainties in the 

values of Cu, Ni, P, and fluence used in the 

calculations. 

Action: No action is required. The above 

comment was inserted for clarity. 

Task 1.4 Change in where the standard deviation on copper and on nickel is sampled in 

the FAVOR looping structure

The two figures below are taken from Appendix D of NUREG-1807. These graphs (and the related text 

in NUREG-1807 Appendix D) provide the technical basis for the standard deviation of both copper and 

nickel within a particular sub-region (i.e., within a particular weld). To be consistent with this data basis, 

FAVOR should sample these standard deviations once per major weld region in each simulated vessel. 

A-10
 

This, however, is not what is done in FAVOR 05.1. FAVOR 05.1 simulates the Cu and Ni standard 

deviations inside of both the flaw and the vessel loops. The effect of this sampling protocol is that the 

standard deviation of Cu and Ni is modeled as varying point-wise throughout a particular weld. 

Action: ORNL is requested to modify the location where the standard deviation on Cu and Ni for welds 

is sampled in FAVOR. The standard deviations for Cu and for Ni should be sampled inside of 

the vessel loop, but outside of the flaw loop. 

Task 1.5 Change the embrittlement trend curve (RTShift equation)

Action: Add the following embrittlement trend curve as an option to FAVOR. Note that the units of 

TTS are F. The technical basis for this equation is currently being documented by Nanstad, 

Eason, and Odette and should be available in April 2006. 

TTS MDterm  CRPterm

   e RCS MDterm A T tPMn 471.2  001718.01  130.61

    e e e

RCS tNiCugPCuf T CRPterm B Ni ,,,  1.543

769.31

100.1

191.1 



 



  





























for welds 10x417.1

platesfor 10x561.1

forgingsfor 10x140.1

7

7

7

A































for welds 0.155

manufactur CEin platesfor 2.135 vesselsed

manufactur CE-nonin platesfor 5.102 vesselsed

 forgingsfor 3.102

B

A-11
 





















 













 



 10

2595.0 10

10

103925.4for 103925.4

103925.4for 

  



 t

t

te

Note: The relationship for te is limited as follows: te = MAX(3t). 

    



 



    

6287.0

12025.184483.01390.1log tanh

2

1

2

1 ,, 10 t Cu Ni tNiCug e e

e e

 

   

  



















  

  





072.0for 0.008)-(359.1072.0 008.0

072.0for 072.0 008.0

072.0for 0

, 0.6679

0.6679

Cu P Cu Pand

Cu Cu Pand

Cu

PCuf

e

e e















  wt%072.0for  wt%072.0for 0

CuCu

Cu

Cue





























flux) L1092 with welds(all wt%0.75 Nifor 301.0

 wt%0.75 Ni 0.5for 2435.0

 wt%0.5 Nifor 370.0

)(CuMax e

The following items should be noted when implementing this formula in FAVOR: 

 Flux () is estimated by dividing fluence (t) by the time (in seconds) associated with the 

analysis. Time is calculated from EFPY. 

 The effective fluence (te) is limited to a maximum value of three times the fluence (i.e., 3t). 

 When estimating values of TTS for an embedded flaw having a crack-tip located z inches from 

the ID, the values flux () and fluence (t) at location z should be estimated as follows before the 

effective fluence (te) at location z is calculated: 

1. ID fluence:  ID , determined from the BNL fluence map 

2. ID flux: 

t

tID

ID

   , where t is determined from EFPY 

3. Fluence at z: tt  z IDz     24.0exp

4. Flux at z:  z IDz     24.0exp

5. Effective fluence at z: 





















 













 



 10

2595.0 10

10

)( 103925.4for 103925.4

103925.4for 

z z

z z

ze t

t

t

  





   ze z t  3MAX t )(

Task 1.6 Manganese sampling protocols and uncertainty

In order to complete Task 1.5, information on the uncertainty in Mn data and sampling protocols for these 

data is needed. Mn data were obtained from the following sources: 

A-12
 

1. Combustion Engineering Owners Group, “Fracture Toughness Characterization of C-E RPV 

Materials,” Draft Report, Rev. 0, CE NSPD-1118, 1998. 

2. VanDerSluys, W.A., Seeley, R.R., and Schwabe, J.E., “An Investigation of Mechanical 

Properties and Chemistry within a Thick MnMoNi Submerged Arc Weldment,” Electric Power 

Research Institute Report, EPRI NP-373, February 1977. 

3. Stelzman, W.J., Berggren, R.G., and Jones, T.N. Jr., “ORNL Characterization of HSST Program 

Plates 01, 02, and 03,” NUREG/CR-4092, March 1985. 

4. Wang, J.A., “Analysis of the Irradiation Data for A302B and A533B Correlation Monitor 

Materials,” NUREG/CR-6413, November 1995. 

5. Fyfitch, S., and Pegram, J.W., “Reactor Vessel Weld Metal Chemical Composition Variability 

Study,” B&W Nuclear Technologies Report, BAW-2220, June 1995. 

These citations contained enough repeated measurements of Mn to enable estimation of the variability in 

Mn at both a global and a local level. Global and local variability are defined as follows: 

 Global variability occurs over an area referred to as a region in FAVOR. A region is any 

individual weld, plate, or forging. Regions have ID areas on the order of 102

 to 103 square inches. 

 Local variability occurs over an area referred to as a “sub-region” in FAVOR. A sub-region is 

completely contained within a region and corresponds to an area of the vessel that has within it 

relatively minor variation in fluence. Sub-regions have ID areas on the order of 100

 to 101 square 

inches. 

Appendix D of NUREG-1807 provides a more complete description of how FAVOR simulates global and 

local variability in composition variables. 

The data from these four citations are summarized in the table and the figure below. Based on this 

information, the following conclusions can be made: 

 The variability (standard deviation) of Mn is approximately independent of mean Mn level. 

 The local variability of welds is less than the global variability of welds. 

 The global variability of forgings is less than that of welds and plates. The global and local 

variability of forgings is approximately equal. 

Regarding sampling/resampling protocols, the following shall be implemented in FAVOR for Mn: 

 The distinction between region and sub-region uncertainty that is currently made with regard to 

sampling of Cu, Ni, and P shall now also be made for Mn. 

 The recommendations of Task 1.4 for Cu and Ni shall be applied to Mn as well. 

 For welds, Cu, Ni, and P are resampled from the global (or region) uncertainty in the IGA 

Propagation Sub-Model each time the propagating crack extends past a 1/4T boundary. These 

same protocols shall be followed for resampling Mn in welds. 

Citation Data ID Product 

Form 

Global or 

Local 

Variability 

Number of Mn 

Measurements 

Mean 

Mn 

Mn 

Standard 

Deviation 

Plate 01-K Plate Global 9 1.356 0.095 

Plate 01-MU Plate Global 3 1.403 0.032 

NUREG/CR-4092 

Plate 02-FB Plate Global 3 1.490 0.010 

A-13
 

Global or Mn Product Number of Mn Mean Citation Data ID Form Local Standard 

Variability Measurements Mn Deviation 

Plate 03-E Plate Global 5 1.348 0.052 

B, OS, F1 Forging Local 4 0.648 0.005 

B, 1/4, F1 Forging Local 5 0.644 0.005 

A, 1/2, F1 Forging Local 5 0.636 0.011 

A, 3/4, F1 Forging Local 4 0.648 0.010 

A, IS, F1 Forging Local 4 0.650 0.008 

All F1 Data Forging Global 22 0.645 0.009 

B, OS, F2 Forging Local 2 0.720 0.014 

B, 1/4, F2 Forging Local 3 0.737 0.006 

A, 1/2, F2 Forging Local 3 0.740 0.017 

A, 3/4, F2 Forging Local 3 0.760 0.010 

All F2 Data Forging Global 13 0.736 0.020 

Flux A Weld Global 15 1.415 0.021 

Flux B Weld Global 11 1.554 0.048 

B, OS, W Weld Local 10 1.548 0.028 

B, 1/4, W Weld Local 9 1.494 0.017 

A, 1/2, W Weld Local 6 1.445 0.010 

A, 3/4, W Weld Local 4 1.423 0.022 

EPRI NP-373 

A, IS, W Weld Local 2 1.390 0.014 

A302B Plate Global 4 1.375 0.037 

HSST-01 Plate Global 16 1.392 0.090 

HSST-02 Plate Global 10 1.479 0.053 NUREG/CR-6413 

HSST-03 Plate Global 6 1.333 0.059 

27204-B03 Weld Global 13 1.292 0.038 

12008/13253-C08 Weld Global 13 1.282 0.078 

3P7317-T07 Weld Global 13 1.452 0.043 

90136-G11 Weld Global 13 1.067 0.034 

33A277-D08 Weld Global 13 1.153 0.038 

83637-N10 Weld Global 13 1.509 0.057 

10137-E08 Weld Global 13 1.291 0.048 

33A277-C19 Weld Global 13 1.220 0.055 

27204-B03 Weld Local 5 1.264 0.018 

12008/13253-C08 Weld Local 5 1.266 0.011 

3P7317-T07 Weld Local 5 1.448 0.013 

90136-G11 Weld Local 5 1.096 0.023 

33A277-D08 Weld Local 5 1.162 0.024 

83637-N10 Weld Local 5 1.498 0.008 

10137-E08 Weld Local 5 1.274 0.015 

CE NPSD 944-P 

Rev. 2 

33A277-C19 Weld Local 5 1.184 0.017 

10137 Weld Global 20 1.132 0.089 

21935 Weld Global 7 1.489 0.050 

20291/12008 Weld Global 29 1.252 0.079 

33A277 Weld Global 38 1.136 0.093 

10137 Plate Global 12 1.259 0.057 

BAW-2220 

21935 Plate Global 7 1.404 0.067 

A-14
 

Global or Mn Product Number of Mn Mean Citation Data ID Form Local Standard 

Variability Measurements Mn Deviation 

20291/12008 Plate Global 17 1.341 0.101 

33A277 Plate Global 24 1.348 0.088 

0.00

0.02

0.04

0.06

0.08

0.10

0.6 0.8 1.0 1.2 1.4 1

Mean Mn

Mn Standard Deviation

.6

 Plate - Global

 Forging - Global

 Forging - Local

 Weld - Global

 Weld - Local

Actions: Model variability in Mn at both the global and local level by sampling from distributions as 

described in the following table. The original data used to generate these values will be 

supplied to ORNL for further analysis. 

Regarding sampling/resampling protocols, the following shall be implemented in FAVOR for Mn: 

 The distinction between region and sub-region uncertainty that is currently made with regard to 

sampling of Cu, Ni, and P shall now also be made for Mn. 

 The recommendations of Task 1.4 for Cu and Ni shall be applied to Mn as well. 

 For welds, Cu, Ni, and P are resampled from the global (or region) uncertainty in the IGA 

Propagation Sub-Model each time the propagating crack extends past a 1/4T boundary. These same 

protocols shall be followed for resampling Mn in welds. 

Condition 

Value Global Variability 

in Plates 

Global Variability 

in Welds 

Global Variability in Forgings and 

Local Variability in all Product Forms 

Mean Standard Deviation 0.0617 0.0551 0.0141 

Standard Deviation of 

Standard Deviations 0.0278 0.0217 0.0063 

A-15
 

Task 1.7 Change coefficients in upper-shelf model

Work has continued in developing a model of upper-shelf fracture toughness and in establishing the 

relationship between upper-shelf and transition fracture toughness. As a result of this ongoing 

development work, some of the coefficients in the upper-shelf fracture toughness model implemented in 

FAVOR need to be changed, as detailed below. 

Eq. 19: The 50.1 and 0.794 coefficients used in Eq. 19 (current version below) should be changed to 

48.843 and 0.7985, respectively. The data supporting this change are given after the 

equation. 

Fit to All Static Data

TUS = 0.7985*To + 48.843

R2

 = 0.9812

-150

-100

-50

0

50

100

150

200

-200 -150 -100 -50 0 50 100 150 200

T o [o

C]

TUS [oC]

All Static

Old

New

Linde 80

Dynamic

Linear (All Static)

Eq. 21: The 2.09 coefficient used in Eq. 21 (current version below) should be changed to 1.75. The 

data supporting this change are given after the equation. 

A-16
 

-250

0

250

500

750

1000

-150 -100 -50 0 50 100 150 200 250 300

Temperature [oC]

JIc - 

JIc(288) [kJ/m2

]

Old

New

ZA Fit to Data, alpha=1.75

Eq. 23: The 62.023 and -0.0048 coefficients used in Eq. 23 (current version below) should be 

changed to 51.199 and -0.0056, respectively. The data supporting this change are given after 

the equation. 

y = 51.199e-0.0056x

R2 = 0.862

0

20

40

60

80

100

-150 -100 -50 0 50 100 150 200 250 300

Temperature [oC]

Standard Deviation of 

JIc 

Values [kJ/m2

]

A-17
 

Task 1.8 Enhance output

Modify FAVOR as necessary to enable the user to output the following results for each vessel iteration: 

 the RTEPISTEMIC value sampled for that vessel iteration 

 for each T-H transient simulated for that vessel for that vessel iteration: 

 the number of axial cracks that initiated 

 the number of circumferential cracks that initiated 

 the CPCI for axial cracks 

 the CPCI for circumferential cracks 

 the CPTWC for axial cracks 

 the CPTWC for circumferential cracks 

 the TWCF contribution from each T-H transient for that vessel iteration 

Also, modify FAVOR to print out values of RTMAX-AW, RTMAX-PL, and RTMAX-CW for each major region in 

the vessel beltline. Formulas for each value, taken from Eq. 8-1 through Eq. 8-3 of NUREG-1806, are as 

follows: 

RTMAX-AW is evaluated for each of the axial weld fusion lines using the following formula. 

In the formula, the symbol tFL refers to the maximum fluence occurring along a 

particular axial weld fusion line, and T30 is the shift in the Charpy V-notch 30 

ft-lb energy produced by irradiation at tFL. 

     FL  axialweld axialweld

FL uNDT

plate plate

AWMAX uNDT RT   RTMAX )(  30  , RTtT )(  30 tT

RTMAX-CW is evaluated for each of the circumferential weld fusion lines using the following 

formula. In the formula, the symbol tMAX refers to the maximum fluence 

occurring over the ID in the vessel beltline region, and T30 is the shift in the 

Charpy V-notch 30 ft-lb energy produced by irradiation at tMAX. 

     MAX  circweld circweld

MAX uNDT

plate plate

CWMAX uNDT RT   RTMAX )(  30  , RTtT )(  30 tT

RTMAX-PL is evaluated for each plate using the following formula. In the formula, the 

symbol tMAX refers to the maximum fluence occurring over the ID in the vessel 

beltline region, and T30 is the shift in the Charpy V-notch 30 ft-lb energy 

produced by irradiation at tMAX. 

  MAX

plate plate

PLMAX uNDT RT  RT )(  30 tT

Task 1.9 Temperature-dependent thermal-elastic properties

In FAVOR Version 05.1 (and previous versions), the thermal-elastic material properties (Young’s 

Modulus, Poisson’s Ratio, and the coefficient of thermal expansion) were modeled conservatively as 

being temperature-invariant properties. The 06.1 version of FAVOR should be modified to implement 

temperature dependencies in these properties as described in the following reference: 

 M. Niffengger, “The Proper Use of Thermal Expansion Coefficients in Finite Element 

Calculations,” Laboratory for Safety and Accident Research, Paul Scherrer Institute, 

Wurenlingen, Switzerland. 

A-18
 

Also, the clad-base stress free reference temperature and the through-wall weld residual stress profile 

models used in FAVOR Version 05.1 (and previous versions) were estimated assuming temperatureinvariant thermal-elastic material properties (for information on this estimation, see T.L. Dickson, W.J. 

McAfee, W.E. Pennell, and P.T. Williams, “Evaluation of Margins in the ASME Rules for Defining the 

P-T Curve for an RPV,” NUREG/CP-0166, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 

Proceedings of the Twenty-Sixth Water Reactor Safety Meeting 1, 1999, pp. 47–72). For consistency, the 

FAVOR model for the clad-base stress free reference temperature should be rederived using temperaturedependent thermal-elastic material properties. 

A-19
 

Action 2: Issue FAVOR Version 06.1 

Once the tasks requested under Action 1 are complete and all consistency checks and internal software 

verifications have been performed, ORNL is requested to issue a new version of FAVOR, which will be 

designated as Version 06.1. Revised versions of the Theory manual, the users manual, example problems, 

and the distribution disks will be issued to the NRC project monitor for review and comment. All 

manuals will be prepared in NUREG/CR format. 

After the manuals have been modified to address the NRC project monitor’s comments, they shall be reissued and distributed to individuals/organizations taking part in the verification and validation (V&V) 

effort. Following V&V, any errors, inconsistencies, and anomalies identified will be fixed (subject to 

concurrence of the project monitor), and the manuals will be revised and re-issued.

A-20
 

Action 3: Reanalyze the Base-Case for the Three Study Plants 

Using FAVOR 06.1 

Input: Repeat the analyses documented in ORNL/NRC/LTR-04/18 using FAVOR Version 06.1. Prior 

to performing this analysis, the input files should be changed only in the following manner: 

1. Change the initiating event frequencies for primary side pipe breaks to be consistent with the 

information provided in NUREG-1829. Alan Kolaskowski of SAIC will provide the necessary 

input files. 

2. Ensure that the global fluence uncertainty is coded as 11.8% and local fluence uncertainty is 

coded as 5.6% in the input files. 

3. The embrittlement trend curve described in Task 1.4 should be selected. Input values of Mn for 

the various plates, forgings, and welds in the three study plants are detailed in the table appearing 

at the end of Action 3. 

4. Change the current percentage of repair flaws in the flaw distribution from 2% to 2.3%. 

Basis for Item 4: NRR correctly points out that the decision to include 2% repair flaws in the flaw 

distribution used in the baseline PTS analysis was a judgment made on the basis that a 2% repair weld 

volume exceeded the proportional volume of weld repairs to original fabrication welds observed in any of 

PNNL’s work (the largest volume of weld repairs relative to original fabrication welds was 1.5%). 

However, flaws in welds are almost always fusion line flaws, which suggests that their number scales in 

proportion to weld fusion line area, not in proportion to weld volume. To address this, RES tasked PNNL 

to reexamine the relative proportion of repair welds that occur on an area rather than a volume basis. 

PNNL determined that the ratio of weld repair fusion area to original fabrication fusion area is 1.8% for 

the PVRUF vessel. Thus, the input value of 2% used in the FAVOR calculations can still be regarded as 

bounding. 

FAVOR makes the assumption that a simulated flaw is equally likely to occur at any location through the 

vessel wall thickness. During discussions between RES and NRR staff regarding the technical basis 

information developed by RES, NRR questioned the validity of this assumption for the case of flaws 

associated with weld repairs. After further consideration, RES has determined that this assumption is 

incorrect, as evidenced by the following information. The figure below shows that if a flaw forms in a 

weld repair, it is equally likely to occur anywhere with respect to the depth of the excavation cavity. 

However, the second figure below shows weld repair areas occur with much higher frequency close to the 

surfaces of the vessel then they do at mid-wall thickness. Taken together, this information indicates that a 

flaw due to a weld repair is more likely to be encountered close to the ID or OD surface than it is at the 

mid-wall thickness. 

A-21
 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80 1.00

Depth of Flaw from Cavity Surface (fraction)

Cummulative distribution ( faction)

Random distribution 

of flaw locations

 Weld Repair Mouth Weld Repair Root 

NUREG/CR-6471, Vol.2

y = 1.1066e-0.558x

R2 = 0.9773

0%

20%

40%

60%

80%

100%

012345678

Depth of Repair Excavation [inches]

Percent of Repair 

Excavations Extending to 

this Depth or Greater

Repair made from ID (26 observations)

Repair made from OD (26 observations)

Combined (52 Observations)

Expon. (Combined (52 Observations))

FAVOR currently uses as input a “blended” flaw distribution for welds. The flaws placed in the blended 

distribution are scaled in proportion to the fusion area of the different welding processes used in the 

vessel. Because of this approach, it is not possible to specify a through thickness distribution of repair 

weld flaws that is biased toward the surfaces while maintaining a random through thickness distribution 

of SAW and SMAW weld flaws. Therefore, to account for the nonlinear through thickness distribution of 

weld flaws the 2% blending factor currently used for repair welds will be modified on the following basis: 

 In FAVOR, only flaws within 3/8T of the inner diameter can contribute to the vessel failure 

probability. Because PTS transients are dominated by thermal stresses, flaws buried in the vessel 

wall more deeply than 3/8T do not have a high enough driving force/low enough fracture 

toughness to initiate. 

A-22
 

A-23

 On the graph above, 3/8T corresponds to 3 in. The curve fit to the data on this graph indicates 

that 79% of all repair flaws occur within from 0 to 3/8T of the outer surfaces of the vessel. The 

figure above also indicates that 7% of all repair flaws occur between 5/8T and 1T from the outer 

surfaces of the vessel. Therefore, 43% ((79%+7%)/2) of all repair flaws occur between the ID 

and the 3/8T position in the vessel wall. 

 FAVOR’s current assumption of a random through-wall distribution of repair flaws indicates that 

37.5% of all repair flaws occur between the ID and the 3/8T position in the vessel wall. Thus, 

FAVOR underestimates the 43% value based on the data given above. 

 To account for this underestimation, the 2% blend factor for repair welds will be increased to 

2.3% (i.e., 2%43/37.5). 

Output: Document the results of the PFM analyses performed with FAVOR 06.1 in the same format as 

that used in ORNL/NRC/LTR-04/18 and provide to the NRC project monitor for review and 

comment. Additionally, as soon as it is practicable after the FAVOR analyses are complete, and 

preferably in advance of issuance of the electronic archive letter report, provide results in MS 

Excel spreadsheets to the NRC project monitor for analysis. 
Table of plant-specific input values for use in FAVOR calculations revised to include mean Mn values. This table w

Appendix D in the FAVOR Theory manual and as Appendix C in NUREG-1807. 

RTNDT(u) [

oF] Composition(2

Product Form Heat Beltline 

flow(u)

 [ksi] RTNDT(u)

Method 

RTNDT(u)

Value 

(u)

Value Cu Ni P 

Beaver Valley 1, (Designer: Westinghouse, Manufacturer: CE) Coolant Temperature = 547 F, Vessel Thickness = 7-7/8 in. 

C4381-1 INTERMEDIATE SHELL B6607-1 83.8 MTEB 5-2 43 0 0.14 0.62 0.01C4381-2 INTERMEDIATE SHELL B6607-2 84.3 MTEB 5-2 73 0 0.14 0.62 0.01C6293-2 LOWER SHELL B7203-2 78.8 MTEB 5-2 20 0 0.14 0.57 0.01

PLATE 

C6317-1 LOWER SHELL B6903-1 72.7 MTEB 5-2 27 0 0.2 0.54 0.0

305414 LOWER SHELL AXIAL WELD 20-714 75.3 Generic -56 17 0.337 0.609 0.01

LINDE 1092 WELD 

305424 INTER SHELL AXIAL WELD 19-714 79.9 Generic -56 17 0.273 0.629 0.01

LINDE 0091 WELD 90136 CIRC WELD 11-714 76.1 Generic -56 17 0.269 0.07 0.01

Oconee 1, (Designer and Manufacturer: B&W) Coolant Temperature = 556 F, Vessel Thickness = 8.44-in.

FORGING AHR54 (ZV2861) LOWER NOZZLE BELT (4) B&W Generic 3 31 0.16 0.65 0.00

C2197-2 INTERMEDIATE SHELL (4) B&W Generic 1 26.9 0.15 0.5 0.00C2800-1 LOWER SHELL (4) B&W Generic 1 26.9 0.11 0.63 0.01C2800-2 LOWER SHELL 69.9 B&W Generic 1 26.9 0.11 0.63 0.01C3265-1 UPPER SHELL 75.8 B&W Generic 1 26.9 0.1 0.5 0.01

PLATE 

C3278-1 UPPER SHELL (4) B&W Generic 1 26.9 0.12 0.6 0.0

1P0962 INTERMEDIATE SHELL AXIAL WELD SA-1073 79.4 B&W Generic -5 19.7 0.21 0.64 0.02299L44 INT./UPPER SHL CIRC WELD (OUTSIDE 39%) WF-25 (4) B&W Generic -7 20.6 0.34 0.68 (361782 NOZZLE BELT/INT. SHELL CIRC WELD SA-1135 (4) B&W Generic -5 19.7 0.23 0.52 0.0171249 INT./UPPER SHL CIRC WELD (INSIDE 61%) SA-1229 76.4 ASME NB- 2331 10 0 0.23 0.59 0.0272445 UPPER/LOWER SHELL CIRC WELD SA- 1585 (4) B&W Generic -5 19.7 0.22 0.54 0.018T1762 LOWER SHELL AXIAL WELDS SA-1430 75.5 B&W Generic -5 19.7 0.19 0.57 0.01

LINDE 80 WELD 

8T1762 UPPER SHELL AXIAL WELDS SA-1493 (4) B&W Generic -5 19.7 0.19 0.57 0.01

A-24
A-25

RTNDT(u) [oF] Composition(2

Product Form Heat Beltline flow(u) [ksi] RTNDT(u)

Method 

RTNDT(u)

Value 

(u)

Value Cu Ni P 

8T1762 LOWER SHELL AXIAL WELDS SA-1426 75.5 B&W Generic -5 19.7 0.19 0.57 0.01

Palisades, (Designer and Manufacturer: CE) Coolant Temperature = 532 F, Vessel Thickness = 81⁄2 in.

A-0313 D-3803-2 (4) MTEB 5-2 -30 0 0.24 0.52 0.0B-5294 D-3804-3 (4) MTEB 5-2 -25 0 0.12 0.55 0.0C-1279 D-3803-3 (4) ASME NB- 2331 -5 0 0.24 0.5 0.01C-1279 D-3803-1 74.7 ASME NB- 2331 -5 0 0.24 0.51 0.00C-1308A D-3804-1 (4) ASME NB- 2331 0 0 0.19 0.48 0.01

PLATE 

C-1308B D-3804-2 (4) MTEB 5-2 -30 0 0.19 0.5 0.01

LINDE 0124 WELD 27204 CIRC. WELD 9-112 76.9 Generic -56 17 0.203 1.018 0.01

34B009 LOWER SHELL AXIAL WELD 3-112A/C 76.1 Generic -56 17 0.192 0.98 (3W5214 LOWER SHELL AXIAL WELDS 3- 112A/C 72.9 Generic -56 17 0.213 1.01 0.01

LINDE 1092 WELD 

W5214 INTERMEDIATE SHELL AXIAL WELDS 2-112 A/C 72.9 Generic -56 17 0.213 1.01 0.01

Notes:

(1) Information taken from the July 2000 release of the NRC’s Reactor Vessel Integrity (RVID2) database. (2) These composition values are as reported in RVID2 for Cu, Ni, and P and as reported in RPVDATA for Mn. In FAVOR calcu

should be treated as the central tendency of the Cu, Ni, P, and Mn distributions detailed in Appendix D. 

(3) No values of phosphorus are recorded in RVID2 for these heats. A generic value of 0.012 should be used, which is the mean o

taken from the surveillance database used by Eason et al. to calibrate the embrittlement trend curve. 

(4) No strength measurements are available in PREP4 for these heats (PREP). A value of 77 ksi should be used, which is the mea

values reported in this appendix. 

(5) No values of manganese strength in RPVDATA for these heats (ref). A generic value of 0.80 should be used, which is the me

forgings taken from the surveillance database used by Eason et al. to calibrate the embrittlement trend curve. 
 

Action 4: Perform Sensitivity Studies on Subclad Cracking 

In the spring of 2006, FAVOR 06.1 will be modified to run on the ORNL supercomputer cluster. At that 

time, ORNL is requested to work with the NRC project monitor to define a set of PFM analyses that can 

be used to quantify the effect of subclad cracks on TWCF. It is anticipated that the total scope of the 

effort will include approximately 8–10 PFM analyses (likely two plants, each run at 4 to 5 different 

EFPY). Reporting of results is needed to the same level of detail as was done for the subclad cracking 

sensitivity study performed by ORNL using FAVOR Version 05.1. 

A-26
APPENDIX B 

REVIEW OF THE LITERATURE ON SUBCLAD FLAWS AND A 

TECHNICAL BASIS FOR ASSIGNING SUBCLAD FLAW 

DISTRIBUTIONS 
B-1

TECHNICAL LETTER REPORT

Review of the Literature on Subclad Flaws 

and a Technical Basis for 

Assigning Subclad Flaw Distributions 

 

PNNL Project Number: 43565 

JCN Y6604 

Task 4: Flaw Density and Distribution in RPVs 

F.A. Simonen 

February 2005 

W.E. Norris, NRC Project Manager 

Prepared for 

Division of Engineering Technology 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

DOE Contract DE-AC06-76RLO 1830 

NRC JCN Y6604 

Pacific Northwest National Laboratory 

P.O. Box 999 

Richland, WA 99352 
Review of Literature on Subclad Flaws and 

Technical Basis for Assigning Subclad Flaw Distributions 

F.A. Simonen 

Pacific Northwest National Laboratory 

Richland, Washington 

January 31, 2005 

Introduction 

Pacific Northwest National Laboratory (PNNL) has assisted the U.S. Nuclear Regulatory Commission 

(NRC) in the efforts to revise the Pressurized Thermal Shock (PTS) Rule. In this role PNNL has 

provided Oak Ridge National Laboratory (ORNL) with inputs for the FAVOR code to describe 

distributions of fabrication flaws in reactor pressure vessels. These inputs, consisting of computer files, 

have been important to probabilistic fracture mechanics calculations with FAVOR. The flaw inputs have 

addressed seam welds, cladding and base metal materials, but had excluded subclad flaws associated with 

the heat-affected zone (HAZ) from the welding processes used to deposit stainless steel cladding to the 

inner surface of the vessel. 

To address concerns expressed by a peer review committee, ORNL was requested by NRC to evaluate the 

potential contribution of subclad flaws to reactor pressure vessel failure. Based on information in 

available documents, PNNL estimated the number and sizes of subclad flaws in a forged pressure vessel, 

and provided input files to ORNL for sensitivity calculations. These sensitivity calculations predicted 

that subclad flaws could contribute significantly to calculated vessel failure probabilities. PNNL was then 

requested to continue its review of the literature for additional information on subclad flaws and to 

propose a refined basis for inputs to the FAVOR code. 

The major sections of the present report: 

1. describe the technical basis for the original subclad flaw input files that PNNL provided to ORNL for 

use with the FAVOR code 

2. summarize results of a literature review performed by PNNL for information on characteristics of 

subclad flaws 

3. propose and describe an improved method for generating distributions for subclad flaws and present 

results of example calculations 

4. recommend future work to improve the flaw distribution model and the simulation of subclad flaws 

by the FAVOR code 

References (as listed at the conclusion of this report) provide information on a range of topics, including 

the metallurgical mechanisms that cause subclad cracks, measures that can prevent cracking, and fracture 

mechanics calculations that have evaluated the significance of subclad cracks. The main focus in the 

present report is on the characteristics of observed subclad flaws and more specifically on available data 

and prior estimates of the sizes and numbers of subclad flaws. 

Technical Basis for Prior Subclad Flaw Distributions 

For welds, base metal, and cladding, PNNL has examined material and has used the data on observed 

flaws in the different material types to establish statistical distributions for the numbers and sizes of flaws. 

However, none of the examined material showed evidence of subclad flaws. Therefore, the numbers and 

sizes of subclad flaws for a vessel susceptible to such cracking were estimated from a preliminary review 

B-2
of the literature. The primary source was a comprehensive paper summarizing European work during the 

1970s (A. Dhooge et al., 1978). This paper was based mainly on experience with vessel cracking in 

Europe and subsequent research programs conducted during the 1970s. The paper was considered to be 

relevant to U.S. concerns with older vessels that may have been fabricated with European practices. 

The survey of the literature showed that subclad cracks: 

1. are shallow flaws extending into the vessel wall from the clad-to-base metal interface, and 4 mm is 

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 

4. extend to depths limited by the depth of the heat-affected zone 

Figures in the cited paper show networks of cracks with flaw depths estimated from a micrograph being 

significantly less than the cited bounding 4-mm depth. The cracks extended perpendicular to the direction 

of welding and were clustered where the passes of the strip clad overlapped. Subclad flaws were said to 

be much more likely to occur in 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 inputs during the cladding process also enhance the 

likelihood of subclad cracking. Other details of the cladding process are also important, such as singlelayer versus two-layer cladding. 

The number of cracks per unit area of vessel inner surface was estimated from Figure 1, taken from the 

Dhooge paper. Cracking was shown to occur in bands estimated to have a width of 4 mm. This 

dimension was used to estimate the bounding lengths 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. Counting the 

number of cracks pictured in a small region of vessel surface gave a crack density of 80,512 flaws per 

square meter. 

Figure 1 Location and Orientation of Underclad Crack; (a) Transverse Section; 

 (b) Plan View of Cracks 

B-3
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 the assumption for 

flaws in seam welds, the amount by which flaw lengths exceed their corresponding depth dimension 

was taken to be a uniform distribution from 0 to 4 mm. Thus, the extreme length for a flaw with a 

depth dimension of 4 mm was 8 mm. The 4-mm deep flaws therefore had lengths ranging from 4 to 8 

mm (aspect ratios from 1:1 to 2:1). Flaws with depths of 1 mm had 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 using the total volume of metal in the vessel wall. 

4. The file prepared for FAVOR assumed that the code would simulate flaws for the total vessel wall 

thickness, rather than just the Category 1 and 2 regions, which address only the inner three-eighths of 

the wall thickness. ORNL then accounted for this concern during the FAVOR calculations. 

A very large number of flaws (> 130,000) per vessel was predicted based on the photograph of one small 

area of a vessel surface. The implication was that this area was representative of the entire vessel. 

Although it is possible that subclad flaws can occur nonuniformly in patches of the vessel surface, it is 

generally understood that flaws occur in a widespread manner. Large numbers of flaws have been 

reported when the proper conditions for subclad cracking have existed. Based on PNNL’s limited review 

of documents, it was therefore difficult to justify reductions of the estimated flaw density. However, 

sensitivity calculations should be performed to see if refinement of the estimated flaw density has a 

significant effect on the FAVOR calculations. 

The estimated depth dimensions of the subclad flaws were thought to be conservative. The depth of 

4 mm was based on statements regarding bounding flaw depths, with no other evidence such as 

micrographs 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 was then taken as a limitation on flaw depth. Alternatively, 

the 4-mm depth could be the extreme depth of some observed subclad flaws. The preliminary review 

showed some examples from metallography of subclad flaws, which showed only flaws of much smaller 

depths (< 2 mm). It is therefore suggested that sensitivity studies assumed subclad flaws with a bounding 

depth of 2 mm. The resulting FAVOR calculations included only flaws in the “first bin” corresponding to 

sizes 0 to 1 percent of the vessel wall thickness and predicted only small contribution for subclad flaws to 

vessel failure probabilities. 

In summary, PNNL’s preliminary estimates of subclad flaw distributions were based on a rather limited 

review of available literature, with a particular focus on the Dhooge 1978 paper. It was recommended 

that the scope of the literature review be expanded to seek sources of additional information. PNNL also 

proposed to review notes from past sessions with expert elicitation panels that have addressed reactor 

vessel fabrication and flaw distributions for the NRC. The critical need was information on the depth 

dimensions of subclad flaws. It was possible that the depth dimension of 4 mm is uncharacteristic of 

most subclad flaws, but is rather a bounding dimension based on consideration of heat-affected zones. It 

was possible that 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. 

B-4
Results of Literature Review

Individual papers and reports are summarized below. 

Welding Research Council Bulletin No. 197 

During the early 1970s, data on subclad cracking were assembled by the Task Group on Underclad 

Cracking under the Subcommittee on Thermal and Mechanical Effects of the Fabrication Division of the 

Pressure Vessel Research Committee. The following paragraphs from the report of the Task Group are 

extracted from Welding Research Council Bulletin No. 197 (Vinckier and Pense, 1974). 

Underclad cracks were defined as intergranular separations no less than about 3 mm (0.12 

in.) deep and 3 mm (0.12 in.) long found in the coarse-grained heat-affected zone of lowalloy steels underneath the weld-cladding overlay. Grain-boundary decohesions of sizes 

less than this were also included in the investigation. They are generally produced during 

postweld heat treatment. The combination of three factors that promote underclad 

cracking are a susceptible microstructures, a favorable residual-stress pattern and a 

thermal treatment bringing the steel into a critical temperature region, usually between 

600 °C (1112 and 1202 °F) where creep ductility is low. Weld-overlay cladding with 

high-heat input processes provides the susceptible microstructure and residual-stress 

pattern, particularly where weld passes overlap, and postweld heat treatment provides the 

critical temperature. 

High-heat-input weld-overlay techniques tend to increase the incidence of underclad 

cracks. Most underclad cracking was found in SA508 Class 2 steel forgings with some 

forged material chemical compositions found to be more sensitive than others. These 

forgings were clad with one-layer submerged-arc strip electrodes or multi-electrode 

processes. It was not reported in SA533 Grade B plate, nor was it produced when 

multilayer overlay processes were used. 

Underclad cracking can be reduced or eliminated by a variety of means, but the most 

feasible appears to be by using a two-layer cladding technique, controlling welding 

process variables (e.g., low-heat-input weld processes) or renormalizing the sensitive 

heat-affected-zone region prior to postweld heat treatment. Control of welding process 

variables alone may not prevent all grain-boundary decohesions. Another solution would 

be to use materials that do not show the combination of a susceptible microstructure and 

low creep ductility or, where feasible, eliminate the thermal postweld heat-treatment 

cycle. 

Other significant findings were: 

 Underclad cracking can include less severe manifestations of the same damage mechanisms as 

underclad cracks, but in the form of incipient cracks, microcracks, intergranular separations, pores, 

etc. 

 Underclad cracks are restricted to overlap of the clad passes and occur in the pattern and orientation 

as indicated in Figure 2. 

 Fracture mechanics evaluations established that subclad flaws with dimensions of 5 mm by 10 mm 

are not critical to safe operation. 

 Underclad cracking was widely reported in an industry survey as occurring in SA 508 Class 2 

forgings. No cases of cracking were reported for SA 533 Grade B. One case of cracking was 

reported for SA 508 Class 3 consisting of separations less than 0.1-mm deep. 

B-5
For purposes of the present review, it is noted that WRC Bulletin 197 has no information on reported 

depths of underclad cracks. There was, however, much discussion of the factors that govern the 

susceptibility of materials to underclad cracking along with descriptions of the material selections and 

welding procedures that can prevent underclad cracking. 

Figure 2 Section of Clad Plate Showing Cracks 

French Work 

Underclad cracking has been observed in a number of reactor pressure vessels fabricated for French 

nuclear power plants. The French evaluation methods and requirements for vessel integrity (Pellissier 

Tanon et al., 1990; Buchalet et al., 1990; ASME, 1993; Moinereau et al., 2001) are based on several 

categories of reference defects. These defects address different defect locations, different mechanisms for 

the origin of defects, and a range of probabilities of defect occurrence. One of the categories is that of 

underclad defects, which are defects that have been of particular concern to French vessels. In terms of 

occurrence probabilities, the French evaluations have defined the following three defect classes. 

 Envelope defects—those that have actually been observed during manufacturing, but with a size that 

cannot be exceeded realistically (1>P>10-2). 

 Exceptional defects—those of the same type as envelope defects, but with a larger size to cover all 

the largest defects even seen in large primary circuit components (10-2>P≥10-4). 

 Conventional defect—covers configurations of very low probability (P<10-4). 

Figure 3 shows the full scope of reference defects, with only the underclad crack being of interest to this 

discussion. For the envelope category, the underclad defect has a 3-mm through-wall dimension and a 

length of 60 mm. For the exceptional category, the underclad defect has a 6-mm through-wall dimension 

and a length of 60 mm. 

Many of the original source documents for the French requirements were not available for the present 

review. However, ASME Section XI, with support by EPRI, has issued reports that provide information 

that is otherwise available only from the French literature. These ASME sources permitted the current 

review to be completed. 

The French characterization of flaws was not specifically formulated for use in probabilistic fracture 

mechanics calculations, but has rather been used in France for deterministic calculations. The following 

B-6
discussion nevertheless provides some interpretations in the context of inputs for probabilistic 

calculations such as with the FAVOR code. 

The probability values as cited above do not define units as needed to estimate flaw frequencies in terms 

of flaws per unit area or flaws per unit volume. The French publications imply that that probability 

values can be interpreted as the probability of having one or more flaws of the given sizes in a beltline 

vessel weld. This definition is difficult to apply to underclad cracks because these cracks occur in base 

metal rather than in welds. However, forged vessels such as those applicable to the French experience 

would have at most two circumferential welds in the beltline. It was therefore assumed that the 

probabilities can be treated as flaws per vessel. With this interpretation: 

 A flaw distribution for underclad cracks would have a maximum flaw depth of 3 mm and maximum 

flaw length of 60 mm. The probability range of 1>P>10-2 can be interpreted to mean that between 

1 percent to 100 percent of a population of vessel welds would be subject to underclad cracking. 

 The probability range of 10-2>P≥10-4 can be interpreted to mean that between 1 percent to 0.01 

percent of the vessels with underclad cracks will have a maximum flaw depth of 6 mm. 

 The probability of P<10-4 can be interpreted to mean that one vessel in 10,000 would have a 

fabrication surface flaw that extends through the entire clad and then into the base metal to give a 

total flaw depth of 13.5 mm. Such a flaw is outside the scope of the present discussion of underclad 

cracking, but has been addressed by ORNL as a low probability surface flaw. 

Sensitivity studies by ORNL for underclad flaws were performed for maximum flaw depths of 2 mm and 

4 mm. The 4-mm flaw is conservative in the context of the French work, because the French work could 

only support the assumption of a 3-mm maximum flaw depth. Uncertainty analyses could consider flaw 

depths as great as 6 mm, but this flaw depth should be weighted by a factor of 10-2 to 10-4 in constructing 

an uncertainty distribution. 

It was noted that the French work used information on fabrication flaws collected from European 

manufacturers of vessels. For the underclad flaws, the exceptional defect depth of 6 mm came from 

considerations of the repair of underclad cracks. The French work indicated that the orientations of 

underclad cracks are expected to be longitudinal and that the use of a two-layer cladding will minimize 

the likelihood of underclad cracking. 

Westinghouse Submittals 

Two topic reports from Westinghouse Electric were submitted to NRC to address the impact of underclad 

cracks on reactor pressure vessel integrity (Mager et al., 1971; Bamford and Rishel, 2000). The most 

recent report revisits concerns for underclad cracking to cover the period of license extension from 40 

years to 60 years, and concludes that underclad cracks are of no concern relative to structural integrity of 

the reactor pressure vessel for a period of 60 years. Both the 1971 and 2000 WCAP reports were 

reviewed by NRC staff. A regulatory guide on weld cladding was issued (NRC, 1972). The NRC review 

of WCAP-15338 resulted in a request for addition information (NRC, 2002a) and a safety evaluation 

report (NRC, 2002b). 

Because the 1971 Westinghouse report and RG 1.43 were not available to PNNL, the review was limited 

to the 2000 WCAP report and NRC’s response to this report. Only limited information for estimating 

flaw distributions for PTS evaluations was found in the Westinghouse and NRC documents. The main 

focus was on deterministic fracture mechanics evaluations that covered such issues as fatigue crack 

growth, with no attention given to PTS evaluations. The fracture mechanics calculations assumed 

deterministic sizes of underclad cracks, with little documentation for the flaw size assumptions. 

The 2000 WCAP report reviews the history of underclad cracking, including 1970 reports of “reheat 

cracking” and 1979 experience with “cold cracking.” Early reports of reheat cracks were limited in the 

B-7
United States with vessels fabricated by the Rotterdam Dockyard Manufacturing Company. Cold 

cracking was limited to a select group of six U.S. vessels. Reheat cracking has occurred with single-layer 

cladding using high heat input welding onto ASME SA-508 Class 2 forgings. The cracks are numerous 

and are confined to a depth of 0.125 inch (3 mm) and a width of 0.4 inch (10 mm). 

Circumferential Direction: 1, 2, 8, 10, 11 

Longitudinal Direction: 3, 4, 5, 6, 7, 9, 12 

Figure 3 Reference Defects for Vessel Beltline from French Evaluations (dimensions in mm) 

Cold cracking has been reported for ASME SA-508 Class 3 forgings after deposition of the second or 

third layer of cladding. Crack depths have varied from 0.007 inch (0.2 mm) to 0.295 inch (7.5 mm) and 

lengths have varied from 0.078 inch (2 mm) to 0.59 inch (15 mm). The WCAP reports indicate that cold 

cracking has not been observed in the vessel beltline, but rather at other locations such as nozzle bore 

regions. No occurrences of underclad cracks have been reported for plate materials or for SA-533B, SA302E, or SA-302B forging materials. 

B-8
NRC Expert Panels 

Two expert panels were formed as part of an NRC project during the 1990s to address concerns with 

flaws in reactor pressure vessels. The overall objective of this project was to review and expand the 

technical basis of the flaw distribution model of the PRODIGAL computer code (Chapman and Simonen, 

1998) as developed in the United Kingdom by Rolls Royce and Associates. A meeting during 1994 

focused on flaws in vessel seam welds. A followup meeting during 1996 focused on clad region flaws, 

including a discussion of underclad cracking. Although the experts provided useful and interesting 

insights and information on underclad cracking, the input from the experts was insufficient to provide the 

quantitative inputs needed to model underclad cracking in the PRODIGAL computer code. 

The minutes of the two meetings (Simonen, 1994; Simonen, 1996) along with informal notes were 

reviewed. The following insights were expressed by the experts during the meetings: 

 Underclad cracking should be addressed from the standpoints of two timeframes, (1) cracking when 

the clad is deposited by welding and (2) cracking when a post-weld heat treatment is performed. 

 Reheat cracks can occur in coarse grained regions of 508 steel when post-weld heat treatment is 

performed. 

 Reheat cracks occur in clusters and have small depths of about 1 mm that cover the clad surface of the 

forging. 

 Reheat cracks form in the base metal and not in weld fill material. Reheat cracks never extend into 

the cladding material. 

 There should be no interaction of underclad cracks with other cracks due to lack of side wall fusion. 

 There is little reason for interaction between underclad cracks and previous HAZ cracks. 

 Post-weld reheat cracks can also occur along the HAZ of the side wall of the weld fill. The 

occurrence of underclad cracks would often be correlated with HAZ along the sidewall. 

 The same metallurgical cracking phenomena can occur for both underclad cracks and HAZ cracks 

with both occurring during stress relief post-weld heat treatment. Cracking is likely to occur (if it 

does occur) both as underclad and as HAZ, because the composition of the material is susceptible. 

 Some heats of material will be more susceptible than others due to material differences. The primary 

variable is chemical composition, and the occurrence of cracking is not much impacted by heat 

inputs. 

 Cracking actually occurs during post-weld heat treatment. The locations of cracks are related to weld 

beads. 

 The PRODIGAL weld simulation model could account for the compositions of forgings (508), and 

this information could be used to establish susceptibilities to underclad cracking. Utilities know 

forging composition, which could be used with a method described in an ASME paper which 

describes “Nakwuma Number” as the basis to predict susceptibility to reheat cracking (Horiya et al., 

1985). 

 A Framatome case of cold cracking (H2 cracking) was described that gives cracks parallel to the 

surface as an example of underclad cracks due to the heat inputs used in cladding. This cracking 

occurs only if there is a second layer of clad applied without preheat. B&W and CE were aware of 

the potential problem, which can occur in both the 533 and 508 materials, but is less likely to occur in 

weld metal. Cracking will also be in the form of a lack of bonding of the clad to base metal. 

B-9
2000 Vessel Flaw Expert Judgment Elicitation 

The NRC has funded a number of efforts to re-evaluate the guidance and criteria in the Code of Federal 

Regulations as it relates to reactor vessel integrity, specifically pressurized thermal shock, which 

challenges the integrity of the reactor pressure vessel’s inner wall. One element of the re-evaluation 

required an accurate estimate of fabrication flaws, and this identified the need for the development of a 

generalized flaw distribution for domestic reactor pressure vessels. In order to develop the flaw 

distribution and resolve technical issues for which scientific uncertainty existed, an expert judgment 

process was used. The expert judgment process assisted the NRC staff in developing a generalized flaw 

distribution for domestic vessels, which has been used as input into probabilistic fracture mechanics 

calculations. 

Although underclad cracking was not specifically addressed by the elicitation, some of the discussions 

with the experts provided some information of interest. The following remarks were compiled from 

detailed notes taken during interviews with the experts: 

 Other experts should address underclad cracking. It is estimated that there is a 1 in 50 probability of 

conditions for underclad cracking. 

 508 Class 2 materials had some problems with lack of bonding of clad to base metal. U.S. vessels did 

not have bonding problems with Class 2. The U.S. Navy stayed with the Class 2 material. The 

French changed to 508 Class 3. 

 One expert believed that Babcock and Wilcox had some cases of underclad cracking. 

 There can be underclad cracks for single-layer clad if the heat input is too high. There can also be 

underclad cracks with a two-layer clad without heat treatment between layers. 

 One expert had concerns with underclad cracks in 508 forgings. An EPRI report on French 

experience was mentioned. 

 Only 508 forgings are susceptible to underclad cracking reheat cracks. One of the experts did 

research and wrote a NUREG for NRC/ORNL about 7 years ago. 

 No reheat underclad cracking has been reported for plate materials. None of the experts was aware of 

H2 underclad cracking for plates. One expert estimated relative probabilities for underclad cracks for 

plates versus forgings. 

Canonico/ORNL Report on Underclad Cracking 

Canonico (1977) reviews research on reheat cracks and the significance of such cracks to the integrity of 

reactor pressure vessels. The focus is on cracking in the heat-affected zones of seam welds rather than on 

underclad cracking. This report provides no specific information on the dimensions of cracks observed in 

nuclear vessels. 

Frederick and Hernalsteen 

Frederick and Hernalsteen (1981) summarize experience with underclad cracking and evaluations of the 

significance of these cracks to vessel integrity. The information provided in this paper does not add to 

what is available in other more comprehensive review papers such at WRC Bulletin 197. 

Dhooge et al. 

Dhooge et al. (1978) provide an extensive review of experience and research in the area of reheat 

cracking in nuclear reactor pressure vessels, both underclad cracks and cracking of structural welds. The 

paper emphasizes European experience and research. Topics covered in the review paper are 

B-10
(1) incidence of cracking, (2) mechanism of cracking, (3) detection of reheat cracking, (4) tests for reheat 

cracking, (5) control of reheat cracking, and (6) significance of reheat cracking to structural integrity. 

Figure 1 from Dhooge et al. (1978) shows the typical locations and orientations of underclad cracks. 

Cracks occur only at locations that are heated twice by welding or, as in Figure 1, the areas of the overlap 

zone of the cladding weld passes. In this zone, the material is heated to a critical temperature by the 

second pass. The following paragraph on the sizes of underclad cracks is quoted: 

The underclad cracks range in size from the short grain boundary separations only a few 

austenitic grains long and deep (0.2 mm) to a maximum of about 10 mm long and 4 mm 

deep. The usual depth is about 2.5 mm or less, the depth beneath the fusion boundary 

being governed by the depth of the grain coarsened HAZ and thus principally by the 

particular cladding procedure. 

The Dhooge-reported incidence of cracking is consistent with the conclusions of WRC Bulletin 197. 

Dolby and Saunders 

Dolby and Saunders note that subclad cracks often refer to conditions such as grain boundary separations 

or decohesions and in other cases to a series of micro voids. Therefore the term “crack” is subject to 

interpretation. A topical report issued by Babcock and Wilcox (Ayres et al., 1972) is cited for 

information on crack depth dimensions. Maximum reported depths of cracking are 4 mm, but depths are 

usually 2.5 mm or less, being governed by the extent of the heat-affected zone. 

Other Papers 

A number of other papers are listed as references to the report. These papers were reviewed, but were 

found to provide little information that is important to the focus of the present report or to repeat and 

reinforce information from the other papers that have been discussed above. 

Subclad Crack Sensitivity Study 

Input files for subclad flaw distributions were used by Oak Ridge National Laboratory and NRC staff to 

perform a sensitivity study (EricksonKirk, 2004). This sensitivity study was formulated as follows: 

1. One set of forging properties was selected based on the Sequoyah 1 and Watts Bar 1 RPVs (RVID2). 

2. One hypothetical model of a forged vessel was constructed based on an existing model of the Beaver 

Valley vessel. 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 were analyzed at three 

embrittlement levels, 32 EFPYs, 60 EFPYs, and Ext-B. Thus, a total of three FAVOR analyses were 

performed (1 material property definition x 1 vessel definition x 3 embrittlement levels). 

At 32 and 60 EFPYs, the through-wall crack frequency (TWCF) of the forging vessels was ~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 results indicate that a more detailed 

assessment of vessel failure probabilities associated with subclad cracks would be warranted should a 

subclad cracking prone forging ever in the future be subjected to very high embrittlement levels. 

B-11
The subclad flaws for the sensitivity study of Table 1 assigned half of the flaws to have depths of 4 

percent of the vessel wall thickness and the remaining flaws to have depths of 2 percent of the vessel wall 

thickness. Calculations for these flaw depths predicted substantial contributions from subclad flaws, 

whereas other calculations (not reported in NUREG-1808) for a bounding flaw depth of 2 percent of the 

vessel wall predicted small contribution of subclad flaws to vessel failure frequencies. 

It is noted here that the flaw input files used for the ORNL/NRC flaw sensitivity calculations had an error 

that understated the estimated number of subclad flaws by a factor of about 25. Details of this error and 

the correction of this problem are described below. The net effect would tend to underestimate the effects 

of subclad flaws on calculated failure frequencies for embrittled forged vessels. 

Table 1 Results of Subclad Crack Sensitivity Study 

EFPY Base FCI 

Forging 

Subclad 

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 9.60E8 0.17 6.15E-9 1.09E-9 0.18 

Ext-Bb 9.00E-6 1.31E-5 1.46 3.81E7 3.95E-6 10.37 

The baseline for all analyses was Beaver Valley as reported by [EricksonKirk, 2004b].

Proposed Flaw Distribution Model 

The updated flaw distribution model includes: 

1. a correction to the equation that converts flaw density from flaws per unit area to flaws per unit 

volume of vessel material 

2. changes to parameters of the flaw distribution using insights from the literature review along with a 

treatment of the uncertainties in estimating these parameters 

The proposed model has been implemented into the PNNL flaw distribution algorithm. The results of 

example calculations are described below. The discussion concludes with recommendations for further 

development of the model. 

Corrections for Flaw Density 

PNNL determined that flaw input files used for the ORNL/NRC flaw sensitivity had an error that 

understated the number of subclad flaws by a factor of about 25. An error was made in converting flaw 

rates from flaws per unit area of vessel surface to an equivalent number of flaws per unit volume of 

forging material. The effect of the underestimated flaw densities has not been evaluated by comparison 

calculations with the FAVOR code. However, even the incorrect density assigned a very large number of 

subclad flaws, such that each sub-region of the vessel inner surface was predicted to have several subclad 

flaws. Whereas predicted failure frequencies are in most cases roughly proportional to the number of 

flaws in the vessel, this trend should saturate at very high levels of flaw density. In this case, all regions 

of the vessel with lower bound toughness levels will have one or more subclad flaws of bounding size. 

The primary conclusion drawn from the results of Table 1 should not change for a corrected version of the 

flaw input file. That is, subclad flaws can substantially increase failure frequencies for embrittled forged 

vessels, and more detailed evaluations should be performed if such vessels become of concern to future 

vessel integrity evaluations. 

B-12
Flaw Distribution Parameters 

This section describes a proposed model for subclad cracks in the beltline regions of reactor pressure 

vessels. The model is based on the information described above and also addresses uncertainties in 

knowledge of the underclad cracks that could exist in a specific vessel. The model includes the following 

parameters: 

1. flaw frequency expressed in terms of flaws per unit area of the vessel inner surface 

2. the maximum (or bounding) through-wall depth dimension of the subclad flaws 

3. the conditional distribution of the through-wall depth dimensions expressed as a fraction of the 

bounding depth dimension 

4. the conditional distribution of the length dimensions of the subclad flaws 

It is assumed that vessel specific evaluations have been performed based on considerations of 

material/welding parameters (and possibly of inspection findings) to establish whether there is a potential 

for subclad cracking for the vessel of concern. For purposes of the preliminary model, this occurrence 

probability has been assigned to be one. As the flaw distribution model is further refined, expert 

judgment could be applied to better estimate a probability of subclad cracking for each given vessel. 

Maximum Through-Wall Dimensions of Cracks—This parameter defines the bounding depth dimension 

for the subclad cracks in a given simulated vessel. As described below, a conditional depth distribution is 

also defined for the individual cracks. The conditional depth distribution is truncated at the bounding 

crack depth. The model features a bounding flaw depth dimension for each simulated vessel. This 

bounding depth is assumed to be related to details of the cladding procedure (e.g., heat inputs for the 

welding process) along with the susceptibility of the vessel’s forging material to subclad cracking (e.g., 

the chemistry of the vessel specific heat of material). 

Figure 4 shows the assumed distribution function for the bounding flaw depth dimension. Vessel-tovessel variability for the bounding crack depth is addressed by using the French work (Pellissier Tanon 

et al., 1990; Buchalet et al., 1990; ASME, 1993; Moinereau et al., 2001) and the paper by Dolby and 

Saunders (1977) for guidance. On this basis, the probability for the maximum depth being greater than 

3 mm is assigned to be less than 10-1 (envelope defect of Figure 3), and the probability of the defect being 

greater than 6 mm is assigned to be two orders of magnitude less (less than 10-3 for the exceptional defect 

of Figure 3). The distribution of bounding flaw depths (Figure 4) is described by uniform distribution of 

the logarithm of the probability over the range of 0–6 mm. 

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Bounding Flaw Depth, mm

Probability Greater Than Depth

Figure 4 Probabilities for Bounding Depth of Subclad Flaws 

B-13
Conditional Flaw Depth Distribution—The conditional distribution of depth dimensions of subclad flaws 

for a given vessel is assumed to be relatively uniform and is described by a uniform distribution over the 

range of 50 percent to 100 percent of the bounding size as shown by Figure 5. This assumption is the 

same as for the prior input files provided to ORNL/NRC for the sensitivity calculations for subclad flaws. 

The uniform distribution is a reflection of the lack of information on measured flaw depth dimensions. 

The approach therefore conservatively assigns a large fraction of the flaws to have depth dimensions 

equal to about the bounding dimension. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Flaw Depth/Bounding Flaw Depth

Probability Greater Than Depth

Figure 5 Conditional Depth Distributions of Subclad Flaws 

Maximum Length Dimensions of Cracks—The envelope and exceptional defects of Figure 3 were first 

considered the basis for a conditional distribution for flaw length dimensions. With this approach, the 

probability of a defect with a 60-mm length would be assigned as 10-2 for both a 3-mm and 6-mm 

bounding depth of flaw. This approach (based on the 60-mm length) would be significantly more 

conservative than that for the prior flaw input files of the ORNL/NRC sensitivity calculations for subclad 

flaws. The French publications provide no data or rationale for the 60-mm flaw length, whereas other 

publications show subclad flaws (see Figure 1) that have lengths much less than 60 mm. Furthermore, 

discussions of the mechanisms of subclad cracking state that flaws are confined to the overlap region of 

the heat-affected zones of adjacent passes of the strips of cladding. This mechanistic model would also 

give flaw lengths much less than the 60-mm (2.4-inch) flaw of the French publications. 

The length distribution of Figure 6 as adopted for the updated model was the same as that assumed for the 

prior ORNL/NRC sensitivity calculations. A uniform distribution was used to simulate the numerical 

differences between the flaw length and depth dimensions. The uniform distribution ranged from 0 mm 

to 5 mm. For each category (or bin) of the flaw depth dimension, the generated input files for FAVOR 

have a distribution table for flaw aspect ratios. 

Number of Cracks per Unit Area of Vessel Inner Surface—The past PNNL estimate for the frequency of 

underclad cracks was 80,512 flaws per square meter. This density was derived from an analysis of the 

flaws shown in Figure 1, which was then assumed to depict a region of a vessel surface with a severe case 

of subclad cracking. This density was treated as a conservative or upper bounding estimate of the flaw 

occurrence frequency with the lower bound assigned to an order of magnitude less as a lower bound 

estimate. It was assumed that the distribution function was a uniform distribution for the logarithm of the 

flaw frequency between these bounding values. Figure 7 shows the resulting distribution of flaw 

frequency. 

B-14
0.0

0.2

0.4

0.6

0.8

1.0

1.2

012345

Flaw Length minus Flaw Depth, mm

Probability Greater Than Value

Figure 6 Conditional Distributions for Flaw Length 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20,000 40,000 60,000 80,000 100,000

Flaws per Square Meter

Probability Greater Than Density

Figure 7 Flaw Frequency Distribution 

 

Example Calculations 

The proposed flaw distribution model was implemented into a computer program, and an output file is 

provided as an appendix to this report. This output has results for the first 10 of the 1000 simulated 

vessels that are addressed by the full input file for the FAVOR code. Significant differences were seen in 

the predicted flaw distributions compared to the prior PNNL work. A large part of these differences came 

from correcting the original conversion from flaws per unit area to flaws per unit volume. 

Table 2 summarizes results from both the prior model (Tables 2a through 2d) and the updated model 

(Tables 2e and 2f). Results are presented both in terms of flaw density (flaws per cubic foot) and total 

number of flaws in a vessel considering only the beltline region (assuming a surface area of 627 square 

feet corresponding to a vessel in a typical FAVOR calculation). The flaws are further categorized in 

terms of their through-wall depth dimensions (0–2 mm, 2–4 mm, and 4–6 mm). Table 2 shows very large 

numbers for subclad flaws, ranging up to a few million flaws per vessel. This means that if even a small 

fraction of the vessel inner surface is exposed to the peak levels of embrittling neutron fluence, these local 

regions will still have thousands of subclad flaws. It is therefore expected that the effect of flaw density 

B-15
on vessel failure frequency will become insensitive to flaw density. Failure frequency will then become 

more sensitive to the simulated bounding sizes of the subclad flaws. 

Table 2(f) illustrates some significant aspects of the new proposed model relative to the prior model. For 

example, only vessel #8 of the first 10 simulated vessels has any flaws with depth dimensions greater than 

2 mm. The sensitivity calculations performed by ORNL with FAVOR predicted zero failure probability 

for a 2-mm flaw depth, even though many 2-mm flaws were present in the beltline regions. Therefore, 

only 1 of the 10 vessels of Table 5(f) would have a 2–4 mm flaw, and only these vessels would be 

expected to fail. In contrast, for the prior flaw distribution of Table 2(d), all vessels had many 4-mm 

flaws, and a large fraction of the simulated vessels were predicted to fail. 

B-16
Table 2 Summary of Results for Subclad Flaws—Prior Model Versus Proposed Model 

Total 0-2 mm 2-4 mm 4-6 mm

456 233 223 0

Total 0-2 mm 2-4 mm 4-6 mm

190,608 97,394 93,214 0

Total 0-2 mm 2-4 mm 4-6 mm

10,958 5,599 5,359 0

Total 0-2 mm 2-4 mm 4-6 mm

4,580,310 2,340,378 2,239,932 0

Total 0-2 mm 2-4 mm 4-6 mm

Average of 1000 Vessels 6,329 5,444 850 35

Vessel #1 5,580 5,580 0 0

Vessel #2 10,701 10,701 0 0

Vessel #3 4,272 4,272 0 0

Vessel #4 8,312 8,312 0 0

Vessel #5 2,554 2,554 0 0

Vessel #6 10,615 10,615 0 0

Vessel #7 6,351 6,351 0 0

Vessel #8 1,784 1,606 178 0

Vessel #9 1,190 1,190 0 0

Vessel #10 7,718 7,718 0 0

Total 0-2 mm 2-4 mm 4-6 mm

Average of 1000 Vessels 2,645,522 2,275,592 355,300 14,630

Vessel #1 2,332,440 2,332,440 0 0

Vessel #2 4,473,018 4,473,018 0 0

Vessel #3 1,785,696 1,785,696 0 0

Vessel #4 3,474,416 3,474,416 0 0

Vessel #5 1,067,572 1,067,572 0 0

Vessel #6 4,437,070 4,437,070 0 0

Vessel #7 2,654,718 2,654,718 0 0

Vessel #8 745,712 671,308 74,404 0

Vessel #9 497,420 497,420 0 0

Vessel #10 3,226,124 3,226,124 0 0

Flaw Depth Dimension

(c) Prior Model - Corrected Values

(Flaws per Cubic Foot)

(a) Prior Model - Uncorrected Values

(Flaws per Cubic Foot)

(b) Prior Model - Uncorrected Values

(Flaws per Vessel)

Flaw Depth Dimension

Flaw Depth Dimension

(d) Prior Model - Corrected Values

(Flaws per Vessel)

Flaw Depth Dimension

(f) Proposed Model

(Flaws per Vessel)

Flaw Depth Dimension

(e) Proposed Model

(Flaws per Cubic Foot)

Flaw Depth Dimension

B-17
References 

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EPRI TR-100251, prepared by ASME Section XI Task Group on Reactor Pressure Vessel Integrity 

Requirements, prepared for ASME Section XI Working Group on Operating Plant Criteria, published by 

Electric Power Research Institute. 

Ayres, P.S., et al. 1972. Babcock and Wilcox, Topical Report, BAW-10012-A, October 1972. 

Bamford, W., and R.D. Rishel. 2000. A Review of Cracking Associated with Weld Deposited Cladding 

in Operating PWR Plants, WCAP-15338, Westinghouse Electric Company, Pittsburgh, Pennsylvania, 

March 2000. 

Buchalet, C., W.L. Server, and T.J. Griesbach. 1990. “U.S. and French Approaches to Reactor Vessel 

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June 1990. 

Canonico, D.A. 1977. Significance of Reheat Cracks to the Integrity of Pressure Vessels for Light-Water 

Reactors, ORNL/NUREG-15, prepared by Oak Ridge National Laboratory for the NRC. 

Canonico, D.A. 1979. “Significance of Reheat Cracks to the Integrity of Pressure Vessels for LightWater Reactors,” Welding Research Supplement to the Welding Journal, May 1979. 

Chapman, O.J.V., and F.A. Simonen. 1998. RR-PRODIGAL—A Model for Estimating the Probabilities 

of Defects in Reactor Pressure Vessel Welds, NUREG/CR-5505, prepared by Pacific Northwest 

Laboratory the NRC, October 1998. 

Dhooge, A., R.E. Dolby, J. Sebille, R. Steinmetz, and A.G. Vinckier. 1978. “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. 

Dolby, R.E., and G.G. Saunders. 1977. “Underclad Cracking in Nuclear Vessel Steels—Part 1 

Occurrence and Mechanism of Cracking,” Metal Construction, Vol. 9, No. 12, pp. 562–566, December 

1977. 

Dolby, R.E., and G.G. Saunders. 1978. “Underclad Cracking in Nuclear Vessel Steels—Part 2 Detection 

and Control of Underclad Cracking,” Metal Construction, Vol. 9, No. 12, pp. 20–24, January 1978. 

Dumont, P., M. Bieth, and J.P. Launay. 1987. “French Developments in the Ultrasonic Examination of 

Pressure Vessels,” International Journal of Pressure Vessels and Piping, Vol. 28, pp. 19–23. 

EricksonKirk, M., et al. 2004. Technical Basis for Revision of the Pressurized Thermal Shock (PTS) 

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Fracture Mechanics Model Used in FAVOR, NUREG-1808 (available Febuary 2010). 

Frederick, G., and P. Hernalsteen. 1981. “Underclad Cracking in PWR Reactor Vessels,” AIM 

International Meeting: Modern Electric Power Stations, Liege, Paper 20. 

Gonnet, B. 1982. “How Framatome Has Dealt with the Cracking Problem,” Nuclear Engineering 

International, Vol. 27, No. 322, January 1982, pp. 21–24. 

Horiya, T., T. Takeda, and K. Yamata. 1985. “Study of Underclad Cracking in Nuclear Reactor Vessel 

Steels,” ASME Journal of Pressure Vessel Technology, Vol. 107, February 1985, pp. 30–35. 

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 Vessels, MEB-00-01, PRAB-00-01, NRC, September 2000. 

B-18
B-19

Lauerova, D., M. Brumovsky, P. Simpanen, and J Kohopaa. 2003. “Problems of Underclad Type 

Defects in Reactor Pressure Vessel Integrity Evaluation,” Transactions of the 17th International 

Conference on Structural Mechanics in Reactor Technology (SMIT 17), Paper #G02-2, Prague, Czech 

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Lopez, H.F. 1987. “Underclad Cracking of Pressure Vessel Steels for Light-Water Reactors,” Scripta 

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Electric, WCAP-7733, July 1971. 

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Evaluation: Recent Improvements in French RPV PTS Assessment,” International Journal of Pressure 

Vessels and Piping, Vol. 78, pp. 69–83. 

Pellissier Tanon, A., J. Grandemange, B. Houssin, and C. Buchalet. 1990. French Verification of PWR 

Vessel Integrity, EPRI NP-6713, prepared by Framatome, Paris, France, for Electric Power Research 

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Rockville, Maryland, prepared for the NRC by Pacific Northwest National Laboratory. 

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Rockville, Maryland, prepared for the NRC by Pacific Northwest National Laboratory. 

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1.43. 

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Reactor (PWR) Plants Westinghouse Owners Group, NRC, September 25, 2002. 

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Components, Welding Research Council Bulletin No. 197, Welding Research Council, New York, 

August 1974. 

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International, Vol. 25, No. 294, January 1982, pp. 27–29. 
Example Output from Proposed Subclad Model 

GENERATION OF FLAW DISTRIBUTION INPUT FILE FOR THE ORNL FAVOR CODE 

 NAME OF REGION = SUBCLAD FLAWS JANUARY 3, 2005 WELD FLAW/FT^3 PVRUF BEAVER VALLEY 

 NUMBER OF SUBREGIONS = 1 

 UNCERTAINTY CALCULATION 

 NUMBER OF MONTE CARLO SIMULATIONS = 1000 

 VESSEL TOTAL WALL THICKNESS (MM) = 203.99 

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

 WELD DENSITY OPTION - FLAWS PER UNIT VOLUME 

 BASE_METAL APPROXIMATION NOT USED 

 OUTPUT FILE REFORMATED FOR INPUT TO ORNL FAVOR CODE 

 SUBREGION NUMBER 1 

 VOLUME FRACTION = 1.0000 

 PVRUF VESSEL PARAMETERS 

 SAW (SUBMERGED METAL ARC WELD) 

 BEAD SIZE (MM) = 4.76 

 FACTOR ON FLAW FREQUENCIES = 1.0000 (DEFAULT = 1.0) 

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

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

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

 TRUNCATION ON FLAW DEPTH (MM) = 100.0000 

B-20
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 1 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .55808E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-21
FLAW DISTRIBUTION FOR SIMULATION NUMBER 2 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .10701E+05 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-22
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 3 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .42724E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-23
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 4 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

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B-24
FLAW DISTRIBUTION FOR SIMULATION NUMBER 5 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

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B-25
FLAW DISTRIBUTION FOR SIMULATION NUMBER 6 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .10615E+05 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-26
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 7 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .63516E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-27
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 8 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .16060E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .17877E+03 19.124 19.124 38.248 23.504 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

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 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-28
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 9 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .11909E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-29
 FLAW DISTRIBUTION FOR SIMULATION NUMBER 10 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .77182E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-30
 LARGEST OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .11167E+05 100.000 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .10106E+05 100.000 19.124 38.248 23.504 .000 .000 .000 .000 .000 .000 .000 

 3 .61631E+04 100.000 31.873 36.253 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-31
 MEDIAN OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .53317E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-32
 MEAN OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .54444E+04 8.247 6.247 12.494 24.989 24.989 23.034 .000 .000 .000 .000 .000 

 2 .84989E+03 76.707 5.508 11.015 6.769 .000 .000 .000 .000 .000 .000 .000 

 3 .35210E+02 98.637 .637 .725 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 99.999 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-33
 SMALLEST OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .00000E+00 6.375 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 2 .00000E+00 19.124 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 31.873 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-34
 25TH PERCENTILE OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .27131E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 19.124 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-35
 75TH PERCENTILE OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .80896E+04 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .37132E+03 100.000 19.124 38.248 23.504 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-36
 5TH PERCENTILE OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .92667E+03 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .00000E+00 19.124 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

B-37
B-38

 95TH PERCENTILE OF EACH ELEMENT FOR 1000 SIMULATIONS 

 N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-10.0 10.0-15.0 >15.0 

 1 .10661E+05 6.375 6.375 12.749 25.499 25.499 23.504 .000 .000 .000 .000 .000 

 2 .51625E+04 100.000 19.124 38.248 23.504 .000 .000 .000 .000 .000 .000 .000 

 3 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 4 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 5 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 6 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 7 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 8 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 9 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 10 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 11 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 12 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 13 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 14 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 15 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 16 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 17 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 18 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 19 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 20 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 21 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 22 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 23 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 24 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 25 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 26 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 27 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 28 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 29 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 30 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 31 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 32 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 33 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 34 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 35 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 36 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 

 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 
APPENDIX C 

SENSITIVITY STUDY ON AN ALTERNATIVE EMBRITTLEMENT 

TREND CURVE 
Sensitivity Study on an Alternative Embrittlement Trend Curve 

Subsequent to the development of FAVOR Version 06.1 as per the change specification in Appendix A, 

Eason developed an alternative embrittlement trend curve of a slightly simplified form (Eason 07). This 

alternative relationship is very similar in form to that which appears as Eq. 3-4 in the main text of this 

report, and is provided below for reference. 

Eq. C-1 30  CRPMDT

   e RCS AMD T tPMn 47.2  001718.01  13.61

     e e e 77.31 ,,, tNiCugPCufNiBCRP 191.1 





























for welds 10x417.1

platesfor 10x561.1

forgingsfor 10x140.1

7

7

7

A































for welds 0.155

manufactur CEin platesfor 2.135 vesselsed

manufactur CE-nonin platesfor 5.102 vesselsed

 forgingsfor 3.102

B





















 













 



 10

2595.0 10

10

1039.4for 1039.4

1039.4for 

  



 t

t

te

Note: Flux () is estimated by dividing fluence (t) by the time (in seconds) that 

the reactor has been in operation. 

    



 



   

629.0

log 120.18448.0139.1 tanh

2

1

2

1 ,, 10 t Cu Ni tNiCug e e

e e

 

   

  



















  

  





072.0for 0.008)-(359.1072.0 008.0

072.0for 072.0 008.0

072.0for 0

, 0.668

0.668

Cu P Cu Pand

Cu Cu Pand

Cu

PCuf

e

e e

    













  ,min wt%072.0for 

 wt%072.0for 0

CuMaxCu Cu

Cu

Cu e

e

CuMax e )(  0.243 for Linde 80 welds, and 0.301 for all other materials. 

Since FAVOR 06.1 had been coded and the through-wall cracking frequency (TWCF) values reported in 

Table 3.1 had been calculated before the development of Eq. C-1 there was a need to assess the effect, if 

any, of using Eq. C-1 instead of Eq. 3-4 in the FAVOR calculations. Eq. C-1 was therefore coded into 

C-1
C-2

FAVOR, and four different embrittlement conditions, as summarized in Table C.1, were analyzed. In 

Figure C.1, the TWCF and reference temperature (RT) values from Table C.1 are compared to the 

baseline results from FAVOR 06.1 (Figure 3.4). This comparison shows that changing from the Eq. 3-4 

to the Eq. C-1 trend curve does not produce any significant effect on the TWCF values estimated by 

FAVOR and, consequently, has no significant effect on the TWCF and RT screening limits proposed in 

the main body of this report. 

Table C.1. FAVOR TWCF Results Using Eq. F-1 for the Embrittlement Trend Curve

RT Values [oF] % TWCF due to ... 95th Percentile TWCF

Condition RTAWMAX

RTPLMAXRTCWMAX

Axial 

Weld 

Flaws 

Plate 

Flaws 

Circ 

Weld 

Flaws 

Total Axial 

Weld Plate Circ Weld 

BV200 251 339 339 21.77 66.79 11.44 2.82E-06 6.14E-07 1.88E-06 3.23E-07 

PAL 500 421 391 397 97.42 2.35 0.23 9.09E-05 8.86E-05 2.14E-06 2.09E-07 

OCO32 160 74 179 100.00 0.00 0.00 2.16E-15 2.16E-15 0 0 

OCO1000 294 205 322 99.12 0.28 0.60 3.69E-07 3.66E-07 1.03E-09 2.21E-09 
August 2006

FAVOR 06.1

1.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 650 750 850

Max. RT AW [R]

95th %ile TWCF - Axial Weld Flaws Beaver Oconee Palisades Fit

AlternateTrend Curve

August 2006

FAVOR 06.1

1.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 650 750 850

Max. RT PL [R]

95th %ile TWCF - Plate Flaws Beaver Oconee Palisades Fit

AlternateTrend Curve

August 200

FAVOR 06.

1.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03

550 65

M

95th %ile TWCF - Circ Weld Flaws

BeavOconPalisFitAlterTrend 

Figure C.1. FAVOR 06.1 baseline results from Figure 3.4 compared with TWCF values estimated using Eq. C-1 

C-3
C-4
APPENDIX D 

TECHNICAL BASIS FOR THE INPUT FILES TO THE FAVOR CODE 

FOR FLAWS IN VESSEL FORGINGS 
Technical Basis for the Input Files to the 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 (RPVs). 

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 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 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 planar cracks. Therefore, their categorization 

as simple planar or 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 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. 

D-1
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 show 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% of the vessel wall thickness. Also seen is the effect of 

truncating the flaw distribution at a depth of 11 mm (about 5% of the wall thickness). 

D-2
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 

D-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 

D-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 V

(cumulative flaw density is the ws per cubic meter of equal or 

greater size) 

alidated Flaw Density and Size Distribution for Three Forging Specimens 

number of fla

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 

D-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 

D-6
D-7
1. REPORT NUMBER 

(Assigned by NRC, Add Vol., Supp., Rev., 

and Addendum Numbers, if any.)

NUREG-1874

3. DATE REPORT PUBLISHED

MONTH YEAR 

2. TITLE AND SUBTITLE 

Recommended Screening Limits for Pressurized Thermal Shock (PTS) 

4. FIN OR GRANT NUMBER

6. TYPE OF REPORT 

 Technical 

5. AUTHOR(S) 

M.T. EricksonKirk1 and T.L. Dickson2

7. PERIOD COVERED (Inclusive Dates)

1-2005 to 2-2007

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 

NRC FORM 335

(9-2004) 

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION

BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

March 2010

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 provides two options for using the updated technical basis described herein to develop PTS screening limits. 

Calculations reported herein show that the risk of through-wall crackin is low in all operating pressurized-water reactors, and

current PTS regulations include consderble implicit margin. 

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