ML15222A848
| ML15222A848 | |
| Person / Time | |
|---|---|
| Site: | Indian Point  |
| Issue date: | 08/10/2015 |
| From: | Entergy Nuclear Operations |
| To: | Atomic Safety and Licensing Board Panel |
| SECY RAS | |
| References | |
| RAS 28134, ASLBP 07-858-03-LR-BD01, 50-247-LR, 50-286-LR | |
| Download: ML15222A848 (161) | |
Text
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. Erickso nKirk 1 T.L. Dickson 2 2Oak Ridge National La boratory Oak Ridge, TN 37831-6170 1Office of Nuclear Regulatory Research
ii Abstract During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron radiation, resulting in localized em brittlement of the vessel st eel and weld mat erials in the core area. If an embrittled RPV had a flaw of critical size and certai n severe system transients were to occur, the flaw could propagate very rapidly through the vessel, re sulting in a through-wall crack and challenging t he integrity of the RPV. The severe transi ents of c oncern, known as pressurized ther mal shock (PTS) events, are chara cterized by a rapid cooling of the internal RPV surface in combination with repressu rization of the RPV. Advancem ents in its unde rstanding and knowledge of materi als behav ior, its abilit y to model realistically plant sy stems and operational charact eristics, and its abilit y to better evaluate PTS transients to estimate loads on vessel walls led the U.S. Nuclear Regulatory Commission to realize that t he analysis conducted in the course of developing the PTS Rule in the 1980s c ontained significant conservatism
- s. This report pr ovides two options for using the update d technical basis described herein to develop PTS screening li mits. Calculations reporte d herein show that the risk of through-wall cracking is low in all operating pre ssurized-w ater reactors, an d current PTS re gulations include considerable i mplicit margin.
Paperwork Reduction Act Statement The inform ation collections contained in this NUREG are subject to the Paperwork Reduction Act of 1995 (44 U.S.C. 3501 et seq.)., which w ere approved by the Office of Managem ent and Bud get, approval number 3150-0011. Public Protection Notification The NRC may not co nduct or sponsor, and a person is not required to respond t o, a request for information or an inform ation collection requirement unless the requesting document displa ys a currently valid OMB control number. iii iv Foreword The reactor pressure vessel (RPV) in a nuclear power plant is expos ed to neutron radiation duri ng normal operation. O ver time, the vessel steel beco mes more brittle in the region adjacent to the core.
If a vessel had a preexisting flaw of critical size and certain sever e system transients wer e to occur, this flaw could propagate rapidly through the wall of the vessel. The severe tran sients of concern, known as pressurized thermal shock (PTS) event s, are charact erized by a rapid cooling (i.e., thermal shock) of t he internal RPV surface that may be combined with repressurization.
Advancements in the state of knowledge in the m ore than 20 years since the U.S. Nuclear Reg ulatory Commission (NRC) prom ulgated its PTS Rule, (i.e.,
Title 10, Section 50.61, "Fracture Toughness Require ments for Pr otection against Pressurized Thermal Shock Events
," of the Code of Federal Regulatio ns (10 CFR 50.61)) suggest that the embrittlemen t screening limits imposed by 10 CFR 50.61 are overly conservative.
Therefore the NRC conducted a study to develop t he technical basis for revising the PTS Rule i n a manner consistent with the NRC's guidelines on risk-informed regulation. In early 2005, th e Advisory Committee on Reactor Safeguards (ACRS) endorsed the staff's approach and its pro posed techni cal basis. The staff docu mented the technical basis in an extensiv e set of reports (Section 4.1 of this report provides a com plete list),
which were then subjected to further internal reviews. Ba sed on these reviews, the st aff decided to m odify certain aspects of the probabilistic calculat ions to refine and improve the model. This report documents these changes to the model and the results o f an updated s et of probabilistic calculations, which sh ow the follow ing: For Plate-We lded Pressurized-Water R eactors (PWRs
): Assuming that current o perating cond itions are maintained, the risk of PTS failure of the RPV is very low. Over 80 percent of operating PWRs have estim ated thro ugh-wall cracking frequency (TWCF) values below 1x1 0-8/ry, even after 60 years of operation.
After 40 years of operation the highest ri sk of PTS at any PWR is 2.0x10
-7/ry. After 60 years of operation this risk increase s to 4.3x10
-7/ry. If the referenc e temperature screening limits proposed herein, which are based on limiting the yearly through wall cracking frequency to below a value of 1x 10-6, are adopte d, and if curr ent operating practices are maintained then no plant will get within 30 F of the reference te mperature limits withi n 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-For ged PWRs: Assuming that current oper ating conditi ons are maintained, the risk of PTS failure of the RPV is very low. All oper ating PWRs h ave estimated TWCF values below 1x10
-8/ry, even after 60 y ears of operation. After 40 years of operation the highest risk of PTS at any P WR is 1.5x10-10/ry. After 60 years of operation this risk increase s to 3.0x10
-10/ry. If the reference temperature screening lim its proposed he rein, whic h 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 li mits within the fi rst 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 curren tly in operation in the United States. This report describes two options by which these findings can be incorporat ed into a revised version of 10 CFR 50.61.
Brian W. Sheron, Director Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission v
vi Contents Abstract.......................................................................................................................
.................................
iii Foreword.......................................................................................................................
................................
v Contents.......................................................................................................................
...............................
vii Executive Summary
..............................................................................................................
.......................
xi 1 Background a nd Objective
.......................................................................................................
...1 2 Changes to the PTS Model.......................................................................................................
...3 2.1 RTNDT Epistemic Uncertaint y Data Basis
...................................................................................
3 2.1.1 Review Finding
.................................................................................................................
......3 2.1.2 Model Change
...................................................................................................................
......3 2.2 FAVOR Sampling Procedures on RT NDT Epistemic Uncertainty
...............................................
4 2.2.1 Review Finding
.................................................................................................................
......4 2.2.2 Model Change
...................................................................................................................
......4 2.3 FAVOR Sampling Pr ocedures 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 Ther mal 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 Demonstratio n That the Fla ws That Contribute to TWCF are Det ectable by NDE Performed to ASME SC VIII Supplem ent 4 Requirem ents.........................................
8 2.10.1 Review Finding
.................................................................................................................
..8 2.10.2 Reply..........................................................................................................................
.........
8 3 PTS Screening Lim its...........................................................................................................
....13 3.1 Overview.......................................................................................................................
............
13 3.2 Use of Plant-Specific Resu lts to Develop Generic RT
-Based Scr eening Lim its......................
13 3.2.1 Justification of Approach
......................................................................................................
13 3.2.2 Use of Reference Tem peratures 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 Lim its 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 Se nsitivity Study
.........................................................................................
29 3.4.3 Modification for Thick-Walled Vessels
................................................................................
31 3.5 Options for R egulatory 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 Con servatisms
........................................................................................................
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 Betw een FAVOR Version 05.1 a nd FAVOR Version 06.1.---A-1 Appendix B
- Review of the Litera ture on Subclad Fla ws and a Technical Basis for Assigning Subclad Flaw Distributions---
.-B-1 Appendix C
- Sensitivit y Study on an Alt ernative Embrittlement Trend Curve-----
.C-1 Appendix D
- Technical Ba sis for the Input Files to the FAVOR Cod e for Flaws in Vess el Forgings..D-1 viii Figures Figure 1.1
. Structure of d ocumentation summarized by this report and by (EricksonKirk-Sum)
. The citations for these reports in the text appear in italicized boldfac e to distingui sh them from literature citatio ns..............................................................................................
1 Figure 2.1
. Data on which the RT NDT 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 descriptor s adopted in FAVOR...........................................
9 Figure 2.5.
Distribution of through-w all position of cracks that initiate
...............................................
9 Figure 2.6
. Flaw depths that contribute to crack initi ation probabil ity in Beaver Valley Unit 1 when subjected to (left) medium
- and large-diameter pipe break transients and (right) stuck-open valve tr ansients at two different em brittlement levels.........................
10 Figure 2.7.
Analysis of Palisades tr ansients #65 (repressurization transient) and #62 (large-diameter primary-side pipe break transient) to illustr ate what co mbinations of flaw size and location lead to non-zero conditional probabilities of crack initiation
.......10 Figure 2.8.
Probabilit y of detection curve (Becker 0 2).......................................................................
11 Figure 3.1
. TWCF distributions f or Beaver Valley Unit 1 estimated for 32 E FPY and for a much higher level of em brittlement (Ext-B). At 32 EFPY the height of the "zero" bar is 62 percent.
.............................................................................................................
..20 Figure 3.2.
The percentile of the TWCF distri bution corresponding to m ean TWCF values at various levels of em brittlement
.........................................................................................
20 Figure 3.3.
Dependence of TWCF due to various tra nsient classes on em brittlement as quantified b y the param eter RTMAX-AW (curves are hand-drawn to ill ustrate trends)
........23 Figure 3.4
. Relationship between TWCF and RT d ue to various flaw populati ons (left: axi al weld flaws, c enter: plate flaws, right: circ umferential weld flaws).
Eq. 3-5 provi des the mathematical form of the fit curves shown here.
........................................................
24 Figure 3.5.
Graphical rep resentation 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 outerm ost corner shown in the bottom diagram. (These diagra ms are provided for visualization purposes only
- they are not a co mpletely accurate re presentation of Eqs. 3-5 and 3-6 particularly in t he very steep regions at the edges of the TWCF = 1x10
-6 surface.)
..26 Figure 3.6.
Maximum RT-based scre ening criterion (1 E-6 curve) for plate-wel ded vessels based on Eq. 3-6 (le ft: screening criterion relative to currently operating PWRs after 4 0 years of operation; right:
screening crit erion relative to currently operating PWRs after 60 years of operation)
...............................................................................................
27 Figure 3.7.
Distribution o f 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 v essel wall thickn ess on th e TWCF of v arious transients in Beaver Valley (all analyses at 60 EFPY). This figure origin ally 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 vess el wall thickness on th e TWCF of forgings having underclad flaw s compared with results for plate-welded vessels (see Figure 3.7)
......................................
31 Figure 3.1
- 1. Estimated distributio n of TWCF for currently operatin g PWRs using the procedu re detailed in Section 3.5.1
....................................................................................................
37 Figure 3.1
- 2. Comparison of the distrib utions (red an d blue hist ograms) of the various RT values characteristic of beltline m aterials in the current operating fleet proj ected to 48 EFPY with the TWCF vs. RT relationships (curves) used to define the proposed
ix PTS screening lim its (see Figure 3.4 and Figure 3.9 f or the original presentation of these relati onships).......................................................................................................
41 Figure 3.1
- 3. Graphical co mparison of the RT limits for plate-welded plants de veloped 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 vessel s having wall thic knesses between 10.5 and 11.5 in............................
47 Figure 3.1
- 4. Graphical co mparison of the RT limits for ring-for ged plants devel oped 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 R esults Reported in (Dickson 07b)
........................................
22 Table 3.2.
Results of a Sensitivity Study Assessing the Effect of Underclad Flaws on the TWCF of Ring-For ged 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 Estim ated Using the Procedure Described in Section 3.5.1
...............................................................................
40 Table 3.5.
..................................................................................................
.......46 Table 3.6.
Non-Best-Est imate Aspects of the Mode ls Used to De velop the RT-Based Screening Limits for PTS
.................................................................................................
51 Table 3.7.
.................................................................................................
........53 x Executive Summary From 1999 through 2007, the U.S. Nuclear Regulatory Commission (NRC) conducted a study t o develop the technical basis for revising the Pressurized Ther mal Shock (PTS) Rule, as se t forth in Title 10, Section 50.61, "Fracture Toughness Requirem ents for Protec tion against Pr essurized Ther mal Shock Events,"
of the Code of Federal Regulatio ns (10 CFR 50.61) in a manner co nsistent with the NRC's guidelines on risk-informed regulation. In early 2005, the Advisory Committee on Reactor Saf eguards (AC RS) endorsed the staff's approach and its pro posed techni cal basis. The staff docu mented the technical basis in an extensiv e set of reports (Section 4.1 of this report provides a com plete list),
which were then subjected to further internal reviews. Ba sed on these reviews, the st aff decided to m odify certain aspects of the probabilistic calculat ions to refine and improve the m odel. This report documents these changes and the results of probabili stic calculatio ns that provi de the technica l basis for the staff' s developm ent of a voluntar y 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 ves sel (RPV). T his is follo wed by a summary of the current regulatory approach to PTS, whic h leads directly to a discus sion of the motivations for conducting t his project. F ollowing t his introductory information, the exec utive summary describes the approach used to c onduct the study, a nd summarizes key findings and recommendations, which include a proposal for a revision to the PTS screening limits.
To provide a complete perspective on th e current und erstanding of the risk of RP V failure arising from PTS, this executive summary draws not only on information presented in t his report but also f rom the other technical basis reports listed in Section 4.1 of this report.
Description of PTS During the operation o f a nuclear power plant, th e RPV walls are exposed to neutron radiation
, resulting in localized embrittlement of the vessel steel and weld ma terials in the area ad jacent to the reactor core. If an embrittled RPV had an existing flaw of critical size and certain seve re system transients were t o occur, the flaw could propagate very rapidly through the vessel, resulting in a through-wall crack and challenging the integrity of the RPV. Th e severe transients of concern, known as PTS events, are characterized b y a rapid cooling (i.e.,
thermal shock) of the intern al RPV surface and downcomer, which may be follo wed by repressuriz ation of the RPV. Thus, a PTS event pos es a potentially significant challenge to the structural integrity of the RPV in a pressurized-water reactor (P WR). A number of abnormal events and pos tulated accident s have the pot ential to ther mally 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-clos es (causing re-pressurizat ion of the primary
), or a break of the ma in 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 provi de makeup water in the primar y system to prevent overheating of the f uel in the core. However, the makeu p water is much colder than that held in the primary system. As a r esult, the temperature d rop produced by rapid depressurization, coupled with the near-ambient temperature of the makeup water, produces sig nificant thermal stresses in the hotter thick section steel wall of the RPV. For embrittled R PVs, these str esses could be sufficient to initiate a running crack, wh ich could propagate all the way through the vessel wall. Such through-wall cr acking of the RPV could result in core dam age or, in rare cas es, a large early release of radioactive material to the envi ronment. Fortunately, the coincident occurrence of critical-size f laws, embrittled vessel steel and weld material, and a severe PTS tr ansient is a very low-probabilit y event. In fact, onl y a few opera ting PWRs are projected to even come cl ose to the xi current statutor y limit (10 CFR 50.61) on the level of embrittlement during the fi rst 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 m onitor the em brittlement of their RPVs using a reactor vessel material surveillance pr ogram qualified under Appendix H, "Reactor Vessel Material Surveillance Program Requirements," to 10 CFR Part 50, "Do mestic Licensing of Production and Utilization Facilities."
The surveillance results are then used together with the form ulae and tables in 10 CFR 50.61 to estim ate the fracture toughness transition tem perature (RT NDT) of the steels in the vessel's beltline and how those transition tem peratures 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 esti mates of the effe ct of irradiation dam age to estimate the value of RTNDT that will occur at end of license (EOL), a value called RT PTS. The screening lim its provided in 10 CFR 50.
61 restrict the maxim um values of RT NDT permitted during the plant's operational life to
+270 F (132 C) for axial welds, plates, and forgi ngs, and +300 F (149 C) for circumferential welds.
These scr eening limits were selected based upon a limit of 5x10
-6 events per year on the annual probabilit y of developing a throu gh-wall crack (RG 1.154).
Should RT PTS exceed these scre ening limits, 10 CFR 50.61 requires the licensee to either take acti ons to keep RT PTS below the scre ening limits. These actions include i mplementing "reasonably practicable" flux reductions to reduce the em brittlement rate or by deembrittling the vessel by annealing (R G 1.162), or perform ing plant-specific analy ses 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 curr ently operating PWR has an RT PTS value that is projected to exceed the 10 CFR 50.61 screening li mits before EOL, several plants are close to the limit (3 ar e within 2 F, while 10 are within 20 F). Those plants are likely to exceed the screen ing limits during the 20-y ear license rene wal period that many operators are currently seeking or have alr eady received.
Moreover, some plants maintain their RTPTS values below the 10 CFR 50.61 sc reening lim its by implementing flux reductions (low-leakage cores, ultra-low-leakage co res), which ar e fuel management strategies that can be econo mically deleterious in a deregulated m arketplace. Thus, the 10 CFR 50.61 screening limits can re strict both the licensable an d economic lifetim e of PWRs.
Motivation for This Project It is now wid ely recognize d that the state of knowledge and data li mitations in the early 1980s necessitated conservative treat ment of several key parameters and models used in the probabilistic calculations that provided the technical basis for the current PTS Rule. The m ost prominent of these conservatis ms includes the following fa ctors: highly simplified treat ment of plant trans ients (very coarse grouping of m any operational sequences (on the or der of 10
- 5) into very few groups (approxim ately 10), necessitat ed by limitations in the computational resources needed to perfor m multiple ther mal-hydraulic (TH) cal culations) lack of any significant credit for operator action characterization of fracture toughness using RT NDT, which has an in tentional cons ervative bias use of a flaw distribution that places all flaws on th e interior surface of the RPV, and, in
- general, contains larger flaws than those usually detected in se rvice xii a modeling approach that t reated the RP V as if it were made entirely from the most brittle of i ts constituent materials (weld s, plates, or forgings) a modeling approach that assessed RP V 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 lim its are unnecessarily conservative. Consequently, the NRC sta ff believes t hat reexamining the technical basis for these screening lim its, based on a modern unders tanding of all the factors that influence PTS, would most likely provide strong justific ation for s ubstantially relaxing these lim its. For these reasons, the NRC undertook this st udy with the objective of d eveloping t he technical basis to support a risk-informed revision of the PTS Rule and the associat ed PTS screening lim its. Approach As illustrated in the foll owing figure, thr ee main models (shown as solid bl ue squares), taken together, permit estimation of t he annual frequency of through-wall cracking in an RPV: probabilistic risk assessment (P RA) event sequence analy sis TH analysis probabilistic f racture mechanics (PFM) analy sis PRA EventSequenceAnalysis(SAPPHIRE)ThermalHydraulicAnalysis(RELAP)ProbabilisticFractureAnalysis(FAVOR)SequenceDefinitionsSequenceFrequenciesfreqConditionalProbability ofThru-WallCracking, CPTWCP(t), T(t), &HTC(t)YearlyFrequency ofThru-WallCracking[CPTWC]x[freq]Probabilis tic Estimation of Through-Wall Cracking FrequencyVessel damage, age, or operational metricYearly Frequency ofThru-Wall CrackingScreening LimitAcceptance Criterion for TWC FrequencyEstablished consistent with*1986 Commission safety goal policy statement*June 1990 SRM*RG1.174Screening Limit Development Schematic sho wing how a probabilisti c estimate of TWCF is combined with a TWCF acceptance criterion to a rrive at a proposed rev ision of the PTS screeni ng 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 est imates the temporal variation o f temperature, pressure, and heat-transfer coefficient in the RPV downcomer, whic h is character istic of each sequence definition.
These tem perature, pressur e, and heat-transfer coefficient histories are then passed to a PFM m odel that uses the TH output, al ong with other information concerning RPV design and construc tion materials, to es timate the time-dependent "driving force to fracture" produced by a particular event sequence. The PFM model then co mpares this est imate of fractu re-driving forc e to the fracture toughness, or fracture re sistance, of the RPV ste el. Perfor ming this co mparison for m any simulated vessels and xiii flaws per mits estimation of the probabilities that a cra ck 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 anal ysis involves a sim ple matrix multiplicatio n of the probability distribution of through-wall cracking (from the PFM analy sis) with the distribution of frequencies at which a particular event sequence could occur (as defined b y the PRA an alysis). This product establishes an estim ate of the distributi on of the annual frequency of thro ugh-wall cracking that could occ ur 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 summe d for all event sequences to estimate the total annual frequency distribution of t hrough-wall cracking for the vessel. Perf ormance of such analy ses for various operating lifetimes provides an estimate of how the distribution of annual fre quency of through
-wall cracking would vary over the lifetime of the plant. Performance of the probabilistic calculat ions just d escribed establishes the tec hnical basis for a revised PTS Rule w ithin an integrated s ystems analysis framework. The staff's approach considers a broad range of factors that influence the likelihood of vessel failure during a PTS e vent, while accounting for uncertainties in these factors across a breadth of tec hnical disciplines. Two central features o f this approach are a focus on the use of realistic input valu es and models (wherever pos sible), and an explicit treatment of uncertainties (using currently available uncertainty analysis tools a nd techniques). Thus, the current approach i mproves upon that employ ed in SECY-82-465, "
Pressurized T hermal Shock," dated November 23, 198 2, which included in tentional and unquantified c onservatism s in many aspects of the analysis, and treated uncert ainties implicitly by incorporating them into the m odels. Key Findings The findin gs from this study are divided into five t opical areas-(1
) the expected m agnitude of the TWCF for currentl y anticipated operational lifetimes, (2) th e material factors that dom inate PTS risk, (3) the transient classes that do minate PTS risk, (4) the appl icability of these findings (based on detailed analy ses of three PWRs) to PWRs in general, and (5) the an nual limit on TWCF established consistent with current guidelines on risk-inform ed regulation.
In this summary
, the conclusions are presented in boldface italic
, while the supporting information is shown in regular type. TWCF Magnitude for Currentl y Anticipated Operational Lifetimes The degree of PTS challenge is low for curr ently anticipated lif etimes and operating conditions. o For Plate-We lded PWRs
- Assuming that current oper ating cond itions are maintained, the risk of PTS failure of the RPV is very low. Over 80 percent of operating PWRs have esti mated TWCF values below 1x10
-8/ry, even after 60 years of operatio
-7/ry. After 60 years of operation this risk increase s to 4.3x10
-7/ry. If the R T screening limits proposed herein
, which are based on limiting the y early through wall cracking frequency to below a value of 1x 10-6, are adopted, and if current operating practices are maintained then no pla nt will get within 30 F of the RT lim its within the fir st 40 years of operation. Af ter 60 years of operation, t he most embrittled plant wi ll still be 17 F away from the RT limits. o For Ring-For ged PWRs: Assuming that current oper ating cond itions are maintained, the risk of PTS failure of the RPV is very low. All operating PWRs have est imated TWCF values below 1x10-8/ry, even after 60 years of operatio
- n. After 40 years of operation the h ighest risk of PTS at any PWR is 1.5x10-10/ry. After 60 years of operation this risk increase s to 3.0x10
-10/ry. If the RT screening li mits proposed herein, which are b ased on lim iting the yearly through wall crackin g xiv frequency to below a value of 1x 10-6, are adopted, and if current operating practices ar e maintained then no plant will get within 59 F of the RT limits within the first 40 years of operation. Af ter 60 years of operation, t he most embrittled plant wi ll still be 47 F away from the RT limits. Material Fa ctors and Their Contri butions to PTS Risk Axial flaws, and the toughness proper ties 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 prop agate through the RPV wall because the applied fr acture-driving for ce increases continuously with increasing crack depth for an a xial flaw. Conversely
, circumferentially oriented flaws experience a driving-force peak mid-wall, provi ding 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 li kely (relative to axially oriented flaws). The toughness properties that can be ass ociated with axial flaws co ntrol nearly all of the TWCF. These include the t oughness 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 P WRs because these can be associat ed only with circumferentially oriented flaws.
o Ring-Forged Vess els As with plate
-welded PWRs, axial flaw s are again much more likely than circumferential flaws to propagate through the RPV wal
- l. However, because there are no axial welds in ring-forged vessels, the axial flaws that can be associat ed with th ese welds are absent
. However, for particular co mbinations of forgi ng chemistry and cladding heat input, underclad cracks can form in the forging.
As implied by the na me, these cracks form in the forging just below the cladding l ayer, and they form perpendicular to the direction in which the clad weld lay er was deposite d (i.e., axially). Therefore, the t oughness properties that can be asso ciated with these axial fla ws (i.e., that of the forg ing) control nearly a ll of the TWCF in ring-forged vessels.
Transients and Their Contributions to PTS Ri sk Transients in volving primary-side faults are th e dominant contributors to TWCF, while transients involving sec ondary-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 cont rols the resistan ce of the vess el to fracture pressure retai ned in the primary system, which controls the pressure stress in the RPV wall o The significance of a transient (i.e., how much it cont ributes to PTS risk) depends on these three factors and the likelihood t hat the transient will occur.
o The analy sis considered transi ents in the following classe s: primary-side pipe breaks stuck-open va lves on the pr imary side main stea mline breaks xv stuck-open va lves on the secondar y side feed-and-bleed steam generator tube ru pture mixed primary and secondary initiators o Of these, transients in the first two categories were responsible fo r 90 percent or more of the PTS risk, while transients in th e third category were responsible for nearly all of th e remainder. For medium- to large-diameter pri mary-side pipe breaks, the fast-to-moderate co oling rates and low downcomer temperatures (generated by rapid depressurization and emergency injection of low-tem perature makeup water direct ly to the primary system) combine to produce a high-severity transient. Despite the moderate-to-low lik elihood that these transients will occur, their severity (if they do occur) makes the m significant contributors to the total TWCF. For stuck-ope n primary-side valves that later reclos e, the repressuriz ation associat ed with valve reclosure coupled with low tem peratures in the primary system combine to produce a high-severit y transient. Thi s, coupled wit h a high likelihood of transi ent occurrence, makes stuck-open pr imary-side valves that may later reclose significant con tributors to the total TWCF. The small or negligible co ntribution of all secondary-side transien ts (main steamline break, stuck-open secondary valves) results d irectly from the lack of low temperatures in the primary system. For these transient s, the minimum temperature of the prim ary system for times of relevance is controlled by the boiling poi nt of water in the secondary sy stem (212 F (100 C) or above). At these tem peratures, the fracture toughness of the em brittled RPV steel is still sufficiently high to resist ve ssel failure in most cases. Applicability of These Findings to PWRs in General Credits for operator action, while included in th e analysis, do not influence these findings in any significant way.
Operator action credits can influence dra matically the risk-significance of individual transients. Therefore, a "be st estimate" analysis needs to include appropriate credits fo r operator action because it is not possible to establish a priori if a particular transient will make a large contr ibution 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 tota l TWCF, for reasons detailed below.
o Medium- and Large-Dia meter Primary-Side Pipe Brea ks: No operator actions are modeled for any break diameter because, for these events, the safety injection systems do not fully refill the upper regi ons of the reactor coolant sy stem. Consequentl y, operators would never take act ion to shut off the pumps. o Stuck-Open Pri mary-Side Valves That May Later Reclose
- The PRA model includes reason able and appropria te credit for operator actions, such as throttling of the high-pressure injection (HPI) system. However, these cr edits have a s mall influence on the estimated values of vessel failure probabilit y attributable to t ransients caused by a stuck-open valve in the prim ary pressure circuit (SO-1 transients) because the credited operator actions only prevent repressurization when SO-1 transients initiate fro m hot zero power (HZP) cond itions and the operators act prom ptly (within 1 minute) to thr ottle the HPI. Com plete 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 pre dicted to occur betwee n 10 and 15 minutes after tra nsient initiation because the thermal st resses associated with the rapi d cooldown reach their maxi mum within this xvi timeframe. Thus, all of the long-term effects (isolation of feedwater flow, timing of the high-pressure safety injection control) that can be influenced b y 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 cont ainment) can influence the conditional probability of through-wall cracking (CPTWC), and operator actions do not influe nce 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 genera l, the TWCF re sults presented herein can be used with confidence to develop revised PT S screening crit eria that apply to the entire fleet of operating PWRs. o Medium- and Large-Dia meter Primary-Side Pipe Brea ks: For these break diamet ers, the fluid in the pri mary system cools faster than the wall o f 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. Perturba tions in the fluid co oldown rate controlled b y break diameter, break location, and season of the year do not pla y a significa nt 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. Consequentl y, the TWCF contributi on 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 Pri mary-Side Valves That May Later Reclos e: A major contributor t o the risk-significance of SO-1 transients is the return to full s ystem pressure once the valve reclose
- s. The operating and safety relief valve pressures of all PWRs ar e similar. Additionally
, as previously noted, operator action credits affe ct only slightly the to tal TWCF associat ed with this transient class.
o Main Steamline Breaks: Since main steamlin e breaks fail early (within 10-15 minutes after transient initiation), only factors affectin g the initial cooling rate can have any influence on the CPTWC values. Operator actions do not influence these fa ctors, which include the plant pow er level at event initiation and the location of the br eak (inside or outsi de of containment), in any way. Sensitivity st udies performed on the TH and PFM m odels to investigate the effect of credi ble model variations on the predicted TWCF values rev ealed that only vessel wall thickness was a factor so significant as to require modification of the base line results for th e three detail ed study plants.
This finding resulted in the revi sed PTS screening lim its being expressed as a function of RPV wall thickness. An investigation of design and operational characteristics for five additional PWRs re vealed no difference s in sequence progression, sequence fr equency, or plant TH response significant enough to call into question the applicability of the TWCF result s from the th ree detailed plant analyses to PWRs in gene ral. An investigation of potenti al external initiatin g events (e.g., fires, earthquakes, floods) revealed that the contribution of those event s to the total TWCF can be re garded as ne gligible.
xvii Annual Limit on TWCF The current guidance pro vided by Regulatory Guid e 1.174 f or large early rel ease is conservatively applied to setting an acceptable annual TWCF limit of 1x10-6 events/year.
o While many post-PTS accident prog ressions led only to core damage (which suggests a TWCF lim it of 1x10-5 events/y ear in ac cordance wit h Regulatory Guide 1.17 4, Revision 1, "
An Approach for Using Probabilistic Risk Assessment in Risk-Info rmed Decisions on Plant-Specific Changes to the Licensing Basis," issued Novem ber 2002), un certainties in the accident progression analysis led to the recommendation to adopt the more conserv ative limit of 1x10
-6 events/year based on the large earl y release fr equency. Recommended Revision of the PTS Screening Li mits The NRC staff reco mmends using differ ent RT-metrics to characte rize the resist ance of an RPV to fractures in itiating from different fl aws at different l ocations in the vessel. Specifical ly, the staff recommends an RT for flaws occurring along axial weld fusion li nes (RTMAX-AW), another for the embedded flaws occurring in plates (RT MAX-PL), a third for flaws occurring along circu mferential weld fusion lines (RT MAX-CW), and a fourt h for embedded and/or underclad cracks in forgings (RT MAX-FO). These values can be esti mated based mostly on the in formation in the NRC' s Reactor Ves sel Integrity Database (RVID). The st aff also reco mmends usin g these different RT values together to c haracteriz e the fracture resi stance of the vessel' s beltline region, r ecognizing that the probability of a vessel fracture initiating from different flaw populations varies considerably in response to factors that a re both understood a nd predictabl
- e. Correlations between these RT values and the TWCF attributable to different flaw populations show little p lant-to-plant variabilit y because of the general si milarity of PTS challenges am ong plants.
This report proposes a formula to estim ate the tota l TWCF for a vessel base d only on these RT values and on the vessel wall th ickness, a nd uses this formula to estim ate the TWCF values for all operating PWRs.
Currently none of these estimates exceeds the 1x10-6/ry limit during either current or extended (thr ough 60 years) operations. One option that may be considered when im plementing these results i n a revised version of 10 CFR 50.61 is to sim ply require license es to ensure that these TWCF esti mates remain below the 1x10
-6/ry limit. An alternative i mplementation option is to use the equation presented herein that relates T WCF to the various RT-metrics to transform the 1x10
-6/ry limit into limits on the various R T 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 li mits along with an assessment of all operating plat e-welded PW Rs relative to the proposed lim its at the end of license exte nsion (the projected plant RT-values for EOLE reported in this figure are premised on the assu mption that current Plate Welded Plants at 48 EFPY (EOLE)050100150200250300350400050100150200250300RTMAX-AW [oF]RTMAX-PL [oF]1x10-6/ry TWCF limitSimplified ImplementationRTMAX-AW269F, andRTMAX-PL356F, andRTMAX-AW+ RTMAX-PL538F.Comparison of RT-based screening limits (curves or dashed lines
) with assessment points fo r operating pla te-welded PWRs at EOLE. Limit s are shown for vessels having wall thicknes ses of 9.5 inches or less. This report prov ides similarly defined limits for thicker v essels and for ring
-forged vessels. xviii operating pra ctices are maintained). In this figure, the region of the graphs between the red locus and the origin has TWCF values below the 1x 106/ry acceptance criterion
, so the staff would consider these combinations of RTs to be acceptable and require no furt her analy sis. By contrast, the region of the graph outside of either the red locus has TWCF values abov e the 1x10
-6/yr acceptanc e criterion, indicating the need for addit ional anal ysis or other m easures to ju stify contin ued plant operation
. Clearly
, operating PWRs will not exceed the 1x10 6/ry limit, even after 60 years of op eration. This separation of operating plants from the screening li mits contrast s markedly with the current regulatory situation in which several plants are wit hin 1 F (0.5 C) of the scr eening lim its set forth in 10 CFR 50.61 after only 40 years of operation.
Aside fro m relying on RT-metrics that differ fro m 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 approxim ately) factors that occur in application, but that were not c onsidered in the a nalysis upon which the screening limits are base
- d. For example, the current 10 CFR 50.61 m argin term accounts for uncerta inty in copper, nickel, and initial R TNDT values. However, the model adopted in this study explicitly considers uncertainty in all of these variables and models these uncertainties as being larger (a conservat ive represen tation) than would be a ppropriate in any plant-specific application. Cons equently, use of the 10 CFR 50.61 m argin term with the new screening lim its proposed her ein is inappro priate. In gen eral, the follo wing three r easons suggest that use of any margin term with the proposed screen ing limits is inapprop riate: (1) The TWCF values used to establish the scr eening li mits are 95th percentile values.
(2) The results from the staff's three plant-speci fic analy ses apply to PWRs in general.
(3) While certain aspects of the modeling cannot reasonabl y be represented as "best estimates," there is, on balance, a conservative bias to these non-best-es timate aspects of the anal ysis because r esidual conservatisms in the m odel far outweigh residual no nconservatisms.
Assessing the Continued Appropriat eness of the Recommended PTS Screening Limits As described in this and in companion reports, th e screening lim its the staff has reco mmended for PTS are premised on the view that the mathemati cal model of PTS we have described is an appropriate representatio n of PTS eve nts, both in te rms of the lik elihood of their occurance as well and in ter ms of their effect on the RPV were they to occur. Becau se the appropria tness of the staff' s model of PTS may change in the future due to changes in operating pr actice, changes i n initiating event frequencies, changes in radiation d amage mechanism s, and potential changes in other factors, the staff should periodically evaluate the PTS m odel described here for appropriat eness. Shoul d these evaluations reveal a significant departure between this model and phy sical 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) st aff completed a series of reports detailing the technical basis for a risk-informed revision of the pressurized ther mal shock (PTS)
Rule (Title 10, Section 50.
61, "Fracture To ughness Requirem ents for Protection against Pressuri zed Thermal Shock Events," of the Code of Federal Regulat ions (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 Saf eguards (ACRS) (ACRS 05) critiqued and appr oved the reports (see Appendix B t o NUREG-1806 (EricksonKir k-Sum) for details). Following ACRS revie w, these reports were then subjected to further inte rnal reviews.
Based on these reviews, the s taff decided to m odify certain aspects of the probabilistic calculations to refine and improve the m odel. The purpose of t his report is threefold-(1) to document the changes made to the PTS m odels based on the post-ACRS reviews, (2) to report the results of the new computations, and (
- 3) to make recommendations on the us e of these res ults to revise screeni ng limits for PTS. Chapter 2 of this report det ails changes t o the model since publication of NUREG-1806 (
EricksonKirk-Sum) while Chapter 3 describes the res ults of the calculations and recommendations on revised screening lim its for PTS. This r eport does not pr ovide a comprehensive summary of NRC activities undertaken over the last 7 years to develop t he technical basis for a risk-inform ed revision to 10 CFR 50.61 (see (EricksonKirk-Sum) for these details).
Summary Report -NUREG-1806*Procedures, Uncertai nty, & 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 w ith 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,"NUREG-1808. *TH Model: Bessette, D., "Thermal Hydraulic Analysis of Pressurized Thermal Shock,"NUREG/1809.*RELAP Procedures & Experimental Validation: Fletcher, C.D., et al., "RELAP5/MOD3.2.2 Gamma Assessment for Pressurized Thermal Shock Applications,"NUREG/CR-6857.*Experimental Benchmarks: Reyes, J.N., et. al., "Final Report for the OSU APEX-CE Integral Test Facility,"NUREG/CR-6856.*Experimental Benchmarks: Reyes, J.N., "Scaling Analysis for the OSU APEX-CE Integral Test Facility,"NUREG/CR-6731.*Uncertainty: Chang, Y.H., et 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/CR-6859.*Uncertainty Analysis Methodology: Siu, N., "Uncertainty Analysis and Pres surized 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 Cont ribution to Pressurized Thermal Shock Risk"*Generalization: Whitehead, D.W., et al., "Generalization of Plant-Specific PTS Risk Results to Additional Plants"ResultsModels, Validation, & ProceduresPFMPRATH Figure 1.1.
Structure of documentation summariz ed by this report and by (EricksonKirk-Sum). The citations for these reports i n the text appear in italicized boldface to disting uish them fro m literature citations
. 1 2
Chapter 2 - Changes to the PTS Model
2.1.1 Review
Finding Following A CRS review a nd acceptanc e of the staff's methodology for developing probabilistic estimates of the risk of thr ough-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 subject ed to further intern al reviews an d quality control checks. On the basis of these revie ws, the NRC staff decided that certain as pects of the probabilistic calculations should be refined or improved. These aspe cts, which are list ed below, are described in both the remainder of this chapter and in Appendix A to this re port. From the descriptions of t he parameters RTLB (lower bound reference tem perature) an d To (fracture toughness referen ce temperature) provided in the docum entation, it seems that these two param eters should have a m ore systematic rel ationship and, in particular, that RTLB should always be greater than or equal to To. Nevertheless, Figure 2.1, which dis plays the data on which the RT NDT epistemic uncertainty correction is based, shows that RT LB can be considerably less than T
- o. Is there a proble m with our u nderstanding of how RTLB and To relate to one another, or is there some inconsistency in the data sh own in Fig ure 2.1? Section 2.1
- Data basi s for the reference temperature n il ductilit y (RTNDT) epistemic uncertainty correction
-250-200-150-100-50050-200-150-100-50050To [oF]RTLB [oF] Data RTLB = To Section 2.2
- RTNDT epistemic uncertain ty correction: sam pling procedures Section 2.3
- Fracture Analysis of Vessels: Oak Ridge (FAVOR
) computer code sampling procedures on ot her variables Section 2.4
- The distributi on of flaws in repair welds Section 2.5
- The distributi on of subclad flaws in forgings Section 2.6
- The relationship used to pr edict embrittlement based on exposure and on composition variables Figure 2.1. Data on which the RTNDT epistemic uncertainty c orrection is bas ed Section 2.7
- The upper-sh elf fracture toughness m odel 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 c orrectly identifies that the data in Figure 2.1 for which RT LB falls below T o are erroneous. The change specification for the Fracture Anal ysis of Vessels-Oak Ridge (FAVOR) Code detailed in Appendix A provides a de tailed explanation of t he origins of these erroneous data and develops a revised epistemic uncertainty correction for RT NDT that does not rely on these data.
Additionall y, while not resulting i n 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 RT NDT fracture toughness indexing parameter and a Master Curve Approach fracture t oughness indexing parameter (To) to estimate material toughness properties. The sam pling of the RT NDT-To correction para meter 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 sam ple the correction out side of the flaw loop so t hat the correction is sa mpled once for each material for each vess el simulation. 2.2.2 Model Change The review finding correctly identifies that it is more appropriate to sam ple the uncertainty in the RTNDT-To correction param eter outside of the flaw loop (but still inside t he vessel loop). The previous sampling procedure simulated a degree of uncertainty in the unirradiated fracture toughness transition tem perature that is unrealistic, a deficiency reconciled by the new sampling procedure. The FAVOR change specification details both t he rationale supportin g this change and how it is implemented in FAVOR V ersion 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 uncertain ty correction is sampled, the location of ot her sampled parameters (e.g., cop per, copper variabil ity, nickel) may not be m ost appropriately placed within the flaw loop.
2.3.2 Model Change The NRC performed a co mprehensive review of the FAVOR uncertainty sam pling strate gy. On the basis of this review, the staff decided that, in addition t o the RTNDT epistemic uncertainty discussed in Section 2.2, the uncertainty on the following variables is more appropriatel y sampled outside of the flaw loop, requiring a modification of FAVOR 04.1:
the unirradiat ed value of RT NDT standard deviation on co pper standard deviation on nickel The FAVOR change specif ication details both the rationale supporting these changes and how they are i mplemented in FAVOR Version 06.1. 2.4 Distribution of Re pair Flaws 2.4.1 Review Finding To develop t he sample flaw distributio ns as input to the FAVOR code, Pacific North west National Laboratory (PNNL) assu med that 2 percent of t he volume of weld seams consisted of repair wel ds. The repair welds wer e assumed to be unif ormly distributed through the submerged metal arc w eld (SMAW) thickness.
Since repairs typically intersect the surfa ce, it is possible that flaws associated with repairs would be preferentia lly located adjacent to the outside diameter (OD) or inside dia meter (ID) surfaces of the RPV.
The extra flaws as sociated with repairs are ty pically located at the deepest point of the repair.
Examination of the repairs detailed in Section 5.
7 of NUREG/CR-6471, Vo lume 2, "Characterization Of Flaws in U.S. Reactor Pressure V essels: Density and Distribution of Flaw Indications in PVRUF," indicates the deepest part of the excavation cavity would be more often as sociated with the surface (o r within 2 inches of the surface) tha n 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 v alue. The hig her value should be associat ed with the t ypical area 4 density of weld repair alon g weld seams. The current approach uses a 2-percent contribution, which was ch osen so that it would be a b ound to the observed 1.5-percent p roportion of weld repair in the Pressure V essel Research Users Facility (PVRUF) vessel. The 1.5-perc ent value seems to have been calculated on a vol ume basis. (1) What is the p roportion of weld repair associated with the weld sea ms on the PVRUF ves sel near the ID surface of the vessel on an area rather tha n a volume basis? (2) What is the expected or calculated effec t of this change in the assu mptions regarding repair flaw distributions o n the TWCFs?
2.4.2 Model Change Regarding th e first question in Section 2.4.1, it is correctly noted that the j udgment to in clude 2-percent repair flaws in the flaw distribution used in the baseline PTS analy sis was made on the basis that a 2-percent repair weld volum e exceeded the proporti onal volume of weld repairs to original fabrication welds obs erved in any of the PN NL work (the largest volume of weld repairs relative to original fabrication welds was 1.5 percent). However, flaw s in welds are almost alway s fusion-line flaws, which suggests that their num ber scales in proportion to weld fusion li ne area and not in proportion to weld volum
- e. To address this issue, PNNL reexamined the relative proportio n of repair wel ds that occur on an area rather than on a volum e 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 boun ding. Regarding th e second question in Section 2.4
.1, FAVOR does assumes that a si mulated flaw is equally likel y to occur at an y location through the vessel wall thickness.
Upon further consideration the staff has deter mined that this model is inco rrect 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 any where with respect t o the depth of the excavation cavity. However, Figure 2.
3 shows that weld repair areas occur with much higher frequenc y close to the surfaces of th e vessel than they do at mid-wall thic kness, as noted in Section 2.4.1. Taken together, this infor mation indicates that a flaw from a weld repair is m ore likely to be encountered close to the ID or OD surface than it is at the m id-wall thickness, a fa ct not well modeled by the approach adopted i n FAVOR Version 04.1.
FAVOR currently uses as input a "blended" flaw distribution for welds. The flaws plac ed in the blended distri bution are scaled in pro portion to the fusion area of the different welding processes used to fabricate the vessel. B ecause of this approa ch, it is not possible, without significant recoding, t o specify a through thickness distribution of re pair weld flaws that is biased toward the surfaces while maintaining a random through-thickness distribution appropriate for subm erged are weld (SAW) and SMAW flaws. Therefore, to account for the nonlinear thr ough-thickness distributio n 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 dia meter can contribute to the vesse l failure probability.
Because PTS transients are dominated by thermal stre sses, flaw s buried in the vessel wall more deeply than 3/8T do not have a hi gh enough driving force/low enough fracture toughness to initiate.
In Figure 2.
3, 3/8T corresp onds to 3 inches on the x-axis. The curve fit to the data indicates that 79 percent of all repair fla ws 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 t he vessel. There fore 43 percent (i.e., (79%+7%)/2) of all repair flaws o ccur between the ID and the 3/8T position in the vessel wall. 5 FAVOR's current assu mption of a random through-wall distributio n of repair flaws generates 37.5 percent of all repair flaws between the ID and 3/8T.
Thus, FAVOR underesti mates the 43-percent value based on the data gi ven above. To account fo r this underestimation, the 2-percent blend factor for repair welds will be increased in future analy ses to 2.3 percent (i.e., 2%43/37.5) (see Appendix A).
00.10.20.30.40.50.60.70.80.910.000.200.400.600.801.00Depth 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 6y = 1.1066e-0.558xR2 = 0.97730%20%40%60%80%100%012345678Depth of Repair Excavation [inches]Percent of Repair Excavations Extending to this Depth or GreaterRepair made from ID (26 observations)Repair made from OD (26 observations)Combined (52 Observations)Expon. (Combined (52 Observations)) Figure 2.3. Distribution of weld repa ir flaws through the vessel wall thickness 2.5 Distribution of Underclad Flaws in Forgings 2.5.1 Review Finding Very shallow flaws w ere created on some forged vessels by underclad crack ing that occurred during or following the cladding process. What is the effect o f underclad fl aws on TWCF, and how does this affect RT-based PTS screening limits for ring-forged vessels?
2.5.2 Model Change Dr. Fredric Sim onen of PNNL perform ed a literature review to establish a distributi on for underclad flaws suitable for use within t he probabilistic f racture mechanics code FAVOR.
Appendix B i s a report summarizing Dr. Simonen's findings.
When unfavo rable welding cond itions (hig h-heat inputs) and material conditions (chem istries having high proportions of impurity elements) coincide, underclad cracks can appear in forgi ngs. When underclad cracks appear they do so as dense arrays (typical intercrack s pacing is 1 or 2 millimeters). They will ha ve depths on t he order of 1 millimeter, but in rare cases can ext end into the ferritic steel of the RPV wall by as much as 6 millimeters. Underclad cracks are oriented perpendicular to the directi on in which t he weld cladding was deposited, wh ich is to say axially in the vessel. While the conditions unde r which underclad cracks form are not believed t o typify those charact eristic of most or all of the 21 forged PWRs now in service, the staff was not able to establish a criteria t hat could differentiate, with a high degree of confidence, those vessels that are belie ved to be prone to underclad cracking from those that are not. For this reason, the staff decide d to perform sensitivity studies at different levels of embrittlement using FAVOR, along with Dr. Simonen's underclad flaw distributio n on forged vessels. In these analy ses the staff assumed that underclad cracks exist. Section 3.4 of this report summarizes the results of these sensitivity studies and uses these results t o develop RT-based scr eening lim its for forged vessels.
2.6 Embrittlement Trend Curve
2.6.1 Review
Finding FAVOR uses an em brittlement 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 beltli ne region of operating PWRs. Versi on 04.1 of FAVOR uses an em brittlement trend curve (Kirk 03) that differs fro m both the trend curve reco mmended by the American Society for Testing and Materials (ASTM) (ASTM E900) as well as from the tren d curve m ost recently recommended by NRC contractors (Eas on 07).
Should the staff consider an y revisions t o the trend curve adopted by FAVOR? 2.6.2 Model Change Both the em brittlement 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 t hrough approximately 2004. For this reason, FAVOR Version 06.1 will be based on the trend curve in (Eason 07), a s detailed in the change specification (see Appendix A). A description of the basis for this relationship is available elsewhere (Eason 07).
Subsequent t o the develop ment of FAVOR 06.1, in accordance with the change specificat ion in Appendix A, Eason developed an alternative embrittlement trend curve of a slightl y simplified form (Eason 07). The results reported in Appendi x C demonstrate that the effect of this alternative tre nd 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 L OCA break 7
frequencies needed as part of a risk-infor med revision to 10 CFR 50.46, "Acceptance Criteria for Emergency Core Cooli ng Systems for Light-Water Nucle ar Power Rea ctors." These frequencies were docu mented in NUREG-1829 (Tregoning 05). Have the calculations documented by the vario us reports listed in Section 4.1 used these most recent esti mates 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) docum ent. The FAVOR 06.1 results
, which are detailed in Chapter 3, make use of the LOCA break frequencies fro m the (Tregoning
- 05) document. 2.8 Tempe rature-Dependent Thermal Elastic Properties
2.8.1 Review
Finding FAVOR 04.1 adopts tem perature-invariant thermal elastic properties despite well-documented evidence, as re flected by American Society of Mechanical En gineers (AS ME) codes, that these properties depend on temperature.
Is the FAVOR 04.1 m odel appropriate?
2.8.2 Model Change The NRC staf f does not believe that the FAVOR 04.1 m odel is app ropriate.
Temperature-dependent the rmal elastic properties have been adopt ed in FAVOR 06.1, as detailed in Appendix A and in (Willia ms 07).
2.9 Upper-Shelf Fr acture Toughness Model 2.9.1 Review Finding Since FAVOR 04.1 was finalized, further work has been publ ished on an upper-shelf fracture toughness model for ferritic steels (Eri cksonKirk 06a; EricksonKirk 06b).
Should the FAVOR 06.1 model incorporate these new re sults? 2.9.2 Model Change The NRC staf f believes that the FAVOR 06.1 model should incorporate t hese new results. As detailed in Appendix A, F AVOR 06.1 adopts the latest finding s on the u pper-shelf fracture toughness model described in (EricksonKirk 06a) and (Eri cksonKirk 06 b). 2.10 Demonstration Th at the Flaw s That Cont ribute to TWCF are Detectable by NDE Performed to ASME SC VIII Supplement 4 Requireme nts 2.10.1 Review Finding NUREG-1806 (EricksonKirk-Sum) indicates that a low density of flaws is one m ajor factor in keeping the total risk associated with PTS low.
The state of knowledge of t he flaw densities in the 70 in dividual PWR plants now in se rvice is based primari ly on detailed destructive examinations of a sm all number of welds and plates fro m four vessels (but m ostly from two vessels), cou pled with expert elicitation and physical modeling. Anot her potential source of information on flaw density is the in-service inspections perfor med at 10-y ear intervals on each operating vessel. It would be very helpful if those inspections could provide evi dence to support t he assumptions in the current analy sis. Specifically
, it is important to know the significance of a flaw to the FAVOR anal ysis (based on its size and through-wall location) as well as the probabilit y 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 de monstrate th at the flaws that co ntribute to PTS risk are (1) all 8
located within approxim ately 1 inch of the vessel inner dia meter and (2) alm ost invariably have a 2a (or throug h-wall extent) dim ension of 0.5 inch or less. To examine the flaw size/l ocation com binations that contribut e to PTS risk in further det ail, the staff perfor med a series of deterministic analyses by locating flaws of various size s axially in the Palisades RP V. Analy ses were perfor med of both a repressurization transient (#65) and of a large-dia meter primary-side pipe break transient
(#62) to addr ess the two types of loadings that collectively are responsible for m ore than 90 percent of the PTS risk. A dditionall y, the staff performed analy ses for embrittlement conditions ranging from those charact eristic of current service to those that would be needed to produce a TWCF equal to the 1x 10-6/ry limit. The results of these analyses at 60 effe ctive full-power y ears (EFPY) and at an em brittlement level characteristic of the 1x10
-6/ry limit appear in Figure 2.7
. Consistent with the conclusi ons based on the probabilistic analyses, these results also indicate that s mall flaws located cl ose to the ID will dom inate PTS risk.
9 Probability of Detect ion Historically
, the inspection of PWR vessels has been conduct ed from the ID. Before 1986, the inspections were conducted with ultrason ic 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, b egan to require that the inspection of the vessel m ust be conducted usi ng a techniqu e that was effective for the ID near-surface zone of the vesse
- l. This new require ment was based on results from the Program for Inspection of Steel Components (PISC). PISC II showed that inspection sensitivity needed to be inc reased fro m 50-percent distance a mplitude correction (DAC) to 20-percent DAC and a special technique is required for this ID near-s urface zone using the increased sensitivity
. PISC II showed that a technique usi ng 70 dual-L wave probes would accomplish this. Subseque ntly, the NRC has required the im plementation of Appendix VIII, leading to t he availability of im proved data to document the effectivenes s 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 wa ll thickness, whichever is larger.
Thus, Supplement 4 or Appendix VIII of the ASME Code addresse s the flaw locations and sizes of interest for PTS.
tWALLtCLAD2aIDODL2c Figure 2.4. Flaw dimension and position descriptors adopted in FAVOR 024680.0000.1250.2500.375Distance of Inner Crack Tip from Clad/Base Interface, L/twall% of Flaws Predicted to InitiateBeaver Valley at Ext-BbPalisades at Ext-Pb Figure 2.
- 5. Distributi on 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 subjecte d to (left) me dium- and large-diameter pipe break transients and (right) stuck-open valve transients at two different em brittlement levels 0.00.51.01.52.02.50.00.51.01.52.02a [inches](note: c=6a)L [inches]In a probabilistic analysis, almost all of the TWCF comes from this shaded region.Re-pressurization transientat 10-6/ry TWCF limitat 60 EFPYLarge diameter pipe break transientCPI 0CPI > 0tWALLtCLAD2aIDODL2cat 60 EFPYat 10-6/ry TWCF limit Note: Each curve i n the figur e above divides the gr aph into two regions: The region a bove each curv e represents combinations of flaw location (L) and flaw size (2a) that cannot produce crack initi ation for the embrit tlement an d loading conditions represe nted by the curve. The region b elow each curve represents combinations of flaw location (L) and flaw size (2a) that produce some finite pro bability of crack initia tion for the em brittleme nt and loading conditions represented by the curve.
Figure 2.7. Analysis of Palisades transients #65 (repressurization transient) and #62 (large-diameter primary-side pipe brea k transient) to illustrate what combinatio ns of flaw size and location lead to non-zero conditional probabilities o f crack initiatio n 10 In 2002, Becker docum ented the performance of inspectors that have gone t hrough the Supplement 4 qualification process (Becker 02).
Becker's paper describes t he findings of the U.S.
Performance Demonstratio n Initiative (P DI), which has manufactured 20 RPV mockups that, in total, conta in in excess of 300 flaws.
Since its inception in 1994, the PDI has perform ed over 10 separate autom ated demonstrations as well as numerous manual qualifications. The w elds examined include both shell welds and the m ore difficult to exa mine nozzle
-to-shell and nozzle-inner-radius welds. Figure 2.8, digitized from Figure 2 of B ecker's paper, shows the probabilit y of detection as a function of crack depth (here called throug h-wall extent) considering p ooled data fro m 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 deriv ing a POD curve is regarded as being overl y optimistic; the inclusion of passed plus fai led candidates is taken to pro vide a lower-bound estim ate of expected inspection performance.
Summary Combining the information on POD fro m Figure 2.8 with the inform ation on the flaw siz es that are needed to produce non-zero crack initiation probabilities (
Figure 2.5 thr ough 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 foc us on detection of flaws having a thro ugh-wall extent of 0.3-0.4 inches and larger beca use these are the f laws that make the greatest contributi on to the non-zero probabilit y of crack initiation from PTS loading.
Performing RPV inspections in accordance with ASME Code, Appendix VIII, Supplement 4 requirem ents results in a 99-percent or greater probability that such flaws can be detect ed. If a vessel were to be em brittled to the point that it challenged the 1x10
-6/ry limit on TWCF and if an inspection were to be performed that inspection should f ocus on detection of f laws having a throu gh-wall extent of appr oximately 0.1 inch and larg er because thes e are the flaws that make the greatest contributio n to the non-zero probabilit y of crack initiation from PTS loading.
Performing RPV inspections in accordance w ith ASME Code, Appendix VIII, Supple ment 4 requirem ents results in an 80-percent or greater probabilit y that such flaws c an be detected.
Based on the inform ation presented in this section it see ms highly likely that the flaw siz es of importance to PTS can be detected if inspections are perfor med in accordance with ASME Code, Appendix VI II, Supplem ent 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%0.00.20.40.60.81.0Through-Wall Extent [in]Probability of Detection for ID Exam Figure 2.8. Probability of detectio n 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). FAVO R Version 04.1, which was used to develop the TWCF esti mates reported in N UREG-1806 (EricksonKirk-Sum
), was revis ed in accordance with this specification to produce FAVOR Version 06.1 (Willia ms 07; Dickson 07a). Additionally, a special version of FAVOR 06.1 was developed to run on the Oak Ridge National Laboratory super-co mputer cluster to faci litate efficient simulation of large populations of underclad cracks. Detailed results fro m the FAVOR V ersion 06.1 a nalyses of plate-welded and ring-forged vessels can be found in (Dickson 0 7b). Information in this chapter is organized as follows:
Section 3.2 re views the rationale first put forward in NUREG-1806 for using plant-specific TWCF versus RT results to develop RT-based scr eening lim its useful for assessing the PTS risk of a ny PWR curr ently operating in t he United States.
Section 3.3 e xamines the FAVOR 06.1 results for Be aver Valley Unit 1, Oconee Unit 1, and P alisades (Dickson 0 7b). Similarity to the FAVOR 0 4.1 results reported in N UREG-1806 is assessed, and the FAVOR 06.1 results a re used to establish relationships betw een TWCF and RT-metrics for plate-welded PWRs currently in operation.
Section 3.4 e xamines the FAVOR results for ring-forged vessels (Dickson 07b). These results are us ed to establish relationships between TW CF and RT-metrics for ring-forged PWRs currently in operation.
Section 3.5 c ombines the inform ation in Sections 3.3 a nd 3.4 to produce two opti ons for regulatory im plementation of these results. The first option pla ces a limit on the estimated TWCF value while the second option places lim its on the RT values associated with the various steels fro m which the reactor beltline is constructed.
These options are completely equivalent, as they both derive directly from the results presented in Sections 3.3 a nd 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 scre ening 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 re sult of various flaw populati ons. The section concludes with a discussion of the need for m argin when using the pr oposed approa ch. 3.2.1 Justification of A pproach Chapter 8 of NUREG-1806 (EricksonKirk-Sum) estimates the variati on of TWCF with embrittlement level in the t hree study pl ants (Oconee Unit 1, Beaver Va lley Unit 1, a nd Palisades). NUREG-1806 reported the following m ajor findi ngs: Only the m ost severe pri mary-side transients (medium- to large-dia meter pipe breaks and stuck-open va lves that later reclose) contribute in any significant m anner to the risk of vessel failure fro m PTS. At lower embrittlement levels stuck-open valves are the dominant risk contribut ors. However, at the embrittlement levels n eeded to produce an estimated TWCF equal to the 10
-6/ry limit, medium- to large-diam eter pipe breaks dominate. Severe secondary
-side tran sients (e.g., a break of the main stea mline) do not contribute significantly to the risk of vessel failure fro m PTS. These transients have 13 extremely rapid initial cool ing rates, which generate high thermal stre sses close to the vessel inner dia meter. Nevertheless, the minimum temperature in the prim ary system that occurs during these transients, the boiling poi nt of water, is not low enough to produce a significant risk of brittle fracture in the RPV steel. Additionally
, a conservatism of the TH m odels adopted for the main stea mline break (MSLB) (i.e., not accounting for the fact that pressurizatio n of containment caused by the break will raise the boiling point of water by 30-40 F above that assu med, 212 F, in the TH analysis) suggests strongl y that reported TWCF values for this transient class overestimate those that can actually occur. Collectively
, these findings demonstrate that only the most severe transi ents contribute significantly to the estimate d risk of RPV failure caused by PTS. Inform ation presented in NUREG-1806 dem onstrates that the nature of these transien t classes is not expected to vary greatly among the po pulation of currentl y operating PW Rs. This information is summarized below:
Medium- to Large-Dia meter Primary-Side Pipe Breaks
- To be risk significant the break dia meter needs to exceed approximately 5 inches. The si milarity of PWR vessel s izes in the operating U.S.
reactor fleet suggests that different plants will have nominally equivalent reactor coolant s ystem (RCS) cooling rates for these large break dia meters. Additionally
, the cooling rate of the RCS inventory for these large breaks e xceeds that a chievable by the RPV steel, which is lim ited by its thermal conductivit y of the vessel steel and does not vary from vessel to vessel because it is a physical property of the m aterial.
Consequentl y, any small plant-to-plant variabilit y that may exist in RCS inventory cooling rate cannot be transm itted to the cooling rate of the RPV steel, which controls the thermal st resses in the RPV wall. T he only possible operator action in response to such a large break is to ma ximize injection flow to keep t he core covered, so no plant-to-plant differences ari sing from different human responses is expect ed. (See NUREG-1806, Section 8.
5.2 for details.
) Stuck-Open Pri mary-Side Valves: For this class of transi ents to be risk significant two criteria must be met-(1) t he valve m ust remain stuck open long enough that the temperature o f the RCS inventory approaches that of the injection water and (2) once the valve reclose s the prim ary system must repressuriz e to the safety valve setpoint. Both of these para meters (injection water temperature and safe ty valve setpoint pressure) ar e input t o the RELAP analy sis and so are not influenced significantly by RELAP modeling uncertainties. Moreo ver, neither parameter varies much within t he population of currently ope rating PWRs.
The modeling of this transient class refl ects credible operator actions. These actions do alter some details of the pr edicted pressure and temperature transients and do vary somewhat based on the RPV vendor because training pr ograms are vendor specific.
Nevertheles s, the analy sis demonstrated that most differen ces caused by operator actions do not appreciably influenc e the risk significance of the transient. Operator actions only matter if repr essurization of the primary system can be pre vented after valve reclosure. If the operator throttles injection within 1 m inute of being allowed, and if the transient was initiated unde r HZP conditi ons then repressurization can be prevented.
Because HZP accounts for onl y a small percentage of the plant' s operating tim e, the total effect of the m odeled operator actions on the estima ted risk significance of thes e transients is small. (See NUREG-1806, Section 8.5.
3 for details.)
Main Stea mline Breaks: As discussed earlier, even t hough these transients produce an extrem ely rapid initial c ooling 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 lev el of fracture toughness in t he vessel wal l, thereby preventing MSLB transients fro m 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 resistanc e of the material s in the vessel a t the location of the flaws in the vessel is nee ded. RT values characterize the r esistance of a ferritic steel to cleav age crack initiation and arr est and to ductile crack initiation (EricksonKirk
-PFM). NUREG-1806 prop osed both weighted and maximum RT metrics. W eighted RT metrics accounted for differences i n weld length and plate volum e between different plants, while maximum RT metrics did not. However, because of the si milarities in the size of all domestic PWRs, the weighted RT metrics did not provide significantl y better correlations with the TWCF data than did t he maximum RT metrics. Further more, 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 dra wings. While this inf ormation is available, it is not currently compiled for all plants in a single location. For these reasons
, this report restricts its attention t o maximum RT metrics.
contributi ng significantl y to the total T WCF estimated for a plant. The size of the main steamline is s ufficiently large that the cooling rate of the RPV wall is lim ited by the thermal conductivit y of the vessel st eel, which does n ot vary from plant to plant. In the rare insta nce that through-wall crack ing does arise fro m an MSLB transient, it will occur within 10-15 minutes after transient initiation, l ong before any operator actions can credibly be expected to occur, so plant-specific operator action diff erences cannot be expected to alter the TWCF associat ed with this transient class. (
See NUREG-1806, Section 8.5.4 for deta ils.) With one sm all exception, the "generaliz ation study," in which the plant characteristics that can influence PTS severity of five additi onal high embrittlement plants were investig ated, validated these expectations. (See (
Whitehead-Gen) and Section 9.
1 of NUREG-1806 for details.) The reco mmended PTS screening limits present ed in Section 3.5 account f or this exception.
In summary
, the NRC' s study demonstrates that risk-significant PTS transi ents do not have any appreciable plant-specific differences w ithin the population of PWRs currentl y operating in the United States
. These findings m otivate the development of generic screening lim its that can be applied to all operating PWRs. Formulae for the three maximum RT metrics proposed in NUREG-1806 (RT MAX-AW, RTMAX-PL, and RTMAX-CW) are repeated below (the algebraic expression of these for mulae have been modified slightl y from the form reported in NUREG-1806 to im prove clarity
): 3.2.2 Use of Reference Temperatu res to Correlate T WCF RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found along t he axial weld fusion lines. It is evaluated us ing the following form ula for each axial weld fusion line within the beltline region of the v essel (the part of the for mula inside the
{-}). The value of RT MAX-AW assigned to the vessel is the highest of the reference temperature v alues associated with any individual axial weld fusion line. In evaluating the T30 values in this for mula the composition properties reported in the RVI D database ar e used for copper, nickel, and ph osphorus. An independent esti mate of the manganese content of each weld and plate evaluated is also neede
- d. Eq. 3-1 FLipladjipladjuNDTFLiawadjiawadjuNDTtTRTtTRT)(30)()()(30)()(AWFL(i)n1iAWMAX,MAXRTMAXAWFL where 15 nAWFL is the num ber of axial weld fusion lines i n the beltline region of t he vessel, i is a counter that ranges from 1 to nAWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT of the weld adjacent to the i th axial weld fusion line,
)()(iawadjuNDTRT is the unirradiated RT NDT of the plate adjacent to the i th axial weld fusion line,
)()(ipladjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th axial weld fusion li ne, and )(30iawadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion li ne. )(30ipladjTRTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in plates that are not associate d with welds. It is evalua ted using the following form ula 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 associ ated with any individual plate. In evaluating the T30 values in this form ula the co mposition pr operties reported in t he RVID database are used for copper, nick el, and phosphorus. An i ndependent estim ate of the manganes e content of each weld and plate evaluate d is also needed.
Eq. 3-2 )()(30)()(n1iPLMAXMAXPLRTiPLMAXiPLiPLuNDTtTRT where nPL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to nPL, is the maximum fluence occurring over the vessel ID occupied by a particular plate,
)(iPLMAXt is the unirradiated RT NDT of a particular plate, and
)()(iPLuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to of a particular plate.
)(30iPLT)(iPLMAXtRTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along t he circumferential weld fusion lines. It is evaluated using the following form ula for each circumferential weld fusion line within the beltline region of the ve ssel (the part of the formula insid e the {-}). Then the value of RT MAX-CW assigned to the vessel is t he highest of the reference t emperature val ues associ ated with any individual circumferential weld fusion line. In evaluating the T30 values in this form ula the composition properties reported in the R VID database are used for copper, nicke l, and phosphorus.
An independe nt estimate of the manganese content of each weld, plate, and forging evaluated is also needed.
16 Eq. 3-3 FLifoadjifoadjuNDTFLipladjipladjuNDTFLicwadjicwadjuNDTtTRTtTRTtTRT)(30)()()(30)()()(30)()(CWFL(i)n1iCWMAX,,MAXRTMAXCWFL where nCWFL is the num ber of circum ferential weld fusion lines in t he beltline region of the vessel, i is a counter that ranges from 1 to nCWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular circumferential weld fusion line, is the unirradiated RT NDT of the weld adjacent to the i th circumferential weld fusion line,
)()(icwadjuNDTRT is the unirradiated RT NDT of the plate adjacent to the i th circumferential weld fusion line (if there is no adjace nt plate this term is ignored),
)()(ipladjuNDTRT is the unirradiated RT NDT of the forging adjacent to the i th circumferential weld fusion line (if ther e is no adjacent forgi ng this term is ignored),
)()(ifoadjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th circumferential weld fusion line,
)(30icwadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion line(if there is no adjacent plate this term is ignored), and
)(30ipladjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the forging adjacent to the i th axial weld fusion line(if ther e is no adjacent forging this term is ignored).
)(30ifoadjT The T30 values in Eq. 3-1 to Eq.
3-3 are deter mined as follows:
f Eq. 3-4 CRPMDT30 eRCStPMnTAMD471.2130.61001718.01 eeeRCStNiCugPCufTNiBCRP,,,1.543769.31100.1191.1 f 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 10x417.1platesfor 10x561.1forgingsfor 10x140.1777A for welds 0.155 vesselsedmanufactur CEin platesfor 2.135 vesselsedmanufactur CE-nonin platesfor 5.102 forgingsfor 3.102B 102595.01010103925.4for 103925.4103925.4for ttte Note: Flux () is estim ated by dividing fluence (t) by the tim e (in seconds) that the reacto r has been in o peration. 6287.012025.184483.01390.1logtanh2121,,10NiCuttNiCugeeee 008.0072.0for 0.008)-(359.1072.0 008.0072.0for 072.0 072.0for 0,0.66790.6679PandCuPCuPandCuCuCuPCufeee wt%072.0for wt%072.0for 0CuCuCuCue 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)(eCuMax NUREG-1806 proposes the use of these three different RTs in recognition of the fact t hat the probability of vessel fra cture initiating from different flaw pop ulations varies considerably as a result of the following known factor s: The degree of irradiation d amage suffered by the material at the flaw tips varies wi th location in the vessel bec ause of differences in chemistry and fluence.
These differe nces indicate that it is im possible for a single RT value to represent ac curately the resistanc e of the RPV to fracture in the general case. Indeed, this is precisely the liability associated with the RT val ue currently adopted by 10 CFR 50.61, the RTPTS. The RT PTS, as defined in 1 0 CFR 50.61, is the maxim um RTNDT of any region in the vessel (a r egion is an axial weld, a circu mferential weld, a plate, or a forging) evaluated at the peak fluence occurring in that region
. Consequentl y, the RTPTS value currently assigned to a vessel may only coincidentally correspond to the toughness Different regions of the ves sel have flaw populations that differ in size (weld flaws are considera bly larger tha n plate flaws)
, density (weld flaws ar e more numerous than plate flaws),
and orientatio n (axial and circumferential welds have flaws of corresponding orientations
, whereas plate flaws may be either a xial or circumferential). The drivi ng force to fracture depends bot h on flaw size and orientation, s o different ve ssel regions experience different fracture-driving forc es. 18 properties of the material region respons ible for the bulk of the TWCF, as i llustrated by the following exa mples: Out of 71 operating PWRs, 14 have t heir RTPTS values established based on circumferential weld properties (RVID2).
However, the results in NUREG-1806 show that the proba bility of a vessel failing as a consequence of a crack in a circu mferential weld is extre mely remote because of the lack of throu gh-wall fracture drivin g force associated with circum ferentially oriented cracks. For these 14 vesse ls, the RT PTS value is unrelated to any material that ha s any significant chance of causing vessel failure. Out of 71 operating PWRs, 32 have t heir RTPTS values established based on plate properties (RVID2). Certainly
, plate properties influence vessel failure probabilit y; however, the 10 CFR 50.61 practice of evaluating RT PTS at the peak fluence occurring in the pla te is likely to estimate a toughness value that cannot be associated with any large flaws bec ause the location of th e peak fluence may not correspond to an axial weld fusion line.
While the RT PTS value for these 32 vesse ls is based on a material that si gnificantly contributes to the vessel fai lure probability, it is likel y that RTPTS has been overesti mated (perhaps significantly so) because the fluence assu med in the RT PTS calculati on does not corr espond to t he fluence at a likely flaw location. Out of 71 operating PWRs, 15 have t heir RTPTS values established based on axial weld properties (RVI D2). It is only for these vess els that the RT PTS value is clea rly associated with a material r egion that contributes significantly to the vessel fai lure probabilit y and is evaluated at a fluence that is clearly associated with a potential location of large flaws.
For these reas ons, the use of the three RT-metrics propo sed here (RT MAX-AW, RTMAX-PL, and RTMAX-CW) is expected to increas e the accuracy with which the TWCF in a vessel c an be estimated rela tive to the current 10 CFR 50.61 procedure, which uses a single RT-metr ic (RTPTS). 3.3 Plate-Welded Pl ants 3.3.1 FAVO R 06.1 Results Detailed re sults from the FAVOR 06.1 analy ses of Oconee Unit 1, Beaver Valley Unit 1, and Palisades c an be found in a separate r eport by (Dickson 07b
). Table 3.1 i ncludes a summary of these results, which have been reviewed and found to be consistent in most respects with the findings presented in NUREG-1806. T his section highli ghts two ke y findings t hat support the use of these results to develop RT-based screening li mits applicable to all plate-welded plants. Characteristics of TWCF Distributions Section 8.3.
2 of NUREG-1 806 reported that the TWCF distributions calcul ated previously b y FAVOR Version 04.1 were heavily skewed towards zero or very low values, and that this skewness oc curs as a natural consequence of (1) the rarity of multiple unfavorable factors combining to produce a high failure probabilit y and (2) the fa ct that the distributio ns of both cleavage crack initiatio n and cleavage crack arrest fra cture toughness have finite lower bounds. Figure 3.1 dem onstrates that th e changes made to the FAVOR code (se e Appendix A) have not qualitatively altered this situation. However, as illu strated in Figure 3.2, the percentile of the TWCF distribution correspondin g to the m ean 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 em brittlement. Conversely, the mean TWCF values esti mated using FA VOR 06.1 correspo nded to between the 80th a nd 99th percentile. The percentile associat ed with the mean TWCF has been reduced in FAVO R 06.1 results for the following two reasons:
19 (1) The change in the data basis for the RT NDT epistemic uncertainty correction (see Tas k 1.1 in the FAVOR change specification in Appendix A) and the chang e in the embrittlement trend curve (see Task 1.5 in the FAVOR c hange specification in Appendix A) have increase d the embrittlement level associ ated with each EFPY analy zed. This incr ease in embrittlement reduces the TWCF percentile associated with the mean along t he same trend line established by the FAVOR 0 4.1 analyses (see Figure 3.2). Indeed, the percentile associated with the mean should reduce with increased em brittlement because, for m ore embrittled material s, fewer zero failure probability vessels are simulated, lea ding to a less skewed distributio n of TWCF. (2) The change in the RT NDT epistemic uncertainty sam pling procedure (in FAVOR 04.1, the RTNDT epistemic uncertainty was sampled inside the flaw loop; in FAVOR 06.1, this sampling was m oved outside o f the flaw loop-see T ask 1.3 in the FAV OR change specification in Ap pendix A) ha s pushed more of the densit y of the TWCF distributio ns to occur in t heir upper tails, thereby broadening them
. This change was motivated by the observation that the FAVOR 04.1 procedure sim ulated an uncertainty in RT NDT for an indivi dual major-region of a si mulated vessel (a major-region is an i ndividual weld, plate, or forging) having a total range in excess of 150 F. This range is much larger than t hat measured in laboratory tests, so FAVOR was modified to bring its si mulations int o better accord with observations.
NUREG-1806 uses mean TWCF values in the TWCF versus RT regressi ons because the percentile associated with the mean exceeded 90 percent in all case s (see Figure 3.2). As explained earlier, this is no longer the case, and it is not appr opriate 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 underestim ated. Consequ ently, the foll owing sections of this report use 95th percentile TWCF values in the TWCF versus RT regressi ons. Use of 95th percentile values makes the probabilit y that the TWCF is underestimated accept ably small (1 chan ce out of 20).
0%5%10%15%20%25%30%35%zero<= E-16E-15E-14E-13E-12E-11E-10E-9E-8E-7E-6E-5E-4TWCF ValuePercent of Simulated Vessels32 EFPYExt-B Figure 3.1. TWCF distributions for Beaver Valley Unit 1 estimated for 32 EFPY and for a much hi gher level of embrittlement (Ext-B). At 32 EFPY the height of the "z ero" bar is 62 perce nt. 0102030405060708090100100200300400Maximum RTNDT Along Axial Weld Fusion Line [oF]Percentile of Mean TWCF ValueOconeeBeaver ValleyPalisadesShaded Symbols: FAVOR 04.1(NUREG-1806)Solid Symbols: FAVOR 06.1(This Report) 0102030405060708090100100200300400Maximum RTNDT Along Axial Weld Fusion Line [oF]Percentile of Mean TWCF ValueOconeeBeaver ValleyPalisadesShaded Symbols: FAVOR 04.1(NUREG-1806)Solid Symbols: FAVOR 06.1(This Report) Figure 3.2. The percentile of the TW CF distribution c orresponding to mean TWCF values at various levels o f embrittlement 20 Dominant Transients As reported in Section 8.
5 of NUREG-1 806 and summarized in Section 3.
2.1 of this rep ort, only the most severe transients make any significant contribution to the total esti mated risk of through-wall cracking from PTS. Examination of the results in (Dickson 0 7b) shows tha t the risk-dominant transients listed in Tables 8.7, 8.8, and 8.9 of NUREG-1806 also dom inate the risk in the current (i.e., FAVOR 06.1) analy ses. 21 Figure 3.3 shows the dependence of the TWCF resulting fro m the two do minant transient classes (medium- to large-diameter primary-side pipe breaks, and stuck-ope n primary valves that may later recl ose) and of MSLBs on embrittlement level (as quantified by RTMAX-AW). The tren ds in these figures agree w ell with those reported previo usly in Section 8.
5 of NUREG-1806, i.e.:
Stuck-open primary-side valves dom inate the TWCF at lower em brittlement levels.
As embrittlement increases, medium- to large-dia meter primary-side pipe breaks become the dominant trans ients. In combination these transient classes constitute 90 percent or m ore of the total TWCF irrespective of em brittlement level. MSLBs are responsible fo r virtuall y all of the remaining risk of through-wall crack ing. It should, however, be remem bered that the models of MSLBs are intentionall y conservative. More accurat e modeling of MSLB transients is theref ore expected to further reduce their percei ved risk significance.
None of the other transient class es (small-diameter primary-side breaks, stuck-open secondary valves, feed and bleed, steam generator tub e rupture) are severe enough to significantl y 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 respecti ve flaw populations-axial fusion line flaws in axial welds, axial a nd circum ferential flaws in plates, and circu mferential flaws i n circumferen tial welds. The following tren ds, demonstrated b y the data in thi s figure agree well with those reported prev iously in Section 1 1.3.2 of NUREG-1806:
The TWCF produced by axial weld flaws dominates the PTS risk of plate-welded PWRs. The TWCF produced by plate flaw s makes a more limited contributi on to PTS risk than do axial weld flaws. This is because the plate flaws, w hile more numerous than axial weld flaws, a re considerably smaller.
Additionally
, half of the pla te flaws ar e oriented circumferentially and half are oriented axially.
The TWCF produced by circu mferential flaws is e ssentially negligible. At the highest RT MAX-CW currently expected for any PWR after 60 years of operation (25 8 F or 718R), circu mferential weld flaws are responsible for approxim ately 0.04 percent of the 1x 10-6/ry TWCF limit prop osed in Chapter 10 of NUREG-1806.
The equations of the curves in Figure 3.4 all share the sa me form, which is as follows:
Eq. 3-5 bRTRTmTWCFxxTHxxMAXxxlnexp95 In Eq. 3-5, the 95 subscript denotes the 9 5th percentile; while the "xx" subscript indi cates the flaw populati on (xx is AW for axial weld flaws, CW for circumferential weld flaws, and PL for plate flaws).
The value RT TH-xx is a fitting coefficient that per mits Eq. 3-5 to have a lower vertical asy mptote on a se mi-log plot.
Values of temperature are expressed i n absolute de grees (Rankine = Fahrenheit + 459.6
- 9) to prevent a logarithm from being taken of a negativ e number. Val ues of the best-fit coefficie nts for Table 3.1. Summary of FAVOR 06.1 Results Reported in (Dickson 07 b) TWCF Partitioned by Flaw Population (% of total TWCF)
TWCF Partition ed by Transient Class (
% of total TWCF) 95th %ile TWCF (/ry) Plant EFPY RTMAX-AW [oF] RTMAX-CW [oF] RTMAX-PL [oF] MEAN FCI (/ry) Mean TWCF (/ry) %ile of Mean TWCF Primary Stuck-Open Valves Axial Welds Circ. Welds Plates Primary Pipe Breaks Main Steam-line Breaks Secondary Stuck-Open Valves 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 0.09 0.00 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 0.87 0.00 Ext-A 221 284 284 2.31E-06 4.08E-08 87.2 1.52E-07 53.88 5.30 40.83 49.25 47.63 3.08 0.00 Beaver 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 9.98 0.00 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 0.00 0.00 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 0.00 0.00 Ext-A 253 277 158 3.19E-07 2.84E-08 93.1 4.63E-08 99.91 0.07 0.03 9.10 90.89 0.00 0.00 Oconee 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 0.00 0.00 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 1.43 1.25 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 1.88 9.82 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 2.94 6.29 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 4.67 12.54 22 August 2006FAVOR 06.11.E-141.E-13 1.E-12 1.E-11 1.E-101.E-091.E-081.E-07 1.E-06 1.E-05 1.E-04550650750850Max. RTAW [R]95th Percentile TWCF Due to Primary Side Pipe BreaksBeaverOconeePalisadesAugust 2006FAVOR 06.11.E-141.E-13 1.E-12 1.E-11 1.E-101.E-091.E-081.E-07 1.E-06 1.E-05 1.E-04550650750850Max. RTAW [R]95th Percentile TWCF Due to Primary Side Pipe BreaksBeaverOconeePalisadesAugust 2006FAVOR 06.11.E-141.E-13 1.E-121.E-111.E-10 1.E-09 1.E-08 1.E-071.E-061.E-05 1.E-04550650750850Max. RTAW [R]95th Percentile TWCF Due to Stuck
-Open Primary ValvesBeaverOconeePalisadesAugust 2006FAVOR 06.11.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-07 1.E-061.E-051.E-04550650750850Max. RTAW [R]95th Percentile TWCF Due to Main Steam Line BreaksBeaverOconeePalisades 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 August 2006FAVOR 06.11.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03550650750850Max. RTAW [R]95th %ile TWCF - Axial Weld FlawsBeaverOconeePalisadesFitAugust 2006FAVOR 06.11.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03550650750850Max. RTPL [R]95th %ile TWCF - Plate FlawsBeaverOconeePalisadesFitAugust 2006FAVOR 06.11.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03550650750850Max RTCW [R]95th %ile TWCF - Circ Weld FlawsBeaverOconeePalisadesFit 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 each flaw po pulation, esta blished by least-squares analy sis 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 RT TH-xx the value of TWCF95-xx is undefined an d should be taken as zero. 3.3.2 Estimation of T WCF Value s and RT-Based Limits for Plate-W elded PWRs Similar to the procedure described in NUREG-1806, the fits to the TWCF 95-xx versus RT MAX-xx relationships shown in Fig ure 3.4 and quantified by Eq. 3-5 are combined to develop t he following form ula that can be used to estimate the TWCF of any currentl y operating plat e-welded PWR in the United States: Eq. 3-6 CWCWPLPLAWAWTOTALTWCFTWCFTWCFTWCF95959595 Here the values of TWCF 95-xx are esti mated using Eq.
3-5. The factors are introduced to prevent under estimation of TWCF95 at low embrittlement levels fro m stuck-open va lves on the primary side that may later reclos e (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 6252505.15.2xxMAXRT Reduction of as embrittlement (RT) increases is justified because the generalization st udy only revealed the potential for the severity of stuck-open valve tr ansients to be slightl y underrepresented, and stuc k-open valves make only small contributions to the total TWCF 95 at high embrittlement levels.
Eqs. 3-5 and 3-6 define a r elationship be tween RTMAX-AW, RTMAX-PL, and RTMAX-CW and the resultant value of TWCF
- 95. Eqs. 3-5 an d 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 insi de the surface therefore have TWCF 95 values below 1x 10-6. Eqs. 3-5 and 3-6 can be us ed, together with values of RT MAX-AW, RTMAX-PL, and RTMAX-CW determined from information in the RVID database, to e stimate the TWCF of any plate-welded PWR currently operating in t he United States. (See S ection 3.3.3 for a necess ary modification to these formulae for RPVs having wall thicknesses above 9.5 inches.) These calculations (see Se ction 3.5.1 for details) show that no operating PWRs are expected to exceed or approach a TWCF of 1x 10-6/ry after either 40 or 60 years of operation.
The two-dimensional version of t he three-dimensional graphical representation of Eq. 3-6 provided inFigure 3.5 can be used to de velop RT-based scr eening lim its for plate-wel ded plants. As was done in NUREG-1806, RT limits can be establi shed by setting the total T WCF in Eq. 3-6 equal to the reactor vessel failure frequency acceptance criter ion of 1x10-6 events/year proposed in Chapter 10 of that document. Plate vess els are made up of axial welds, plates, and circum ferential 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 T able 3.3, the contributi on of flaws in circumferential welds to TWCF is negligi ble. The highest RTMAX-CW anticipated for an y currentl y operating PWR after 60 years of operation (assu ming current operating conditions are maintained) is 258 F. At this embrittlement level flaws in circumferential welds would contrib ute approximately 0.04 percent of the 1 x10-6/ry limit. In view of this ver y minor contribution of flaws in circu mferential welds to the overall risk, RT-base d screening limits for plate
-welded plants are developed as follows:
25 (2) Set TWCFTOTAL to the 1x10
-6/ry limit proposed in Chapter 10 of NUREG-1806.
(1) Set TWCF95-CW to 1x10-8/ry (this corresponds to an RT MAX-CW value of 312 F, which far exceeds the highest va lue expected for any currently operating PWR after 60 years of operation.
(3) Solve Eq.
3-6 to establish (RT MAX-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 di agrams is 1x10-6. The top diagr am 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 completel y accurate represe ntation 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 th e locus of (RT MAX-AW, RTMAX-PL) pairs that define the horizo ntal cross-section of the three-dimensional surface depicted in Figure 3.5 at an RT MAX-CW value of 312 F. In the region of t he graph between the red loci and the origin, t he TWCF is below the 1x10
-6 acceptanc e criterion, so these co mbinations of RT MAX-AW and RTMAX-PL would satisfy the 1x 10 6/ry limit on TWCF. I n the region of the graph o utside of the red loci, the esti mated TWCF excee ds the 1x10-6/ry limit, indicating the need for additional analysis or other measures to justif y continued plant operatio
- n. 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 1.15 4, "Format and Content of Pl ant-Specific Pres surized Thermal Shock Safety Analysis Reports for Pressurized Water
- Reactors,
" issued January 1987.
Figure 3.6 also shows asses sment points (blue circles and blue triangles), one representing each plate-welded PWR after 40 and 60 years of operation. T he coordinates (RT MAX-AW, RTMAX-PL) for each plant were esti mated from information in the RVID database (
see Table 3.3). Com parison of the as sessment points for the indivi dual plants to the (proposed) 1 x10-6 and (current) 5x10
-6 limits in Figure 3
.6 supports the following conclusions:
The risk of P TS failure is low. Over 80 percent of op erating PWRs have estim ated TWCF values below 1x1 0-8/ry, even after 60 years of operation.
After 40 years of operation the highest ri sk of PTS at any PWR is 2.0x10
-7/ry. After 60 years of operation this risk increase s to 4.3x10-7/ry. The current regulations assume that plants have a TWCF risk of appr oximately 5x10 6/ry when they are at the 10 CFR 50.61 RTPTS screening lim its. Contrary to the current situation in which several plants are thought to be within fractional degrees Fahrenheit of these li mits, the staff' s calculations show that when realistic models are adopted n o plant is clos er 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)050100150200250300350400050100150200250300RTMAX-AW [oF]RTMAX-PL [oF]1E-81E-71E-65E-630oF53oF Plate Welded Plants at 48 EFPY (EOLE)050100150200250300350400050100150200250300RTMAX-AW [oF]RTMAX-PL [oF]1E-81E-71E-65E-617oF40oF Figure 3.6. Maximum RT-based screening criterion (1E-6 c urve) for plate-welded vessel s based on Eq. 3-6 (left: screening criteri on relative to currently operating PWRs after 40 years of operation; right: screening criterion relative to currently operating P WRs 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 in ches. The three vessels analyzed in detail in this study are all in this range and thus represent the vast majority of the op erating 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 embrittl ement levels) because of the higher thermal stresses th at occur in the thicker vessel walls. Figure 3.8 reproduces the results o f a sensitivity study on wall thickness reported in NUREG-1806
. These result s show that for PTS-dominant transients (the 16-in ch hot leg break and the stuck-open safety
/relief valve) the TW CF in a thick (11 to 11
.5 inch) wall vessel will increase by approximately a factor o f 16 over the values presented in this report for vessels having wall thicknesses between 8 and 9.5 inches. To account for this increase d driving force to fracture in thick-walled vessels the staff recommends that the TWCF estimated by Eq. 3-6 b e increased by a factor of 8 for each inch of thickness by which the vessel wall exceeds 9.5 in ches. Section
3.5 provid
es a formula that formally implements thi s recommendation. 0510152025306.57.07.58.08.59.09.510.010.511.011.5Vessel Wall Thickness [in]Number of PWRs Figure 3.7.
Distribution of RPV w all thicknesses for PWRs current ly in service (R VID2). This figure originally appeared as Figure 9.9 i n NUREG-1806. 01020304050789101112Vessel Wall Thickness [in]TWCF / TWCF for 7-7/8-in. ThicBeaver Valley Vessel at 60 EFPBV9 - 16" Hot Leg BreakBV56 - 4" Surge Line BreakBV102 - MSLBBV126 - Stuck open SRV, re-closes after 100 minutes Figure 3.8.
Effect of vessel wall thickness on the TWCF of vari ous transients i n Beaver Valley (all analyses at 60 E FPY). This figure originally appeared as Fi gure 9.10 in NURE G-1806. 3.4 Ring-Forged Plants All three of the detailed study plants are plate-welded vessel
- s. However, 21 of the currently operating PWRs have be ltline regions made of ring forgings. As such, these vess els have no axial welds. The lack of the large, axially oriented axial flaws fro m such vessels indicates that they may have much lower values of TWCF than a com parable plate vessel of equivalent embrittlement. However, forgings have a population of embedded flaws that is particular in densit y and size to their method of manufacture.
Additionall y, under certain rare conditions for gings may contain underclad cracks that ar e produced by the deposition of the austenitic stai nless steel cladding la yer. Thus, to investigate the applicability of the result s reported in Section 3.3 to forged vessels
, the staff perfor med a number of analyses on vessels using properties (RTNDT(u), copper, nickel, phosphorus, manganese) and flaw popul ations appropriate to forgings.
Appendices B a nd D detail the tec hnical basis for the distributions of flaws used in these sensitiv ity 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 (Schust er 02). These flaw s 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 previo usly in NUREG-1808 (EricksonKirk-SS) and will not be repeated here. This study showed that the similarities in flaw size and densit y between forgings and plates allow the relationship between RT MAX-PL and TWCF 95 (Eq. 3-6) to be used for forgi ngs containin g embedded flaws.
For forgings t he RT metric is defined as follows:
RTMAX-FO characterizes the resist ance of the RPV to fracture initiating fr om flaws in forgings that are not associ ated with wel ds. It is evaluated using the foll owing formula for each forging within the beltline region of the vessel. The value of RT MAX-FO assigned to the vessel is the highest of the referenc e temperature v alues associated with any individual plate. In evaluating the T30 values in this form ula the co mposition pr operties reported in the RVID datab ase are used for copper, nicke l, and phosphorus. An independent e stimate of the manganese content of each weld and plate evaluated is also needed.
Eq. 3-7 )()(30)()(n1iFOMAXMAXFORTiFOMAXiFOiFOuNDTtTRTwhere nFO is the num ber of forgi ngs 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,
)(iFOMAXt is the unirradiated RT NDT of a particular forging, an d )()(iFOuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-lb) energ y (estimated using Eq.
3-4) produced by irradiation to of a particular forging.
)(30iFOT)(iFOMAXt 3.4.2 Underclad Flaw Sensitiv ity Study By May 1973 the causes of underclad cracking were sufficientl y well understood for th e NRC to issue Regulator y Guide 1.
43, "Control of Stainless Stee l Weld Cladding of Low Alloy Steel Components" (RG 1.43). Vessels fabricated aft er this da te would have had to comply with the provisio ns of Regulator y Guide 1.43 and, ther efore, should not be susceptible to underclad cracking. Vessels fabricated before 1973 may have been com pliant as well because the causes of and remediation for underclad cracking wer e widely known before the issuance of the regulatory guide.
Nevertheless, t o provide the inform ation needed to support a comprehensive revision of the PTS Rul e the NRC staff considered it necess ary to establish PTS screening lim its for vessel s containing underclad cracking for t hose situations in which compliance with Regulator y Guide 1.4 3 cannot be demonstrated.
As discussed in detail in A ppendix B, underclad cracks occur as dense arr ays of shallow cracks extending into the vessel wall fro m the clad-to-basemetal interface to dept hs that are limited by the extent of the heat-affect ed zone (approxim ately 0.08 inch (approximately 2 millimeters)). These cracks are oriented normal to the direction of welding for c lad deposition, producing axially oriented cr acks in the vessel bel tline. The y are clustered where the passes of stri p clad contact each other.
Underclad fla ws are much more likely to occur in particular grades of pressure vess el steels that have chem ical compositions that enhance the likelihood of cracking. Forging grades such as A508 are m ore susceptible than plate materials such as A533. High levels of heat input during the cladding process enhance the likelihood of underclad cracking.
The NRC staf f 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 1960 s and early 1970s the understand able focus of the investigations performed at that tim e was to prevent the phenom ena from occurring altogether, not to characteri ze the size and density of the resulting def ects. Because of this lack of infor mation, the flaw distributio n detailed in Appendix B reflects conserv ative judgments. Hypothetical m odels of forged vessels w ere constructed based on the existing m odels of the Beaver Valley Unit 1 and Palisades ves sels. In these hypothe tical forged vessel s both the axial welds and the plates in the beltline region were combined and assigned the following properties, which are cha racteristi c of the forging in Sequoyah Unit 1 (RVID2)-copper = 0.13 percent, nickel = 0.76 perc ent, phosp horus = 0.020 percent, manganese
= 0.70 percent, RTNDT(u) = 73 F, upper-sh elf energy
= 72 ft-lbs (this forging was select ed because it has am ong the most embrittlement sensitive properti es of any forging in the current operating fleet).
Using these properties along with the underclad flaw distribution described in Appendix B, FAVOR analyses were co nducted at a num ber of different EFPY values to investigate the variation of T WCF with em brittlement level. Because of the extre mely high density of underclad flaws assu med by the Append ix B flaw distribution, a super-com puter cluster was used to perform these FAVOR analyses (see (Dickson 07b
) for a full de scription of t he underclad flaw analy sis). Table 3.2 and Figure 3.9 summariz e the results of these analy ses. The rate of increa se of TWCF with increasi ng embrittlement (as quantified by RTMAX-FO) shown in Fig ure 3.9 for underclad crack s is much more rapid than shown previously (see Figure 3.4) for plate and weld flaws. The steepness of t his slope occurs as a direct consequence of the ver y high densit y of underclad cracks assu med in the anal ysis (the mean crack-to-crack spaci ng 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 hi gh 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 sm all increases in embrittlement will lead to l arge increases in TWCF. Beca use of the steepness of the TWCF versus RT MAX-FO relationship, the staff made no attempt to develop a "best fit" to the results.
Instead, the following bounding relation ship (which also appears on Fig ure 3.9) is pr oposed: Eq. 3-8 FOMAXRTFOTWCF185.01379510103.1Table 3.2. Results of a Sens itivity S tudy Assessing the Effect of Undercl ad Flaws on the TWCF of Ring-Forged Vessels Analysis ID RTMAX-FO [oF] 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 T WCF was from ci rcumferenti al weld flaws in thes e analyses 1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-03550650750850Max RTFO [R]95th %ile TWCF for Underclad Flaws FAVOR ResultsBoundFOMAXRTFOTWCF185.01379510103.1 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-w elded vessels, the effect of incr eased ves sel wall thickness on the TWCF in ring-forged vessels must also be quantified. The sensitivity study presented previously for plate-welde d vessels (se e Figure 3.8) can be used to correct for thickness effects in forgings that have onl y embedded flaws (no underclad cracking) because of the sim ilarity in both flaw density and flaw size betw een embedded flaws in forging s 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 increas ed to 11 inches and the analysis was rerun using s ubclad cracks. Figure 3.10 presents the results of these analy ses and compares them with the results presente d previously for plate-welde d vessels (se e Figure 3.7) as well a s to the thickness correctio n recommended in Section 3.3.3. This comparison demonstrates that the thickness correctio n recommended in Section 3.3.3 for plate-welded vessels can also be applied to ring-forged vessels that have underclad cra cks. 31 3.5 Options for Regul atory Implementation of These Results Any future revision of 10 CFR 50.61 m ust include a procedure by which licensees can demonstrate com pliance with the 1x 10-6/ry TWCF limit based on infor mation 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 inform ation presented so far in this chapter.
The first approach places a limit on TWCF of 1x10-6/ry, whereas the s econd approach places a limit on the maxima of the various RT values, or combinations thereof, which would produce a TWCF value at the lim it of 1x10
-6/ry. Equations presented els ewhere in this report are re peated in these sections for clarity
. Adoption of e ither approach in r egulations wo uld be full y consistent with the technical basis information presented in this report, in NUREG-1806, and i n the other companion documents listed in Section 4.1. It should be noted that Step s 1 and 2 are identical in both appr oaches. Additiona lly, Step 2 uses the em brittlement trend curve from the FAVOR 06.1 change specification (Appendix A)
. Eason has d eveloped an alternative em brittlement trend curve of a slightly simplified form (Eason 07). T he results reported in A ppendix C demonstrate that the effect of this alternative tre nd curve on the TWCF values esti mated by FAVOR is insignificant.
Thus, the eq uations in Appendix C c ould be adopted instead of the equations presented in Step 2 of Sections 3.5.1 and 3.5.2 without the need to change an y other part of the pr ocedure.
FFResults from analyses of forge d 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 res ults for plate-welded vessels (see Figure 3.7)
3.5.1 Limitation on TWCF Step 1. Establish the plant characte rization pa rameters, which include the following:
RTNDT(u) [ F] The unirradiated value of RT NDT. Needed for e ach 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 perce nt] Nickel co ntent. Needed for each weld, plate, and forging in the beltline region of the RPV.
P [weight percent]
Phosphor us content. N eeded for each weld, plate, and forging in the beltline region of the RPV.
Mn [weight perce nt] Manganese content. Needed for eac h weld, plate, and forging in the beltline region of the RPV.
t [seconds] The amount of ti me the RPV has been in o peration.
TRCS [ F] The average tem perature of the RCS inventor y in the beltline region under normal operating conditions. tMAX [n/cm2] The maximum fluence on the vessel I D for each plate and forging in the beltline region of the RPV. tFL [n/cm2/sec.] The maximum fluence occurring along each axial w eld and circumferential weld fusion line. Th is value is neede d for each axial weld and circum ferential weld fusion line in the beltli ne region of t he 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 foll owing formulae and the values of the characteri zation para meters fro m Step 1: RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found along the axi al weld fusion lines. It is evaluated using the foll owing form ula for each axial weld fusion line within the beltline region of the vessel (the part of the for mula inside the {-}). The value of RT MAX-AW assigned to the vessel is the highest of the referenc e temperature values as sociated with any individual axial weld fusion line. In evaluating the T30 values in t his formula the com position properties reported in the R VID database are used for copper, ni ckel, and pho sphorus.
An independent e stimate of the manganese content of each weld and plate evaluated is also neede
- d. FLipladjipladjuNDTFLiawadjiawadjuNDTtTRTtTRT)(30)()()(30)()(AWFL(i)n1iAWMAX,MAXRTMAXAWFL where nAWFL is the num ber of axial weld fusion lines i n the beltline region of the vessel, i is a counter that ranges from 1 to nAWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT of the weld adjacent to the i th axial weld fusion li ne, )()(iawadjuNDTRT 32 is the unirradiated RT NDT of the plate adjacent to the i th axial weld fusion li ne, )()(ipladjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th axial weld fusion line, and
)(30iawadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion line. )(30ipladjTRTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in plates that are not associate d with welds. It is evaluated using the following formula for each plate wit hin the beltli ne region of the vessel. The value of RTMAX-PL assigned to the vessel is the hi ghest of the referenc e temperature values associ ated with any individual plate. In evaluating the T30 values in this form ula the composition properties reported in the RVID datab ase are used for copp er, nickel, and ph osphorus. An indepen dent estim ate of the manganese content of each weld and plate evaluated is also neede
- d. )()(30)()(n1iPLMAXMAXPLRTiPLMAXiPLiPLuNDTtTRT where nPL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to nPL, is the maximum fluence occurring over the vessel ID occupied by a particular plate,
)(iPLMAXt is the unirradiated RT NDT of a particular plate, and
)()(iPLuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to of a particular plate.
)(30iPLT)(iPLMAXtRTMAX-FO characterizes the resistance of the RPV to fracture initiating from flaws in forgings that are not associ ated with wel ds. It is evaluated using the following form ula for each forging with in the beltline region of the vessel.
The value of RTMAX-FO assigned to the vessel is the hi ghest of the referenc e temperature v alues associated with any individual plate. In evaluating the T30 values in this form ula the co mposition pr operties reported in t he RVID database ar e used for copper, nickel
, and phosphorus
. An independent estimate of the manganese content of each weld and plate evaluated is also needed.
)()(30)()(n1iFOMAXMAXFORTiFOMAXiFOiFOuNDTtTRT where nFO is the num ber 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,
)(iFOMAXt is the unirradiated RT NDT of a particular forging, and )()(iFOuNDTRT 33 is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to of a particular forging.
)(30iFOT)(iFOMAXtRTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along the circum ferential weld fusion li nes. It is evaluated using the following form ula for each circumferential weld fusion line within the beltline region of the vessel (the part of the form ula inside the {-}). Then the value of RTMAX-CW assigned to the vessel is the hi ghest of the referenc e temperature v alues associated with an y individual circum ferential weld fusion line. In evaluating the T30 values in this formula the com position properties reported in the R VID databa se are used for copper, nicke l, and phosphorus.
An independe nt estimate of the manganese content of each weld, plate, and forging evaluated is als o needed. FLifoadjifoadjuNDTFLipladjipladjuNDTFLicwadjicwadjuNDTtTRTtTRTtTRT)(30)()()(30)()()(30)()(CWFL(i)n1iCWMAX,,MAXRTMAXCWFL where nCWFL is the num ber of circum ferential weld fusion lines in t he beltline region of the vessel, i is a counter that ranges from 1 to nCWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular circum ferential weld fusion li ne, is the unirradiated RT NDT of the weld adjacent to the i th circumferential weld fusion line,
)()(icwadjuNDTRT is the unirradiated RT NDT of the plate adjacent to the i th circumferential weld fusion line (if there is no adjace nt plate this term is ignored),
)()(ipladjuNDTRT is the unirradiated RT NDT of the forging adjacent to the i th circumferential weld fusion line (if ther e is no adjacent forgi ng this term is ignored),
)()(ifoadjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th circumferential weld fusion li ne, )(30icwadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion line(if there is no adjacent plate this term is ignored), and
)(30ipladjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the forging adjacent to the i th axial weld fusion line(if ther e is no adjacent forging this term is ignored).
)(30ifoadjT 34 The T30 values in the preceding equations are deter mined as follows
- CRPMDT30 eRCStPMnTAMD471.2130.61001718.01 eeeRCStNiCugPCufTNiBCRP,,,1.543769.31100.1191.1 for welds 10x417.1platesfor 10x561.1forgingsfor 10x140.1777A for welds 0.155 vesselsedmanufactur CEin platesfor 2.135 vesselsedmanufactur CE-nonin platesfor 5.102 forgingsfor 3.102B 102595.01010103925.4for 103925.4103925.4for ttte Note: Flux () is estim ated by dividing fluence (t) by the tim e (in seconds) that the reacto r has been in o peration. 6287.012025.184483.01390.1logtanh2121,,10NiCuttNiCugeeee 008.0072.0for 0.008)-(359.1072.0 008.0072.0for 072.0 072.0for 0,0.66790.6679PandCuPCuPandCuCuCuPCufeee wt%072.0for wt%072.0for 0CuCuCuCue 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)(eCuMax Step 3. Estimate the 95th percentile TWCF value for each of the axial weld flaw, plate flaw, circumferential weld flaw, and forgin g flaw populatio ns using the RTs from Step 2 and the following form ulae. 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 contributi on of a particular axial weld, plate flaw, cir cumferential weld, or forging is zero if either of the following c onditions are me t: (a) if the result of the subtraction from which the natural logarithm is taken is negative, or (
b)if the beltli ne of the RP V being evaluated does not contain the product form in question.
542.40616ln5198.5exp95AWMAXAWRTTWCF 38.162300ln737.23exp95PLMAXPLRTTWCF 066.65616ln1363.9exp95CWMAXCWRTTWCF 38.162300ln737.23exp95FOMAXFORTTWCF FOMAXRT185.013710103.1 The factor = 0 if the forg ing is com pliant with Regulator y Guide 1.43; otherwise = 1. The factor is determ ined as follows:
If TWALL 91/2 -in, th en = 1. If 91/2 < TWALL < 111/2 -in, then = 1+ 8(TWALL - 91/2) If TWALL 111/2 -in, th en = 17. Step 4. Estimate the total 95th percentile TWCF for the vessel using the following form ulae (note that depending on the type of vessel in question certain ter ms in the following formula will be zero). TWCF 95-TOTAL must be less than or equal t o 1x10-6. FOFOCWCWPLPLAWAWTOTALTWCFTWCFTWCFTWCFTWCF9595959595 is determined as follows:
If RTMAX-xx 625R, then
= 2.5 If 625R <
RTMAX-xx < 875R then 6252505.15.2xxMAXRT If RTMAX-xx 875R, then
= 1 Table 3.3 and Table 3.4 provide the RT s and TWCF95 values esti mated by this procedure for every currentl y operating P WR. In Tabl e 3.4 TWCF95 values are r eported for all ring-forged vessels ba sed on both the assu mption that underclad cracking can occur and o n the assumption that underclad cracking cannot occur. No judgm ent regar ding the incidence (or not) of underclad cracking in an y operating rin g-forged PWR is made in pre senting these values.
However, the se calculations do dem onstrate that for the em brittlement levels currently expected through EOLE the contrib ution of underclad cracks to the total TWCF of ring-forged plants is estimated to be vanishingly small becau se, even at EOLE, the em brittlement levels expected of the ring for gings is low (at EOLE the hi ghest RTMAX-FO of any ring-forge d plant is 199 F). The graphs in Figure 3.
11 summarize the TWCF values provided in these tables for all currently operating PW Rs. Eight y-one percent of plate-welded PWRs (100 percent of ring-f orged PWRs) have esti mated TWCF 95 values that are 36 two orders of magnitude or more below the 1x10-6/ry regulator y limit (i.e., below 1x10
-8/ry), even after 60 y ears of operation. After 40 years of operation t he highest risk of PTS producing a through-wall crack in any plate-welded PWR is 2.0x10-7/ry (for ring-for ged PWRs this value is 1.5x10-10/ry). After 60 years of operation this risk increase s to 4.3x10
-7/ry (3.0x10-10/ry for ring-forged P WRs). Figur e 3.12 pr ovides a perspective on the relative contributi ons to the total TWCF made by the various com ponents (axial welds, circumferential welds, plates, and forgings) from which the beltline regions of the operating n uclear RPV fleet are constructed.
This figure com pares the histograms depicting the distributi ons of the var ious RT valu es characteristic of beltline m aterials in the current operating fleet (projected to EOLE) to the TWCF versus RT relationships used to define the proposed PTS screening lim its (see Figure 3.4 and Figure 3.9). These com parisons show that the level of em brittlement in m ost plants is so low, even when proj ected to EOLE, that the estimated TWCF resulting from PTS is very
, very small. 02468101214Below E-13E-13 to E-12E-12 to E-11E-11 to E-10E-10 to E-9E-9 to E-8E-8 to E-7E-7 to E-6Number of Currently Operating Power Reactors Plate Welded Plants at 48 EFPYRing Forged Plants at 48 EFPY02468101214Below E-13E-13 to E-12E-12 to E-11E-11 to E-10E-10 to E-9E-9 to E-8E-8 to E-7E-7 to E-6Number of Currently Operating Power Reactors Plate Welded Plants at 32 EFPYRing Forged Plants at 32 EFPYEstimated Yearly Through Wall Cracking Frequency All 2E-72E-7 to 4E-7 Figure 3.11.
Estimated distributio n of TWCF for curr ently operating P WRs 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 Sec tion 3.5.1 Values at 32 E FPY (EOL) Values at 48 E FPY (EOLE) RTMAX-AW [oF] RTMAX-PL [oF] RTMAX-CW [oF] 95th Percentile TWCF (/ry) RTMAX-AW [oF] Plant Name RTMAX-PL [oF] RTMAX-CW [oF] 95th Percentile TWCF (/ry) ARKANSAS N UCLEAR 1 121.0 84.0 184.6 3.7E-14 128.7 92.0 193.4 1.0E-13 ARKANSAS N UCLEAR 2 97.9 97.9 97.9 1.3E-13 112.3 112.3 112.3 4.7E-13 BEAVER VALL EY 1 183.3 214.8 214.8 1.3E-09 194.0 230.1 230.1 4.9E-09 BEAVER VALL EY 2 95.4 114.4 114.4 5.7E-13 103.4 126.6 126.6 1.6E-12 CALLAWAY 1 84.7 84.9 84.9 3.8E-14 92.6 92.8 92.8 8.1E-14 CALVERT CLIFFS 1 196.6 149.8 149.8 4.2E-09 213.5 168.1 168.1 2.7E-08 CALVERT CLIFFS 2 174.1 174.1 174.1 1.1E-10 192.4 192.4 192.4 2.5E-09 CATAWBA 2 82.9 82.9 82.9 3.1E-14 90.2 90.2 90.2 6.3E-14 COMANCHE P EAK 1 60.3 60.3 60.3 3.1E-15 69.3 69.3 69.3 8.0E-15 COMANCHE P EAK 2 44.3 44.3 44.3 5.1E-16 52.0 52.0 52.0 1.2E-15 COOK 1 159.1 161.1 204.8 2.4E-11 174.2 175.1 220.1 1.2E-10 COOK 2 160.2 174.1 174.1 6.0E-11 171.9 188.1 188.1 1.8E-10 CRYSTAL RIVER 3 135.4 122.5 193.0 1.2E-12 143.8 130.4 201.8 2.4E-12 DIABLO CANY ON 1 191.3 130.5 130.5 1.9E-09 207.6 144.1 144.1 1.5E-08 DIABLO CANY ON 2 181.4 191.5 191.5 5.1E-10 193.6 205.0 205.0 3.2E-09 FARLEY 1 134.8 164.7 164.7 3.1E-11 147.5 183.1 183.1 1.1E-10 FARLEY 2 153.5 184.4 184.4 1.2E-10 167.1 203.6 203.6 4.2E-10 FORT CALHOUN 204.1 131.1 169.9 1.0E-08 221.6 149.3 187.7 5.6E-08 INDIAN POIN T 2 199.3 208.4 208.4 6.5E-09 219.4 225.0 225.0 4.8E-08 INDIAN POIN T 3 236.8 236.8 236.8 1.7E-07 249.9 249.9 249.9 3.8E-07 MCGUIRE 1 166.0 119.9 119.9 2.6E-12 176.0 128.7 128.7 8.6E-11 MILLSTONE 2 128.1 132.2 132.2 2.5E-12 139.4 144.2 144.2 6.6E-12 MILLSTONE 3 116.1 116.1 116.1 6.6E-13 128.8 128.8 128.8 1.9E-12 OCONEE 1 164.5 77.0 182.8 6.9E-13 174.4 84.3 191.9 5.3E-11 PALISADES 217.2 181.6 207.7 3.8E-08 237.2 200.4 227.5 1.7E-07 PALO VERDE 1 90.6 90.6 90.6 1.1E-12 101.9 101.9 101.9 3.2E-12 PALO VERDE 2 60.6 60.6 60.6 5.4E-14 71.9 71.9 71.9 1.8E-13 PALO VERDE 3 50.6 50.6 50.6 1.8E-14 61.9 61.9 61.9 6.2E-14 POINT BEACH 1 172.5 117.5 222.4 3.4E-11 185.7 125.6 238.8 7.9E-10 ROBINSON 2 136.8 141.8 199.8 5.6E-12 146.4 152.3 213.8 1.4E-11 SALEM 1 212.8 218.2 218.2 2.7E-08 225.9 232.0 232.0 8.0E-08 38 Values at 32 E FPY (EOL) Values at 48 E FPY (EOLE) Plant Name RTMAX-AW [oF] RTMAX-PL [oF] 95th RTMAX-CW RTMAX-AW RTMAX-PL [oF] Percentile
[oF] [oF] TWCF (/ry) RTMAX-CW [oF] 95th Percentile TWCF (/ry) SALEM 2 171.2 153.0 153.0 3.1E-11 185.7 166.7 166.7 7.9E-10 SEABROOK 79.4 79.4 79.4 2.2E-14 88.2 88.2 88.2 5.2E-14 SHEARON HA RRIS 143.0 158.7 158.7 2.0E-11 150.8 169.8 169.8 4.4E-11 SONGS-2 133.8 133.8 133.8 2.9E-12 149.2 149.2 149.2 9.7E-12 SONGS-3 104.1 104.1 104.1 2.3E-13 118.5 118.5 118.5 8.1E-13 SOUTH TEXAS 1 42.4 47.6 47.6 7.5E-16 49.7 56.0 56.0 1.9E-15 SOUTH TEXAS 2 21.3 26.2 26.2 5.7E-17 28.3 34.4 34.4 1.6E-16 ST. LUCIE 1 158.2 143.4 143.4 6.2E-12 169.2 155.2 155.2 2.4E-11 ST. LUCIE 2 124.8 124.8 124.8 1.4E-12 136.0 136.0 136.0 3.4E-12 SUMMER 107.7 107.7 107.7 3.2E-13 119.4 119.4 119.4 8.7E-13 SURRY 1 239.2 138.7 198.7 2.0E-07 252.2 158.0 216.7 4.3E-07 SURRY 2 157.8 114.7 189.2 5.9E-13 169.8 133.3 207.2 1.4E-11 TMI-1 238.3 67.1 240.2 1.9E-07 247.7 74.3 249.4 3.3E-07 VOGTLE 1 72.5 72.5 72.5 1.1E-14 79.9 79.9 79.9 2.3E-14 VOGTLE 2 97.7 97.7 97.7 1.3E-13 108.4 108.4 108.4 3.4E-13 WATERFORD 3 73.6 73.6 73.6 1.2E-14 85.2 85.2 85.2 3.9E-14 WOLF CREEK 72.7 72.7 72.7 1.1E-14 80.0 80.0 80.0 2.4E-14 At 32 EFPY the fluence is the value re ported in (RVID2) at EOL for the vessel ID.
The 48 EFPY fluenc e is estimated as 1.5 time s the 32 EF PY value. Chemistry values are from (RVID2), exc ept that mang anese of 0.70 an d 1.35 weight percent were used, respective ly, for forgings and for welds/plates. These defaults represent the appr oximate averages of the data use d to establish the uncertainty distributions for F AVOR 06.1 (s ee Appendix A). 39 Table 3.4. RT and TWCF Values for Ring-Forged Plants Estimated Using the Procedure De scribed in Section 3.5.1 32 EFPY (EOL) 48 EFPY (EOLE) 95th Percentile TWCF
(/ry) 95th Percentile TWCF
(/ry) RTMAX-FO [oF] RTMAX-CW [oF] Plant Name without Underclad Cracking RTMAX-FO [oF] RTMAX-CW [oF] with Underclad Cracking without Underclad Cracking with Underclad Cracking BRAIDWOOD 1 28.4 85.1 7.5E-17 7.5E-17 32.5 95.3 1.2E-16 1.2E-16 BRAIDWOOD 2 43.5 74.7 4.6E-16 4.6E-16 46.5 82.6 6.6E-16 6.6E-16 BYRON 1 70.7 70.7 9.2E-15 9.2E-15 77.5 77.5 1.8E-14 1.8E-14 BYRON 2 28.7 68.1 7.8E-17 7.8E-17 33.0 81.3 1.3E-16 1.3E-16 CATAWBA 1 41.1 41.1 3.5E-16 3.5E-16 46.2 46.2 6.4E-16 6.4E-16 DAVIS-BESSE 70.6 184.5 1.1E-14 1.1E-14 75.3 193.3 4.2E-14 4.2E-14 GINNA 187.2 196.6 1.4E-10 1.4E-10 195.4 209.8 2.5E-10 2.5E-10 KEWAUNEE 120.3 237.5 3.3E-11 3.3E-11 133.8 258.3 2.4E-10 2.4E-10 MCGUIRE 2 96.6 96.6 1.1E-13 1.1E-13 103.0 103.0 2.1E-13 2.1E-13 NORTH ANNA 1 159.1 159.1 2.0E-11 2.0E-11 168.4 168.4 4.0E-11 4.0E-11 NORTH ANNA 2 164.2 164.2 3.0E-11 3.0E-11 173.4 173.4 5.7E-11 5.7E-11 OCONEE 2 75.6 242.0 5.2E-11 5.2E-11 81.5 251.2 1.3E-10 1.3E-10 OCONEE 3 84.6 186.8 4.2E-14 4.2E-14 91.4 196.0 1.2E-13 1.2E-13 POINT BEACH 2 112.4 219.5 3.9E-12 3.9E-12 123.1 234.9 2.5E-11 2.5E-11 PRAIRIE ISLAND 1 85.1 125.4 3.9E-14 3.9E-14 101.1 148.4 1.7E-13 1.7E-13 PRAIRIE ISLAND 2 91.3 109.6 7.0E-14 7.0E-14 107.6 129.6 3.1E-13 3.1E-13 SEQUOYAH 1 187.3 187.3 1.5E-10 1.5E-10 198.6 198.6 3.0E-10 3.0E-10 SEQUOYAH 2 107.0 107.0 3.0E-13 3.0E-13 115.9 115.9 6.5E-13 6.5E-13 TURKEY POINT 3 102.2 215.8 2.2E-12 2.2E-12 108.9 230.1 1.4E-11 1.4E-11 TURKEY POINT 4 92.9 215.8 2.0E-12 2.0E-12 99.7 230.1 1.4E-11 1.4E-11 WATTS BAR 1 172.2 172.2 5.2E-11 5.2E-11 181.4 181.4 9.8E-11 9.8E-11 At 32 EFPY the fluence is the value re ported in (RVID2) at EOL for the vessel ID.
The 48 EFPY fluenc e is estimated as 1.5 time s the 32 EF PY value. Chemistry values are from (RVID2), exc ept that mang anese of 0.70 an d 1.35 weight percent were used, respective ly, for forgings and for welds/plates. These defaults represent the appr oximate averages of the data use d to establish the uncertainty distributions for F AVOR 06.1 (s ee Appendix A). 40 02 468 10475-500525-550 575-600625-650675-700Max. RTCW [R]# of RingForged PWRs 02 468 10475-500525-550 575-600625-650675-700Max. RTFO [R]# of RingForged PWRs1.E-231.E-21 1.E-19 1.E-17 1.E-151.E-131.E-111.E-09 1.E-07 1.E-05 1.E-03450550650750850Max RTAW [R]95th %ile TWCF - Axial Weld FlawsBeaverOconeePalisadesFit1.E-231.E-21 1.E-19 1.E-17 1.E-151.E-131.E-111.E-09 1.E-07 1.E-05 1.E-03450550650750850Max RTPL or RTFO [R]95th %ile TWCF - Plate FlawsBeaverOconeePalisadesFit02468 10# of PlateWelded PWRs 0
246810# of PlateWelded PWRs 0246810# of PlateWelded PWRs1.E-231.E-21 1.E-19 1.E-17 1.E-151.E-131.E-111.E-09 1.E-07 1.E-05 1.E-03450550650750850Max RTCW [R]95th %ile TWCF - Circ Weld FlawsBeaverOconeePalisadesFitHistograms depict current estimates of RTvalues at EOLE(48 EFPY)1.E-231.E-21 1.E-191.E-171.E-151.E-131.E-111.E-091.E-071.E-051.E-03450550650750850Max RTFO [R]95th %ile TWCF for Underclad FlawsFAVORResultsBound02 468 10# of RingForged PWRs 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 PTS screening limits (see 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 characte rization pa rameters, which include the following:
RTNDT(u) [ F] The unirradiated value of RT NDT. Needed for e ach 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 perce nt] Nickel co ntent. Needed for each weld, plate, and forging in the beltline region of the RPV.
P [weight percent]
Phosphor us content. N eeded for each weld, plate, and forging in the beltline region of the RPV.
Mn [weight perce nt] Manganese content. Needed for eac h weld, plate, and forging in the beltline region of the RPV.
t [seconds] The amount of ti me the RPV has been in o peration.
TRCS [ F] The average tem perature of the RCS inventor y in the beltline region under normal operating conditions. tMAX [n/cm2] The maximum fluence on the vessel I D for each plate and forging in the beltline region of the RPV. tFL [n/cm2/sec.] The maximum fluence occurring along each axial w eld and circumferential weld fusion line. Th is value is neede d for each axial weld and circum ferential weld fusion line in the beltli ne region of t he 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 foll owing formulae and the values of the characteri zation para meters fro m Step 1: RTMAX-AW characterizes the resistance of the RPV to fracture initiating from flaws found along the axi al weld fusion lines. It is evaluated using the foll owing form ula for each axial weld fusion line within the beltline region of the vessel (the part of the for mula inside the {-}). The value of RT MAX-AW assigned to the vessel is the highest of the referenc e temperature values as sociated with any individual axial weld fusion line. In evaluating the T30 values in t his formula the com position properties reported in the R VID database are used for copper, ni ckel, and pho sphorus.
An independent e stimate of the manganese content of each weld and plate evaluated is also neede
- d. FLipladjipladjuNDTFLiawadjiawadjuNDTtTRTtTRT)(30)()()(30)()(AWFL(i)n1iAWMAX,MAXRTMAXAWFL where nAWFL is the num ber of axial weld fusion lines i n the beltline region of the vessel, i is a counter that ranges from 1 to nAWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT of the weld adjacent to the i th axial weld fusion li ne, )()(iawadjuNDTRT 42 is the unirradiated RT NDT of the plate adjacent to the i th axial weld fusion li ne, )()(ipladjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th axial weld fusion line, and
)(30iawadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion line. )(30ipladjTRTMAX-PL characterizes the resistance of the RPV to fracture initiating from flaws in plates that are not associate d with welds. It is evaluated using the following formula for each plate wit hin the beltli ne region of the vessel. The value of RTMAX-PL assigned to the vessel is the hi ghest of the referenc e temperature values associ ated with any individual plate. In evaluating the T30 values in this form ula the composition properties reported in the RVID datab ase are used for copp er, nickel, and ph osphorus. An indepen dent estim ate of the manganese content of each weld and plate evaluated is also neede
- d. )()(30)()(n1iPLMAXMAXPLRTiPLMAXiPLiPLuNDTtTRT where nPL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to nPL, is the maximum fluence occurring over the vessel ID occupied by a particular plate,
)(iPLMAXt is the unirradiated RT NDT of a particular plate, and
)()(iPLuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to of a particular plate.
)(30iPLT)(iPLMAXtRTMAX-FO characterizes the resistance of the RPV to fracture initiating from flaws in forgings that are not associ ated with wel ds. It is evaluated using the following form ula for each forging with in the beltline region of the vessel.
The value of RTMAX-FO assigned to the vessel is the hi ghest of the referenc e temperature v alues associated with any individual plate. In evaluating the T30 values in this form ula the co mposition pr operties reported in t he RVID database ar e used for copper, nickel
, and phosphorus
. An independent estimate of the manganese content of each weld and plate evaluated is also needed.
)()(30)()(n1iFOMAXMAXFORTiFOMAXiFOiFOuNDTtTRT where nFO is the num ber 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,
)(iFOMAXt is the unirradiated RT NDT of a particular forging, and )()(iFOuNDTRT 43 is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to of a particular forging.
)(30iFOT)(iFOMAXtRTMAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along the circum ferential weld fusion li nes. It is evaluated using the following form ula for each circumferential weld fusion line within the beltline region of the vessel (the part of the form ula inside the {-}). Then the value of RTMAX-CW assigned to the vessel is the hi ghest of the referenc e temperature v alues associated with an y individual circum ferential weld fusion line. In evaluating the T30 values in this formula the com position properties reported in the R VID databa se are used for copper, nicke l, and phosphorus.
An independe nt estimate of the manganese content of each weld, plate, and forging evaluated is als o needed. FLifoadjifoadjuNDTFLipladjipladjuNDTFLicwadjicwadjuNDTtTRTtTRTtTRT)(30)()()(30)()()(30)()(CWFL(i)n1iCWMAX,,MAXRTMAXCWFL where nCWFL is the num ber of circum ferential weld fusion lines in t he beltline region of the vessel, i is a counter that ranges from 1 to nCWFL, tFL is the maximum fluence occurring on t he vessel ID along a particular circum ferential weld fusion li ne, is the unirradiated RT NDT of the weld adjacent to the i th circumferential weld fusion line,
)()(icwadjuNDTRT is the unirradiated RT NDT of the plate adjacent to the i th circumferential weld fusion line (if there is no adjace nt plate this term is ignored),
)()(ipladjuNDTRT is the unirradiated RT NDT of the forging adjacent to the i th circumferential weld fusion line (if ther e is no adjacent forgi ng this term is ignored),
)()(ifoadjuNDTRT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the weld adjacent to the i th circumferential weld fusion li ne, )(30icwadjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the plate adjacent to the i th axial weld fusion line(if there is no adjacent plate this term is ignored), and
)(30ipladjT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) produced by irradiation to tFL of the forging adjacent to the i th axial weld fusion line(if ther e is no adjacent forging this term is ignored).
)(30ifoadjT 44 The T30 values in the preceding equations are deter mined as follows
§: CRPMDT30 eRCStPMnTAMD471.2130.61001718.01 eeeRCStNiCugPCufTNiBCRP,,,1.543769.31100.1191.1 for welds 10x417.1platesfor 10x561.1forgingsfor 10x140.1777A for welds 0.155 vesselsedmanufactur CEin platesfor 2.135 vesselsedmanufactur CE-nonin platesfor 5.102 forgingsfor 3.102B 102595.01010103925.4for 103925.4103925.4for ttte Note: Flux () is estim ated by dividing fluence (t) by the tim e (in seconds) that the reacto r has been in o peration. 6287.012025.184483.01390.1logtanh2121,,10NiCuttNiCugeeee 008.0072.0for 0.008)-(359.1072.0 008.0072.0for 072.0 072.0for 0,0.66790.6679PandCuPCuPandCuCuCuPCufeee wt%072.0for wt%072.0for 0CuCuCuCue 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)(eCuMax Step 3. Compare the RTs from Step 2 to the limits in Table 3.5. The lim its on RT MAX-CW given in this table correspond to a T WCF95 limit of 1x10
-8/ry, not 1x10-6/ry. This m ore restrictive limit was imposed to enable a si mple two-dimensional representati on 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 46multidimensional relationship between the various RT values and TWCF 95 illustrated inFigure 3.
5 while not un duly diminishing the resulti ng 1x10-6/ry limits placed on RTMAX-AW and RTMAX-PL. Adoption of this l ower limit for the TWCF produced by circumferential welds is not expected to have any practical i mpact because the hi ghest projected values RT MAX-CW at EOLE are 250 F and 258 F for plate-welded and ring-forged plants (respectively
), both of whic h are well bel ow the lim its on RTMAX-CW that appear in Table 3.5. S hould changes in operations or other unfores een changes that develop in the future increase a value of RTMAX-CW above the Table 3.5 lim its, the licensee could alway s assess its plant using the approach that place s a limit on TWCF described in Section 3.5.1.
Table 3.5. RT Limits for PWRs Limit on RT v alue for different v alues of T WALL [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 belo w) 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 RT MAX-CW corresponds to a TWCF value of 10
-8/ry. Should these limits on RTMAX-CW be exceeded, the RT MAX-AW, RTMAX-PL, RTMAX-FO, and RTMAX CW values shoul d be used, along with Eq. 3-6, to estimate the total TWCF value.
This total TWCF sh ould be limited to 1x10
-6. Figure 3.1 3 and Figure 3.14 provide a graphical comparison of (1) the RT li mits expressed in Table 3.5, (2) the RT lim its derived from Eqs. 3-6 and 3-8, and (
- 3) the RT values for operating PW Rs 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 lim its at EOLE (these num bers increas e to 94 percent for plate-welded plants and 10 0 percent for ring-f orged plants at EOL). At EOLE, 17 F separates the most embrittled plate-weld ed plant from these screening li mits (this num ber increas es to 30 F at EOL). For ring-forged plants at EOL E, 47 F separates the m ost embrittled plant from the most restricti ve screening li mit (the number increases to 59 F at EOL).
Plate Welded Plants at 48 EFPY (EOLE)050100150200250300350400050100150200250300RTMAX-AW [oF]RTMAX-PL [oF]1x10-6/ry TWCF limitSimplified ImplementationRTMAX-AW269F, andRTMAX-PL356F, andRTMAX-AW+ RTMAX-PL538F.Palo Verde 1, 2, and 3at 48 EFPY (EOLE)050100150200250300350400050100150200250300RTMAX-AW [oF]RTMAX-PL [oF]1x10-6/ry TWCF limitSimplified ImplementationRTMAX-AW222F, andRTMAX-PL293F, andRTMAX-AW+ RTMAX-PL445F. Figure 3.13. Graphical comparison of the RT limits fo r 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 bo ttom graph is for vessels having wall thicknesses between 10.5 and 11.5 in. Ring Forged Plants at 48 EFPY (EOLE)050100150200250300350400050100150200250300RTMAX-CW [oF]RTMAX-FO [oF]TWCF = 1x10-6/rylimit if not in compliance with Reg. Guide 1.43TWCF = 1x10
-8/ry limitTWCF = 1x10-6/rylimit if in compliance with Reg. Guide 1.43 Figure 3.14. Graphical comparison of the RT limits for ring-forge d 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 lim its proposed in Section 3.
5 differ from the current 10 CFR 50.61 R TPTS screening li mits by the absence of a "
margin term." Use of a margin term is appropriate to account (at least approximately
) for fact ors that occur in appli cation that were not considered in the analy ses upon which t hese proposed screening lim its 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 (EricksonKir k-PFM), the NRC model explicitl y considers uncertainty in all of these variables and represents these uncert ainties as bei ng larger (a conservati ve representat ion) than would be characteristic of any plant-specific as sessment application.
Consequentl y, use of the 10 CFR 50.61 m argin term with the screening limits proposed in this rep ort would be inappropriate.
The following additional reasons suggest that use of any margin term with the proposed screening li mits is inappropriate:
47 (1) The TWCF values used to establish the screening li mits 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 fro m the three plant-specific analyses apply to PWRs in general.
It is correct that certain asp ects of the models used to establish the proposed PTS lim its cannot be considered as "best e stimates." On balance, there is a conservative bias to these non-best-estimate aspects of the analy sis, as discussed in the following section.
Throughout this project, every effort has been made to perfor m a "best estimate" analysis. Nonetheless, comparison of the analy tical models used to asses s risk with the actual situation being asses sed reveals that cert ain features of that situation h ave not been represented a s realistic ally as possible. These parts of the model m ay be judged as pro viding either a conservative representation (i.e.,
tending to increase the esti mated TWCF) or a nonconservat ive representation (i.e., tending to decrease the estimated TWCF) relative to the actual situation in service. Table 3.6 summarizes these conserva tisms and nonconservat isms, which are discussed i n greater detail in Section 3.
6.1 and Sectio n 3.6.2, respectively
. This discussion does not include factors that the models do not accurately represent whe n these inacc uracies have been demonstrated to not significantly influence the TWCF results. This infor mation dem onstrates that, on
- balance, more conservatisms than nonconservat isms remain in the m odel, suggesting the appropria teness of apply ing the proposed screening lim its without an additional margin term
. 3.6.1 Residual Conservatisms In the reactor vessel failure frequency limit- The reactor vessel f ailure frequency limit of 1x10-6 events/reactor y ear was e stablished based on the assumption that through-wall cracking of the RPV will produce a large early release i n all circumstances. As discussed in Chapte r 10 of NUREG-1806 through-wall cracking of the RPV is likely to lead to core da mage, but large early release is unlikely for two reasons: (1) because of re actor safety systems and the multiple barri ers that block radioactive release to the environm ent (e.g., containment), and (2) because if a through wall crack were to develop it w ould happen when the temperature and pressure in the prim ary circuit are low, both of w hich produce a low sy stem energy. Current guidelines on core dam age frequency provided by Regulatory Guide 1.1 74 and the Option 3 fra mework for risk-inform ing 10 CFR Part 50 suggest a reactor vess el failure frequency limit of 1x10
-5 events/reacto r year (RG1.174). Changing from a 1x10-6 to a 1x10-5 limit would increase all of the proposed RT lim its 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 partic ular scenario in, the scenario w as intentionally binned in a conservative manner. Thus, the loading severity has a tendency toward being overest imated. In the PRA model- External initi ating events
. As detailed in Section 9.4 of NUREG-1806 and in (Kolaczkowski-Ext)
, the NRC's analysis has not considered the potent ial for a PTS transient to be started by an initiating event external to th e plant (e.g., f ire, earthquake).
The bounding analy ses performed demonstrate t hat this would increase the TWCF values reported herein b y at most a factor of 2.
However, the bou nding nature of the NRC' s external events analy sis suggests strongl y that the actual effect of ignoring the contribution of external initiating eve nts is much smaller than 2 times. The temperature of water held in the safety injection accum ulators was assumed to be 60 F (15.6 C). These ac cumulators ar e 48 inside containment and so exist at temperatures of 80-90 F (26.7-32.2 C) in the winter and above 1 10 F (43.3 C) in the summe
- r. This conservative esti mate of injection w ater temperature increase s the magnitude of the thermal st resses that occur during of pipe breaks and reduces the fracture resi stance of the vessel ste el. When a main stea mline breaks inside of containment, the releas e of stea m from the break pressurizes the conta inment structure to approximately 50 pounds per square inch (psi) (335 kilopascals (kPa). Consequently, the minimum temperature for MSLBs is bounded by t he boiling poi nt of water at approximately 50 psi (335 kPa), or approximately 260 F (126.7 C). However, the NRC's secondar y-side breaks do not account for pressurization of containm ent, so the minimum temperature calculat ed by RELAP for these transient s is 212 F (100 C), or appro ximately 50 F (28 C) too cold. This conservative est imate of the minimum temperature a ssociated with an MSLB increa ses the magnitude of the thermal stresses and reduce s the fracture resistanc e of the vessel ste el. In the fracture model- Once a circumferential crack initiates, it is assumed to instantly propagate 360 around the vessel wa ll. However, full circumferential propagatio n is high ly unlikely because of the azim uthal variati on in fluence, which causes al ternating regions of more embrittled and less em brittled material to exist circu mferentiall y around the vessel wa ll. Thus, the NRC model tends to overestima te the extent of cracking initiated from circu mferentially oriented defects because it ignores this natural crack arrest mechan ism. Once an axial flaw initiates, it is assu med to instantly become infinitely long. In reality, it only propagates to the length of an axi al shell course (approxim ately 8 to 12 feet (approxim ately 2.4 to 3.7 meters)), a t which point, it en counters tough er material a nd arrests. Even though a shell course is very long, flaws of finite length tend to arrest more readily than do flaws of infini te length because of sy stematic diffe rences in the through-wall variation of c rack-driving force. Becau se of this approxim ation, the NRC model tends to overe stimate the likelihoo d of through-wall cracking. As detailed in Section 4.2.
3.1.3 of (EricksonKir k-PFM) and in (English 02), the adopted F AVOR model of how flue nce attenuates through the RPV wall is conservative relative to experi mental data As detailed in Section 4.2.
2.2 of (EricksonKir k-SS) and in Appendix E to (EricksonKirk-PFM),
the statistical distributio ns of copper, nic kel, phosp horus, and RTNDT sampled by FAVOR overestimate the degree of uncertainty in these variable s relative to what can actu ally exist in any particular weld
, plate, or forging. While the FAVOR model corrects (on average) for the sy stematic conservative bias in RTNDT, the model overe stimates the uncertainty associated with the fracture toughness transition tem perature metric. In the flaw model- In the experi mental data u pon which t he flaw distribution is based, all detected defects w ere modeled as being crack-like and, therefore, potentiall y deleterious to the fracture integrity of the vessel. However
, many of these defects a re actually volumetric rather than planar, making them either benign or, at a m inimum, much less of a challenge to the fracture integrity of the vessel. Thus, the NRC model overesti mates the seriousness of the defect population in RPV materials, which leads to overly pessimistic assessments of the fracture resistanc e of the vessel.
49 50 FAVOR inco rporates an interdependence between initiation and arrest fracture toughness values prem ised on phy sical arguments (see Sections 5.3
.1.1 and 5.3.1.2 of (EricksonKirk-PFM)
). While the staff believes these m odels are appropriate, this view is not universally held (see review er comment 40D in Appendi x B of NUREG-1806). The alternative model, with no interdependence between i nitiation and arrest fra cture toughness values, would reduce the est imated values of TWCF. As detailed in Section 9.2.
2.1 of NUREG-1806, the NRC has sim ulated levels of irradiation da mage beyond those occurring over currently anticipated lifeti mes 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 prov ided in Regulatory Guide 1.1 74, which was used to establish the 1x10
-6/ry TWCF li mit, assumes source ter ms that do not re flect scenarios where fuel co oling has been lost, exposing the fuel rods to air (rather than stea m). Should such a situation arise, so me portion of the reactor fuel would eventually be oxidized in a n air environ ment, which would result in relea se fractions f or key fission products (rut henium being of prim ary concern) that may be significantly (e.g., a factor of 20) larger than those as sociated with fuel oxi dation in steam environments. These larger r elease fractio ns could lead to larger num bers of prom pt fatalities than predicted for non-PTS risk-significant scenarios. N onetheless, the accident progression event tree (APET) developed in Chapter 10 of NUREG-1806 dem onstrates that the num ber of scenario s in which air oxidation is possible is extrem ely small, certainly far smaller than the num ber of scenarios in which only core damage (not LERF) is the onl y plausible outcome. Thus, the nonco nservatism introduced b y not explicitl y considering the potential for air oxidation is more than com pensated fo r by the conservatis m of establis hing a TWCF limit based on LERF when m any accident sequences c an only plausibly result in c ore damage. In the PRA model- External initi ating events
. As detailed in Section 9.4 of NUREG-1806 and in (Kolaczkowski-Ext)
, the NRC's analysis has not considered the potent ial for a PTS transient to be started by an initiating event external to th e plant (e.g., f ire, earthquake).
The bounding analy ses performed demonstrate t hat this would increase the TWCF values reported herein b y at most a factor of 2.
However, the bou nding nature of the NRC' s external events analy sis suggests strongl y that the actual effect of ignoring the contribution of external initiating eve nts is much smaller than 2 times.
In the fracture model- Through-wall chem istry layering. As detailed in (EricksonKi rk-PFM), FAVOR models the existe nce of a gradient of properties through the thickness of the RPV because of through-w all changes in copper content. These copper content changes arise from the fact that, given the large volum e of weld metal needed to fill an RPV weld, manufacturers used weld wire from multiple weld wire sp ools (having different am ounts of cop per coating) to completely fill the groove.
The model adopted in F AVOR resamples the mean copper content of the weld at the 1/4T, 1/2T, and 3/4T locations through t he thickness.
This resam pling increases t he probability of crack arre st because it allo ws the si mulation of less irradiation-sensitive material s, which could arrest the runni ng crack before it fails the vessel. If these weld la yers did not occur in a real vess el, the TWCF would increase relative to those reported herein by a small factor (approximately 2.5 based on the limited sensit ivity studies performed).
Table 3.6.
Non-Best-Estimate Aspects of the Models Used to Devel op the RT-B ased Screening Limits for PTS Situation Potential Conservatism in the An alytical Model The model ass umes that all fa ilures produce a large early release; however, in the accident progression event tree (APET) (Ch. 10, NUREG-1806), most seque nces lead only to core damage. An initiated axial crack is ass umed to insta ntly propagate to infinite length. In realit y, the crack len gth will be finite and limited to the le ngth of a sin gle shell course because the crac ks will most lik ely arrest when they encounter higher toughness materials i n either the ad jacent circumfere ntial welds or plates. If the vessel fails, what happens next? An initiated circumferenti al crack is assumed to instantl y propagate 360o around the ves sel ID. In reality, t he crack le ngth is limite d because the azimuthal fluence variati on places strips of tough er materia l in the pat h of the extending crack.
How the many possible PTS initiators are binned, and how TH transients are selected to represent eac h bin to the PFM analysis When uncertainty of how to bin existed, consistently conservative decisions were made. The minimum temper ature of an MSLB inside containment is model ed as approximately 50 oF (28 C) colder than it ca n actually be because containment pressurizes as a result of the steam esca ping from the break.
Characterizati on of secon dary-side failures Stuck-ope n valves on the sec ondary side are conserv atively modeled in Palisades. Through-wall attenuatio n of neutron damage Attenuatio n is assumed to be more sign ificant than meas ured in experiments. Model of material u nirradiated toughness and chemical composition variability The statistical distrib utions sampled produce more uncerta inty than could ever occur i n a specific weld, plate, or forgi ng. Correction for s ystematic c onservative bias in RTNDT Model corrects for mean bias, but overrepr esents uncerta inty in RTNDT. All defects fou nd were assumed to be p lanar. Flaw model Systematically conservative judgments were made when developing the flaw distribution model. Interdependency of between initiation toughness and arrest tough ness Model employed allows all initiated flaws a chance to pro pagate into the vessel. Most conservat ive approach taken (i ncreasing time vs. incre asing unirradiated RTNDT). Extrapolation of irradiati on damage Situation Potential Nonconservatism in the An alytical Model If the vessel fails, what happens next? The potential f or air oxidation has been ignored. External PTS initiators The potential f or external events (e.g., fire s, earthquakes) initiati ng PTS transients has not been modeled explicitly. A conservativ e bounding analysis estim ates the effect of external events to be at most a factor of 2 increase i n TWCF, but the likel y increas e is expected to be much less than 2 times.
Through-wall chemistry layering Model assumes that the mean leve l of copp er can cha nge 4 times throug h the vessel wall thickness. If copper la yering is not present, the TWCF would increase. 51 3.7 Summary This report presents the res ults of FAVOR 06.1 calculations, co mpares them to the FAV OR 04.1 results presen ted in NUREG-1806, and uses the new results to propose two options f or implementing these findings in a revision of the PTS Rule (10 CFR 50.61).
Changes made in FAVOR 06.1 have placed a greater dens ity in the upper tail s of the TWCF distributio ns, resulting in the agency' s adoption of the 95th percentile of the TWCF distribution for use in the analy ses that produced the reco mmended implementation o ptions. Nevertheles s, as was reported prev iously in NUREG-1806, t he NRC again finds that only the most severe tra nsient classes (i.e.,
medium- to large-dia meter primary-side pipe breaks, valves on the primary side that stick open an d may suddenly reclose later) contribute significantly to the TWCF. The minor plant-t o-plant variat ion of the thermal hydraulic characteristi cs of such transients cannot signifi cantly alter the stresses bor ne by the vessel wall, and thus cannot significantl y alter the TWCF. Thus, the results pres ented herein can be regarded as being generally applicable to all PWRs currently operati ng in the United States
. Also, the current results reinforce the findin g from NUREG-1806 that it is the material properties a ssociated with axially oriented flaws that dom inate PTS risk.
Thus, the embrittlement properties of axial welds and plates in plate-welded vess els and of forgings in ring-forged vessels are the most important indicators of PTS risk. Conversely
, the much lower probabi lity that cracks initiated from circumferentially oriented flaws will propagate through wall makes the embrittlement properties of circumferential welds much less i mportant contributors t o the total PT S risk. The two recommended implem entation options include either (1) lim iting the TWCF est imated for an operati ng plant to a total value no greater than 1x10-6/ry or (2) l imiting RT values of the various m aterials in the RPV beltline so that their total TWCF is not per mitted to exceed 1x10-6/ry. These options are co mpletely equivalent and interchangeable because they are both based on the sa me formula, provide d herein, that estimates the to tal TWCF from the RT values for the material s in the RPV beltline-RT values that can be determ ined from information in the NRC's RVID database, and surveillance program information (to develop an estimate for manganese content). Table 3.7 provides the r ecommended RT lim its (i.e.,
implementation o ption 2. Assuming that current operating pra ctices are maintained, the status of currently operating PWRs relative to these li mits is as follows:
For plate-wel ded PWRs- The risk of PTS failure of the RPV is very low. Over 80 percent of op erating PWRs have estim ated TWCF valu es below 1x1 0-8/ry at EOLE.
At EOL the highest risk of PTS at any P WR is 2.0x10-7/ry. At EOLE this risk increas es to 4.3x10-7/ry. Eighty-five percent of all plants are 50 F or more away from the proposed RT scre ening limits at EOLE (this num ber increas es to 94 percent at EO L). At EOLE, 17 F separat es the most embrittled plant from these screening li mits (this num ber increases to 30 F at EOL).
For ring-for ged PWRs- The risk of PTS failure of the RPV is very low. All oper ating PWRs h ave estimated TWCF values below 1x1 0-8/ry at EOLE.
At EOL the highest risk of PTS at any P WR is 1.5x10-10/ry. At EOLE this risk increases to 3.0x10-10/ry. Ninety percent of all plant s are 50 F or more away from the most restrictive of the proposed RT screening li mits at EOLE (this number increases to 100 percent at EOL).
At EOLE 47 F separat es the most embrittled plant from these screening li mits (this num ber increases to 59 F at EOL).
52 Table 3.7. RT Limits for PWRs Limit on RT v alue for different v alues of T WALL [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 belo w) 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 RT MAX-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 sh ould be limited to 1x10
-6. 53 54 Chapter 4
- References 4.1 PTS Technical B asis Citations The following three sections provi de the citations that, together wit h this report, comprise the technical basi s for risk-infor med revision of the PTS R ule. When these reports ar e cited in the text, the citations appear in italicized boldface to distinguish the m from the related literature citat ions. 4.1.1 Summary EricksonKirk
-Sum EricksonKirk, M.T., et al.,
"Technical B asis for Revis ion of the Pressurized T hermal Shock (PTS) Screening Lim its in the PTS Rule (10 CFR 50.
61): Summary Report," NUREG-1806, U
.S. Nuclear Regulatory Commission.
4.1.2 Probabilis
tic Risk Assessmen t Kolaczkowski-Oco Kolaczkowsk i, A.M., et al., "Oconee Pre ssurized Ther mal Shock (PTS) Probabilistic Risk Assessment (PRA)," Septem ber 28, 2004, available in the NRC' s Agencywide Docu ments Access and Management System (ADAMS) under Accession #ML0428 80452. Kolaczkowski-Ext Kolaczkowsk i, A. et al., "Esti mate of Ex ternal Events Contribution to Pressurized Thermal Shock (PTS) Risk," Letter Report, October 1, 2004, available in ADAM S under Accession #ML042880476.
Siu 99 Siu, N., "Uncertainty A nalysis and Pressurized Therm al Shock: An Opinion," U.S. Nuclear Reg ulatory Commission, 1999, available in ADAMS under Accession
- ML992710066.
Whitehead-PRA Whitehead, D.L. and A.M.
Kolaczkowsk i, "PRA Procedures and Uncertainty for PTS Anal ysis," NUREG/CR-6859, U.
S. Nuclear Regulatory Commission, December 31, 200
- 4. Whitehead-BV Whitehead, D.L., et al., "Beaver Vall ey Pressurized T hermal Shock (PTS) Probabilistic Risk Assessmen t (PRA),"September 28, 2004, available in ADAMS under Accession
- ML042880454.
Whitehead-Gen Whitehead, D.W., et al., "Generalization of Plant-Specific Pressurized T hermal Shock (PTS) Risk Results to Additional Plants," Octo ber 14, 2004, available in ADAMS under Accession
- ML042880482. Whitehead-Pal Whitehead, D.L., et al., "Palisades Pre ssurized Ther mal Shock (PTS)
Probabilistic Risk Assessment (PRA),
" October 6, 2004, availabl e 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 Ther mal-Hydraulic Analy sis to Support P TS Evaluations for the Oconee-1, Beaver V alley-1, and Palisades Nuclear Power 55 Plants," NUREG/CR-6858, U.S. Nuclear Regulator y Commission, September 30, 200
- 4. Arcieri-SS Arcieri, W.C.
, et al., "RELAP5
/MOD3.2.2 Gamma Results for Palisades 1D Downcomer Sensitivit y 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. P our-Gol, "Therm al-Hydraulic Uncertainty Analysis in Press urized Ther mal Shock Risk Assessment: Methodolo gy and Implementation o n 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/M OD3.2.2 Assessment for Pressurize d Thermal Shock Applications," NUREG/CR
-6857, U.S. Nuclear Regulatory Commission, Septem ber 30, 200
- 4. Junge "PTS Consistency Effort," Staff Le tter Report to file, October 1, 2004, available in ADAM S 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, 200
- 4. Reyes-Scale Reyes, J.N., et al., "Scaling Analy sis for the OSU AP EX-CE Integral Test Facility
," NUREG/CR-6731, U.S.
Nuclear Regulatory Commission, Novem ber 30, 200
- 4. 4.1.4 Probabilis tic Fracture Mecha nics Dickson-Bas e Dickson, T.L., and S. Yin, "Electronic A rchival of the Results of Pressurized T hermal Shock Analy ses for Beaver Valley, Oconee, and Palisades Reactor Pres sure Vessels Generated with the 04.1 Version of FAVOR,
" ORNL/NRC/LT R-04/18, October 15, 2004, available in ADAMS under Accession
- ML042960391 Dickson-UG Dickson, T.L., and P.T. William s, "Fracture Analy sis of Vessel s Oak Ridge, FAVOR v04.1, Com puter Code:
User's Guide," NUREG/
CR-6855, U.S. Nuclear Regulator y Commission, October 21, 2004. EricksonKirk
-PFM EricksonKirk, M.T., "Probabilistic Fract ure Mechanics: Models, Parameters, and Uncertainty Treat ment Used in FAVOR Version 04.1," NUREG-1807, U.S.
Nuclear Reg ulatory Commission, January 26, 2005. EricksonKirk
-SS EricksonKirk, M.T., et al.,
"Sensitivity Studies of the Probabilistic Fracture Mec hanics Model Used in FAVOR V ersion 03.1,"
NUREG-1808, U.S. Nuclear Regulatory Commission, Novem ber 30, 2004. 56 Kirk 12-02 EricksonKirk, M.T., "Technical Basis fo r Revision of the Pressurized T hermal Shock (PTS) Screening Lim its in the PTS Rule (10 CFR 50.61)," December 2002, available in ADAMS under Accession #ML0300 90626. Malik Malik, S.N.M., "FAVOR C ode Versi ons 2.4 and 3.1: Verification and Validation Summary Report," NUREG-1795, U.
S. Nuclear Regulatory Commission, October 31, 2 004. Simonen Simonen, F.A., S.R. Doctor, G.J. Schuster, and P.G. Heasl er, "A Generalized Procedure for Genera ting Flaw Related Inputs for t he FAVOR Code," NURE G/CR-6817, Rev. 1, U.S. Nuclear Regulator y Commission, October 2003, available in ADAMS under Accession
- ML051790410. Williams Williams, P.T., and T.L.
Dickson, "Fracture Analy sis of Vessel s Oak Ridge, FAVOR v04.1: C omputer Code: Theor y and Implementation of Algorithm s, Methods, and Corre lations," NUREG/CR-6854, U.
S. Nuclear Regulatory Commission, October 21, 20
- 04. 57 4.2 Literature Citations 10 CFR 50.61 Title 10, Section 50.61, "Fracture Toughness Requirem ents for Protection against Pressuri zed Thermal Shock Events
," of the Code of Federal Regulati ons, promulgated June 26, 19
- 84. 10 CFR 50 A pp. H Appendix H to Part 50, "R eactor Vessel Material Surveillance Program Requirem ents," of the Code of Federal Regulations, promulgated December 31, 200
- 3. ACRS 05 ACRSR-2116, Letter from Graham Wallis to Luis Rey es entitled "Pressurized Ther mal Shock (PTS) Reevaluation Project: Technical Basis for Rev ision of the P TS Screening Criterion in t he PTS Rule,"
available in ADAMS under Accession
ASME S4 AVIII ASME Boiler and Pressure Vess el Code,Section XI, Division I, 1989 Edition, 1989 Addenda, A ppendix VIII, Supple ment 4. ASTM E900 ASTM E900-02, "Standard Guide for Pr edicting Radiation-Induced Transition Tem perature Sh ift in Reactor Vess el Materi als," American Society for Testing and Mate rials, Philadelphia, Pennsylvania, 2002. Becker 02 Becker, L., "Reactor Pressure Vessel Inspection Reliability
," Proceedings of the Joint EC-IAEA Tech nical Meeting on Improvements in In-Service Inspection Effectivene ss, Petten, Netherlands, Novem ber 2002.
Dickson 07a Dickson, T.L., P. T. Willia ms, and S. Yin, "Fracture Analy sis of Vessels-Oak Ridge FAVOR, v06.1, Com puter Code: User's Guide," ORNL/TM-2007/
0031, Oak Rid ge Natinoal Laborator y, 2007. Dickson 07b Dickson, T.L.
, and S. Yin, "Electronic A rchival of the Results of Pressurized T hermal Shock Analy ses for Beaver Valley, Oconee, and Palisades Reactor Pres sure Vessels Generated with the 06.1 Version of FAVOR,
" ORNL/NRC/LT R-07/04.
Eason 07 Eason, E.D.,
G.R. Odette, R.K. Nanstad
, and T. Yama moto, "A Physically Based Correlati on of Irradiati on-Induced Transition Temperature Shifts for RPV Steels,"
Oak Ridge National Laborator y, ORNL/TM-2 006/530. English 0 2 English, C., a nd W. Server, "Attenuation in US RPV Steels-MRP-56," Electric Power Research Institute, June 2002.
EricksonKirk 06a EricksonKirk, Mark and M arjorie Eric ksonKirk, "An Upper-Shelf Fracture Toughness Master Curve for Ferritic Steels,
" International Journal of Pr essure Vessels and Pipi ng 83 (2006) 571-583. EricksonKirk 06b EricksonKirk, Marjorie and Mark Erick sonKirk, "Th e Relationship between the Transition and Upper-Shelf Fracture Toughness of Ferritic Steels,"
Fatigue Fr act Engng Mater Struct 29 (2006) 672-684. Kirk 03 Kirk, Mark, Cayetano Santos, Ernest Eason, Jo yce Wright, and G. Robert Odette, "Updated E mbrittlement Trend Curve for Reactor Pressure V essel Steels,"
Transactions of the 17th I nternation al 58 Conference o n 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 W eld 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. Nuclea r Regulatory Commission, February 1996. RG 1.154 Regulatory Guide 1.1 54, "Format and Content of P lant-Specific Pressurized T hermal Shock Safety Analysis Reports for Pressurized-Water Reactors," U.S. Nuc lear Regulatory Commissi on, Novem ber 2002. RG 1.174 Re v 1 Regulatory Guide 1.1 74, Rev. 1, "An Ap proach for Using Probabilistic Risk Assessment in Risk-Inform ed Decisions on Pla nt-Specific Cha nges to the Licensing Basis
," U.S. Nucle ar Regulatory Commission, January 1987. RVID2 Reactor V essel Integrity Database, Version 2.1.1, U.S. Nuclear Regulatory Commission, Jul y 6, 2000. Schuster 02 Schuster, G.J., "Technical Letter Report-JCN-Y6604-Validated Flaw Density and Distribution within Reactor Pressur e Vessel Base Metal Forged Rings," Pacific Northwest National Laborator y, for U.S. Nuclear Regulatory Commission, December 20, 200
- 2. Schuster 98 Schuster, G.J., S.R. Doctor, S.L. Crawford, and A.F. P ardini, 19 98, "Characterization of Flaws in U.S. React or Pressure V essels: Density and Distribution of Flaw Indications in PVRUF,"
, Vol. 2, U.S. Nuclear Regulatory Commission, Washington, D.C.
Tregoning 05 Tregoning
, R., and P. Scot t, "Estimating Loss-of-Coolant Accident (LOCA) Freq uencies through the Elicita tion Process," NUREG-1829, U.S. Nuclear Regulator y Commission, June 2 005. Williams 07 Williams, P.T., T.L. Dickson, and S. Yin, "Fracture Analy sis of Vessels-Oak Ridge FAVOR, v06.1, Com puter Code: Theor y and Implementation of Alg orithms, Methods, and Correlations,"
ORNL/TM-2 007/0030, Oak Ridge Natinoal Laborato ry, 2007. 59 60 APPENDIX A CHANGES REQUESTED BETWEEN FAVOR VERSION 05.1 A ND FAVOR VERSION 06.1
24 March 20 06 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, OR NL Subj: Changes req uested bet ween FAVOR Version 05.1 and FAVOR Ver sion 06.1 Dear Terry
- As you are aware, over the past eight months staff from the NRC's Office of N uclear Reactor Regulation (NRR) have reviewed the technical basis RES has pro posed for a ri sk-inform ed revision of the pressurized ther mal shock (
PTS) rule (10 CFR 50.61).
As a consequence of this review, I am requesting that ORNL take the followi ng actions:
- 1. Make certain changes to FAVOR 05.1.
- 2. Issue a new v ersion of FAVOR, Ve rsion 06.1, in cluding revisions to both the Theory and the Users manual
- s. 3. Re-analyze the base-c ase for the three study plants (Oconee Unit 1, Beaver V alley Unit 1, and Palisades) using certain new input data and issue the results to the NRC.
- 4. Perform sensitivity studies to asses s the effects of sub clad cracking on the through wall cracki ng frequency associated with forged vessels and issue the results to the NRC.
The purpose of this m emorandum is to docum ent in de tail the particular tasks you are requested to take within each of these actions, and (in the case of changes made to the FAVO R code) docum ent the technical basi s for the requested changes
. Should you have any questions or requir e clarifica tion 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: Ch ange FAVOR 05.1 Note: Information provided at the beginning of each of the following tasks establishes th e technical basis/motivation for the requested change to FAVOR. At the end of each task writeup, the specific requested change can be foun d in a box highlighted, as is th is one, in p ink. 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 informat ion in Table 4.2 that is eventually used in FAV OR because it is only for this subset of materials for which enou gh KIc data are av ailable to establish a RT LB value. There is a discrepancy between the To value given in these table s for HSST Plate 03 (shaded in gold in the tables). Table 4.1 gives a value of -21 F, while Table 4.2 gi ves a value of +31 F. What is the reason for the discr epancy? Answer 1:
The values were cal culated from different sets of K Jc data, which is the reason they are different. However, the +31 F value in Table 4.2 is n ot considered valid per AS TM E1921 procedures because all of the K Jc values were measured at a temperature t hat is more than 90 F below T
- o. The value of
-21 F, which is valid per ASTM E192 1, should therefore be used.
Action: In the FAVOR Theory manual (Tab le 10), change the value of T o for HSST Plate 03 to -
21 F, and change the resultant R TNDT-To value to +41 F. A-2 Table 4.1 Summary of U nirradiated RPV Materi als 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 13 41 Marston, T.U.
1978 A508 Cl. 2
-6 65 71 Marston, T.U.
1978 A508 Cl. 2
-60 51 111 VanDerSluy s, 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 31 68 Ishino, S.
1988 Generic Plate 13 68 CEOG 1998 A533B Cl. 1 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 58 -19 Ishino, S.
1988 76 22 CEOG 1998 -126 -80 46 Ramstad, R.K.
1992 HSST 73W 29.2 48 McCabe, D.E.
1994 Midland Noz zle -32 27 59 Ramstad, R.K.
1992 HSST 72W 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 R eference Transitio n Temperatures Defined Using the ORNL 99/27 KIc Database A-3 Reference Temperatures Uncert. Terms Property Set ID Material Description Product Form Sample Size RTNDT(u) T0 RTLB RTNDT(u) - T0 RTLB 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 77.8 21 97.8 4 HSST 03 Plate 9 20 31 -71.5 -11 91.5 5 A533 Cl. 1 Plate 13 65 121.4139 186.4 6 HSST 02 Plate 69 0 2.1 17 2.1 7 A533B Weld 10 151 -187.2106 142.2 8 A533B Weld/HAZ 6 0 -132 -162.4132 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 15.4 60.6 6 13 HSSI 73W Weld 10 -29.2 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 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 I rr. Plate 4 0 -8 from other sources -62.3 8 62.3 A-4 Question 2: When the R TLB data in Table 4.2 are plotted versus T o (using the corre cted value of T o identified in Question 1), the plot shown below res ults. (Note that three T o values have been added to the original table f or materials 16-18; these values are backed in blue.) Is the re a reason why 7 of the data points have RT LB values that are lower than To (these data are indicated in re d print in Table 4.2 above
), while 11 of the values have RTLB values higher than T o? -250-200-150-100-50050-200-150-100-50050To [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 The ory Manual, indic ates that RT LB is established for a particular data set using the foll owing procedure:
- 1. Identify a set of ASTM E399 valid K Ic data for which you want to identify RTLB and for which RT NDT is known.
- 2. Plot the K Ic data, and also plot the ASM E KIc curve located using RT NDT. 3. Shift the ASME K Ic curve downward b y 9.5 ksiin. and call this curve the Adjusted Lower Bound ASME KIc Curve. 4. Shift the Adj usted Lower Bound ASM E KIc Curve leftward until it intersects t he first measured KIc value. Call the am ount by which the curve has been translated RTLB. 5. RTLB is now defined as RT LB = RTNDT - RTLB. A-5 For data sets such as those shown in the figure above (i.e., those having K Ic values measured over a range of temperatures), the RT LB value will alway s exceed the T o value. This is illustrated in the figure at the top of the next page, where 100 K Jc values are randomly simulated over the te mperature ran ge of -150 C T-To +75 C. The 11 a ctual sets of data for which RT LB exceeds To all have K Ic values measured over a wide range of tem peratures and so can be expected to have RT LB > To. We used the Master Curve to simulate 100 data sets of 100 K Jc values over the tem perature range of -150 C T-To +75 C (-270 F T-To +135 F). The 100 sim ulated RTLB values es timated fro m these simulated data excee ded To by, on average, 38 F (with a standard deviation of 19 F). This sim ulated amount by which RT LB exceeds T o is in good agr eement with the 11 actual data sets for which RT LB exceeds T o by 41 F (on average). From this analy sis, we draw the following conclusions:
RTLB should exceed To. For well-populated data se ts where K Ic or KJc values are measured in transition, RTLB will be estimated to exceed T
- o. The average amount by which RTLB exceeds T o for the 11 data sets shown in bl ack type in T able 4.2 is in good agree ment with our si mulation based on the Master C urve. A-6 050100150200250-200-150-100-50050100T-To [oC]KJc [MPa*m0.5]KJc simulated based on MC 2.5% MC Bound Median MC 97.5% MC BoundRTLB Curve, RTLB = To + 25C The seven data sets shown in red type in Table 4.2 d o not have m easured KIc values distributed over a wide range of tem peratures. In general, t he measured K Ic 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 i llustrated 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 RT LB to fall below T
- o. To investigate the degree to which RT LB can be expected to fall below T o for data sets of this t ype, we used the M aster Curve to sim ulate 100 data sets of 20 K Jc values over the tem perature range of -11 1 C T-To -83 C (-200 F T-To -150 F). The 100 simulated RTLB values esti mated from these simulated data fell below T o by, on average, 77 F (with a standard deviation of 4 9 F). This sim ulated amount by which RT LB falls below T o is well within one standard deviation of the s even actual data sets that h ave only KIc values on the lower shelf. These data sets, shown in red type in Figure 4.2
, have RTLB values that fall below T o by 43 F (on average). From this analy sis, we draw the following conclusions:
050100150200250-200-150-100-50050100T-To [oC]KJc [MPa*m0.5]KJc simulated based on MC 2.5% MC Bound Median MC 97.5% MC BoundRTLB Curve, RTLB = To -45C RTLB will fall below T o if the only KIc data available for analy sis lie on or near the lower shelf.
A-7 The result RT LB < To is anomalous. It arises as a conseque nce of a limited am ount of data that li e only on the lower shelf and
, therefore, does not capture the tem perature dependence inherent to transition fracture. RT LB < To does not reflect any thing intrinsic abo ut the material that shoul d be simulated in FAVOR. Mo reover, the K Ic values esti mated when RT LB falls below T o become nonconservat ive at higher t emperatures.
The data sets shown in red type in Table 4.2 should therefore not be used in the e stimation of the RTEPISTEMIC value sam pled in FAVOR to represent the difference between a known value of RTNDT and a simulated value of RT LB. The plot belo w shows the relationship (o r lack thereof) between RT LB and RTNDT for the 11 da ta sets in black type shown in Table 4.2. For purposes of illustration only, a nonparametric CDF derived from these data is a lso shown on the next page.
Action: Modify the data basis for t he RTEPISTEMIC distribution used by FAVOR. The data used to establish the RTEPISTEMIC distributio n should include only those data sets fro m Table 4.2 (see pages 4 and 5 of this m emorandum) for which RT LB > To. Also, include the three new T o values given for materials 16, 17, and 18 in the FAVOR Theory manual. The analy sis methodolog y used to establish the RTEPISTEMIC distribution fr om these data should be the same as that used c urrently. -150-100-50050-100-50050100RTNDT [oF]RTLB [oF] A-8 0.000.250.500.751.00-50050100150200RTEPISTEMIC = RTNDT - RTLB [oF]Cumulative Probability Task 1.2 Change in where the uncerta inty in RTNDT(u) is sampled in the FAVOR looping structure The uncertainty assigned to a value of RT NDT(u) is a variable input t o FAVOR. In practice, RT NDT(u) uncertainty is onl y assigned a nonzero value when the input value of RT NDT(u) is determ ined by the so-called generic method. In FAVOR Version 05.1, RT NDT(u) uncertainty is sam pled inside of bot h the flaw and the vessel loops. Because FAVOR si mulates the existence of hundreds of t housands of fl aws in a particular major region in a particular vessel, the curre nt sampling strategy implies that RT NDT(u) can vary point-wise thr oughout any one weld, plate, or forgin
- g. This sim ulation is inco nsistent with the ASME definition of RT NDT(u). Per ASME, the value of RT NDT(u) assigned to a particular weld, plate, or forging must be the highest of any value calculat ed from all of the Charpy V-notch and nil-ductilit y temperature measurements made for the weld, plate, or forgin g in question. Per ASME, RT NDT(u) should therefore be single-valued for each major region in each si mulated vessel.
Action: To reconcile this problem
, ORNL is req uested to m odify the location where the RT NDT(u) uncertainty is sa mpled in FAVOR. RT NDT(u) uncertainty shoul d be sampled inside of the vessel loop, but outside of the fla w loop.
Task 1.3 Change in where RTEPISTEMIC is sampled in th e FAVOR looping stru cture The FAVOR program includes a series of nested FORT RAN DO-loops that are used to perform a Monte Carlo simulation. Of these, the outerm ost loop is called the vessel loop. Immediately inside t he vessel loop is t he flaw loop. I n FAVOR Version 05.1, a ne w value of RTEPISTEMIC is sampled from the RTEPISTEMIC distribution for each new flaw si mulated. The sa mpled RTEPISTEMIC value is used to estimate the r eference temperature for the fractur e toughness transition curve in the following way
- tPNiCuRTRTRTRTSHIFTEPISTEMIC uNDTIrradiated,,,)( For any particular simulated vessel, hundreds of thousa nds of individual flaws may be simulated to exist within a particular weld, plate, or forging (i.e., w ithin what FAVOR refers to as a major region). Thus, A-9 the uncertainty sim ulated by FAVOR Ve rsion 05.1 in the RTIrradiated value will be as large as th e 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 sam ples were r emoved 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 reque sted to m odify the location where the RTEPISTEMIC distribution is sam pled in FAVOR. RTEPISTEMIC should be sampled inside of the vessel loop, but outside of the flaw loop.
No changes to the FAVOR code shoul d be made inside the flaw loop t o simulate the uncertaint y associated with RTIrradiated. Once the acti ons requested in Tasks 1.2 and 1.3 are ta ken, there will be no uncertainty sim ulated within the flaw loop in either of the following variables, RT NDT(u) and RTEPISTEMIC
. However, there is uncertaint y within the flaw loop in the RTShift value. This unc ertainty arises as a consequence of uncertainties si mulated in the Cu, Ni, P, and fluenc e values. The graph below shows the effect of thes e simulated uncertainties on the resultant uncertainty in RTShift and, consequentl y, the resultant uncertainty in RT Irradiated. It can be observed that, except at low mean co pper values, FAVOR simulates more uncertainty in RT Shift (and, consequent ly, in RT Irradiated) than is reflected in either the data from which Eason derived the embrittlement shift model or than is characteristic of uncertaint y in the To reference temperature (AS TM E1921).
If FAVOR simulates a neg ative RTShift value, it instead sets the RTShift used in the calculation to zero, w hich is why the simulated uncertainty in the low copper shift values is so small. The general overesti mation by FAVOR of the uncertainty in RTShift occurs because information on chem ical composition uncertainty from many sources had to be combined to obtain enough data to establish a distribution (se e discussion in Appendix D of NUREG-1 807). This procedure tends to overestimate the variabilit y in chemical composition t hat would characteriz 0102030405060012345Fluence / 1019 [n/cm2]Standard Deviation of 1000 Simulated Shift Values [oF]Mean Cu = 0.05Mean Cu = 0.10Mean Cu = 0.20Mean Cu = 0.30Standard deviation of Eason model for weldse any individual weld.
Because of these fa ctors, there is no need to add logic insi de the flaw loop to sim ulate the uncertainty associated with RTIrradiated; this uncertainty is already accounted for i n 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 sta ndard deviat ion on co pper and on nickel is sampled in the FAVOR looping structure The two figur es below are t aken from Appendix D of NUREG-1807. These graphs (and the r elated text in NUREG-1 807 Appen dix D) provi de the technical b asis for the standard deviation of both copper and nickel within a particular sub-region (i
.e., within a par ticular weld). To be consist ent with this data basis, FAVOR should sam ple these standard deviations onc e per major weld region in each simulated vessel.
A-10 This, however, is not what is done in FA VOR 05.1.
FAVOR 05.1 si mulates the Cu and Ni standard deviations ins ide of bot h the flaw and the vessel loops.
The effect of this sam pling prot ocol is t hat the standard deviation of Cu a nd Ni is m odeled as varying point-wise throug hout a particular weld
. Action: ORNL is req uested to m odify the location wher e the standard deviation on C u and Ni for welds is sampled in FAVOR. Th e standard deviations for Cu and for Ni s hould be sampled inside of the vessel loop, but outside of the flaw loop.
Task 1.5 Change the embrittlement trend cu rve (RTShift equation)
Action: Add the following em brittlement 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 sho uld be available in April 2 006. CRPtermMDtermTTS eRCStPMnTAMDterm471.2130.61001718.01 eeeRCStNiCugPCufTNiBCRPterm,,,1.543769.31100.1191.1 for welds 10x417.1platesfor 10x561.1forgingsfor 10x140.1777A for welds 0.155 vesselsedmanufactur CEin platesfor 2.135 vesselsedmanufactur CE-nonin platesfor 5.102 forgingsfor 3.102B A-11 102595.01010103925.4for 103925.4103925.4for ttte Note: The relationship for te is limited as f ollows: te = MAX(3t). 6287.012025.184483.01390.1logtanh2121,,10NiCuttNiCugeeee 008.0072.0for 0.008)-(359.1072.0 008.0072.0for 072.0 072.0for 0,0.66790.6679PandCuPCuPandCuCuCuPCufeee wt%072.0for wt%072.0for 0CuCuCuCue 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)(eCuMax The followin g items should be noted when implementing t his formula in FAVOR:
Flux () is estim ated by dividing fluence (t) by the time (in secon ds) associat ed with the analysis. Time is c alculated from EFPY. The effective fluence (te) is limited to a maxi mum value of three ti mes the fluen ce (i.e., 3t). When esti mating values of TTS for an em bedded 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 flue nce (te) at location z is cal culated:
- 1. ID fluence:
ID, determined from the BNL fluence map 2. ID flux:
ttIDID, where t is determ ined from EFPY 3. Fluence at z:
zttIDz24.0exp 4. Flux at z:
zIDz24.0exp 5. Effective flue nce at z:
102595.01010)(103925.4for 103925.4103925.4for zzzzzettt zzett3MAX)( Task 1.6 Manganese sampling protocols and uncertainty In order to com plete Task 1.5, inform ation on the uncertainty in Mn data and sam pling protocols for these data is neede
- d. Mn data were obtained from the following sources:
A-12
- 1. Combustion Engineering Owners Grou p, "Fracture Toughness Characterization of C-E RPV Materials," Draft Report, Rev. 0, CE NS PD-1118, 1998. 2. VanDerSluy s, W.A., Seeley, R.R., and Schwabe, J.E
., "An Investigation of Me chanical Properties and Chem istry within a Thick MnMo Ni Submerged Arc Weld ment," Electric Power Research Institute Report, EPRI NP-373
, Februar y 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 198
- 5. 4. Wang, J.A., "Analy sis of the Irradiation Da ta for A302B and A533B Correlation Monitor Materials," NUREG/CR-6413, No vember 1995.
- 5. Fyfitch, S., a nd Pegram
, J.W., "Reactor Vessel Weld Metal Chem ical Composition Variability Study," B&W Nuclear Technologies Report, BAW-2220, June 1995. These citatio ns contained enough repea ted measur ements of Mn to enable esti mation of the variability in Mn at both a global and a l ocal level. Globa l and loc al variability are defined as follows: Global variabilit y occurs over an area referred to as a region in FA VOR. A regi on is any individual weld, plate, or forging.
Regions have ID areas on the order of 10 2 to 103 square inches. Local variability occurs over an area r eferred to as a "sub-region" in FAVOR. A sub-region is completely contained within a re gion and corresponds to an area of the vessel that has within it relatively minor variation i n fluence. Su b-regions hav e ID areas on the order of 1 00 to 101 square inches. Appendix D of NUREG-1 807 provides a more complete description of how FAVOR si mulates global and local variability in com position variables.
The data from these four citations are s ummarized 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 m ean Mn level. The local variability of welds is less than the global variability of welds. The global va riability of forgings is less than th at of welds and plates. The global and local variabilit y of forgings is approxim ately equal. Regarding sam pling/res ampling protocols, the follo wing shall be im plemented in FAVOR for Mn: The distinctio n between region an d sub-region uncertainty that is currentl y made with regard to sampling of Cu, Ni, and P shall now also be m ade for Mn. The recommendations of T ask 1.4 for C u and Ni shall be applied to Mn as well. For welds, Cu, Ni, and P a re resampled from the global (or region) uncertainty in the IGA Propagation Sub-Model e ach time the propagating crack extends past a 1/4T b oundary. These same protocols shall be followed for resam pling Mn i n 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 0.000.020.040.060.080.100.60.81.01.21.41Mean MnMn Standard Deviation.6 Plate - Global Forging - Global Forging - Local Weld - Global Weld - Local Actions: Model variabilit y 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 analy sis. Regarding sam pling/res ampling protocols, the follo wing shall be im plemented in FAVOR for Mn: The distinctio n between region an d sub-region uncertainty that is currentl y made with regard to sampling of Cu, Ni, and P shall now also be m ade for Mn. The recommendations of T ask 1.4 for C u and Ni shall be applied to Mn as well. For welds, Cu, Ni, and P a re resampled from the global (or region) uncertainty in the IGA Propagation Sub-Model e ach time the propagating crack extends past a 1/4T b oundary. These same protocols shal l be followed for resam pling 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 coefficien ts in upper-shelf model Work has continued in developing a m odel of uppe r-shelf fracture toughness and in establishing the relationship between upper-shelf a nd transition fracture toughness. As a result of this ongoing development work, som e of the coefficie nts in the upper-shelf fract ure toughness m odel implemented in FAVOR need to be change d, as detailed below.
Eq. 19: The 50.1 and 0.794 coefficients used in E
- q. 19 (current version belo w) should be changed to 48.843 and 0.7985, respectively. The da ta supportin g this change are given after the equation.
Fit to All Static DataTUS = 0.7985*To + 48.843R2 = 0.9812-150-100-50050100150200-200-150-100-50050100150200To [oC]TUS [oC]All StaticOldNewLinde 80DynamicLinear (All Static) Eq. 21: The 2.09 coefficient used in Eq.
21 (current version b elow) should be changed to 1.75. The data supporti ng this chang e are given after the equation.
A-16
-25002505007501000-150-100-50050100150200250300Temperature [oC]JIc - JIc(288) [kJ/m2]OldNewZA Fit to Data, alpha=1.75 Eq. 23: The 62.023 and -0.0048 coefficients used in Eq. 23 (current version below) shoul d be changed to 5 1.199 and -0.0056, respectively.
The data supportin g this change are given after the equation.
y = 51.199e-0.0056xR2 = 0.862020406080100-150-100-50050100150200250300Temperature [oC]Standard Deviation of JIc Values [kJ/m2] A-17 Task 1.8 Enhance output Modify FAVOR as nec essary to enable the user to output the following results for each vesse l iteration:
the RTEPISTEMIC value sampled for that vessel iter ation for each T-H transient si mulated for th at vessel for that vessel iter ation: the number of axial cracks that initiated the number of circu mferential cracks that initiated the CPCI for axial cracks the CPCI for circu mferential cracks the CPTWC for axial cracks the CPTWC for circu mferential cracks the TWCF contribution from each T-H transient for that vessel iter ation Also, modify FAVOR to print out values of RT MAX-AW, RTMAX-PL, and RTMAX-CW for each major region in the vessel bel tline. Form ulas for each value, take n from Eq. 8-1 through Eq.
8-3 of NUREG-1 806, are as follows:
RTMAX-AW is evaluated for each of the axial weld fusion lines using the following form ula. In the form ula, the sy mbol tFL refers to the maxim um fluence occurring along a particular axial weld fusion line, and T30 is the shif t in the Charpy V-notch 30 ft-lb energ y produced by irradiation at tFL. FLaxialweld axialweld uNDTFLplateplateuNDTAWMAXtTRTtTRTMAXRT30)(30)(, RTMAX-CW is evaluated for each of the circu mferential weld fusion lines using the following formula. In the form ula, the symbol tMAX refers to the maxi mum fluence occurring ove r the ID in the vessel beltli ne region, and T30 is the s hift in the Charpy V-notch 30 ft-lb energy produced by irradiati on at tMAX. MAXcircweldcircwelduNDTMAXplateplateuNDTCWMAXtTRTtTRTMAXRT30)(30)(, RTMAX-PL is evaluated for each plate using the following form ula. In the form ula, the symbol tMAX refers to the maxi mum fluence occurring over the ID in the vessel beltline region, and T30 is the shift in t he Charpy V-notch 30 ft-l b energy produced b y irradiation at tMAX. MAXplateplateuNDTPLMAXtTRTRT30)( Task 1.9 Temperature-dependent thermal-elastic properties In FAVOR Version 05.1 (a nd previous versions),
the therm al-elastic material properties (Young's Modulus, P oisson's Ratio, and the coefficient of th ermal expansion) were modeled conservatively as being tem perature-invariant properties. The 06.1 ve rsion of FAVOR should be modified to im plement temperature d ependencies i n these prope rties as des cribed in the following reference:
M. Niffengger, "The Proper Use of Thermal E xpansion Coefficients in Finite El ement Calculations," Laboratory for Safety and Accident Resear ch, Paul Scherrer Insti tute, Wurenlingen, Switzerland.
A-18 Also, the clad-base stre ss free reference temperature and the through-wall weld residual stress profile models used in FAVOR Ve rsion 05.1 (and previous versions) were estimated assuming temperature-invariant thermal-el astic material properties (for info rmation on this esti mation, see T.L. Dick son, W.J.
McAfee, W.E. Pennell, and P.T. Williams, "Evaluati on of Margins in the ASME Rules for Defining t he P-T Curve for an RPV," N UREG/CP-01 66, Oak Ri dge National La boratory, Oak Ridge, Tennesse e, Proceedings of the Twenty
-Sixth Water Reactor Saf ety Meeting 1, 1999, pp. 47-72)
. For consistency
, the FAVOR model for the clad-base stress free reference temperature should be rederived using te mperature-dependent the rmal-elastic material prop erties. A-19 Action 2: Issue FAVOR Versi on 06.1 Once the task s requested under Action 1 are complete and all consi stency checks and internal software verifications have been performed, ORNL is request ed to issue a new version of FAVOR, wh ich will be designated as Version 06.1
. Revised versions of th e Theory manual, the users manual, exam ple problem s, and the distri bution 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 m odified to address the NRC project monitor's comment s, they shall be re-issued and di stributed to i ndividuals/or ganizations taking part in the verification and validatio n (V&V) effort. Following V&V, any errors, inconsistencies, and anomalies identified will be fixed (s ubject to concurrence of the project monitor), and the manuals will be revised and re-issued.
A-20 Action 3: Reanal yze the Base-Case for the Three Study Plants Using FAVOR 06.1 Input: Repeat the an alyses documented in ORNL/NRC/
LTR-04/18 using FAVOR Version 06.1.
Prior to perform ing this analy sis, the inpu t files should be c hanged only in the followi ng manner: 1. Change the initiating event frequencies for prim ary side pipe breaks to be consistent with the information provided i n NUREG-1829.
Alan Kolaskowski of SAIC will provide the necessar y input files.
- 2. Ensure that the global fluence uncertaint y is coded as 11.8%
and local fluence uncertainty is coded as 5.6
% in the inpu t files.
- 3. The embrittlement trend curve described in Task 1.4 should be selected. Input values of Mn for the various pl ates, forgings, and welds in the three study plants are detailed in the table appear ing at the end of Action 3.
- 4. Change the current percentage of repair flaws in the flaw distributio n from 2% to 2.3%. Basis for Ite m 4: NRR correctly points out that the decision to include 2% repair flaws in the flaw distribution used in the baseline PTS analy sis was a judgment made on the basis that a 2% repair weld volume exceeded the pro portional vol ume of weld repair s to origina l fabrication welds observed in an y of PNNL's work (the largest volum e of weld repairs re lative to ori ginal fabrication welds was 1.5%).
However, fla ws in welds a re almost always fusion line flaws, whic h suggests that their num ber scales in proportion to weld fusion li ne area, not in proportion to weld volum
- e. To address this, RES tasked PNNL to reexam ine the relative proportio n of repair welds th at occur on an area rather than a volum e 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 assu mption that a sim ulated flaw is equally likely to occur at any location through the vessel wall thickness. During discussions between RE S and NRR staff regarding the technical basis information developed by RES, NRR questioned th e validity of this assu mption for the case of flaws associated with weld repairs. After further consid eration, RES has determined that this assu mption is incorrect, as e videnced by the following information. The figure be low shows that if a flaw for ms in a weld repair, it is equally likely to occur any where with respect to th e depth of the excavation cavit
- y. However, the second figur e below shows weld repair areas occur with m uch higher frequency close to the surfaces of the vessel then they do at m id-wall thickness.
Taken together, this information indicates that a flaw due to a weld repair is m ore likely to be encountered close to the ID or OD surface than it is at the mid-wall thic kness. A-21 00.10.20.30.40.50.60.70.80.910.000.200.400.600.801.00Depth of Flaw from Cavity Surface (fraction)Cummulative distribution ( faction)Random distribution of flaw locations Weld Repair Mouth Weld Repair Root NUREG/CR-6471, Vol.2y = 1.1066e-0.558xR2 = 0.97730%20%40%60%80%100%012345678Depth of Repair Excavation [inches]Percent of Repair Excavations Extending to this Depth or GreaterRepair 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 distr ibution for w elds. The flaws placed in the blended distribution are scal ed in proportion to the fusion ar ea of the different welding processes used in the vessel. Because of this approach, it is not possible to specify a through thicknes s distribution of repair weld flaws th at is biased toward the surfaces while maintaining a r andom through thickness di stribution of SAW and SMAW weld flaws. Theref ore, to acc ount for the nonlinear through thickness di stribution of weld flaws th e 2% blending factor currentl y used for repair welds will be m odified on the f ollowing 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 ves sel wall more deeply than 3/
8T do not have a high en ough driving force/low enough fracture toughness to i nitiate.
A-22 A-23 On the graph above, 3/8T corresponds to 3 in. The curve fit to the data on this g raph indicates that 79% of all repair flaws occur within from 0 to 3/8T of the outer surfaces of t he vessel. The figure above also indicates that 7%
of all repair flaws occur between 5/8T an d 1T from the outer surfaces of the vessel. The refore, 43% ((79%+7%)
/2) of all repair flaws occur be tween the ID and the 3/8T position in the vessel w all. FAVOR's current assu mption of a random through-wall distribution of repair flaws indicates t hat 37.5% of all repair flaws o ccur between the ID and the 3/8T position in the vessel wall. Thus, FAVOR underesti mates the 43% valu e 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 re sults of the PFM analy ses performed wi th FAVOR 06.1 in the same for mat as that used in O RNL/NRC/LTR-04/18 an d provide to the NRC project m onitor for review and comment. Additionall y, as soon as it is practicab le after the FAVOR analy ses are co mplete, and preferably in advance of issuance of the electr onic archive letter report, provide r esults in MS Excel spreads heets to the NRC project monitor for analy sis.
Table of plant-specific input values for use in FAVOR calculations revised to include mean Mn values. This table will appear a s 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) ValueCu Ni P Mn USE(u) [ft-lb] 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 5-2 430 0.140.620.0151.490C4381-2 INTERMEDIATE SHELL B6607-2 84.3 MTEB 5-2 730 0.140.620.0151.484C6293-2 LOWER SHELL B7203-2 78.8 MTEB 5-2 200 0.140.570.0151.384PLATE C6317-1 LOWER SHELL B6903-1 72.7 MTEB 5-2 270 0.20.540.011.3180305414 LOWER SHELL AXIAL WELD 20-714 75.3 Generic -5617 0.3370.6090.0121.4498LINDE 1092 WELD 305424 INTER SHELL AXIAL WELD 19-714 79.9 Generic -5617 0.2730.6290.0131.44112LINDE 0091 WELD 90136 CIRC WELD 11-714 76.1 Generic -5617 0.2690.070.0130.964144Oconee 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 331 0.160.650.006(5)109C2197-2 INTERMEDIATE SHELL (4) B&W Generic 126.9 0.150.50.0081.2881C2800-1 LOWER SHELL (4) B&W Generic 126.9 0.110.630.0121.481C2800-2 LOWER SHELL 69.9 B&W Generic 126.9 0.110.630.0121.4119C3265-1 UPPER SHELL 75.8 B&W Generic 126.9 0.10.50.0151.42108PLATE C3278-1 UPPER SHELL (4) B&W Generic 126.9 0.120.60.011.26811P0962 INTERMEDIATE SHELL AXIAL WELD SA-1073 79.4 B&W Generic -519.7 0.210.640.0251.3870299L44 INT./UPPER SHL CIRC WELD (OUTSIDE 39%) WF-25 (4) B&W Generic -720.6 0.340.68(3) 1.5738161782 NOZZLE BELT/INT. SHELL CIRC WELD SA-1135 (4) B&W Generic -519.7 0.230.520.0111.4048071249 INT./UPPER SHL CIRC WELD (INSIDE 61%) SA-1229 76.4 ASME NB-2331 100 0.230.590.0211.4886772445 UPPER/LOWER SHELL CIRC WELD SA-1585 (4) B&W Generic -519.7 0.220.540.0161.436658T1762 LOWER SHELL AXIAL WELDS SA-1430 75.5 B&W Generic -519.7 0.190.570.0171.4870LINDE 80 WELD 8T1762 UPPER SHELL AXIAL WELDS SA-1493 (4) B&W Generic -519.7 0.190.570.0171.4870 A-24 A-25RTNDT(u) [oF] Composition (2) Product Form Heat Beltline flow(u) [ksi] RTNDT(u) Method RTNDT(u) Value (u) ValueCu Ni P Mn USE(u) [ft-lb] 8T1762 LOWER SHELL AXIAL WELDS SA-1426 75.5 B&W Generic -519.7 0.190.570.0171.4870Palisades, (Designer and Manufacturer: CE) Coolant Temperature = 532 F, Vessel Thickness = 81/2 in.
A-0313 D-3803-2 (4) MTEB 5-2 -300 0.240.520.011.3587B-5294 D-3804-3 (4) MTEB 5-2 -250 0.120.550.011.2773C-1279 D-3803-3 (4) ASME NB-2331 -50 0.240.50.0111.293102C-1279 D-3803-1 74.7 ASME NB-2331 -50 0.240.510.0091.293102C-1308A D-3804-1 (4) ASME NB-2331 00 0.190.480.0161.23572PLATE C-1308B D-3804-2 (4) MTEB 5-2 -300 0.190.50.0151.23576LINDE 0124 WELD 27204 CIRC. WELD 9-112 76.9 Generic -5617 0.2031.0180.0131.1479834B009 LOWER SHELL AXIAL WELD 3-112A/C 76.1 Generic -5617 0.1920.98(3)1.34111W5214 LOWER SHELL AXIAL WELDS 3-112A/C 72.9 Generic -5617 0.2131.010.0191.315118LINDE 1092 WELD W5214 INTERMEDIATE SHELL AXIAL WELDS 2-112 A/C 72.9 Generic -5617 0.2131.010.0191.315118 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 calculations, these values 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 of 826 phosphorus values 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 mean of other flow strength 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 mean value of manganese for forgings taken from the surveillance database used by Eason et al. to calibrate the embrittlement trend curve.
Action 4: Perform Sensitivit y Studies on Subclad Cracking In the spring of 2006, FA VOR 06.1 will be m odified to run on the ORNL superco mputer cluster. At that time, ORNL is requested to work with the NRC projec t monitor to define a set of PFM analy ses that can be used to quantify the effect of subclad cracks on TW CF. It is anticipated that the total scope of the effort will include approximately 8-10 PFM analy ses (likely two plants, each run at 4 to 5 different EFPY). Reporting of results is needed to the sam e 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 A SSIGNING SUBCLAD FLAW DISTRIBUTIONS
B-1 TECHNICALLETTERREPORT Review of the Literature on Subclad Flaws and a Technical Basis for Assigning Subclad Flaw D istributions PNNL Project Num ber: 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 Re gulatory Research U.S. Nuclear Regul atory 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 Flaw s and Technical Basis for Assigning Subclad Flaw Distributions F.A. Simonen Pacific North west National Laboratory Richland, Washington January 31, 2005 Introduction Pacific North west National Laboratory (PNNL) has a ssisted the U.
S. Nuclear Re gulatory Commission (NRC) in the efforts to revise th e Pressur ized Ther mal Shock (PTS)
Rule. In this role PNNL has provided Oak Ridge National Laboratory (ORNL) wi th inputs for the FAVOR c ode to describe distributions of fabrication flaws in reactor pressure vessels. These inputs, consisting of com puter files, have been important to probabilistic fracture mechani cs calculations with FAVOR. The flaw inputs have addressed se am welds, clad ding and base metal materials, but had e xcluded subclad flaws as sociated with the heat-affec ted zone (HA Z) from the welding pro cesses used to deposit stainless steel cl adding to the inner surface of the vessel.
To address concerns expressed by a peer review co mmittee, ORNL was request ed by NRC to evaluate the potential contribution of subclad flaws t o reactor pressure vessel f ailure. Based on inform ation in available documents, PNN L estimated the num ber and sizes of subclad flaws in a forged pressure vessel, and provided input files to ORNL for sensitivit y calculations. The se sensitivity calculations predicted that subclad flaws could contribute significantly to calculated vessel failure proba bilities. PNNL was then requested to continue its re view of the literatur e for additional inf ormation on su bclad flaws and to propose a refined basis for inputs to the FAVOR code.
The major se ctions of the present report:
- 1. describe the technical basis for the original subclad flaw input files t hat PNNL provided t o 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 im proved method for generating distributions for subc lad flaws and present results of exam ple calculat ions 4. recommend future work to im prove the flaw distri bution model and the sim ulation of su bclad 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 caus e subclad crac ks, measure s that can prevent cracking, and fracture mechanics calculations that have evaluated the signi ficance of subc lad cracks. The main focus in the present report is on the cha racteristi cs of observed subcla d flaws an d more specifically on available data and prior estimate s of the sizes and numbers of subclad flaws.
Technical Basis for Prior Subclad Flaw Distributions For welds, base metal, and cladding, PN NL has exa mined material and has used the data on observed flaws in the different material types to establish statisti cal distributions for the num bers and siz es of flaws.
However, none of the examined material showed evid ence of subclad flaws. Therefore, the num bers and sizes of subcl ad flaws for a vessel susc eptible to such cracking wer e estimated from a preliminary review B-2 of the literature. The primary source was a co mprehensive paper summari zing European work during the 1970s (A. Dhooge et al., 1978). T his paper was ba sed mainly on experience wit h vessel cracking i n Europe and s ubsequent research pr ograms conducted during the 1970s. Th e 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 fl aws extending into the vessel wall fro m the clad-to-base metal inter face, and 4 mm is cited as a bounding through-wall depth dimension
- 2. have orientations norm al to the direction of welding for clad deposition, gi ving axial cracks in a vessel beltline
- 3. occur as dens e arrays of small cra cks extending into the vessel wa ll 4. extend to dep ths limited by the depth of the heat-affected zone Figures in the cited paper show network s of cracks wi th flaw depth s estimated from a micrograph being significantly less than the c ited bounding 4-mm depth.
The cracks e xtended perpendicular to the direction of welding and were cluste red where the passes of the strip clad overlapped. Subclad flaws w ere said to be much more likely to occur in grades of pressure vessel steels th at have che mical compositions that enhance the likelihood of cracking. For ging grades such as A508 are more susceptible than p late materials such as A533. H igh levels of heat inputs during t he cladding process also enhance the likelihood of subclad crack ing. Other de tails of the cladding process are also i mportant, such as single-layer versus t wo-layer cladding.
The number of cracks per unit area of vessel inner su rface was estimated fro m Figure 1, taken from the Dhooge pape
- r. Cracking was shown to occur in ba nds estimated to have a width of 4 mm
. This dimension was used to estimate the bounding lengths of subclad cracks. The longest indivi dual cracks in Figure 1 were about 2 mm versus the 4-mm width di mension of th e zone of cracking.
Counting the number of cr acks pictured in a s mall region of vessel surface gave a crack densit y of 80,512 flaws per square meter. Figure 1 Location and O rientation of Underclad C rack; (a) Transverse S ection; (b) Plan View of Cracks B-3 The flaw input files as provide to ORNL were based on the foll owing assum ptions: 1. The crack depth dim ensions were described b y a uniform statistical distributi on from 0 to 4 mm with no cracks greater than 4 mm in depth.
- 2. The crack lengths were als o described by a uniform statistical distri bution. Like the assumption for flaws in seam welds, the am ount by which flaw lengths exceed their correspondi ng depth dimension was taken to be a uniform distributio n from 0 to 4 mm
. Thus, the extrem e length for a flaw with a depth dim ension of 4 mm was 8 mm. The 4-mm deep flaws therefore had lengt hs ranging fr om 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 wa s converted (for purposes of the FAVOR code) to flaws per unit volum e using the total volume of metal in the vessel wall.
- 4. The file prepared for FAV OR assumed that the c ode would sim ulate flaws for the total vessel wall thickness, rather than just the Category 1 and 2 re gions, which address only the inner three-eighths of the wall thickness. ORNL then accounted for this concern during t he FAVOR calculations.
A very large number of flaws (> 130,000) per vessel was predicted based on the photograph of one small area of a vess el surface. T he implication was that this area was representative of the entire vessel.
Although it is possible that subclad flaws can occur no nuniformly in patches of the vessel surf ace, it is generally understood that fl aws occur in a widespr ead manner. Large num bers of flaws have been reported when the proper conditions for subclad crack ing have existed. Based on PNNL' s limited review of documents, it was therefore difficult t o justify reductions of the estimated flaw density
. However, sensitivity calculations should be pe rformed to see if refinement of the esti mated flaw density has a significant effect on the FAVOR c alculations. The estim ated depth dimensions of the subclad flaw s were thought to be conserv ative. The depth of 4 mm was based on statements regarding boundi ng flaw depths, with no other evidence such as micrographs or data on m easured de pth dimensions presented. The depth of 4 mm could be an esti mate for the size of the heat-affe cted zone, which was then taken as a lim itation on flaw depth. Alter
- natively, the 4-mm depth could be the extreme depth of som e observed subclad flaws. The prelim inary review showed so me examples from metallograph y of subclad flaws, whic h showed only flaws of much smaller depths (< 2 mm). It is therefore suggested that sensitivit y studies a ssumed subclad flaws with a bounding depth of 2 mm. The resulting FAVOR calculations include d only flaws in the "first bin" corresponding to sizes 0 to 1 percent of the vessel w all thickness and pr edicted only small contribution for subc lad flaws to vessel failure probabilities.
In summary
, PNNL's preliminary estimates of subcla d flaw distributions were based on a rather li mited review of available literature, with a particular focus on the Dhooge 1978 paper.
It was reco mmended that the scope of the literature revi ew be expanded to seek sources of additional inform ation. PNNL also proposed to review notes from past sessions with expe rt elicitation panels that have addressed reactor vessel fabrication and flaw distributions for the N RC. The critical need was infor mation on the depth dimensions of subclad flaws. It was possible that the depth dim ension of 4 mm is uncharacteristic of most subclad flaws, but is rather a bounding dim ension based on consideration of heat-affect ed zones. It was possible that this dept h has also been used in the literature for determ inistic fracture mechanics calculations and coul d therefore reflect the conservativ e nature of i nputs used fo r such calculations.
B-4 Results of Literature Review Individual papers and reports are su mmarized below.
Welding Research Council Bulletin No. 197 During the early 19 70s, data on subclad cracking we re assembled by the Task Group on Underclad Cracking under the Subcommittee on Therm al and Mechan ical Effects of the Fabrication Division of t he Pressure Vessel Research Committee.
The following paragraphs from the report of the Task Group are extracted from Welding Resear ch Council Bulle tin No. 197 (Vinckier and Pense, 1974).
Underclad cr acks were defined as intergranular separations no less than about 3 mm (0.12 in.) deep and 3 mm (0.12 i n.) long found in the coarse-grained heat-affected zon e of low-alloy steels underneath the weld-cladding overl ay. Grain-boundar y decohesions of sizes less than this were al so included in the inves tigation.
They are generally produced during postweld heat treatm ent. The com bination of three factors that pro mote underclad cracking are a susceptible microstructur es, a favorable residual-str ess pattern an d a thermal treatment bringing the steel into a critical te mperature reg ion, usually between 600 °C (1112 and 1202 °F) where creep ductilit y is low. Weld-overlay cladding with high-heat input processes provides the s usceptible microstructure a nd residual-stress pattern, particularly where weld passe s overlap
, and postweld heat treat ment provides the critical te mperature. High-heat-input weld-over lay techniques tend to incr ease the incid ence of underclad cracks. Most underclad cracking was found i n SA508 Class 2 steel forgings with some forged material chemical compositions found to be more sensitive than others. T hese forgings were clad with one-lay er submerged-arc stri p electrodes or m ulti-electrode processes. It was not reported in SA533 Grade B plate, nor was it pr oduced when multilayer overlay processes wer e used. Underclad cr acking can be reduced or eli minated by a variety of means, but the most feasible appears to be by using a two-la yer cladding technique, controlling welding process variables (e.g., low-heat-input weld processes) or renor malizing the sensitive heat-affe cted-zone region prior to postweld heat treat ment. Control of welding process variables alone may not prevent all grain
-boundary decohesions. Another soluti on would be to use m aterials that do not show the combination of a susceptible microstruct ure and low creep ductility or, where feasible, el iminate the ther mal postweld heat-treat ment cycle.
Other significant findin gs were: Underclad cr acking can include less sev ere manifestations of the sa me damage mechanisms as underclad cracks, but in the form of incipient crack s, microcracks, intergranular separations, pores, etc. Underclad cr acks are r estricted to overlap of the clad passes and occur in the pattern and orientation as indicated in Figure 2. Fracture mechanics evaluations established that subcl ad flaws with dimensions of 5 mm by 10 mm are not critical to safe operation. Underclad cr acking 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 th at WRC Bulletin 197 has no information on r eported depths of u nderclad cracks. There was, however, much discussion of the factors that govern the susceptibility of m aterials to underclad cracking along with descriptions of the m aterial selecti ons and welding proc edures that can prevent u nderclad cracking.
Figure 2 Section of Clad Plate Showing Cracks French Work Underclad cr acking has been observed in a num ber of reactor press ure vessels f abricated for French nuclear power plants. The French evaluation m ethods 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 referenc e defects. These d efects address different defect locations, different mechanisms for the origin of defects, and a range of probabilities of de fect occurrence. One of the categories is that of underclad defects, which ar e defects that have been of particular concern to French vessels. In ter ms of occurrence probabilities, the French evaluations have defined the following three defect classes. Envelope def ects-those that have actually been observed during manufacturing, but with a size that cannot be exceeded realisti cally (1>P>10-2). Exceptional defects
-those of the same t ype as envelope defects, but with a larger size to cover all the largest defects even seen in large pri mary circuit com ponents (10
-2>P10-4). Conventional defect-covers configura tions of ver y low probabilit y (P<10-4). Figure 3 sho ws the full scope of reference defects, with only the underclad crack being of interest to this discussion. F or the envelo pe category
, the undercla d 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 sourc e documents for the Fr ench requirements were not available for the present review. However, ASME Section XI, with supp ort by EPRI, has issued reports th at provide inf ormation that is otherwise available only from the French literature. These ASME sources per mitted the current review to be co mpleted. The French characterization of flaws was not specifi cally formulated for use in probabilistic f racture mechanics calculations, but has rather been used in France for determ inistic cal culations. The following B-6 discussion nevertheless provides some interpretations in the context of inputs for probabilistic calculations s uch as with the FAVO R code. The probabili ty values as cited above do not define units as needed to estimate flaw frequencies in term s of flaws per unit area or flaws per unit volum
- e. The French public ations im ply that that proba bility values can be interpreted as the probability of havi ng one or more flaws of the given sizes in a beltline vessel weld. This definition is difficult to apply to underclad crack s because th ese cracks occur in base metal rather t han in welds.
However, forged vessels s uch as those a pplicable to the French experience would have a t most two circu mferential welds in the beltline. It was therefore assu med that the probabilities can be treated as flaws per vessel. With this interpretation: A flaw distribution f or underclad cracks would have a maximum flaw depth of 3 mm and maximum flaw length of 60 mm
. The probabilit y range of 1>P
>10-2 can be interpreted to mean that bet ween 1 percent to 100 percent of a population of vessel we lds would be s ubject to underclad cracking. The probabili ty range of 1 0-2>P10-4 can be interpreted to m ean that between 1 percent to 0.01 percent of the vessels with underclad cracks will have a maximum flaw depth of 6 mm. The probabili ty of P<10
-4 can be interpreted to m ean that one vessel in 10,000 would have a fabrication surface flaw that extends through t he entire clad and then into t he base metal to give a total flaw depth of 13.5 m
- m. Such a fla w is outside the scope of the present disc ussion of underclad cracking, but has been addressed by ORNL as a low probability surface flaw.
Sensitivit y studies by ORNL for under clad flaws were performed for maxim um flaw depths of 2 mm and 4 mm. The 4-mm flaw is conservative in the contex t of the French work, becau se 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 d epth shoul d be weighted by a factor of 10
-2 to 10-4 in constructing an uncertainty distribution.
It was noted that the French wo rk used inform ation on fabrication flaws colle cted from European manufacturer s of vessels.
For the underclad flaws, th e exceptional defect depth of 6 mm came from considerations of the repair of un derclad cracks. The French work indicated that the orientations of underclad cracks are expected to be longitudinal and that the use of a two-lay er cladding will minimize the likelihoo d of underclad cracking.
Westinghouse Submittals Two topic reports from Westinghouse E lectric were s ubmitted to NRC to address the i mpact of underclad cracks on reactor pressure vessel integrity (Mager et al., 1971; Bamford and Rishel, 2000)
. The most recent report revisits conce rns for underclad crack ing to cover the period of lice nse extension from 40 years to 60 years, and concludes that underclad cra cks are of no concern relative t o structural integrity of the reactor pressure ves sel 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 revie w of WCAP-15338 resulted i n a request for addition information (NRC, 2002a) and a safety evaluation report (NRC, 2002 b). Because the 1971 Westinghouse report and RG 1.43 were not available to PNNL, the review was li mited to the 20 00 WCAP report and NRC's response to thi s report. Onl y limited inform ation for esti mating flaw distributions for PTS evaluations was found in the Westinghouse and NRC documents. The main focus was on deter ministic fracture mechanics evalua tions that cove red such issues as f atigue crack growth, with no attention given to PTS e valuations
. The fracture mechanics calculations assumed deterministic sizes of underclad cracks, with little documentation for the flaw size assu mptions.
The 2000 WCAP report reviews the history of u nderclad crackin g, includ ing 1970 reports of "reheat cracking" and 1979 experience with "cold cracking."
Early reports of reheat cracks were lim ited in the B-7 United States with vessels fabricated by the Rotterdam Dockyard Manufacturing Com pany. Cold cracking was limited to a select group of six U.S. vessel
- s. Reheat cracking has occurred with single-lay er cladding using high heat input welding onto ASME SA-508 Class 2 forgings. T he cracks ar e numerous and are confined to a dept h of 0.125 inch (3 mm) and a width of 0
.4 inch (1 0 mm). Circumferential Direction: 1, 2, 8, 10, 11 Longitudinal Direction: 3, 4, 5, 6, 7, 9, 12 Figure 3 Referenc e Defects for Ves sel 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. Cr ack depths have varied from 0.007 inch (0.2 mm) to 0.295 i nch (7.5 mm) and lengths have varied from 0.078 inch (2 mm) to 0.59 i nch (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 o f underclad cracks have been reported for plate materials or for SA-533B, SA-302E, or SA-302B forg ing materials.
B-8 NRC Expert Panels Two expert panels wer e formed as part of an NRC project during t he 1990s t o address concer ns with flaws in rea ctor pressure vessel
- s. The overall objectiv e of this project wa s to review and expand the technical basis of the flaw distributio n model of the PRODIGAL computer code (Chap man and Sim onen, 1998) as deve loped in the United Kingd om by Rolls Royce and Associates. A meeting durin g 1994 focused on flaws in vessel seam welds.
A followup meeting during 1996 focus ed on clad region flaws, including a discussion of u nderclad cracking.
Although the expert s provided useful and inter esting insights and i nformation on un derclad cracking, the i nput from the experts was insufficient to provide t he quantitative i nputs needed to model underclad cracking in t he PRODIGAL com puter code.
The minutes of the two m eetings (Sim onen, 1994; Simonen, 1996) along with i nformal notes were reviewed. The following insights were expressed by the experts during the mee tings: Underclad cr acking shoul d be addressed from the stan dpoints of two tim eframes, (1) cracking when the clad is deposited b y welding and (2) cracking when a post-weld heat treat ment is performed. Reheat cr acks can occur in coarse graine d regions of 508 steel when post-weld heat treat ment is performed. Reheat cracks occur in clusters and have small depths of about 1 mm that cover the clad surface of the forging. Reheat cr acks form in the base metal and not in weld fill material.
Reheat cr acks 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 int eraction between underclad cracks and previous HAZ cracks. Post-weld reheat cracks can also occur along t he HAZ of the side wall of the weld fill. T he occurrence of underclad cracks would o ften be correlated with HAZ along the si dewall. The same metallurgical cra cking phenomena c an occur for both underclad cracks and HAZ cr acks with both occurring during stress relief post-weld h eat treatment. Cracking is likely to occur (if it does occur) both as underc lad and as HAZ, because t he composition of the material is susceptible. Some heats o f material will be more susceptible th an others due to material differences. The primary variable is che mical composition, and the occurrence of cracking is not m uch impacted by heat inputs.
Cracking actually occurs during post-weld heat treatme nt. The locations of cracks are rel ated to weld beads. The PRODIGAL weld simulation m odel could accoun t for the compositions of f orgings (5 08), and this inform ation could be used to establish susceptibilities to under clad cracking. Utilities know forging com position, whic h could be used with a met hod described in an ASME paper which describes "Nakwuma Nu mber" as the basis to predict susceptibility to reheat cracking (Horiy a et al.,
1985). A Framatome case of cold cracking (H 2 cracking) was described that gives cracks parallel to the surface as an exam ple of underclad cracks due to t he heat inputs us ed in cladding. This cracking occurs onl y if there is a second la yer of clad applied without preheat. B&W and CE were aware of the potential problem, which can occur in both the 533 and 508 m aterials, but is less likely to occur in weld metal. Cracking will also be in the form of a lack of bondi ng of the clad to base metal. B-9 2000 Vessel Flaw Expert Judgmen t Elicitation The NRC has funded a n umber of efforts to re-evaluate the guidance and criteria in the Code of Federal Regulatio ns as it relates to reactor vess el integrity
, specifically pressurized therma l shock, whic h challenges the integrity of the reactor pressure ves sel's inner wall. One ele ment of the re-evaluation required an accurate e stimate of fabricat ion flaws, a nd this identified the need for the development of a generalized fl aw distribution for dom estic reactor pressure vessel
- s. In order to develop the fla w distribution and resolve technical issues for which sci entific uncertainty existed, an expert judgment process was used. The expert judgm ent process assist ed the NRC staff in developing a genera lized flaw distribution f or domestic vessels, which has been u sed as input int o probabilistic f racture mechanics calculations.
Although underclad cracking was not specifically addressed by the elicitation, some of the discussions with the experts provided s ome information of i nterest. The following remarks were co mpiled from detailed notes taken durin g interviews wi th the experts: Other experts should address underclad cracking. It i s 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. vessel s 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 s ome cases of underclad cracking. There can be underclad cracks for single-lay er clad if the heat input is too hi gh. There can also be underclad cracks with a two-lay er clad without heat t reatment between lay ers. One expert had concerns with underclad cracks in 508 forgings. An EPRI report on French experience w as mentioned. Only 508 forgings are susceptible to underclad cr acking reheat cracks. One of the experts did research and wrote a NUREG for NRC/
ORNL about 7 years ago. No reheat underclad crack ing has been r eported for pl ate materials.
None of the experts was aware of H2 underclad cracking for plates. One expert estim ated relative probabilities for underclad cracks for plates versus forgings.
Canonico/ORNL Report on Underclad Crackin g Canonico (1977) reviews resear ch on reheat cracks and the signifi cance of such cracks to the integrit y of reactor pressu re vessel
- s. The focus is on cracking in the heat-affect ed zones of sea m welds rat her than on underclad cracking. T his report prov ides no specific in formation on the dim ensions of cracks observed in nuclear vesse ls. Frederick a nd Hernalsteen Frederick and Hernalsteen (1981) summarize experience with underclad cracking and evalua tions of the significance of these cra cks to vessel integrity
. The information provided in this paper does not add to what is available in ot her more co mprehensive review papers such at WRC Bulletin 19
- 7. Dhooge et al.
Dhooge et al. (1978) provide an extensive review of experience an d research in the area of reheat cracking in nuclear rea ctor pressure vess els, both unde rclad cracks and cracking of structural welds. The paper emphasizes Europea n experience and research
. Topics covered in the review paper are B-10 (1) incidence of cracking, (2) mechanis m of cracking, (3
) detection of reheat cra cking, (4) tests for reheat cracking, (5) control of reh eat cracking, and (6) si gnificance of reh eat cracking to structural integrity.
Figure 1 from Dhooge et al. (197
- 8) shows the typical locations and orientations of underclad cracks.
Cracks occur only at locations that are heated twic e by welding or, as in Figure 1, the areas of the overlap zone of the cladding weld passes. In this zone, the material is heat ed to a critical tem perature by the second pass. The following paragraph on the sizes of underclad cracks is quoted:
The underclad cracks range in size fro m the short grai n boundary separations only a few austenitic grains long and deep (0.2 mm) to a m aximum of about 10 mm long and 4 mm deep. The us ual depth is a bout 2.5 mm or less, the depth beneath t he fusion boundar y being governed by the depth of the grain coarsened HAZ and thu s principall y by the particular cladding procedure. The Dhooge-reported incid ence of crack ing is consis tent with the conclusions of WRC Bulletin 19
- 7. Dolby and Saunders Dolby and Saunders note t hat subcla d cracks often refer to conditions such as grain boundar y separations or decohesions and in other case s to a ser ies of micro voids. Therefore the ter m "crack" is subje ct to interpretation. A topical report issued b y Babcock and Wilcox (A yres et al., 1972) is cited for information on crack depth dimensions. Maxim um reported depths of cracking are 4 mm, but depths are usually 2.5 mm or less, being g overned by the extent of the heat-affected zone.
Other Papers A number of other papers are listed as r eferences to the report. These papers were reviewed, but were found to provide little infor mation that is im portant to the focus of t he present report or t o repeat and reinforce inform ation from the other pap ers that have been discussed above.
Subclad Crack Sensitivity Study Input files for subclad flaw distributio ns were used by Oak Ridge National Labor atory and NRC staff to perform a sensitivity study (EricksonKirk, 2004).
This sensitivity study was formulated as fo llows: 1. One set of forging properties wa s selected based on the Sequoy ah 1 and Watts Bar 1 RPVs (
RVID2). 2. One hypothet ical model of a forged vessel was constr ucted based on an existing model of the Beaver Valley vessel. The hypothetical forged vessel w as constructed by removing the axial welds and combining these regions w ith the surrounding plates to make a forging. This forging was assi gned the properties from Step 1.
- 3. A FAVOR analysis of each vessel/forging com bination from Steps 1 and 2 were analy zed at three embrittlement levels, 32 EFPYs, 60 EF PYs, and Ext-B. Thus, a total of three FAVOR analyses were performed (1 materi al proper ty definition x 1 vessel definition x 3 e mbrittlement levels).
At 32 and 60 EFPYs, the through-wall crack frequency (TWCF) of the forging vessel s was ~0.2 percent and 18 percent of the plate welded vessels. Howeve r, at the much higher em brittlement level r epresented 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 em brittlement. While these very high embrittlement levels are unlikely to be approached in the foresee able future, these result s indicate that a more detail ed assessment of vessel failure proba bilities associated with subclad cracks would be warranted sh ould a subclad crack ing prone forging ever in t he 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 t hickness and the re maining flaws to have depths of 2 percent of the vessel w all thickness. Calculations for these flaw de pths pred icted substantial contribut ions from subclad flaws, whereas other calculations (not reported in NUREG-1 808) for a bounding flaw depth of 2 percent of the vessel wall predicted s mall contribution of subclad flaws to vessel f ailure frequencies.
It is noted her e that the flaw input files used for the ORNL/NRC flaw sensitivity calculations had an error that understated the estim ated number of subclad flaws b y a factor o f about 25. Details of this error and the correction of this pr oblem are described below. Th e net effect w ould tend to underesti mate the effects of subclad flaws on calculated failure freque ncies for em brittled forged vessels.
Table 1 Results of Subclad Crack Sensitivity Stu dy 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, 200 4b]. Proposed Flaw Distribution Model The updated f law distribution m odel includes:
- 1. a correction to the equatio n that convert s flaw density from flaws per unit area to flaws per unit volume of vessel material
- 2. changes to param eters of the flaw distribution using insights from the literature review along with a treatment of the uncertainties in esti mating these parameter s The proposed model has been im plemented into t he PNNL flaw distributio n algorithm. The results of example calculations are described below. The discussion concludes with reco mmendations 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 num ber of subclad flaw s by a factor o f about 25. An error was made in conver ting flaw rates fro m flaws per unit area of vessel s urface to an equivalent num ber of flaws per unit volume of forging m aterial. The effec t of the underesti mated flaw densities has not been evaluated b y comparison calculations with the FAVOR code. However, even the incorrect density assigned a very large num ber 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 roughl y proportional to the n umber of flaws in the vessel, this tre nd should saturate at very high levels of flaw density
. In this case, all regions of the vessel with lower bound t oughness levels will ha ve one or more subclad flaws of bounding size.
The primary conclusion dr awn from the results of Table 1 should not change for a corrected v ersion of the flaw input fil
- e. That is, subclad flaws can substa ntially increase failure frequencies for em brittled forged vessels, and more detailed evaluations should be perf ormed if such vessels beco me of concer n to future vessel integrity evaluations.
B-12 Flaw Distribution Parameters This section describes a pr oposed model for subclad cracks in the beltline regions of reactor pressure vessels. The model is based on t he information described above and also addresses uncertaint ies in knowledge of the underclad cracks that could exist in a specific vessel. The model includes the following parameters: 1. flaw frequenc y expressed in terms of fla ws per unit area of the vess el inner surface
- 2. the maxim um (or bounding) through-wall depth d imension of the su bclad flaws
- 3. the conditional distribution of the through-wall depth dim ensions expressed as a fraction of the bounding depth dimension 4. the conditio nal distributio n of the len gth dimensions of the subclad flaws It is assu med that vessel sp ecific evaluat ions have been perform ed based on considerations of material/weld ing parameters (and po ssibly of inspectio n findings) to establish whether there is a potential for subclad cracking for the vessel of concern. Fo r purposes of the preli minary model, this occ urrence probability ha s been assigned to be one. As the fl aw distribution model is furt her refined, expert judgment could be applied to better estimate a probabilit y of subclad cracking for each given vessel.
Maximum Through-Wall D imensions of Cracks
-This param eter defines the bou nding depth dimension for the subclad cracks in a given sim ulated vessel. As described below, a conditi onal depth distribution is also defined for the indi vidual cracks. The conditio nal depth distribution is tr uncated at the bounding crack depth.
The model features a bounding flaw depth dim ension for each si mulated vessel.
This bounding depth is assu med to be rela ted to details of t he cladding procedure (e.g., heat inputs f or the welding proc ess) along with the susceptibilit y of the vessel
's forging m aterial to subclad crack ing (e.g.,
the chemistry of the vessel specific heat of material).
Figure 4 shows the assu med distribution function fo r the bounding flaw depth dimension. Vessel-to-vessel variabi lity for the bounding crack depth is a ddressed by using the French work (Pellissier Tanon et al., 1990; Buchalet et al., 19 90; ASME, 1993; Moinereau et al., 2001) an d the paper by Dolby and Saunders (1977) for guidance. On this basis, the probabilit y for the maximum depth being greater than 3 mm is as signed to be less than 10
-1 (envelope defect of Figure 3)
, and the probabilit y of the defect being greater than 6 mm is a ssigned to be two orders of m agnitude 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 probabilit y over the range of 0-6 mm. 1.E-041.E-031.E-021.E-011.E+001.E+010.01.02.03.04.05.06.07.0Bounding Flaw Depth, mmProbability Greater Than Depth Figure 4 Probabilities for Bounding Depth of Subclad Flaws B-13 Conditional F law Depth Di stribution
-The conditional distributi on of depth dimensions of subclad flaws for a given ve ssel is a ssumed 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. T his assumption is the same as for the prior input f iles provided to ORNL/NRC for the sensitivit y calculations for subc lad flaws.
The uniform distributio n is a reflection of the lack of information on m easured flaw depth dimensions.
The approach therefore conservatively assigns a large fraction of the flaws to have depth dim ensions equal to abou t the bou nding dimension.
0.00.20.40.60.81.01.20.00.20.40.60.81.01.2Flaw Depth/Bounding Flaw DepthProbability Greater Than Depth Figure 5 Conditional Depth Distribu tions of Subclad Flaws Maximum Length Dim ensions of Cracks
-The envelope and exceptional defects of Figure 3 w ere first considered the basis for a conditi onal distribution for flaw length di mensions. With this appr oach, 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. T his approach (based on the 60-mm length) would be significantl y more conservative than that for t he prior flaw input fil es 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 s how subclad flaws (see Figure 1) that have lengths much less than 60 mm
. Further more, discussions of the mechani sms of subcla d cracking stat e that flaws a re confined to the overlap region of the heat-affec ted zones of adjacent p asses of the strips of cladding.
This mechani stic model would also give flaw lengths m uch less than the 60-mm (2.4-inch) flaw of the French public ations. The length di stribution of Figure 6 as adopted f or the updated m odel was the same as that assumed for the prior ORNL/NRC sensitiv ity calculations. A unifor m distribution was used to si mulate the numerical differences b etween the fl aw length and depth dimensions. The uniform distribution ranged from 0 mm to 5 mm. For each categor y (or bin) of the flaw depth dim ension, the generated input files for FAVOR have a distribution table fo r flaw aspect ratios.
Number of Cracks per Uni t Area of Ves sel Inner Surface
-The past PNNL estimate for the frequenc y of underclad cracks was 80,512 flaws per square meter. This densit y was derived from an analysis of the flaws shown in Figure 1, which was then assu med to depict a region of a vessel s urface with a severe case of subclad cracking. This density was treated as a conservative or upper bou nding estimate of the flaw occurrence fr equency with the lower bound assigned to an order of magnitude less as a lower bound estimate. It was a ssumed that the distribution functi on was a uniform distribution for t he logarithm of the flaw frequency between these boundi ng values. Figur e 7 shows the resulting dist ribution of fla w frequency
. B-14 0.00.20.40.60.81.01.2012345Flaw Length minus Flaw Depth, mmProbability Greater Than Value Figure 6 Conditional Distributions for Flaw Length 0.00.20.40.60.81.01.2020,00040,00060,00080,000100,000Flaws per Square MeterProbability Greater Th an Density Figure 7 Flaw Frequen cy Distribution Example Calculations The proposed flaw distribution m odel was im plemented into a computer progra m, and an out put file is provided as an appendi x to this report.
This outp ut has results for the first 10 of the 1000 simulated vessels that a re addressed by the full input file for th e FAVOR code. Significa nt differences were seen in the predicted flaw distributions com pared to the prior PNNL work. A large part of these differences c ame from correcting the ori ginal conversion f rom flaws per unit area to f laws per unit volum
- e. Table 2 summarizes results fro m both the prior m odel (Tables 2a through 2d) and the u pdated model (Tables 2e and 2f). Results are pres ented both in te rms of flaw density (flaws per cubic foot) and total number of flaws in a vessel considering only the beltline region (assum ing a surfa ce area of 627 square feet correspo nding to a ves sel in a typical FAVOR calculation). The flaws a re further categorized in terms of their throu gh-wall depth dimensions (0-2 m m, 2-4 mm, and 4-6 mm). Table 2 sho ws very large numbers for subclad flaws, ranging up to a few million fl aws per vessel. This means that if even a sm all fraction of the vessel inner surface is ex posed to the peak levels of em brittling neutron fluenc e, these local regions will still have thousands of subclad flaws. It is therefore ex pected that the effect of flaw density B-15 on vessel failure frequency will beco me insensitive to flaw density
. Failure frequency will the n become more sensitiv e to the sim ulated bounding sizes of the subclad flaws.
Table 2(f) illustrates so me significant aspects of the ne w proposed m odel relative to the prior model. For example, only vessel #8 of the first 10 sim ulated vessels has any flaws with depth dim ensions greater than 2 mm. The sensitivity calculations perfor med by ORNL with FAVOR predicted zero failure probability for a 2-mm flaw depth, even though m any 2-mm flaws were present in the beltline regions. The refore, 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 contra st, for the prior flaw distribution of Table 2(d), all ve ssels had many 4-mm flaws, and a large fraction of the sim ulated vessels w ere predicted to fail.
B-16 Table 2 Summary of R esults for Su bclad Flaws-Prior Model Versus Proposed Mod el Total0-2 mm2-4 mm4-6 mm4562332230Total0-2 mm2-4 mm4-6 mm190,60897,39493,2140Total0-2 mm2-4 mm4-6 mm10,9585,5995,3590Total0-2 mm2-4 mm4-6 mm4,580,3102,340,3782,239,9320Total0-2 mm2-4 mm4-6 mmAverage of 1000 Vessels6,3295,44485035Vessel #15,5805,58000Vessel #210,70110,70100Vessel #34,2724,27200Vessel #48,3128,31200Vessel #52,5542,55400Vessel #610,61510,61500Vessel #76,3516,35100Vessel #81,7841,6061780Vessel #91,1901,19000Vessel #107,7187,71800Total0-2 mm2-4 mm4-6 mmAverage of 1000 Vessels2,645,5222,275,592355,30014,630Vessel #12,332,4402,332,44000Vessel #24,473,0184,473,01800Vessel #31,785,6961,785,69600Vessel #43,474,4163,474,41600Vessel #51,067,5721,067,57200Vessel #64,437,0704,437,07000Vessel #72,654,7182,654,71800Vessel #8745,712671,30874,4040Vessel #9497,420497,42000Vessel #103,226,1243,226,12400Flaw 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 DimensionFlaw 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 ASME. 1993.
White Paper on Reactor Vessel Integri ty Requirements for Level A and B Conditions
, EPRI TR-100251, prepared by ASME Section XI T ask Group on Reactor Pressur e Vessel Integrit y Requirements, prepared for ASME Section XI Worki ng Group on Operating Plant Criteria, pu blished b y Electric Power Research Institute.
Ayres, P.S., e t al. 197
- 2. Babcock and Wilcox, Topi cal Report, BAW-10012-A
, October 197
- 2. Bamford, W., and R.D. Rishel. 20
- 00. A Review of Cracking Associated with W eld Deposited Claddin g in Operating PWR Plants
, WCAP-1533 8, Westingho use Electric Company, Pittsburgh, Pen nsylvania, March 2000.
Buchalet, C., W.L. Server, and T.J. Griesbach. 1990
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Example Output from Pr oposed 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 8.0-1 0.0 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 8.0-1 0.0 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 .
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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 8.0-1 0.0 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 8.0-1 0.0 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 8.0-1 0.0 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 8.0-1 0.0 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 8.0-1 0.0 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 .
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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 8.0-1 0.0 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 .
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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 8.0-1 0.0 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 8.0-1 0.0 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 t o the develop ment of FAVOR Version 0 6.1 as per the change specif ication in Appendix A, Eason developed an alternative em brittlement trend curve of a slightl y simplified form (Eason 07). This alternative rel ationship is very similar in form to that which appears as Eq. 3-4 in the m ain text of this report, and is provided below for referen ce. Eq. C-1 CRPMDT30 eRCStPMnTAMD47.213.61001718.01 eeetNiCugPCufNiBCRP,,,77.31191.1 for welds 10x417.1platesfor 10x561.1forgingsfor 10x140.1777A for welds 0.155 vesselsedmanufactur CEin platesfor 2.135 vesselsedmanufactur CE-nonin platesfor 5.102 forgingsfor 3.102B 102595.010101039.4for 1039.41039.4for ttte Note: Flux () is estim ated by dividing fluence (t) by the tim e (in seconds) that the reacto r has been in o peration. 629.0120.18448.0139.1logtanh2121,,10NiCuttNiCugeeee 008.0072.0for 0.008)-(359.1072.0 008.0072.0for 072.0 072.0for 0,0.6680.668PandCuPCuPandCuCuCuPCufeee wt%072.0for ,min wt%072.0for 0CuCuMaxCuCuCuee )(eCuMax0.243 for Linde 80 welds, and 0.301 for all other m aterials.
Since FAVOR 06.1 had been coded and the throu gh-wall cracking frequency (TWCF) values reported in Table 3.1 had been calculat ed before the developm ent of Eq. C-1 there wa s a need to assess the effect, if any, of using Eq. C-1 inste ad of Eq.
3-4 in the FAVOR calculations. Eq. C-1 w as therefore c oded into C-1 C-2FAVOR, and four different em brittlement conditi ons, as su mmarized in Table C.1
, were analyzed. In Figure C.1
, the TWCF and referenc e temperature (RT) values from Table C.1 are compared to the baseline resul ts 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 o n the TWCF values esti mated by FAVOR and, consequentl y, has no signi ficant effect o n the TWCF and RT screening lim its proposed in the main body of this report.
Table C.1.
FAVOR TWCF Results Us ing Eq. F-1 for the Embrittlement Tre nd Curve RT Values [
oF] % TWCF due to -
95th Percentil e TWCF Condition RTAW-MAX RTPL-MAX RTCW-MAX 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 2006FAVOR 06.11.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-03550650750850Max. RTAW [R]95th %ile TWCF - Axial Weld FlawsBeaverOconeePalisadesFitAlternateTrend CurveAugust 2006FAVOR 06.11.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-03550650750850Max. RTPL [R]95th %ile TWCF - Plate FlawsBeaverOconeePalisadesFitAlternateTrend CurveAugust 2006FAVOR 06.11.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-03550650750850Max RTCW [R]95th %ile TWCF - Circ Weld FlawsBeaverOconeePalisadesFitAlternateTrend Curve Figure C.1. FAVOR 06.1 baseline results from Figure 3.4 compared with TWCF values estimated using Eq. C-1 (red circles)
C-3 C-4 APPENDIX D TECHNICAL BASIS FOR THE INPU T FILES TO THE FAVOR CODE FOR FLAWS IN VE SSEL FORGINGS
Technical Basis for the Input Files to the FAVOR Code for Flaws in Vessel Forgings F.A. Simonen Pacific North west National Laboratory Richland, Washington July 28, 2004 Pacific North west National Laborator y (PNNL) has been funded b y the U.S. Nu clear Regulator y Commission (NRC) to generate data on fabrication flaw s that exist in reactor pressure vess els (RPVs).
Work has focused on flaws in welds, but with some at tention also to flaws in the base metal regions. Data from vessel examinat ions, along with insights from an expert judgment elicitation (MEB-00-01) and from applications of the P RODIGAL flaw sim ulation model (NUREG/CR-5505, Chapm an et al., 199 8), have been used to generate input files (
see NUREG/CR-6817, Si monen et al.,
2003) for probabilistic fracture mechanics cal culations perform ed with the FAVOR code by Oak Ridge National Labor atory. NUREG/CR-6817 addresses onl y flaws in plate m aterials and provi ded no guidance for esti mating the numbers and sizes of flaw s in forging m aterials.
More recent studies have exa mined forging material, which has provided data on flaws that were detected and sized in the exa mined mate rial. At the request of NRC staff, PNNL has used these more recent data to supplem ent insights from the expert judgment elicitation to generate FAVOR code input files for forging flaws. The discussion below des cribes the technical basi s and results for the forging flaw model. Nature of Base Metal F laws 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 onl y part of the forging that had been re moved from the top of the fo rged ring as scrap not intended for the vessel. This material was expected to have more than the aver age flaw density
, and as such may contribute to the conservatism of any derived flaw distribution.
Figures 1 and 2 show m icrographs of s mall flaws in plate and forging m aterials. These flaws are inclusions rather than por osity or voids. They are al so not planar cracks. Theref ore, their cate gorization as simple planar or volumetric flaw s is subject to ju dgment. The plate flaw of F igure 1 has many sharp and crack-like features, wh ereas such features are not r eadily identified for the particular forging flaw seen in Figure 2. It should, however, be e mphasized that the PNNL exa mined only a lim ited volum e of both plate and forgin g material and foun d very few flaws in exa mined material. I t is not possible to generalize fro m such a small sample of flaws. Ac cordingly, the flaw m odel makes assumptions that may be somewhat conservative, due to the lim ited data on the flaw chara cteristics. Flaw Model for Forgin g Flaws The model for generating distributions of forging fl aws for the FAVOR code uses the same approach as that for m odeling plate fla ws as describ ed in NUREG
/CR-6817.
The quantitati ve results of the expert elicitation are used along w ith available data fro m observed forging flaws. The flaw data were used as a "sanity check" on the results of the expert elicitati on. Figure 3 sum marizes results of the expert elicitation. Each expert wa s asked to estimate r atios between fla w densities in base metal compared to the corresponding flaw densities observed in the weld me tal of the PVRUF vessel. Separate ratio s were requested for plate material and forging material. D-1 As indicated in Figure 3, the parameters for forging fl aws are similar to those for plate flaws.
The forging and plate m odels 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" flaw s in forging material is somewhat gre ater than the density of flaws in plate m aterial. The factor of 0.025 for the flaw density is replaced by a factor of 0.07 for forging flaw
- s. 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 exa minations show that these factors are consistent with the available data. It is noted that the assu mption for the 0.07 factor is supported b y only a single data point cor responding to the largest observed forgi ng flaw (with a depth dimension of 4 mm). The factors of 0.1 and 0.07 ca me from the reco mmendations from the expert elicitation on vessel flaw
- s. As noted below, the very limited data from PNNL's examinations of forging m aterial show that these factors are consistent with the data, although the 0.07 factor is supported b y only one data po int for an observed forg ing flaw with a 4-mm depth dim ension.
Comparison w ith Data on Observed Flaw s The PNNL e xaminations of vessel materials included both plate materials and forging m aterials. For plate flaws less than 4 mm in through-wall depth dim ension, Figur e 4 shows data fro m NUREG/CR-6817 that show frequencies for plate flaws.
Also shown for comparison are the flaw frequencies f or the welds of the PVRUF and Shoreh am vessels.
This plot confirmed results of the expert judgment elicitation (Figure 4) and indicated (1) there are fe wer 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 o n flaws in forgings af ter 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 materi al. There is qualitative agreement with the results of the expert ju dgment elicitat ion (Figure 4)
, which indic ates that (1) plate and forging m aterials have sim ilar frequencie s for small (2 mm) flaws, and (2) f orging material have higher fl aw frequencies fo r larger (> 4 mm) flaws.
Inputs for FAVOR Co de Figure 7 compares the flaw frequencies for plates and fo rgings that were provid ed to ORNL as input files for the FAVOR code. This plot shows mean frequen cies from an uncertainty distribution as described by the flaw input files. It is seen that the cu rves for plate and forgin g flaws are identical for sm all flaws, but show differences for the fla ws larger tha n 3% of th e vessel wall thickness. Also seen is the eff ect of truncating the flaw distribution at a dept h of 11 mm (about 5% of t he wall thickness).
D-2 References Jackson, D.A., and L. Abra mson, 2000.
Report on the Preliminary Results of the Expert Judgment Process for t he Development of a Methodology for a Ge neralized Flaw Size and Density Distribution for Domestic R eactor Pres sure Vessel, MED-00-01, PRAB-00-01, U.S
. Nuclear Reg ulatory Commission.
Schuster, G.J., 200
- 2. "Technical Letter Report-JC N-Y6604-Validated Flaw Density and Distribution Within Reactor Pressure V essel Base Metal Forged Rings," prepared by Pacific Northwest Na tional Laborator y for U.S. Nuclear Regulator y Commission, December 20, 200
- 2. Simonen, F.A., S.R. Doctor, G.J. Schuster, and P.G. Heasl er, 2003.
A Generalized Procedure for Generating Flaw-Related Inputs for t he FAVOR Code
, NUREG/CR-6817, Rev. 1, prepared b y Pacific Northwest National Labora tory for U.S.
Nuclear Regulatory Commission.
Figure 1 Small F law in Plate Material Figure 2 Small F law in Forging Material D-3 Figure 3 Relative Flaw Densities of Base Met al Compared to Weld Metal as Estimated by Expert Judgment Process (from Jackson and Abramson, 2000) 1101001,00010,000100,00002468101214Flaw Depth, mmFlaw Rate- per cubic meter Shoreham Weld PVRUF WeldC:\FLAWDATA\ORNL-FLAW-002.XLSShorehamBase MetalRiver BendBase MetalHope CreekPVRUFBase MetalAverage of Base Metal Figure 4 Flaw Frequencies fo r Plate Material s with Comparisons to D ata for Weld Flaw s D-4 1.E+021.E+031.E+0401234Through-wall size (mm)Cumulative Density (per cubic meter) 5PVRUF plate109-1,2,5109-1,2 Figure 5 V (cumulative flaw density is the ws per cubi c meter of equal or greater siz e) alidated Fla w Density and Si ze Distribution for Three Forging Specimens number of fla1.E+021.E+031.E+04012345Through-wall size (mm)Cumulative Density (per cubic meter)6PVRUF plate109-5109-1109-2 Figure 6 Average of V alidated Cumulative Flaw Density for Forging Material, A508 D-5 1.E-021.E-011.E+001.E+011.E+020123456Flaw Depth Dimension, Percent of WallFlaws per Cubic FootForgingPlate Figure 7 Comparison of Flaw Distributions for Forging and Plate D-6 D-7
- 1. REPORT NUMBER (Assigned b y NRC, Add Vol., Supp., Rev
., and Addendum Num bers, if any.) NUREG-1874 3. DATE REPORT PUBLISHED MONTH YEAR 2. TITLE AND SUBTITLE Recommended Screening Limits for Pressurized T hermal Shock (PT S) 4. FIN OR GRANT NUMBER 6. TYPE OF REPORT Technical 5. AUTHOR(S)
M.T. EricksonKirk 1 and T.L. Dickson2 7. PERIOD COVERED (Inclusive Da tes) 1-2005 to 2-2 007 8. PERFORMI NG ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Com mission, and mailing address; if c ontractor, provide name and mailing address.) 1Division of Fuel, Engineering, and Radiologi cal Research, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, Washington, DC 20555-0001 2Oak Ridge National Labor atory, P.O. Box 2008, Oak Ridge, T N 37831-6075 NRC FORM 335 (9-2004) NRCMD 3.7 U.S. NUCLEAR REGULATORY COMMISSION BIBLIOGRAPHIC DATA SHEET (See instructions on th e reverse) March2010 9. SPONSORING ORGANI ZATION - NAME AND ADDRESS (If NRC, type "Same as above
"; if contractor, provid e NRC Divisi on, 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 l ess) During plant operation, the walls of reactor pr essure vess els (RPVs) are e xposed to neutr on radiation, resulting in localized embrittlem ent of the vessel steel a nd weld materials in the c ore area. If an embrittled RPV had a fla w of critical size and certain severe system transients were to occur, the fla w could very rapidly propagate through the vessel, resu lting in a throug h-wall crack and ch allenging the integrity of the RP V. The severe trans ients of conce rn, known as pressuriz ed thermal s hock (PTS), are characterized by a rapid cooling (i.e., the rmal shock) of the internal RPV surface in co mbination with repressurization of the RPV. Advance ments in our u nderstanding and knowledge of materi als behavior, our ability to realistically model plant systems and operational character istics, and our a bility to better eva luate PTS transie nts to estimat e loads on vessel walls led the U.S. Nuclear Regulatory Commission (NRC) to realize that the earlier analysis, cond ucted in the course of d eveloping the PTS Rule in the 19 80s, contained significant conserv atisms. This report provides t wo options for using th e updated tech nical basis described herein to deve lop PTS screeni ng limits. Calculations reported herein show that the risk of through-wall cracki n is low in all operating pressurized-water reactors
, and current PT S regulations include consderble implicit marg in. 12. KEY WORDS/DESCRIPT ORS (List words or phrases that will assist researchers in locating the report.) Pressuriz ed thermal shock, reactor press ure vessel, pro babilistic fractur e mechanics 13. AVAILABILITY STATEMENT unlimited 14. SECURITY CLASSIFICATION (This Page) unclassified (This Report) unclassified
- 15. NUMBER OF PAGES 16. PRICE NRC FORM 335 (9-20
- 04) PRINTED ON RECYCLED PAPER