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
NU REG-18 7 4 Recommended Screening Limits for Pressurized Thermal Shock (PTS)
Office of Nuclear Regulatory Research NU REG-18 7 4 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 2 Oak Ridge National La boratory Oak Ridge, TN 37831-6170 1 Office of Nuclear Regulatory Research
ii Abstract During plant operation, the walls of reactor pressure vessel s (RPVs) are exposed to neutron radiation, resulting in localized em b rittlem e nt of the vessel st eel and weld mat e rials in the core area. If an em brittled RPV had a flaw of critical size and certai n sev ere sy stem transients we re to occur, the flaw could pr opagate very rapidly through the vessel, re sulting in a through-wall crack and challenging t h e integrity of the RPV. The severe transi ents of c oncern, known as pressurized ther m a l shock (PTS) events, are chara c teri zed by a rapid cooling of the internal RPV surface in com b ination with repressu rization of the RPV. Advancem ents in its unde rstanding and knowledge of materi als behav ior, its abilit y to m odel realistically plant sy stem s and operational charact erist i cs, and its abilit y to better evaluate PTS transients to esti m ate lo ads on vessel walls led the U.S. Nuclear Regulatory Commission to realize that t h e analy s is conducted in the course of developing the PTS Rule in the 1980s c ontai ned 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 ate r reactors, an d current PTS re gulations include considerable i m plici t margin.
Paperw ork Reduction Act Statement The inform ation collections contained in this NUR EG are subject to the Paperwork Reduction Act of 1995 (44 U.S.C. 350 1 et seq.)., which w e re approved b y the Office of Managem e nt and Bud g et, approval num ber 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 inform ation or an inform ati on collection require m e nt unless the requesting document displa y s a currently valid OMB control num ber. iii iv Fore w o rd The reactor pressure vessel (RPV) in a nuclear power plant is expos ed to neutron radiation duri ng norm al operation. O v er time, the vessel steel beco m e s m o re brittle in the region adjacent to the core.
If a vessel had a preexisting flaw of critical size and certain sever e sy stem tr ansients wer e to occur, this flaw could propagate rapidly thr ough the wall of the vessel. The severe tran si e n ts of concern, known as pressurized therm a l shock (PTS) event s , are charact e rized by a ra pi d cooli ng (i.e., thermal shock) of t h e internal RPV surface that may be com b ined with repressurization.
Advancem ents in the state of knowledge in the m o re than 20 y ears since the U.S. Nuclear Reg u lator y Commission (NRC) prom ulgat e d its PTS Rule, (i.e., Title 10, Section 50.61, "Fracture Toughness Require m e nts for Pr otection against Pressurized Thermal Shock Events
," of the Cod e of Federal Regulatio ns (1 0 C F R 5 0.6 1)) suggest th at th e embrittlemen t s c r e e n i n g l i m i t s i m p o s e d b y 1 0 C F R 5 0.6 1 a r e overly conservative.
T h e r e f o r e t h e NRC conducted a stud y to develop t h e technical basis for revising the PTS Rule i n a m a n n e r c o ns i s t e n t w i t h t h e N R C's g u i d e l i n e s o n r i s k-i n f orm e d regulation. In early 2005, th e Advisory Comm itt ee on Reactor Safeguards (ACRS) endorsed the staff's approach and its pro posed techni cal basis. The staff docu m ented the technical basis in an extensiv e set of reports (Section 4.1 of this report provi des a com p lete 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 im prove the m odel. This report documents these changes to the m odel an d the results o f an updated s e t of pr obabil istic calculations, which sh ow the follow ing: For Plate-We lded Pressurized-Water R e actors (PWRs
): Assu m ing that current o p erating cond itions are maintained, the risk of PTS failure of the RPV is very l o w. Over 80 percent of operating PWRs have estim ated thro ugh-wall cracking frequency (TW C F) values below 1x1 0-8/ry, even after 60 y ears of operation.
After 40 y ears of operation the highest ri sk of PTS at any PWR is 2.0x10
-7/r y. A f ter 60 y ears of operation this risk increase s to 4.3x10
-7/ry. If the referenc e te m p er ature screening limits proposed herein, which are based on limiting the y e arly 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 m p eratur e li m its withi n the first 40 y ears of operation. After 60 y ears of operation, the m o st em b r ittled plant will still be 17 F away from the r e feren ce te m p eratur e li m its. For Ring-For g ed PWRs: Assu m ing that current oper a ting conditi ons are m a intained, the risk of PTS failure of the RPV is very l o w. All oper a ting PWRs h a ve estimated TWCF values below 1x10
-8/r y , even after 60 y ears of operation. After 40 y ears of operation the highest risk of PTS at any P W R is 1.5x 10-1 0/ry. After 60 y ears of operation this risk increase s to 3.0x10
-10/r y. If the reference tem p erature screening lim it s proposed he rein, whic h are based on limiting the y e arly through wall cracking frequency to belo w a value of 1x10
-6 , are adopted, and if current operating practices are maintained then no plant will get within 59 F of t h e reference temperature li m it s within the fi rst 40 y ears of operation. After 60 y ears of operation, the m o st em brittl ed plant will still be 47 F away from the ref e r e nce te m p erat ure lim it s. These findings apply to all PWRs curren tly in operati on in the United States. This report describes two options by w h ich these findings can be incorporat ed into a revised version of 10 CFR 50.61.
Brian W. Sheron, Director Office of Nuc l ear 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 RT NDT Epistemic Uncertaint y Data Basis
...................................................................................
3 2.1.1 Review Finding
.................................................................................................................
......3 2.1.2 Model Change
...................................................................................................................
......3 2.2 FAVOR S a mpling Procedures on RT NDT Epistem ic Un certainty...............................................
4 2.2.1 Review Finding
.................................................................................................................
......4 2.2.2 Model Change
...................................................................................................................
......4 2.3 FAVOR S a mpling 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 E m brittlem e n t Trend Curve
......................................................................................................
..7 2.6.1 Review Finding
.................................................................................................................
......7 2.6.2 Model Change
...................................................................................................................
......7 2.7 LOCA Break Fr equencies...........................................................................................................
7 2.7.1 Review Finding
.................................................................................................................
......7 2.7.2 Model Change
...................................................................................................................
......8 2.8 Tem p erature-Dependent Ther m a l 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 De m onstratio n That the Fla w s That Contribute to TWCF are Det ect ab le by NDE Performed to ASME SC VIII Supplem ent 4 Requirem e nts.........................................
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 e ening Lim its......................
13 3.2.1 Justification of Approach
......................................................................................................
13 3.2.2 Use of Reference Tem p erat ures to Correlate TWCF
............................................................
15 3.3 Plate-Welded Plants............................................................................................................
......19 3.3.1 FAVOR 06.1 Results
............................................................................................................
1 9 3.3.2 Esti m a tion of TWCF Values and RT-Based Lim its for Plate-Welded PWRs
......................
25 3.3.3 M o d i f i c a t i o n f o r T h i c k-W a l l e d V e s s e l s....................................................................................
28 3.4 Ring-Forged Plants
.............................................................................................................
......28 3.4.1 E m bedded 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 e gulator y Implem entation of These Results
........................................................
31 3.5.1 Lim itation on TWCF
.............................................................................................................
32 3.5.2 Li m itation on RT...................................................................................................................
42 3.6 Need for Margin
................................................................................................................
........47 3.6.1 Residual Con servatisms
........................................................................................................
4 8 3.6.2 Residual Nonconservatisms
..................................................................................................
50 3.7 Summary........................................................................................................................
...........
52 4 Refere n ces.....................................................................................................................
............
55 4.1 PTS Technical Basis Citations..................................................................................................
55 4.1.1 Summary........................................................................................................................
.......55 4.1.2 Probabilistic Risk Assessment
..............................................................................................
55 4.1.3 Therm a l-Hy draulics.............................................................................................................
.5 5 4.1.4 Probabilistic Fracture Mechanics
..........................................................................................
56 4.2 Literature Citations
...........................................................................................................
........58 Appendix A
- Changes Requested Betw een FAVOR V e rsion 05.1 a nd FAVOR Version 06.1.---A-1 Appendix B
- Review of the Litera ture on Subclad Fla w s and a Technical Basis for Assigning Subclad Flaw Distributions---
.-B-1 Appendix C
- Sensitivit y St udy on an Alt e rn ative E m brittlem e nt 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 o cumentation summarized b y this report and b y (EricksonKirk-Sum). The citations for these reports in the text appear in itali cized boldfac e to distingui s h them fro m literature citatio ns..............................................................................................
1 Figure 2.1. Data on which the RT NDT epistem ic 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 di m e nsi on and positi on descriptor s adopted in FAVOR...........................................
9 Figure 2.5.
Distribution of through-w a ll position of cracks that initiate
...............................................
9 Figure 2.6. Flaw depths that contribute to cr ack initi ation probabil ity in Beaver Valley Unit 1 when subjected to (left) medium- and la rge-dia m eter pipe break transients and (right) stuck-open valve tr ansients at two different em brittlement levels.........................
10 Figure 2.7.
Analy s is of Palisades tr ansients #65 (repressurization transient) and #62 (large-diam eter pri m ary-side pipe break transient) to illustr a te what co mbinations of flaw size and location lead to non-zero conditi onal pr obabilities of crack initiation
.......10 Figure 2.8.
Probabilit y of detection curve (Becker 0 2).......................................................................
11 Figure 3.1. TWCF distributions f o r Beaver Valley Unit 1 estimated for 32 E F PY and for a m u ch higher level of em brittlem e nt (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 n sient classes on em brittlement as quantified b y the param e ter RT MAX-A W (curves are hand-drawn to ill ustrate trends)
........23 Figure 3.4. Relationship between TWCF and RT d u e to various flaw populati ons (left: axi a l weld flaws, c e nter: plate flaws, right: circ u m ferential weld flaws).
Eq. 3-5 provi d es 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 diagram s is 1 x10-6. The top diagram pr ovides a close-up view of the outerm o st corner shown in the bottom diagra m. (Th ese diagra ms ar e provided for visualization purposes only
- the y are not a co m p letel y accurate re presentation of Eqs. 3-5 and 3-6 particularly in t h e ver y steep regions at the edges of the TWCF = 1x10
-6 surface.)
..26 Figure 3.6.
Maxi m u m R T-based scre e n ing criterion (1 E-6 curve) for plate-wel d ed vessels based on Eq. 3-6 (le f t: screening criterion relative to current ly operating PWRs after 4 0 y ears of operation; right:
screening crit erion relative to currently operating PWRs after 60 y ears of operation)
...............................................................................................
27 Figure 3.7.
Distribution o f RPV wall th icknesses for P WRs curr ent ly in serv ice (RVID2). Th is fig u re origin ally app e ared as Figure 9.9 in NUREG-1806.
................................................................
28 Figure 3.8.
Effect of v essel wall thickn ess on th e TWCF of v a riou s transients in Beav er Valley (all analy s es 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 co m p ared wit h results for plate-welded v essel s (see Figure 3.7)
......................................
31 Figure 3.1
- 1. Estim a ted distributio n of T WCF for currently operatin g PWRs using the procedu r e detailed in Section 3.5.1
....................................................................................................
37 Figure 3.1
- 2. Co m p arison of the distrib u tions (red an d blue hist ogr am s) of the various RT values characteristic of beltline m a terials 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 o r the original presentation of these relati onships).......................................................................................................
4 1 Figure 3.1
- 3. Graphical co m p arison of the RT lim its for plate-welded plants de veloped in Section 3.5.
2 with RT values for plants at EOLE (from T a ble 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 m p arison of the RT lim its for ring-for g ed plants devel oped in Section 3.5.
2 with RT values for plants at EOLE (from T a ble 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 g ed 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 a ted Using the Procedure Described in Section 3.5.1
...............................................................................
40 Table 3.5.
..................................................................................................
.......46 Table 3.6.
Non-Best-Est i m ate A s pect s of the Mode ls Used to De velop the RT-Based Screening Limits for PTS
.................................................................................................
51 Table 3.7.
.................................................................................................
........53 x Executive Summary Fro m 1999 th rough 2007, the U.S. Nu clear Regulatory Co mmission (N R C) c ondu cted 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 e n ts for Protec tion against Pr essurized Ther m a l Shock Events,"
of the Code o f Federal Regulatio ns (1 0 C F R 5 0.6 1) i n a manner co nsistent with the NRC's guidelin es on r i s k-i n f orm e d regulation. In early 2005, the Advisory Co mm ittee on Reactor Saf e guards (AC R S) endorsed the staff's approach and its pro posed techni cal basis. The staff docu m ented the technical basis in an extensiv e set of reports (Section 4.1 of this report provi des a com p lete 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 im pr ove 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 al ternative to the PTS Rule.
This e x ecu ti v e sum m a ry be gi ns w it h a de scrip ti on of P TS, h o w it m igh t occ u r, an d its p o ten tial c onse q uences for the reactor pressure ves sel (RPV). T h is is follo wed by a summ a ry of the current regulatory approach to PTS, whic h leads directly to a discus s ion of the m o tivations for conducting t h is project. F o llowing t h is introductory inform ation, the exec ut ive summary describes the approa ch used to c onduc t the study, a n d summ arizes k e y f i n d i n gs and re co m m en d a tio n s , wh i c h in cl u d e a p ro p o s a l fo r a r e v i sio n to th e PTS sc r een in g limits.
To prov ide a co m p lete perspective on th e current und erstanding of the risk of RP V failure arising from PTS, this executive summary draws not onl y on inf o r m a tion presented in t h is report but also f r om the other technical basis reports listed in Section 4.1 of t h is report.
Description of PTS During the op eration o f a n u clear po wer plant, th e RPV walls are exposed to n e u t r on radiation
, resulting in locali zed emb r ittl ement o f t h e v e ssel st ee l and weld ma terials in th e area ad j a cent t o the reactor core. If an e m b r it t l e d RP V had an existing flaw of critical size and certain seve re sy stem tr a n sients were t o occur, the f l a w could propa gate very rapidly through the vessel, resulting in a through-wall crack and challenging the i n t e g r i t y of th e RPV. Th e severe tran sien ts of con c ern, known as PTS ev ents, are characterized b y a r a p i d cooling (i.e., t h erm a l shock) of the intern al RPV surface and downcomer, which may be follo wed by repressuriz a tion of the RPV. Thus, a PTS event pos es a potentially significant challenge to the structural integrity of the RPV in a pressurized-w at er reactor (P WR). A num ber of abnorm a l events and pos tul a ted accident s have the pot ential to ther mally shock t h e vessel (either with o r without sign ifican t in tern al pressure). These ev ents in clud e, among others, a pip e break in t h e pr im a r y p r e s s ure c i rc u i t, a s t uc k-o pe n v a l ve in th e primary pressure circuit that later re-clos es (causing re-pressurizat i on of the primary
), or a break of the ma in steam line. When such events are initiated by a break in the p r i m ary pressu re ci rcu it th e water l e v e l dr o p s a s a r e s u l t of leakage from the bre a k. Automatic sy stems and operators provi de makeup water in the primar y s y s t e m to prevent overheating of the f u el in the core. However, the makeu p water is m u ch colder than that held in the prim ary sy stem. As a r esult, the tem p erature d rop produced by rapid depr essurization, coupled with t h e ne a r-a m b i e n t t e m p e r a t ur e of t h e makeup water, produces sig n ifican t th er mal stresses in t h e hott e r thi c k section s t e e l w a l l o f t h e R P V. F o r em brittled R PVs, these str esses could be sufficient to initiate a running crack, wh ich could propagate all the way thr o ugh the vessel wall. Such through-wall cr acking of the RPV could result in core dam a ge or, in rare cas es, a large early releas e of radioactive m a te rial to the envi ronm ent. Fortunately, the coincident occurrence of critical-size f laws, em brittl ed vessel steel and weld material, and a severe PTS tr ansient is a very l o w-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 lim it (10 CFR 50.61) on the level of em brittlement during the fi rst 40 y ears of operation assu m ing that current operating practices are m a intain ed. 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 mater ial surveillance pr ogram qualified under Appendi x H, "Reactor Vessel Material Surveillance Program Requirements," to 10 C FR Part 50, "Do m esti c Licensing of Production and Utilization Facilities."
The surveillance results are then used together with the form ulae an d tables in 10 CFR 50.61 to estim at e the fracture toughness transition tem p er ature (RT NDT) of the steels in the vessel's beltline and how those transition tem p er atures increase as a result of irradiation damage that accu m u lat es over the operational life of the vessel.
For licensing purposes, 10 CFR 50.61 provides instructions on how to use these esti m at es of the effe ct of irradiation dam a ge to esti m at e the value of RT NDT that will occur at end of license (EOL), a value called RT PT S. The screening lim its provided in 10 CFR 50.
6 1 restrict the maxim u m values of RT NDT perm itted during the plant's operational life to
+270 F (1 32 C) for axial welds, plates, and forgi ngs, and +300 F (149 C) for circu m fer e ntial welds.
These scr eeni ng lim its wer e selec ted based upon a limit of 5x10
-6 e v ents per y ear on the annual probabilit y of developing a throu gh-wall crack (RG 1.154).
Should RT PTS excee d these scre e n ing lim its, 10 CFR 50.61 requires the licensee to ei ther take acti ons to keep RT PTS below the scre e ning limits. These actions include i m plementing "reasonably practicable" flux reductions to reduce the em brittlement rate or by deem brittl ing the vessel by annealing (R G 1.162), or perform ing plant-specific analy ses to demonstrate that operating the plant be y o nd t h e 10 CFR 50.61 s c r e e n i n g l i m i t s d o e s n o t p o s e a n u n d u e r i s k t o t h e p u b l i c (R G 1.15 4). While no curr ently operating PWR has an RT PTS value that is projected to exceed the 10 CFR 50.61 screening li mits b e f o re E O L , s e ve ra l p l a n t s ar e clo s e t o the li mit (3 ar e within 2 F, wh il e 10 are within 20 F). T h os e p l a n ts ar e likely to exceed the screen ing lim its during the 20-y ear license rene w a l period that many operators are currently seeking or have alr eady received.
Moreover, some plants ma intain their RT PTS values below the 10 CFR 50.61 sc reening lim its b y im plem en ting flu x redu ctions (low-leakage cores, ultra-low-leakage co res), which ar e fuel m a nag e m e nt strat e gies that can be econo m icall y deleterious in a deregulated m a rketplace. Thus, the 10 CFR 50.61 screening limits can re str ict both the licensable an d econom ic lifetim e of PWRs.
Motivation for This Project It is now wid e ly recognize d that the state of knowled g e and data li mitations in the early 1 980 s necessit a ted c onservative treat ment of several key pa ra m e t e rs and m odel s used in the probabilistic calculations that provided the technical basis for the current PTS Rule. The m o st prom inent of these conservatis ms includes the following fa ctors: highl y sim p li fied treat m e nt of plant trans ients (very coarse grouping of m a ny oper a tional sequences (on the or der of 10 5) into very few groups (approxim a tely 10), necessitat e d by limitations in the co m putational resources needed to perfor m m u ltiple ther m a l-hy dra u lic (TH) cal culations) lack of any significant credit for operator action characte rizati on 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 m odeling approach that t reated the RP V as if it were m a de entirely from the most brittle of i ts constituent materials (weld s , plates, or forgings) a m odeling approach that assessed RP V em brittlement 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 h at reexa m ini ng the technical basis for these screening lim its, based on a modern unders tanding of all the factors that influence PTS, would m o st likely provide strong justific ation for s ubs tantially relaxing these lim i ts. For these reasons, the NRC undertook this st ud y with t h e objective of d e veloping t h e technical basis to support a risk-inform ed revi sion of the PTS Rule and the associat ed PTS screening lim its. Approach As illustrated in the foll owing figure, thr ee main m odels (shown as solid bl ue squares), taken together, perm it estimation of t h e an nual frequency of thr oug h-wall cracking in an RPV: probabilistic risk assessment (P RA) event sequence analy s is TH analy s is probabilistic f racture mech anics (PFM) analy s is PR A E v e n t S e quence An a l y s i s (SA PPH I R E)Th e r m a l Hy d r a u li c An a l y s i s (R EL A P)P r o b a b ilis t ic Fr ac t u r e An a l y s i s (F A V O R)Se q u enc e De fi ni ti o n s S e qu en ce Fr eq ue nc ie s fr eq C ond it i ona l P r o ba bili t y of Th ru-W al l C r ack ing, CP TW C P(t), T (t), &HT C (t)Ye ar l y Fr eq ue nc y o f Th ru-W al l Crac ki ng[CP TW C]x[fr eq]Probabilis t i c E s t i mat i on of Th rough-W a ll Cracking Fre q ue ncy V e s s e l da m a ge , a ge , o r op eratio n a l me t r i c Yea r l y Fre qu e nc y of Thru-W a l l Cr a ck i n g Scr e eni ng Li mi t Acce pta n ce Cri t e r ion fo r T W C Frequ e ncy Establ ishe d co n s i s te nt w i th*1 98 6 Co m m i ssi on safe ty goal po lic y s t a t e m e n t*J une 1 9 9 0 SRM*R G 1.1 7 4 Sc ree n ing Li mit De v e lo pme n t Schematic sho w i ng ho w a probabilisti c estimate of TWCF is combined w i th a TWCF accep tanc e criterion to a rriv e at a proposed rev i sion of the PTS screeni ng limit Fir s t, a P R A e v ent sequ en c e an aly s is i s pe rfor m e d to po stul at e th e s e q u enc e s of ev e n ts th at may c a us e a PTS challenge to RPV integrity and to esti m ate the f requency with which such sequences mi ght o c c u r. The e v e n t sequence de finitions are th en passed to a TH m odel that est im ates the tem p oral variation o f te m p erature, pressure, and heat-transfer coefficient in the RPV downcomer, whic h is character istic of each sequence definition.
These tem p er ature, pressur e , and heat-transfer coefficient histories are then passed to a PFM m odel that uses the TH output, al ong with other inform a tion c oncerning RPV design and construc tion m a terials, to es tim at e t h e tim e-depe nde nt "dr i vi ng f o r ce to f r act ure" pr o duce d b y a par tic ular event sequence. The PFM m odel then co m p ares this est i m ate of fractu re-driving forc e to the fracture toughness, or fracture re sistance, of the RPV ste e l. Perfor m ing this co m p arison for m a ny simulated vessels and xiii flaws per m its esti m ation of the probabilities that a cra c k c o u l d g r ow t o s u ff ic ie nt s i z e t h a t i t w o u l d pene tr at e all t h e way throu gh the RP V w a ll (a s s u m ing that a p a r ti c ul ar s e quen c e o f ev ent s a c t u a l l y o c c u r s). The final step in the anal y s i s involves a sim p le m a trix m u ltiplicatio n of the proba bilit y distribution of through-wall cracking (from the PFM analy s is) with the distribution of frequencies at which a particular event sequence could occur (as defined b y the PRA an aly s is). T h i s product establishes an estim ate of the distributi on of t h e ann u al frequency of thro ugh-w a ll cracking that could occ u r at a particular plant a f t e r a p a r t i c u l a r peri od of o p erat io n whe n su bjec ted t o a partic ular se quence of e v ents. The a n nual fre que nc y d i s t r i b u t i o n o f t h r o u g h-w a l l cracking is then summe d f o r all event sequences to estimate the total annual frequency distribution of t h rough-wall cracking for the vessel. Perf ormance of such analy ses for various o p e r a t i n g l i f et i m e s p r o v i d e s a n e s t i m a t e of how the distribution of annual fre quen c y of through-wall crack ing would vary over th e li feti me of t h e pl ant. Perfor m ance of the probabilistic calculat ions just d escribed establishes the tec hnical basis for a revised PTS Rule w i thin a n integrated s y stem s analy s is fram e wo r k. T h e staf f's ap pr oac h c o nsi d ers a br oa d ra n g e of f a c t o r s that i n fluence the likelihood of vessel f a ilure during a PTS e v ent, while accounting for uncertainties in these factors across a breadth of tec hnical disciplines. Two central features o f this a p p r o a c h a r e a f o c u s on the use of realistic input valu es and mod e ls (wherever pos sible), and an explicit t r e a tm e n t of un c e r t a i n t i e s (u sing currently available un certainty analysis tools a nd t echniques). Thus, the current approach i m proves upon that employ ed i n SE CY-82-465, "
Pressurized T h er m a l Shock," dated Novem b er 23, 198 2, which included in tentional and u nquantified c onservatism s in m a ny aspects of the analy s is, and treated uncert a inties i m plic itly by incorporating them into the m odels. Key Findings The findin g s from this study are divided into five t opi cal areas-(1) the expected m a g n i t u d e of the TWCF for currentl y anticipated operational lifetimes, (2) th e materi al facto rs that dom inate PTS risk, (3) the transient classes that do m inate PTS risk, (4) the appl icability of the se findings (based on detailed analy ses of three PWRs) to PWRs in general, and (5) the an nual li m it on T W CF established consistent with current guidelines on risk-inform e d regulation.
In this summary , the conclusions are presented in bol dface italic , while the supporting infor m ation is shown in regular type. TWCF Mag nitude for Currentl y Anticipated Operational Lifetimes The degree of PTS challenge is low for curr ently anticipated lif etimes and operating con d itions. o For Plate-We lded PWRs: Assu m ing that current oper a ting cond itions are m a inta ined, the risk of PTS failure of the RPV is very l o w. Over 80 percent of operating PWRs have esti m a ted TW CF values below 1x10
-8/r y, even after 60 y ears of operatio
-7/ry. After 60 y ears of operation this risk increase s to 4.3x10
-7/ry. If the R T screening limits proposed herein , which are based on lim iting the y early through wall cracking frequency to below a value of 1x 10-6 , ar e adopted, and if current operating practices are maintained then no pla n t will get within 30 F of the RT lim it s within the fir s t 40 y ears of operation. Af ter 60 y ears of operation, t h e m o st em brittled plant wi ll still be 17 F away from the RT li m its. o For Ring-For g ed PWRs: Assu m ing that current oper a ting cond itions are m a inta ined, the risk of PTS failure of the RPV is very l o w. All ope rating P W Rs have est i m ated TWCF values below 1x10-8/r y, even after 60 y ears of operatio
- n. After 40 years of operation the h ighe st risk of PTS at any PWR is 1.5x1 0-10/ry. After 60 y ears of operation this risk increase s to 3.0x10
-10/r y. If the RT screening li mits proposed herein, which are b ased on lim iting the yearly through wall crackin g xiv frequency t o below a value of 1x 10-6 , ar e adopted, and if current operating practices ar e maintained then no plant will get within 59 F of t h e RT li m its wit h in the first 40 y ears of operation. Af ter 60 y ears of operation, t h e m o st em brittled plant wi ll still be 47 F away from the RT li m its. 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 Vess els Axial flaws are m u ch m o re likel y than ci rcu m ferential 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 x ial flaw. Conversely , circ um fe rentially oriented flaws experience a driving-force peak m i d-wall, provi ding a natural crack a rrest mechanism. It should be n o ted that crack initiation from circu m ferentially oriented flaws is likely
- only their through-wall propagation is m u ch less li kely (relative to axially orie nted flaws). The toughness properties that can be ass ociated with axial flaws co ntrol nearly a l l o f t h e TWCF. These include the t oughness properties of plates and axial welds at the flaw locations.
Conversely
, t h e toughness properties of both ci rcum ferential welds and forgings have little effect on the TWCF of plate-welded P W Rs becaus e these can be associat ed only with circu m ferentially oriented flaws.
o Ring-Forged Vess els As with plate-welded PWRs, axial flaw s are again much m o re like ly than circumferential flaws to propagate through the RPV wal
- l. Ho wever, because there are no axial welds in ring-forged vessels, the axial flaws that can be associat ed with th ese we lds are absent
. However, for particular co m b inations of forgi ng ch em istry and cladding heat input, undercl a d cracks can for m in the forging.
As i m plied by the na m e , t h ese cra c ks f o rm in the forging just below the cladding l a y e r, and t h ey form perpendicular to the direction in which the clad weld lay e r was deposite d (i.e., axially). Therefore, the t oughness properties that can be asso ciated with these axial fla w s (i.e., that of the forg ing) control nearly a l l o f t h e T W C F 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 s m alle r role. o The seve rity of a transient is controlled by a com b ina tion of three factors: initial cooling rate, which controls the t h erm a l stress in the RPV wall mini m u m te m p erature of the transient, which cont rols the resistan ce of the vess el to fracture pressure retai n ed in the primary sy stem , whic h controls the pressure stress in the RPV wall o The significance of a transient (i.e., how m u ch it cont ributes to PTS risk) depends on these three factors and the likelihood t h at the transient will occur.
o The analy s is considered transi ents in the following classe s: primary-side pipe breaks stuck-open va lves on the pr im ary side main stea mli n e breaks xv stuck-open va lves on the secondar y side feed-and-bleed steam gen e rator tube ru ptur e mixed primary and secondary initiators o Of these, t r an si ent s in th e fi rst two cat e go ries we re resp onsible fo r 90 percent or more o f th e PTS risk, wh ile transients in th e thir d catego ry were responsible for n e arly all of th e remaind e r. For m e diu m- to large-diameter pri m ary-side pipe breaks, the fast-to-m oderate co oling rates and low downcom e r tem p eratures (g ene ra ted b y rap id d e press uriza ti o n a n d em erge nc y i n jec ti o n of low-tem p e rature m a keu p water direct ly to the primary s y stem) c o m b ine to produce a high-s e v e r i t y transi ent. Despit e t h e moderat e-t o-low lik eliho od that th ese t ran si ent s will occu r, th ei r s e ve ri t y (if they do occur) makes the m significant contributors to the total TWCF. For stuck-ope n prim ary-side valves that later reclos e, the repressuriz a tion associat ed with valve reclosure coupled with low tem p eratures in the primary s y stem co m b ine to produce a high-severit y transient. Thi s , coupled wit h a high likeli hood of transi ent occurrence, m a kes stuck-open pr im ary-side valves that may later reclose significant con tributors to th e total TWCF. The sm all or negligible co ntributi on of all secondary-side transien ts (m ain steamline break, stu c k-op en secondary valv es) results d i rectly fro m the lack of lo w temp er atures in the p r imary sy stem. For these transient s , the m ini m u m t e m p er ature of the prim a ry s y stem for times of relevance is controlled by t h e boiling poi n t of water in the secondary sy stem (212 F (100 C) or above). At these tem p er atures, the fracture toughness of the em brittled RPV steel is still sufficiently high to resist ve ssel failure in m o st cas es. 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 m atic all y the risk-significance of individual transients. Therefore, a "be s t esti m at e" ana ly s is n eeds to include appropriate credits fo r operator action because it is not po ssible to establish a pri o ri if a par tic ular trans i ent w ill m a ke a la rge contr i buti on t o t h e total ri sk. No neth el es s, the re sult s of th e ana l y s e s d e monstr at e th at t h es e op er ato r ac tion cr edit s h a v e a sm all overall effect on a plant's tota l T W CF, for reasons detailed below.
o Medium- and Large-Dia m e ter Pri m ary-Side Pipe Brea ks: No operator actions are m odeled for any break diam eter because, for these events, the safety injection sy stems 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 pum ps. o Stuck-Open Pri m ary-Side Valves That May Later Reclose
- The PRA m odel includes reason a ble and appropria te credit for operator actions, such as throttling of the high-pressure injection (HPI) sy stem. How e ver, these cr edits have a s m all in fluence on the estimated values of vessel failure probabilit y attributable to t r ansients caused by a stuck-open valve in the prim ary p r e s s u r e c i r c ui t (SO-1 t ran si e n ts) b e c a us e t h e cr edit ed op er ator a c t ions only prevent r e pr es su riz a t io n w h e n S O-1 transients initiate fro m hot zero power (HZP) cond iti ons and the operators act prom ptly (within 1 minute) to thr o ttle the HPI. Com p lete rem ova l of operator action credits from th e m odel onl y increase s slig htly the total risk associat e d with SO-1 transients.
o Main St ea ml i n e B r eak s: F o r th e overwh e l m ing majo ri ty of tran si ent s cau sed by a main st eaml in e brea k, vesse l failure is pre d icted to occur betwee n 10 a n d 15 m i nutes after tra n sie n t initia tion b ecause the thermal st resse s as socia t ed with the rapi d cooldown reach their maxi m u m wi thin this xvi timeframe. Thus, all o f th e long-term effect s (isolation of feed water flow, timing o f th e high-p r e s s u r e s a f e t y i n j e c t i o n c o n t r o l) that can be influenced b y operator actions have no effect on vessel failure probability be cause s u c h fa c t o r s i n f l ue n c e t h e p r o g r e s s i o n o f t h e tr a n s i e n t a f te r f a i l u r e ha s oc c u r r e d (i f i t oc c u r s a t a l l). Only factors affecting the initial cooling rate (i.e., plant power level at time of transient initiation, break location inside or outside of cont ain m ent) can in flu e n ce th e co n d ition a l p r o b a b ility of t h r ough-wa ll cr ac ki ng (C PTW C), a n d oper a t o r a ct i ons do not influe nc e thes e fa ctors in a n y w a y. Be cau s e th e s e v e r it y o f th e mo st sign ifi c ant t r an si ent s in th e do mi n a nt t r an si ent cla s s e s i s con troll ed by factors that are common to PWRs in genera l, the TWCF re su lts presented herein can be used with confidence to develop revised PT S scre ening crit eria that apply to the entire fleet of operating PWRs. o Medium- and Large-Dia m e ter Pri m ary-Side Pipe Brea ks: For these break diamet ers, the fluid in the pri m ary sy stem coo ls fast er than the wall o f th e RPV. In th is si tuation , only the th ermal c onduct i v i t y o f t h e st eel an d t h e t h i ck n ess o f t h e RP V wal l co n t ro l t h e t h ermal st r esse s an d , t h us, the severity of the fracture challenge. Perturba tions in the fluid co ol down rate controlled b y b r e a k d i a m e t e r , break location, and season of the y ear do not pla y a significa n t role. Therm a l con d u cti v i t y i s a ph ysica l pr ope rt y, so it i s v ery co n si st e n t fo r al l R P V st e els , an d th e th i ck n es s e s o f t h e t h r e e R P V s a n a l y z e d a r e t y p i c a l of m o st PWRs. Consequentl y , t h e TWCF contributi on of m e d i u m- t o l a r g e-d i a m e t e r p r i m a r y-s i d e pi pe brea ks is ex pecte d to b e co nsis ten t f r o m pla n t-to-p l a nt and can be we ll represe nte d for all PWRs b y t h e a n a l y s e s r e p o r t e d h e r e i n. o Stuck-Open Pri m ary-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 y s t e m pressur e once the valve reclose
- s. The operating and safety relief valve pressures of all PWRs ar e si mi lar. Additionally , as previously noted, operator action credits affe ct only slightly the to tal TWCF associat ed with this transient class.
o Main St ea ml i n e B r eak s: Since main steamlin e b r eak s fa il early (within 10-15 minutes after t r a n s i e n t i n i t i a t i o n), only fa ctors affectin g the in itial c ooling rate can have any influence on the CPTWC values. Operator actions do not influence these fa ctors, w h ich 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 b le 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 o p eratio nal char acteristics for five additional PWRs re veale d no difference s in sequence progression, sequence fr e q uency, 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 a l 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 v ided by Regulatory Guid e 1.174 f o r la rge early rel ease is conservatively applied to setting an acceptable annual TWCF limit of 1x10-6 events/year.
o While m any post-PTS accident prog ressions led only to core dam a ge (whic h s u ggests a TWCF lim it of 1x1 0-5 events/y ear in ac cordance wit h Regulatory Guide 1.17 4, Revision 1, "
A n Approach for Using Probabilistic Risk Assessment in Risk-Info rmed Decisions on Plant-Specific Changes to the Licensing Basis," issued Novem b er 2002), un cert a inties in the accident progression analysis led to the recommendation to adopt the m o re conserv a tive lim it of 1x10
-6 events/y ear based on the large earl y release fr equency. Recommended Revision of the PTS Screening Li mits The NRC staff reco mmends using differ e nt RT-m et ri cs to characte rize the resist ance of an RPV to fractures in itiating fro m di fferent fl aws at di fferent l o cation s in th e v e sse l. Specifical ly , the staff r e c o m m e n d s an RT for flaws occurring along axial weld fusion li n es (RT MAX-A W), another for the em bedded flaws occurring in plates (RT MAX-PL), a third for flaws occurring along circu m fer e ntial weld fusion lines (RT MAX-CW), and a fourt h fo r em bedded and/or underclad cracks in forgings (RT MAX-FO). These values can be esti m a t ed based m o stly on the in formation in the NRC' s Re actor Ves sel I n tegrity Databas e (R VID). The st aff also reco mmends usin g th ese different RT values together to c h aracteriz e the fracture resi st ance 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 valu es and the T WCF at tribu t abl e to di f f e r e n t f l a w popul a t i o ns s h o w little p l an t-to-p lan t variabilit y be cause of the general si m il a rity of PTS challenges am ong plants.
This re port proposes a form ula to estim ate the tota l TWCF for a vessel base d only on these RT values and on the ves sel wall th ickness, a n d uses this form ula to estim ate th e TWCF values for all ope rating PWRs.
Currently none of these estim ates exceeds the 1 x 1 0-6/r y lim it during either current or extended (thr ough 60 y ear s) operations. One option that may be considered when im p le m enting these results i n a revised version of 10 CFR 50.61 is to sim p ly require license es to ensure that these TWCF esti m ates re main below the 1x10
-6/r y lim it. An alternative i m plementa tion option is to use the equation presented herein that relates T W CF to the various RT-metrics to transform the 1x10-6/r y lim it into lim its on the various R T values. The staff has e s t a b l i s h e d c a n d i d a t e RT-based scree ning lim its by set t i n g th e to tal TW CF e q u a l t o 1 x 1 0-6/r y. 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 m p tion that current P l at e W el d ed P l an t s at 48 E F P Y (E O L E)0 50 10 0 15 0 20 0 25 0 30 0 35 0 40 0 0 5 0 1 00 15 0 2 00 2 5 0 3 00 RT MA X-A W [o F]RT MA X-P L [o F]1x 10-6/ry TWC F limi t Sim p lif ied Im plem ent a tion RT MA X-A W269 F, and RT MA X-PL35 6 F, and RT MA X-A W+ R T MA X-P L538 F.Comparis on of RT-ba sed scree ning limits (curv es or dashed lines) w i th ass ess ment points fo r op erating pla t e-w e lde d PWRs at EOLE. Limit s are sho w n for v essels hav i ng w a ll thicknes ses of 9.5 inches or less. This report prov ides similarly d e fined limits for thicker v essels and for ring
-for g e d v ess els. xviii operating pra c tices are mai n tained). In this figure, the region of the graphs between the red locus and the origin has TWCF values below the 1x 10 6/ry acceptance criterion , so the staff would consider these co m b inations of RTs to be acceptable and require no furt her analy s is. By contrast, the region of the graph outside of either the red lo cus has TWCF values abov e the 1x10
-6/yr acceptanc e criterion, indicating the need for addit ional anal y s is or other m e asures to ju stify contin ued p lant operation. Clearly , op erating PWRs will not exceed the 1x10 6/r y l im i t, even after 60 y ears of op eration. This separation of operating plants from t h e screening li m its contrast s m a rkedly w ith the current regulatory situation in which several plants are wit h in 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 rel y ing on RT-metrics that differ fro m tho se currently used in 10 CF R 50.61, these proposed im plem entatio n opti ons also d i ff e r f r o m t h e c u rr e n t ap p r o ach in term s of the a b sence of a m a rgin te rm. Use of a m a rgin term is a p propriate to acc ount for (at least approxim ately) fac t ors that occ u r in a p plication, but tha t were not c ons idere d in the a n alysis upon whic h the scr e e ning lim its are base
- d. F o r ex a m p l e , t h e cu r r e n t 10 CFR 50.61 m argin term acco unts for uncerta inty i n c opper, nickel, and initial R T NDT values. However, the m odel ad opted in this study explicitly considers uncertainty in all of these variables and models these uncertainties as being larger (a conservat ive represen ta tion) than would be a ppropriate in any plant-specific application. Cons equentl y , use of the 10 CFR 50.61 m a rg in term with the new screening lim its proposed her e in is inappro p riate. In gen e ral, the follo wing three r e a s o n s s u g g e s t t h a t u s e o f a n y m a r g i n term with th e 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 st aff's three plant-speci fic analy ses apply to PWRs in general.
(3) While certain aspects of the m odeling cannot reasonabl y be represented as "best esti m at es," t h ere is, on balance, a conservative bias to these non-best-es timate aspects of the anal y s is because r esi dual 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 co m p anion reports, th e screening lim its t h e staff has reco mmended for PTS are prem ised on the view that the mathemati cal m ode l of PTS we have described is an appropriate representatio n of PTS eve n ts, both in te r m s of the lik elihood of the ir occurance as well and in ter m s of their effect on the RPV were they to occur. Becau se the appropria tness of the staff' s m odel of PTS may change in the future due to changes in operating pr actice, changes i n initiating event frequencies, changes in radiation d a m a ge mechanism s , a nd po tential changes in other factors, the staff should period ically evaluate the PTS m odel described here for appropriat e ness. Shoul d these evaluations reveal a significant departure between this m o del and phy s i cal reality th en appropriate actions, if any, could be taken.
xix xx Chapter 1 - Background and Objective In early 2005, the U.S. Nuclear Regulatory Co mm is sion (NRC) st aff c o m p let e d a se ries of reports detailing the technical basis for a risk-inform ed revi sion of the pressurized ther mal shock (PTS)
Rule (Title 10, Section 50.
61, "Fracture To ughness Requirem e nts for Protection against Pressuri zed Ther m a l Shock Events," of the Code of Federal Regulat ions (10 CFR 50.61)). Figure 1.1 depicts these reports; Section 4.
1 inclu d es the full references.
Both an external peer review panel and the Advisory Committee for Reactor Saf e guards (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 im prove the m odel. The purpose of t h is 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 co m putations, and (3) to m a ke reco mmendat ions on the us e of these res u lts to revise screeni ng lim its for PTS. Chapter 2 of this report det a ils changes t o the m odel since publication of NUREG-1806 (EricksonKirk-Sum) while Chapter 3 describes the res u lts of the calculations and recommendations on revised screening lim its for PTS. This r e port does not pr ov ide a co m p rehensive summary of NRC activities undertaken over the last 7 y ears to develop t h e technical basis for a risk-inform e d revision to 10 CFR 50.61 (see (E rickso nKirk-Sum) for these details).
Summ a r y Re port -N UR EG-1806*Procedu r es, Uncertai n ty , & E x p eri m en t al Va lid a t io n: Eri cks onKi r k, M.T., et al., "P robabi l i sti c F r act u r e M echani c s: M odel s , Pa r a m e t e r s , and Unc e r t ai nt y Tr eat m e nt U sed i n FA VO R V e r s i on 04.1 ,"NURE G-180 7.*FAVO R*T h eo r y M a n u al: W ill ia ms , P.T., e t a l., "F r a c t u r e A n a l ys i s o f Ve ss el s -O ak R i dge, FAVO R v0 4.1, Co m put e r Cod e: T h e o r y and I m pl em ent a t i on of A l gor i t hm s, M e t hod s , and C o r r el at ion s ,"NURE G/CR-685 4.*U ser's M anual: D ic k s o n , T.L., e t a l., "F r a c t u r e A n a l ys i s o f Ve ss el s -O ak R i dge, FAVO R v0 4.1, Co m put e r Cod e: U ser's G ui de ,"N URE G/CR-6 855.*V&V Repor t: Ma l ik , S.N.M., "F A V O R C ode V e r s i ons 2.4 a nd 3.1 V e r i f i cat i on and V a l i d a t i on Sum m a r y R e po r t ,"NU REG-1 795. *Fl a w Di st r i but i on: S im o n e n , F.A., e t a l., "A Gene r a l i zed Pr o cedur e f o r G e ner a t i ng Fl a w-R el at ed I nput s f o r t h e FA VO R Code,"N UREG/CR-6 817, R e v. 1.*Base l i ne: D ic k s o n , T.L., e t a l., "E l ectr oni c Archi v al of the R esul t s of Pres suri ze d Therm al S hock An al y s es for Beav er V a l l e y, O c on ee, and Pal i sad es Reac t o r Pres sure V ess el s G enerated w i th t he 04.1 v e r s i on of FAVO R,"ORNL/NRC/LTR-04/1 8.*S e n s it iv i t y Stu d i e s: E r ic k s o n K irk , M.T., et al., "S ensi ti v i t y Studi e s of t h e P r o b a b ilis t ic F r a c t u r e Me c h a n ic s Mo d e l Used i n FA VO R Ver s ion 0 3.1 ,"NURE G-180 8. *TH M odel: B esse t t e, D., "Therm al H y dr aul i c Anal y s i s of P r es suri ze d Ther m al S hock ,"NURE G/1 809.*RELAP P r ocedu r es & Ex peri m e ntal Va lid a t io n: Fl et ch er, C.D., e t al., "R ELAP 5/M O D 3.2.2 G a m m a A sse ss m e nt f o r Press uri z ed The r m al Sho ck Appl i cat i ons,"NUR E G/C R-6 857.*E x p e r i m e nt al Benchm ar ks: Rey es, J.N., et. al., "Fi n al Report f o r the O S U APE X-CE I n tegral Test F aci l i ty ,"NUR E G/C R-685 6.*E x p e r i m e nt al Benchm ar ks: Rey es, J.N., "S ca l i ng Anal y s i s for t h e O S U A P E X-CE In tegr al T est Fa cil i t y ,"NURE G/CR-67 31.*U n certai n ty: C h a n g , Y.H., e t a l., "T h e rma l H y d r a u lic U n c e r t a i n t y A n a l y s is in Pres suri ze d Therm al S hock Ri s k Asse ss m e nt,"NUR EG/C R-68 99.*Base l i ne: A r c i e r i, W.C., e t a l., "R E L A P 5 Ther m al Hy dr aul i c Anal y s i s t o Suppo r t PTS E v a l u a t i ons f o r t h e O c one e-1, Beav er V a l l e y-1, and P a l i s a de s Nucl ear Po w e r Pl ant s ,"NURE G/CR-6858.*S e n s it iv i t y Stu d i e s: A r c i e r i, W.C., e t a l., "R E L A P 5/M O D3.2.2 Ga mma Re s u lt s f o r P a l i sad es 1D Do w n com er S ensi t i v i t y St u d y"*Consi s t e ncy Ch eck: J u n g e , M., "P T S Consi s t e ncy E f f or t"*Procedu r es & Unc e rtai nt y: W h i t ehea d, D.W., e t a l., "P R A P r o c e d u r e s a n d Uncer t a int y for PTS An al y s is,"NURE G/CR-685 9.*Uncer t a i nt y Ana l y s i s M e t hodol og y: Si u , N., "U n certai n ty An a l y si s and Pres suri z ed Ther m al S hock , An Opi ni on."*Beav er: W h it e h e a d , D.W., e t a l., "B e a v e r Val l e y P T S P RA"*Oc on e e: Kol a czko w s ki , A.M., et al., "O con ee PTS P RA"*Pal i sad es: Wh it e h e a d , D.W., e t a l., "P al i sad es P TS PRA"*Ext e r n al Ev ent s: K o la c z k o w s k i, A.M., e t a l., "E st i m ate of E x t e r n al Ev ents Cont ri b u t i on t o Pres suri ze d Th er m a l S hock Ri s k"*Ge n e r a li z a t i on: Wh i t e h e a d , D.W., e t a l., "Ge n e r a liz a t io n o f P l a n t-S p e c if ic PT S R i s k Resul t s t o A ddi t i ona l Pl a nt s"Resu lt s M o d el s, V alid atio n, & Pr o cedu r es PFM P RA TH Figure 1.1.
Struc t ure of docume ntat i o n summariz e d by this repor t and by (E r i c ks onK i rk-Su m). The citati ons for these reports i n the te xt appear in ita licized b o l d f a c e to disting u ish 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 m e thodology for developing probabilistic estimates of the risk of thr ough-wall cracking of a pressurized-w ater re actor (PWR) vessel caused by PTS (see the reports detailed in Section 4.1 of this report), these reports were subject e d to further intern al reviews an d qualit y cont rol checks. On the basis of these revie w s, t h e NRC staff decided that certain as pects of the probabilistic calculations should be refined or i m proved. These aspe c ts, which are list e d below, are described in both the remainder of this chapter and in Appendix A to this re port. From the descriptions of t h e param e ters RT LB (lower bound reference tem p erature) an d T o (fracture toughness referen ce tem p eratur e) provided in the docum enta tion, it seems that these two param e t e rs should have a m o r e sy stematic rel a tionship and, in particular, that RT LB should alway s be greater than or equal to T o. Nevertheless, Figure 2.1, which dis p lay s the data on which the RT NDT epistem ic uncertainty correction is based, shows that RT LB can be considerably less than T
- o. Is there a proble m with our u nde rstanding of h o w RT LB and T o relate to one another, or is there so m e inconsistency in the data sh own in Fig u r e 2.1? Section 2.1
- Data basi s for the reference tem p erature n il ductilit y (R T NDT) epistemic uncertainty correction
-2 5 0-2 0 0-1 5 0-1 0 0-5 0 0 50-2 0 0-1 5 0-1 0 0-5 0 0 5 0 T o [o F]RT LB [o F] Da t a RT L B = T o Section 2.2
- F racture A nal y sis of V essels: O ak R idge (FAVOR) co mputer code sam p ling pro cedures on ot her variables Section 2.4
- The distributi on of flaws in repair welds Section 2.5
- The distributi on of su bclad flaws in forgings Section 2.6
- The relationship used to pr edict em brittlement based on exposure and on co m position variables Fi gure 2.1. Da ta o n w h i c h the RT NDT e p istemic uncertainty c o rrection is bas ed Section 2.7
- The upper-sh e lf fracture toughness m odel Section 2.8
- The te m p erat ure dependence of ther m a l-el asti c properties 2.1.2 Model Change Section 2.9
- Loss-of coolant accident (LOCA) break frequencies The review c o rrectly 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 y s is of Vessels-Oak Ridge (FAVOR) Code detailed in Appendix A provides a de tailed explanation of t h e ori g ins of these erroneous data and develops a revised epistem i c uncertainty corre ction for RT ND T 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 exa m ination (NDE) techniques to detect and size the flaws found to be risk-s ignificant for PTS.
2.1 RT ND T Epistemic Uncertainty Data Basis 3 2.2 FA VO R S a m p lin g Pr ocedu r es on RT ND T Epistemic Uncertainty 2.2.1 Review Finding The FAVOR code uses an RT NDT fr actu re toughness indexing parameter and a Master Curve Approach fracture t oughness indexing param e t e r (T o) to estimate materi al toughness properties. The sam p ling of the RT NDT-T o correction para m e t e r in the Monte Carlo process (used in the FAVOR code), may affect the variation that is seen in the results for the exa m ple plants. Currently the correction is sam p led inside the flaw loop so that each flaw is potentially assigned a different correction. It may be m o re appropriate to sam p le the correction out side of the flaw loop so t h at the correction is sa m p led once for each m a t e rial for each vess el si m u l a tion. 2.2.2 Model Change The review finding correctly identifies that it is m o re appropriate to sam p le the uncertainty in the RT NDT-T o correction param e ter outside of the flaw loop (but still inside t h e vessel loop). The previous sampling procedu re sim u lated a degree of uncertainty in the unirradiated fracture toughness transition tem p erature that is unrealistic, a deficiency reconciled by the new sa m p ling procedure. The FAVOR change specification details both t h e rationale supportin g th is change and how it is i m ple m ented in FAVOR V e rsion 06.1.
2.3 FA VO R S a m p lin g Pr ocedu r es on Other Variables 2.3.1 Review Finding Sim ilar to the comment made in Section 2.2.1 regarding the location in FAVOR at which the RT NDT epistemic uncertain ty correction is sam p led, the location of ot h e r sam p led param e ters (e.g., cop p er, copper variabil ity, nickel) may not be m o st ap propriately 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 th e RT NDT epist e m i c uncert a inty discussed in Section 2.2, the uncertainty on the following variables is m o re appropriatel y sam p led outside of the flaw loop, requiri ng a m odific a tion of FAVOR 04.1:
the unirradiat ed value of RT NDT standard deviation on co pp er standard deviation on nick el The FAVOR change specif ication details both the rationale supporting these changes and how they are i m ple m ented in FAVOR Versi on 06.1. 2.4 Distribution of Re pair Fl aw s 2.4.1 Review Finding To develop t h e sam p le flaw distributio ns as input t o the F AVOR code, Pacific North w est National Laboratory (PNNL) assu med that 2 percent of t h e volum e of weld seams consisted of repair wel d s. The repair welds wer e assu med to be unif o rmly distributed throug h the submerged metal arc w e ld (SMAW) thickness.
Since repairs typically intersect the surfa ce, it is possible that flaws a ssociat ed with repairs would be preferentia lly located adjacent to the outside dia m eter (O D) or inside dia m eter (I D) su rface s of the RPV.
The extra flaws as sociated with repairs are ty pically located at the deepest point of the repair.
Exam ination of the repairs detailed in Section 5.
7 of NUREG/CR-6471, Vo lume 2, "Charact eriza tion Of Flaws in U.S. Reactor Pressure V ess els: Density and Distribution of Flaw Indications in PVRUF," indicates the deepest part of the excavation cavity would be m o r e 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 see ms rea s onable to increase the proporti on of the flaw distribution that sh ould be attributed to weld repairs from the current 2 percent to some higher v a lue. The hig h er value should be associat ed with the t y pic a l 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 r oportio n of weld repair in the Pressure V ess el Rese arch Users Facility (PV R UF) vessel. The 1.5-perc ent value seems to have been calculated on a vol ume basis. (1) What is the p r oportio n of weld repair associat ed wi th the weld sea m s on the PVRUF ves s e l near the ID surface of the vessel on an area rather tha n a volum e basis? (2) What is the expected or calculated effec t of this change in the assu m p tions 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 n o ted that the j udgm ent to in clude 2-percent repair flaws in the flaw distribution used in the baseline PTS analy s i s was made o n the basis that a 2-percent repair weld volum e exceeded the proporti onal volum e 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 wa s 1.5 percent). However, flaw s in welds are al most alway s fusion-line flaws, which suggests that their num b er scal es in proporti on t o weld fusion li ne area and not in proporti on t o weld volum
- e. To address this issue, PNNL reexam ined the relative proportio n of repair wel d s that occur on an area rather than on a volum e basis. PNNL deter m ined 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 assu mes that a si m u lated fl aw is equally likel y to occur at an y location th rough the vessel wall thickness.
Upon further consideration the staff has deter m ined that this m odel 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 t o occur any w here with respect t o the depth of the excavation cavity. However, Figure 2.
3 shows that weld repair areas occur with m u ch 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 m ation indicates that a flaw fro m a weld repair is m o re likely t o be encountered close to the ID or OD surface than it is at the m i d-wall thickness, a fa ct not well m odel e d by t h e approach adopted i n FAVOR Version 04.1.
FAVOR currently uses as input a "blended" flaw distribution for welds. The flaws plac e d in the blended distri bution are scaled in pro port ion to the fusion area of the different welding processe s use d to fabricate the vessel. B ecause of this approa ch, it is not possible, without significant recoding, t o spe c ify a thr oug h thickness distribution of re pair weld flaws that is biased toward the surfaces while m a intai n ing a random through-thickness distribution appropriate for subm erged are weld (SAW) and SMAW flaws. Therefore, to account for the nonlinear thr ough-t h ickne ss distributio n of weld flaws the 2-percent blending factor currently used for repair welds will be m odified on the following bases:
Only flaws within 3/
8T of the inner dia m eter can contribute to the vesse l failure probability.
Because PTS transients are dom inated by thermal stre s ses, flaw s buried in the vessel wall m o re de eply than 3/8T do not have a hi gh enou gh dri v ing f o rce/low enough fracture toughness to initiate.
In Figure 2.
3, 3/8T corresp onds to 3 inc h es on the x-axis. The curve fit to the data indicates that 79 percent of all repair fla w s 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 h e 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 w a ll. 5 FAVOR's cu rrent assu m p t i on of a random throug h-wall distributio n o f repair flaws generates 37.5 percent of all repair flaws between the ID and 3/8T.
Thus, FAVOR underesti m at es 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 s e s to 2.3 percent (i.e., 2%43/37.5) (see Appendix A).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.00 0.2 0 0.40 0.60 0.80 1.00 D e p t h o f F l aw f r o m C avi t y S u r f ac e (f r act i o n)C u m m u l at i v e d i st ri b u t i o n ( f act i o n)R a ndom di s t r i bu t i on of f l aw l oc a t i on s Weld Re pa ir M o uth Wel d Repa ir Ro o t Fi gure 2.2. Di stri bu ti o n o f rep ai r fl aw s i n an y w e l d re pai r c avi ty NURE G/CR-6471, V o l.2 6 y = 1.1 066e-0.558x R 2 = 0.9773 0%20%40%60%80%100%0 123 4 56 78 Dept h of R e pai r Exca vat i on [i n c hes]P e r c e n t o f R e p a ir E xcav at i o ns E x t e ndi n g t o t hi s D e pt h o r G r eat er R e pa i r m a de f r om I D (2 6 obs e r v a t i on s)R e pa i r m a de f r om O D (2 6 obs e r v a t i o ns)C o m b i n ed (5 2 O b s e r v at i o n s)E x pon. (C om bi ne d (5 2 O bs e r v a t i ons)) Fi gure 2.3. Di stri bu ti o n o f weld repa i r fla w s thro ug h the v e ssel w a ll thickness 2.5 Distribution of Underclad Flaws in For g in gs 2.5.1 Review Finding Very shallow flaws w e re c reated 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 lim it s for ring-forged vessels?
2.5.2 Model Change Dr. Fredric Sim onen of PNNL perform ed a literature review to establish a distributi o n for underclad flaws suitable for use within t h e probabilistic f racture mech anics code FAVOR.
Appendix B i s a report summarizing Dr. Sim onen's findings.
When unfavo r able welding cond itions (hig h-h eat inputs) and material conditions (chem i stries having high proporti ons o f im purity elements) coincide, underclad cracks can appear in forgi ngs. When underclad cracks appear they d o so as d e nse array s (ty p ical intercrack s p acing is 1 or 2 milli m e t e rs). They will ha ve depths on t h e order of 1 m illi m e t e r, but in rare cases can ext e nd into the ferritic steel of the RPV wall by as much as 6 m illi meters. Underclad cracks are oriented perpendicular to the directi on in which t h e weld cladding was deposited, wh ich is to say a x iall y in the vessel. While the conditions unde r which underclad cracks form are not believed t o t y pif y those charact eristic of m o s t or all of the 21 forged PWRs now in service, the staff was not able to establish a criteria t h at could differentiate, with a high d e gree 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 st udies at different levels of em brittlement using FAVOR, along with Dr. Sim onen's underclad flaw distributio n on forged vessels. In these analy ses the staff assu med that underclad cracks exist. Section 3.4 of this report su mmarize s 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 esti m ate how transition temperature shift depends on b o th com position (copper, ni ckel, phosph orus) and exposure (flux, fluence , tim e) variables for the steels used in the beltli ne region of operating PWRs. Versi on 04.1 of FAVOR uses an em bri ttlem e nt trend curve (Kirk 03) that differs fro m both the trend curve reco mmended by the Am eri can Society for Testing and Materials (ASTM) (ASTM E900) as well as from the tren d curve m o st recently reco mmende d by NRC contractors (Eas on 07). Should the st aff consider an y revisions t o the trend curve adopted b y FA VOR? 2.6.2 Model Change Both the em b r ittlem e nt trend curve adopted in FAVOR Vers ion 04.1 (Kirk 03) and the ASTM E900 trend curve (ASTM E900) are based on an analy s is of surveillance data available through approxim a tel y 2001, whereas the trend curve detailed in (Eason 07) features an analysis of all surveillance data available t h rough approxim a tel y 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 m ent of FAVOR 06.1, in accordance with the change specificat ion in Appendix A, Eason developed an alternative em brittlement trend curve of a slightl y sim p lified form (Eason 07). The results reported in Appendi x C dem onstrate that the effect of this alternative tre nd curve on the TWCF values esti m ated by FAVOR i s insignificant.
2.7 LO CA Break Fre q uencies 2.7.1 Review Finding Recently the NRC staf f conducted an expert elicitation to update the L O CA break 7 frequencies needed as part of a risk-infor med revision to 10 CFR 50.46, "Acc eptance Criteria for Emergency Core Cooli ng S y stem s for Light-Water Nucle a r Power Rea c t ors." These frequencies were docu m ented in NUREG-1829 (Tregoning 0 5). Have the calculations docum ented b y the vario u s reports listed in Section 4.1 used these m o s t recent esti m ates 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 0 5) docum ent. 2.8 Tempe r ature-De pende nt Thermal Elastic Properties 2.8.1 Review Finding FAVOR 04.1 adopts tem p erature-invariant therm a l elasti c properties despite well-docum ented e v idence, as re flected by A m eric an Society of Mechanical En gineers (AS M E) codes, that these properties depend on tem p erature.
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 r opriate.
Tem p erature-dependent the r m a l 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 u pper-shelf fracture toughness m odel for ferritic steels (Eri cksonKirk 06a; EricksonKirk 06b).
S hould the FAVOR 06.1 m odel incorporate these new re sults? 2.9.2 Model Change The NRC staf f believes that the FAVOR 06.1 m odel should incorporate t h ese new results. As detailed in Appendix A, F AVOR 06.1 adopts the latest finding s on the u ppe r-shelf fracture toughness m odel described in (EricksonKirk 06a) and (Eri cksonKirk 06 b). 2.10 De monstration Th at the Flaw s That Cont ribute to TWCF are Detectable by NDE Performed to ASME SC VIII Supplement 4 Requireme n ts 2.10.1 Review Finding NUREG-1806 (EricksonKirk-Sum) indicates that a low density of flaws is one m a jor factor in keeping the total risk associated with PTS low.
The state of knowledge of t h e flaw densities in the 70 in divi d u al PWR plants now in se rvice is based primari ly on detailed destructive exam inations of a sm all num b e r of welds and plates fro m f our vessels (but m o stly from t w o vessels), cou p led with expert elicitation and ph y s ical m o d e ling. Anot h e r potential source of inform ation on flaw density is the in-service inspections perfor m ed at 10-y ear intervals on each operating vessel. It would be very helpful if those inspections could provide evi d ence to support t h e assu m p tions in the current analy s is. Specifically , i t is im portant to know the significance of a flaw to the FAVOR anal y s is (based on its size and through-wall location) as well as the probabilit y of detection for those flaws found, based on the FAVOR anal y s is, to be risk significant.
2.10.2 Reply Flaw Depths Important for PTS Figure 2.4 , Fi gure 2.5, and Figure 2.6 ori g inall y appeared in NUREG-1808 (EricksonKirk-SS) as Figures 4-3, 4-4, and 4-5, respectively.
Collectively these figures de m onstrate th at the flaws that co ntribute to PTS risk are (1) all 8
located within approxim at ely 1 inch of the vessel inner dia m et er and (2) alm o st invariably have a 2a (or throug h-wall extent) dim e n s ion of 0.5 inch or le ss. To exam ine t h e flaw size/l o cation com b inations that contribut e to PTS risk in further det a il, the staff perfor m ed a series of deter m inistic analy ses by locating flaws of various size s axially in the Palisades RP V. Analy ses were perfor m ed of both a repressurization transient (#65) and of a large-dia m et e r prim a ry-side pipe break transient
(#62) to addr ess the two types of loadings that collectively a r e responsible for m o re than 90 percent of the PTS risk. A dditionall y , t h e 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/r y lim it. T h e results of these analyses at 60 effe ctive full-power y ears (EFPY) and at an em brittlement level characte ristic of the 1x10
-6/r y lim it appear in Figure 2.7. C onsistent with the conclusi ons based on the probabilistic analy ses, these results also indicate that s m all fla w s located cl ose to the ID will dom i n ate PTS risk.
9 Probability of Detect io n Historically , the inspection of PWR vessels has been conduct e d from the ID. Before 1986, the inspections were conducted with ultrason ic testing that was quite unreliable for flaw sizes and locations i m portant to PTS. Thus, these exam inations would be of li ttle value when assessing the risk of vessel failure resulting from PTS. In 198 6, t h e ASME Code,Section XI, b e gan to require that the inspection of the vessel m u st 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 Co m ponents (PISC). PISC II showed that inspection sensitivity needed to be inc reased fro m 5 0-percent distance a m plitude 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 7 0 dual-L wave probes would acco m p lish this. Subseque ntly , the NRC has required the im pl ementation of Appendix VIII, leading to t h e availability of im proved data to docum ent the effectivenes s of the NDE for the flaws im portant to PTS.
S upplem ent 4 of Appendix VIII covers the clad-to-base metal region u p to a depth of 1 in ch 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.
t WA L L t CL A D 2a ID OD L 2c Fi gure 2.4. F l aw di mensi o n an d p o si ti on descri pt ors ad opt e d i n FA V OR 0 2 4 6 8 0.000 0.125 0.250 0.375 Di st a n ce of I nne r Cr ac k T i p f r om Cl ad/B as e I nt e r f a c e , L/t wa l l% o f Fl aw s P r ed i ct ed t o I n i t i a t e B e av e r V a ll e y at E x t-B b P a l i sa d e s a t E x t-P b Figure 2.5. Distributi o n of thr o ugh-w a ll positi on o f cra cks tha t initia te Fi gure 2.6. Fl aw dep t hs t h at c o ntri b u te t o cr ack i n i t i a ti on p r o b abi l i t y i n B e a v er Val l e y U n i t 1 when subjecte d to (left) me di um- and lar g e-diame t er pipe bre a k tr an sients and (ri g ht) stuck-open valve tr ansients at tw o different em brittlement levels 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2a [i nch e s](n o t e: c=6a)L [i nches]I n a prob ab ilist i c a n alys is , al mo st a l l o f th e T W CF comes fr o m th is s h a d e d r e g i o n.Re-p ress ur izati on t r ans i ent a t 1 0-6/r y T W C F l i m i t a t 6 0 E F P Y Large diamete r pipe break trans i ent CP I 0 CP I > 0 t WA L L t CL A D 2a ID OD L 2c a t 6 0 E F P Y a t 1 0-6/r y T W C F l i m i t Note: Each curve i n the figur e ab ov e divi des the gr aph i n to t w o re gio n s: T he region a b o v e each curv e repres ents co mbin ations of fl a w loc a tion (L) and fla w s i ze (2a) that cann ot prod uc e crack initi a tio n for the embrit tlement an d lo adi ng co nditi on s represe n ted b y th e curve. T he region b e l o w eac h curve repres ents co mbin ations of fl a w loc a tion (L) and fla w s i ze (2a) that prod uce so me finite pro b a b il ity of crack initia tion for the em brittleme n t and load ing c ond iti ons repres ente d b y the curve.
Fi gure 2.7. An al ysi s of P a l i s ades tra n si ents #6 5 (re p re ssuri z a ti on tr ansi en t) an d #6 2 (l arge-di a meter prima r y-side pipe brea k transient) to illustrate wha t combinatio ns of fla w size a n d lo cation lea d to no n-zero co ndi tio n a l probabilities o f cra ck initiatio n 10 In 200 2, Becker docum ented the performance of inspectors that have gone t h roug h the Supplem ent 4 qualification process (Becker 02).
Becker's paper describes t h e findings of the U.S.
Perform ance Dem onstratio n Initiative (P DI), which has m a nufactured 20 RPV m o ckups that, in total, conta in in excess of 300 flaws.
Since its inception in 1 994, t h e PDI has perform ed over 10 separate autom a ted dem onstrations as well as num erous manual qualifications. The w e lds exa m ined include both shell welds and the m o r e difficult to exa m ine 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 m a nual 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 o p tim istic; the inclusion of passed plus fai led candidates is taken to pro v i d e a lower-bound estim ate of expected inspection performance.
Summary C o m b ining t h e 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 y ears of operation) if an inspection were to be performed that inspection should foc u s on detection of flaws having a thro ugh-wall extent of 0.3-0.4 inches and larger beca use these are the f l aws that make the greatest contributi on t o the non-zero probabilit y of crack initiation from PTS loading.
Perfor m ing RPV inspections in accordance with ASME Code, Appendix VIII, Supplem ent 4 requirem e nts 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/r y lim it on TWCF and if an inspection were to be performed that inspection should f o cus on detection of f laws having a throu gh-wall extent of appr oxim a tely 0.1 inch and larg er because thes e are the flaws that make the greatest contributio n to t h e non-zero probabilit y of crack initiation from PTS loading. Perform ing RPV inspections in accordance w ith ASME Code, Appendix VIII, Supple m ent 4 requirem e nts results in an 80-percent or greater probabilit y t h at such flaws c a n be detected.
Based on the inform ation presented in this section it see ms highly likely that the flaw siz es of im portance to PTS can be detected if inspections are perfor m ed in accordance with ASME Code, Appendix VI II, Supplem ent 4 requirem e nts. N o sam p l e s h ad f l aw s w it h T W E < 0.1-in. P O D c u r v e is e xt r ap o l at e d b e l o w 0.1-i n.[B e cke r 2002]0%20%40%60%80%100%0.0 0.2 0.4 0.6 0.8 1.0 T hr o ugh-W a l l E x t e nt [i n]P r ob abi l i t y of D e t e ct io n f o r ID E x a m Fig u re 2.8. Pro b a b ility of detectio n curv e (Becker 0 2) 11 12 Chapter 3 - PTS Screening Limits 3.1 O v er view 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 m at es reported in N U REG-1806 (EricksonKirk-Sum
), was revis e d in accordance with this specification to produce FAVOR Versi on 06.1 (Willia m s 07; Dickson 07a). Additionally, a special version of FAVOR 06.1 was developed to run on the Oak Ridge National Laboratory super-co m puter cluster to faci litate efficient si m u lation of large populati ons o f underclad cracks. Detailed results fro m t h e FAVOR V e rsion 06.1 a n aly ses of plate-welded and ring-forged vessels can be found in (Dickson 0 7b). Inform ation in this chapter is organized as follows: Section 3.2 re views the rationale first put forward in NUREG-1806 for using plan t-specific TWCF versus RT results to develop RT-based scr eening lim its useful for assessing the PTS risk of a n y PWR curr ently operating in t h e United States.
Section 3.3 e x a m ines the FAVOR 06.1 results for Be aver Valley Unit 1, Oconee Unit 1, and P a lisades (Dickson 0 7b). Sim i l a rity to the FAVOR 0 4.1 results reported in N U REG-1806 is assessed, and the FAVOR 06.1 results a re used to establish relationships betw een TWCF and RT-m etri cs f o r plate-welded PWRs currently in operation.
Section 3.4 e x a m ines the FAVOR r esu lts for ring-forged vessel s (Dicks on 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 o m b ines the inform ation in Sections 3.3 a nd 3.4 to pro duce two opti ons for regulatory im ple m entati on of these results. The first option pla ces a li mit on the estimated TWCF value while the second option places lim it s on the RT values associat ed wi th the various steels fro m which the reactor beltline is constructed.
These options are co m p lete ly equivalent, as they bot h deri ve directly fr om 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 analy ses to develop RT-based scre e ning lim it s 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 a rgin when using the pr o posed approa ch. 3.2.1 Justification of A p proach Chapter 8 of NUREG-1806 (EricksonKirk-Sum) esti m at es the variati on of TWCF with em brittlement level in the t h ree study pl ants (Oconee Unit 1, Beaver Va lley Unit 1, a nd Palisades). NUREG-1806 reported the following m a jor findi ngs: Only the m o s t severe pri m ary-side transients (m ediu m- to large-dia m et er pipe breaks and stuck-open va lves that later reclose) contribute in any si gnificant m a nner to the risk of vessel failure fro m PTS. At lower em brittlement levels stuck-open valves are the dom inant risk contribut ors. However, at the em brittlement levels n eeded to produce an esti m at ed TWCF equal to the 10
-6/r y lim it, medium- to large-diam eter pipe breaks dom inate. Severe secondary-side tran sients (e.g., a break of the main stea mli n e) do not contribute significantly to the risk of vessel failure fro m PTS. These transients have 13 extrem ely rapid initial cool ing rates, which generate high thermal stre s ses clos e to the vessel inner dia m et er. Nev e rtheless, the mini m u m te m p erature in the prim ary sy stem 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 o dels adopted for the main stea mline break (MSLB) (i.e., not accounting for the fact that pressurizatio n of containment caused by t h e break will raise the boiling point of water by 30-40 F above that assu m e d, 212 F, in the TH analy s is) sug g ests strongl y that reported TWCF values for this transient class overesti m at e those that can actually occur. Collectively
, these findings dem onstrat e that only the m o st 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 classe s is not expected to vary greatly am ong the po pulati on of currentl y operating PW Rs. This inform ation is su mmarized below:
Medium- to Large-Dia m e ter Pri m ary-Side Pipe Breaks
- To be risk significant the break dia m et er needs to exceed approxim a tel y 5 inches. The si m ilarity of PWR vessel s izes in the operating U.S.
reactor fleet suggests that different plants will have nominally equivalent reactor coolant s y stem (RCS) cooling rates for these large break dia m et ers. Additionally
, the cooling rate of the RCS inventory for these large breaks e x ceeds that a c hievable by the RPV steel, which is lim ited by its t h ermal conductivit y of the vessel steel and does not vary from ves sel to vessel because it is a phy s ical property of the m a terial. Consequentl y , an y sm all plant-to-plant variabilit y tha t may exist in RCS inventory cooling rate cannot be transm itted to the cooling rate of the RPV steel, which controls the thermal st resse s in the RPV wall. T h e onl y possible operator action in response to such a large break is to ma xim iz e injecti on flow to keep t h e core covered, so no plan t-to-plant differences ari s ing from differ e nt hum an re sponses is expect ed. (See NUREG-1806, Section 8.
5.2 for details.
) Stuck-Open Pri m ary-Side Valves: For this class of transi ents to be risk significant two criteria m u st be met-(1) t h e valve m u st rem a in stuck open lo ng en ough that the te m p erature o f the RCS inventory approaches that of the injection water and (2) once the valve reclose s the prim ary sy stem m u st repressuriz e to the safety valve setpoint. Both of these para m e t e rs (inje c tion water te mper ature and safe ty valve setpoint pressure) ar e input t o the R ELAP analy s i s and so are not influenced significantly by RELAP m odeling uncertainties. Moreo v er, neither parameter varies much within t h e populati on of currently ope rating PWRs.
The m odeling of this transient class refl e c ts credible operator actions. These actions do alter so m e details of the pr edicted pressure and tem p erature transients and do var y so m e what based on the RPV vendor because training pr ogr am s are vendor specific.
Nevertheles s , the analy s is de m onstrated that m o st differen ces c a used by operator actions do not appreciably influenc e the risk significance of the transient. Operator actions only matter if repr essurization of the primary s y stem can be pre v ented 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 sm all 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 m l i n e Breaks: A s 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 m i ni m u m te m p era t ure of the RCS (the boiling point of water) is generally high enough to ens u re a high lev e l of fracture toughness in t h e 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 i n the vessel a t the location of the flaws in the vessel is nee d ed. RT values characterize the r esi stance of a ferritic steel to cleav age crack initiation and arr est and to ductile crack initiation (EricksonKirk-PFM). NUREG-1806 prop osed b o th weighted and maxi m u m R T metrics. W e ighted RT metrics accounted for differences i n weld length and plate volum e between different plants, while maxim u m RT metrics did not. However, because of the si m ilariti es in the size of all dom estic PW Rs, the weighted RT metrics did not pr ovide si gnificantl y be tter correlations with the TWCF data than did t h e m a xim u m RT metric s. Further m ore, m a x i m u m RT me trics can be esti m at ed for all operating PWRs based m o stly on inf o rmation currently contained within the NRC' s RVID database (RVI D2) while weighted RT m e trics require additional inform ation from plant construction dra w ings. While this inf o rmation is available, it is not currently com p iled for all plants in a single location. For these reasons , this report restricts its attention t o m a xi m u m RT m e trics. contributi ng s ignificantl y t o the total T WCF esti m ated for a plant. The size of the m a in stea mline is s u fficiently large that the cooling rate of the RPV wall is lim it ed by the thermal conductivit y of the vessel st eel, which does n o t var y from plant to plant. In the rare insta n ce that through-wall crack ing does arise fro m an MSLB transient, it will occur within 10-1 5 m inutes after transient initiation, l o ng 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. (S ee NU REG-1806 , Section 8.5.4 for deta ils.) With one sm a ll exception, the "generaliz ation study ," in which the plant characte ristic s that can influence PTS severity of five additi onal high em brittlem e nt plants were investig ated, validated these expectations. (See (Whitehead-Gen) and Section 9.
1 of N U REG-1806 for details.) The reco mmended PTS screening lim it s present e d in Section 3.5 account f o r this exception.
In summary , the NRC' s study dem onstra t es that risk-significant PTS transi ents do not ha ve any appreciable plant-specific differences w ithin the populati on of PWRs currentl y o p erating in the United States. These findings m o tivate the developm ent of generic screening lim its that can be applied to all operating PWRs. Form ula e for the three m a x i m u m RT me trics proposed in NUREG-1806 (RT MAX-AW , R T MAX-PL , and RT MAX-CW) ar e repe ated below (the algebraic expression of these for m ulae h a ve been m odified slightl y fro m the form reported in NUREG-1806 to im prove clarity
): 3.2.2 Use of Reference Temperatu res to Correlate T WCF RT MAX-A W characterizes the resistance of the RPV to fracture initiating from flaws found along t h e 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 m ula inside the
{-}). The value of RT MAX-AW assigned to the vessel is the highest of the reference te m p erature v a lues as sociat ed with any indivi dual axial weld fusion line. In evaluating the T 30 values in this for m ul a the co mposition properties reported in the RVI D database ar e used for copper, nickel, and ph osphorus. An independent esti m ate of the manganese c ontent of each weld and plate evaluated is also neede
- d. Eq. 3-1 FL i pl adj i pl adj u NDT FL i aw adj i aw adj u NDT t T RT t T RT)(30)()()(30)()(AWFL(i)n 1 i AW MAX , MAX RT MAX AWFL where 15 n AW FL is the num ber of axial weld fusion lines i n the beltline region of t h e vessel, i is a counter that ranges from 1 to n AW F L , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT o f the weld adjacent to the i th axial weld fusion line,
)()(i aw adj u NDT RT is the unirradiated RT NDT o f the plate adjacent to the i th axial weld fusion line,
)()(i pl adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th axial weld fusion li ne, and )(30 i aw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axial weld fusion li ne. )(30 i pl adj TRT MAX-PL characterizes the resistance of the RPV to fracture initiating from fl aws in plates that are not associate d with welds. It is evalua ted using the following form ul a for each plate within the beltline region of the vessel. The value of RT MAX-PL assi gned to the vessel is the highest of the reference te m p erature valu es associ ated with any individual plate. In evaluating the T 30 values in this form ula the co m position pr operties reported in t h e RVID database are used for copper, nick el, a nd ph osp horus. An i n dependent estim ate of the manganes e content of each weld and plate evaluate d is also needed.
Eq. 3-2 )()(30)()(n 1 i PL MAX MAX PL RT i PL MAX i PL i PL u NDT t T RT where n PL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to n PL , is the m a xi mum fluenc e occurring over the vessel ID occupied by a particular plate, )(i PL MAX t is the unirradiated RT NDT o f a particular plate, and
)()(i PL u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to of a particular plate.
)(30 i PL T)(i PL MAX t RT MAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along t h e circu m fer e ntial weld fusion lines. It is ev aluated using the following form ula for each circu m fer e ntial weld fusion line within the be ltline region of the ve ssel (the part of the form ula insid e the {-}). Then the value of RT MAX-CW a ssigned to the vessel is t h e highest of the reference t e m p erature val u es associ ate d with any individual circu m ferential weld fusion line. In evaluating the T 30 values in this form ula t h e co m position properties reported in the R V ID da tabase are used for copper, nicke l, and phosphorus.
An independe nt esti m ate of the manganese content of each weld, plate, and forging evaluated is also needed.
16 Eq. 3-3 FL i fo adj i fo adj u NDT FL i pl adj i pl adj u NDT FL i cw adj i cw adj u NDT t T RT t T RT t T RT)(30)()()(30)()()(30)()(CWFL(i)n 1 i CW MAX , , MAX RT MAX CWFL where n CW FL is the num ber of circum ferential weld fusion lines in t h e beltline region of the vessel, i is a counter that ranges from 1 to n CW FL , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular circu m ferential weld fusion line, is the unirradiated RT NDT o f the weld adjacent to the i th circu m ferential weld fusion line,
)()(i cw adj u NDT RT is the unirradiated RT NDT o f the plate adjacent to the i th circu m fer e ntial weld fusion line (if there is no adjace nt plate this term is ignored),
)()(i pl adj u NDT RT is the unirradiated RT NDT o f the forging adjacent to the i th circu m ferential weld fusion line (if ther e is no adjacent forgi ng thi s term is ignored),
)()(i fo adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th circum ferential weld fusion line,
)(30 i cw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axial weld fusion line(if there is no adjacent plate this term is ignored), and
)(30 i pl adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the forging adjacent to the i th a x ial weld fusion line(if ther e is no adjacent forging this term i s ignored).
)(30 i fo adj T The T 30 values in Eq. 3-1 to Eq.
3-3 are deter m ined as follows:f Eq. 3-4 CRP MD T30 e RCS t PMn T A MD 471.2 130.6 1 001718.0 1 e e e RCS t Ni Cu g P Cu f T Ni B CRP , , , 1.543 769.3 1 100.1 191.1 f Th e resu lts repo rted in App e nd ix C d e m o n s t r ate th at th e altern ativ e fo rm o f th is relatio nsh i p presen ted in Ch ap ter 7 of (Eason 0 7) h a s n o sign if ican t e ffect o n th e TWCF v a lu es esti m a ted b y FAVOR. 17 for welds 10 x 417.1 plates for 10 x 561.1 forgings for 10 x 140.1 7 7 7 A for welds 0.155 vessels ed manufactur CE in plates for 2.135 vessels ed manufactur CE-non in plates for 5.102 forgings for 3.102 B 10 2595.0 10 10 10 3925.4 for 10 3925.4 10 3925.4 for t t t e Note: Flux () is estim ated by dividing fluence ( t) by the tim e (in seconds) that the reacto r h as been in o p eration. 6287.0 12025.18 4483.0 1390.1 log tanh 2 1 2 1 , , 10 Ni Cu t t Ni Cu g e e e e 008.0 072.0 for 0.008)-(359.1 072.0 008.0 072.0 for 072.0 072.0 for 0 , 0.6679 0.6679 P and Cu P Cu P and Cu Cu Cu P Cu f e e e wt%072.0 for wt%072.0 for 0 Cu Cu Cu Cu e flux) L1092 with welds (all wt%0.75 Ni for 301.0 wt%0.75 Ni 0.5 for 2435.0 wt%0.5 Ni for 370.0)(e Cu Max NUREG-1806 proposes the use of these three different RTs in recognition of the fact t h at 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 a m a ge suffered by the m a teri al at the flaw tips varies wi th location in the vessel bec a u se of differences in chem i s try and fluence.
T hese differe nces indicate that it is im possible for a single RT value to represent ac curat e ly the resistanc e of the RPV to fracture in the general case. Indeed, this is precisely the liability associat ed wi th the RT val u e currently adopted by 10 CFR 50.6 1 , th e RT PTS. The RT PTS, as defined in 1 0 CFR 50.61, is the maxim u m RT NDT of any region in the vessel (a r e gion is an axial weld, a circu m fer e ntial weld, a plate, or a forging) evaluated at the peak fluence occurring in that region
. Consequentl y , the RT PTS value currently assigned to a vessel m a y only coincidentally correspond to the toughness Different regions of the ves sel have flaw populati ons t h at differ in size (weld flaws are considera b ly larger tha n plate flaws), density (weld flaws ar e m o re numerous than plate flaws), and orientatio n (axial and circu m fer e ntial welds have flaws of corresponding orientations , whereas plate flaws may be either a x ial or circu m ferential). The drivi ng force to fracture depends bot h on fl aw 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 m ples: Out of 71 ope rating PWRs, 14 have t h eir RT PTS values established based on circu m ferential 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 m f e ren tial weld is extre m ely rem o te because of the lack of throu gh-wall fracture drivin g fo rce associat ed wi th circum f e re ntially oriente d 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 ope rating PWRs, 32 have t h eir RT PTS 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 esti m ate a toughness value that cannot be associat ed wi th any large flaws bec a use t h e location of th e peak fluence m a y 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 tha t RT PTS has been overesti m ated (perhaps significantly so) because the fluence assu med in the RT PTS calculati on does not corr espond to t h e fluence at a likely flaw location. Out of 71 ope rating PWRs, 15 have t h eir RT PTS values established based on axial weld properties (RVI D2). It is only f o r these vess els that the RT PTS value is clea rly associat ed wi th a material r e gion that contributes significantly to the vessel fai l ure 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 , RT MA X-PL , and RT MAX-CW) is expected to increas e the a ccuracy with which the TWCF in a vessel c a n be esti m ated rela tive to the current 10 CFR 50.61 procedure, which uses a single RT-metr i c (RT PTS). 3.3 Plate-Welded Pl ants 3.3.1 FAVO R 06.1 Results Detailed re sults from the F AVOR 06.1 analy ses of Oconee Unit 1, Beaver Valley Unit 1, and Palisades c a n be found in a separate r e port by (Dickson 07b
). Table 3.1 i n cludes a summary of these results, which have been reviewed and found to be c onsistent in m o st respects with the findings presented in NUREG-1806. T h is section highli ghts two ke y findings t h at 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 a ted previously b y FAVOR Vers ion 04.1 were heavily skewed towards zero or ver y low values, and that this skewness oc c u rs as a natural consequence of (1) the rarity of m u ltiple unfavorable factors co m b ining 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 boun ds. Fig u r e 3.1 dem onstrates that th e changes m a d e to the FAVOR code (se e Appendix A) have not qualitatively alter e d 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 esti m ated 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 m a ted using FA VOR 06.1 correspo nded to between the 80th a nd 9 9 th percentile. The percentile associat ed wi th 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 episte m i c uncertainty corre ction (see Tas k 1.1 in the FAVOR change specification in Appendix A) and the chang e in the em brittlement trend curve (see Task 1.5 in the FAVOR c h ange specification in Appendix A) have increase d the em brittlement level associ ated with each EFPY analy z ed. This incr ease in em brittlement reduces the TWCF percentile associat ed wi th the m e an along t h e sam e trend line established by the FAVOR 0 4.1 analy ses (see Figure 3.2). Indeed, the percentile associated with the mean should reduce with increased em b r ittlem e nt because, for m o r e em brittl ed material s, fewer z e ro fai l ure probability vessels are si m u lated, lea d ing to a less skewed distributio n o f TWCF. (2) The change in the RT NDT epistem ic uncertainty sam pling procedure (in FAVOR 04.1, the RT NDT epistem i c uncertainty was sam p led inside the flaw loop; in FAVOR 06.1, this sampling was m o ved outside o f the flaw loop-see T ask 1.3 in the FAV O R change specification in Ap pendix A) ha s pushed m o re of the densit y of the TWCF distributio ns t o occur in t h eir upper tails, thereby broad e ning them. This change was m o tivated by the observation that the FAVOR 04.1 procedure sim u l a ted an uncertainty in RT NDT for an indivi dual major-region of a si m u lated vessel (a major-region is an i ndivid u al weld, plate, or forging) having a total range in excess of 150 F. T h is range is m u ch larger than t h at mea s ured in laboratory tests, so FAVOR was m odified to bring its si m u l a tions int o better accord with observations.
NUREG-1806 uses m ean TWCF values in the TWCF versus RT regressi ons because the percentile associated with the mean exceeded 90 percent in all case s (se e 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 associat ed wi th a particular RT value is underestim ated. Consequ e ntly, the foll owing sections of this report use 95th percentile TWCF values in the TWCF versus RT regressi ons. Use of 95t h percentile values makes the probabilit y that the TWCF is underestimated accept a bly s m all (1 chan ce out of 20).
0%5%10%15%20%25%30%35%ze r o<= E-1 6 E-1 5 E-1 4 E-1 3 E-1 2 E-1 1 E-1 0 E-9 E-8 E-7 E-6 E-5 E-4 T W C F V a lu e Per c ent of Si m ul a t e d Ve ss el s 3 2 EF PY Ex t-B Fi gure 3.1. T W CF di stri b uti on s f o r B e a v er Valley Unit 1 estimated for 32 E FPY an d f o r a much hi gh e r l e vel of embrit t lem e nt (Ex t-B). At 3 2 EFPY the height of the "z ero" bar is 62 perce nt. 0 10 20 30 40 50 60 70 80 90 100 10 0 200 300 40 0 M axi m u m R T NDT A l ong A x i a l W e l d F u si on L i ne [o F]P e r c e n ti le o f M e a n T W C F V a lu e O c one e B eav er V al l ey P al i s ad es Shad ed S y m b ols: FA V O R 0 4.1 (NUREG-1 8 0 6)Soli d S y m bol s: FA V O R 0 6.1 (T his R e por t) 0 10 20 30 40 50 60 70 80 90 100 10 0 200 300 40 0 M axi m u m R T NDT A l ong A x i a l W e l d F u si on L i ne [o F]P e r c e n ti le o f M e a n T W C F V a lu e O c one e B eav er V al l ey P al i s ad es Shad ed S y m b ols: FA V O R 0 4.1 (NUREG-1 8 0 6)Soli d S y m bol s: FA V O R 0 6.1 (T his R e por t) Figure 3.2. The percentile of the TW CF distribution c o rresponding to mean TWC F va lues at v a r i o us levels o f embrittlement 20 Dominant Transients As reported in Section 8.
5 of NUREG-1 806 and su mmarized in Section 3.
2.1 of this rep o r t, onl y the m o st seve re transients make any significant contribution to the total esti m ated risk of through-wall cracking from PTS. Examination of the results in (Dickson 0 7b) shows tha t the risk-dom inan t transients listed in Tables 8.7, 8.8, and 8.9 of N U REG-1806 also dom inate the risk in the current (i.e., FAVOR 06.1) analy s e s. 21 Figure 3.3 sh ows the dependence of the TWCF resulting fro m the two do minant transient class es (m edi u m- to large-dia m eter pri m ary-side pipe breaks, and stuck-ope n prim ary valves that may later recl ose) and of MSLBs on em brittlement level (as quantified by RT MAX-AW). The tren ds in these figures agree w e ll with those reported previo usl y i n Section 8.
5 of NUREG-1806, i.e.:
Stuck-open p r im ary-side valves dom inate the TWCF at lower em britt lem e nt levels.
As em brittlement increases, m e diu m- to large-dia m et e r prim a ry-side pipe breaks beco m e the dom inant trans ients. In co m b ination these transient class es constitute 90 percent or m o re of the total TWCF irrespective of em b r ittlem e nt lev e l. MSLBs are responsible fo r virtuall y all of the rem a ining risk of through-wall crack ing. It should, ho wever, be remem b ered that the m odels of MSLBs are intentionall y conservative. More accurat e m odeling of MSLB transients is theref ore expected to further reduce their percei ved risk significance.
None of the other transient class es (s mall-dia m eter pri m ary-side breaks, stuck-open secondary val v es, 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 sh ows the relationship between the three RT m e t rics described in Section 3.2.2 (i.e., RT MAX-A W , RT MAX-PL , and RT MAX-CW) and the TWCF resulting from their three respecti v e flaw populati ons-axial fusion line flaws in axial welds, axial a nd circum f e re ntial flaws in plates, and circu m fer e ntial flaws i n circumferen tial welds. The following tren ds, dem onstrated b y the data in thi s figure agree well with those reported prev iousl y in Section 1 1.3.2 of NUREG-1806:
The TWCF produced by axial weld flaws dom inates the PTS risk of plate-welded PWRs. The TWCF produced by plate flaw s m a k es a m o re li m ited contributi on t o PTS risk than do axial weld flaws. This is because the plate flaws, w h ile m o re nu merous than axial weld flaws, a re considerably smaller.
Additionally
, half of the pla t e flaws ar e oriented circumferentially and half are oriented axially.
The TWCF produced by circu m fer e ntial flaws is e ssen tially negligible. At the highest RT MAX-CW currently expected for any PWR after 60 y ears of operation (25 8 F or 718R), circu m ferential weld flaws are responsible for approxim a tely 0.04 percent of the 1x 10-6/r y TWCF l imit prop osed in Chapter 10 of NUREG-1806.
The equations of the curves in Figure 3.4 all share the sa me for m , which is as follows:
Eq. 3-5 b RT RT m TWCF xx TH xx MAX xxln exp 95 In Eq. 3-5, t h e 95 subscript denotes the 9 5 th 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-x x is a fitting coefficient that per m its Eq. 3-5 to have a lower vertical asy mptote on a se mi-log plot.
Values of te m p erature a re expressed i n absolute de grees (Rankine = Fahrenheit + 459.6
- 9) to prevent a logarithm from being taken of a negativ e num ber. Val u es of the best-fit coefficie n ts for Ta ble 3.1. Summa ry of FA VOR 06.1 R e sult s R e po rt ed in (D ickson 07 b) TWCF Pa rtitio ne d by Fla w Po pula t i on (% of total TWCF)
T W CF Partition e d b y T r an sien t Class (% o f total TWCF) 95 th %ile TWCF (/ry) Plant EFPY RT MA X-AW [o F] RT MA X-CW [o F] RT MA X-PL [o F] ME A N FCI (/ry) Mean TWCF (/ry) %ile of Mean TWCF Primary Stu ck-Open Val v es Ax i a l We lds Circ. We lds Plates Primary Pipe Bre aks Main Steam-line Bre aks Se c onda ry Stu ck-Op en Val v es 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-13 100.0 0 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-11 100.0 0 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-07 100.0 1 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 Palis ades 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. RT AW [R]95 th 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. RT AW [R]95 th 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. RT AW [R]95 th 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. RT AW [R]95 th 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. RT AW [R]95 th %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. RT PL [R]95 th %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 RT CW [R]95 th %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 b lished by least-squares analy s is of the data in Figure 3.4, are as follows: Reg r e sso r Va riab le m b RT TH [R] RT MA X-A W 5.519 8 -40.54 2 616 RT MA X-P L 23.73 7 -162.3 6 300 RT MA X-C W 9.136 3 -65.06 6 616 Below the value of RT TH-x x the value of TWCF 95-x x is undefined an d shoul d be ta ken as zero. 3.3.2 Estimation of T WCF Value s and RT-Based Limits for Plate-W eld ed PWRs Sim il a r to the procedure described in NUREG-1806 , the fits to the TWCF 95-x x versus RT MAX-x x relationships shown in Fig u re 3.4 and q u antified b y Eq. 3-5 ar e co m b ined to develop t h e following form ul a that can be used to estimate the TWCF of any currentl y operating plat e-welded PWR in the United States: Eq. 3-6 CW CW PL PL AW AW TOTAL TWCF TWCF TWCF TWCF 95 95 95 95 H ere the values of TWCF 95-xx are esti m ated using Eq. 3-5. The factors are introduced to prevent under estimation of TWCF 95 at low em brittlement levels fro m stuck-open va lves on the prim ary side that may later reclos e (s ee Chapter 9 of NUREG-1806). Values of are defined as follows:
If RT MAX-xx 625R, then
= 2.5 If RT MAX-xx 875R, then
= 1 If 625R <
RT MAX-xx < 875R then 625 250 5.1 5.2xx MAX RT 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 onl y sm all co ntributi ons to the total TWCF 95 at high em brittlem e nt levels.
Eqs. 3-5 and 3-6 define a r e lationship be tween RT MAX-A W , RT MAX-PL , and RT MAX-CW an d 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 RT MAX-A W , RT MAX-PL , and RT MAX-CW that lie insi de the surface therefore have TWCF 95 val u es below 1x 10-6. Eqs. 3-5 and 3-6 can be us ed, together with values of RT MAX-AW , RT MA X-PL , and RT M AX-CW determ ined from inform ati on in t h e RVID database, to e s ti m a te the T W CF of any plate-welded PWR currently ope rating in t h e United States. (See S ection 3.3.3 for a necess ar y m odific a tion 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/r y after either 40 or 60 y ears of operation.
The two-dimensional version of t h e three-dimensional graphical representation of Eq. 3-6 provided inFi gure 3.5 can be used to de velop RT-based scr eening lim its for plate-wel d ed plants. As was done in NUREG-1806, RT lim its can be establi shed by setting the total T W CF in Eq. 3-6 equal to the reactor vessel failure frequency acceptance criter i on of 1x10-6 events/y ear proposed in Chapter 10 of that docum ent. Plate vess els ar e m a de up of axial welds, plates, and circum f e rential welds, so in principle, flaws in all of these regions will contribute to the total TWCF. However, as revealed by t h e RT values reported in T a ble 3.3, the contributi on of flaws in circu m ferential welds to TWCF is negligi b le. The highest RT MAX-CW anticipated for an y currentl y operating PWR after 60 y ears of operation (assu m i ng current operating conditions are maintai n ed) is 258 F. At t h is em brittlement level flaws in circu m ferential welds would contrib u te approxim a tely 0.0 4 percent of the 1 x10-6/r y lim it. In view of this ver y m inor contribution of flaws in circu m ferential welds to the overall risk, RT-base d screening limits for plate-welded plants are developed as follows:
25 (2) Set TWCF TOT AL to the 1x10
-6/r y lim it proposed in Chapter 10 of NUREG-1806.
(1) Set TWCF 95-C W to 1x10-8/r y (this corresponds to an RT MAX-CW value of 312 F, whic h far exceeds the highest va lue expected for any currently operating PWR after 60 y ears of operation.
(3) Solve Eq.
3-6 to establish (RT MAX-A W , RT MAX-PL) pairs that satisfy equality.
Fi gure 3.5. Grap hi cal rep resent a ti on of E q s. 3-5 and 3-6. The TWCF of t h e surf ace in both di agrams is 1 x10-6. T h e top diagr a m pr ovide s a close-up view of the outerm ost corner sh own in the bottom di agr am. (T h e se di a g r a ms are pr o v i d ed f o r vi su al i z ati o n pur pose s on l y; the y are n o t a completel y ac curate represe n tation of Eqs. 3-5 a nd 3-6 pa rticul a rly in th e ver y s t eep regions at the e d ges o f th e T W CF = 1x 10-6 surface.)
26 As illustrated in Figure 3.6, this procedure establishes th e locus of (RT MAX-AW , RT MAX-PL) pairs that define the horizo n tal cross-section of the three-dimensional surface depicted in Figure 3.5 at an RT M AX-CW value o f 312 F. In t h e region of t h e graph between the red loci and the origin, t h e T WCF is below the 1x10
-6 acceptanc e criterion, so these co m b ina tions of RT MA X-AW and RT MAX-PL would satisfy the 1x 10 6/r y lim it on TWCF. I n the region o f the graph o u tside of the red loci, the esti m at ed TWCF excee ds the 1x10-6/r y lim i t, indicating t h e need for additional analy s is or ot her m e asures to justif y co nt inued plant operatio
- n. For reference, Figure 3.
6 shows loci corresponding to o the r TWCF values. Of particular interest is the 5x10
-6 locus, which appears in dark green. A 5x10
-6 TWCF lim it corresponds to that viewed as being acceptable according to the current version of Regulatory Guide 1.15 4, "Form a t and Content of Pl ant-Specific Pres surized Thermal Shock Safety Analy s is Reports for Pressurized Water Reactors," issued January 1987.
Figure 3.6 also shows asses s m ent points (blue circles and blue triangles), one representing each plate-welded PWR after 40 and 60 y ears of operation. T h e coordinates (RT MAX-A W , RT MAX-PL) for each plant were esti m ated fro m inform ation in the RVID database (see Table 3.3). Com p arison of the as sess ment points for the indivi dual plants to the (proposed) 1 x 1 0-6 and (current) 5x10
-6 lim its 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 y ears of operation.
After 40 y ears of operation the highest ri sk of PTS at any PWR is 2.0x10
-7/r y. After 60 y ears of operation this risk increase s to 4.3x 10-7/r y. The current regulations assume that plants have a TWCF risk of appr oxim a tely 5x10 6/ry whe n the y are at the 10 CFR 50.61 RT PTS screening lim its. Contrary to the current situation in which several plants are thought to be within fractional degrees Fahrenheit of these li m its, the staff' s calculations show that when realistic m o dels 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/r y lim it im plicit in RG 1.154.
P l at e W el d ed P l an t s at 32 E F P Y (E O L)0 50 10 0 15 0 20 0 25 0 30 0 35 0 40 0 0 5 0 1 00 15 0 2 00 25 0 3 00 RT MA X-A W [o F]RT MA X-P L [o F]1E-8 1E-7 1E-6 5E-6 30 o F 53 o F P l at e W el d ed P l an t s at 48 E F P Y (E O L E)0 50 10 0 15 0 20 0 25 0 30 0 35 0 40 0 0 5 0 1 00 15 0 2 00 25 0 3 00 RT MA X-A W [o F]RT M A X-PL [o F]1E-8 1E-7 1E-6 5E-6 17 o F 40 o F Fi gure 3.6. Ma xi mum RT-ba s ed scr eeni n g cri terion (1E-6 c u rve) for plat e-w e l d ed vessel s b a se d on E q. 3-6 (left: screening criteri on rel ati v e to c u rre ntly operating PW Rs after 40 year s of ope r ati o n; right: screeni n g cri terion r e lative to cur r e ntly operating P WRs after 60 ye ars of operati on). 27 3.3.3 Modification for Thick-Walled Vessels Figure 3.7 sho w s th at th e v a st majo rity of P WRs curr ent ly in s e r v ic e h a ve wa ll thic knes ses be tw ee n 8 and 9.5 in ch e s. The thr e e ve s s e ls an aly z ed i n det a il in thi s study are all in thi s ran g e and thu s rep r esen t the v a st majori ty of the op erat ing fl eet. As di scu s sed in Section 9.2.2.3 of NUREG-1806, the few PWRs having th ick e r wa ll s can b e e xpec ted to exp e ri en ce higher TW CF than th e thinn e r ve s s e ls an aly zed he re (at equiv a l e nt embrittl ement l e vels) b e cau s e of th e higher thermal stresses th at o c cur in th e thi c k e r v e ssel walls. Figure 3.8 rep r odu ces the results o f a sen s i tivity stud y on wall thi c k n ess repo rt ed i n NUREG-1806. Th ese result s sho w th at for PTS-do m i n a nt transients (the 16-in ch hot leg b r eak and the stu c k-op en safety/rel ie f v a lve) the TW CF in a thick (11 to 11.5 inch) wal l v e ssel wi ll in crease by approximately a factor o f 16 o v er the v a lu es presen ted in th is repo rt fo r v e ssel s h a ving wall thickn esses b e tween 8 and 9.5 inch es. To account for this increase d driving forc e to fra c ture in thic k-wa lle d ves s e l s th e st af f r eco mme n d s that the TW CF estimated by Eq. 3-6 b e in creased by a facto r of 8 for each inch o f th ickn ess by whi c h th e v e ssel wall exceeds 9.5 in ches. Section 3.5 provid e s a formula that formally i m pl ements thi s reco mmendat i on. 0 5 10 15 20 25 30 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 V essel W al l T h i ckn ess [i n]Nu m b e r o f P W R s Fi gure 3.7.
Di stri but i o n of RPV w a l l thi c knesses for PWRs current l y in service (R VID2). T h i s f i gure ori g i n all y appeared as Fi gure 9.9 i n N URE G-180 6. 0 10 20 30 40 50 7 8 9 1 01 11 2 V essel W a l l Thi ckness [i n]TW C F / TW C F f o r 7-7/8-i n. Thi c B eave r Val l ey Vessel at 60 EF P B V 9 - 16" H o t L e g B r ea k B V 56 - 4" S u r g e L i n e B r ea k B V 10 2 - M S L B B V 12 6 - S t u ck o p en S R V , r e-cl o ses af ter 100 m i n u t e s Fi gure 3.8.
E ffect of vessel w a ll thi c kness on the T W CF of vari o us transients i n B e aver Val l ey (al l anal yses at 60 E FPY). T h i s f i gure ori g i n all y appeared as Fi gure 9.10 in NURE G-180 6. 3.4 Rin g-Forge d Plan ts 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 ha ve no axial welds. The lack of the large, axially oriented axial flaws fro m s u ch vessels indicates that the y m a y have m u ch lower values of TWCF than a com p a rable plate vessel of equivalent em brittlement. However, forgings have a populati on of em bedded flaws that is particular in densit y an d size to their method of manufacture.
Additionall y, under certain rare conditions for g ings m a y contain underclad cracks that ar e produced by the deposition of the austenitic stai nless steel cladding la y e r. Thus, to investigate the applicability of the result s reported in Section 3.3 to forged vessels
, the staff perfor m ed a num ber of analy ses on vessels using pr operti es (RT ND T(u), copper, nicke l, phosphorus, manganese) a nd 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 e m bedded forging flaws based on destructive exam ination of an RPV forging (Schust e r 02). These flaw s a re si m ilar in both size and density to plate flaws. A sensitivity study based on the e m bedded forging flaw distribution described in Appendix D was described previo usl y i n NUREG-1808 (EricksonKirk-SS) and will not be repeated here. This study showed that the si m ilarities in flaw size and densit y between forgings and plates allow the relationship between RT M AX-PL and TWCF 95 (E q. 3-6) to be used for forgi ngs containin g em bedded flaws.
For forgings t h e RT m e tric is defined as follows:
RT MAX-FO ch aracte rize s the resist ance of the RPV to fracture initiating fr om flaws in forgings that are not associ ated with wel d s. It is evaluated using the foll o w ing form ula 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 te m p erature v a lues as sociat ed with any indivi dual pla te. In evaluating the T 30 values in this form ula the co m position pr operties reported in the RVID datab ase ar e used for copper, nicke l , and p hosph orus. An independent e s ti m a te of the manganese content of each weld and plate evaluated is also needed.
Eq. 3-7 )()(30)()(n 1 i FO MAX MAX FO RT i FO MAX i FO i FO u NDT t T RTwhere n FO is the num ber of forgi ngs i n the beltline region of the vessel, i is a counter that ranges from 1 to n FO , is the m a ximum fluence occurring over the vessel ID occupied by a particular forging, )(i FO MAX t is the unirradiated RT NDT of a particular forging, an d )()(i FO u NDT RT is the shift in the Charpy V-Notch 30-foot-pou n d (ft-lb) energ y (estimated using Eq.
3-4) p r oduced by irradiation to of a particular forging.
)(30 i FO T)(i FO MAX t 3.4.2 Underclad Flaw Sensitiv ity Study By Ma y 1973 the causes of underclad cracking were sufficientl y well un d e rstood for th e NRC to issue Regulator y Guide 1.4 3 , "Control of Stainless Stee l Weld Cladding of Low Alloy Steel Co m ponents" (RG 1.43). Vessels fabricated aft e r this da te would have had to co m p ly with t h e provisio n s of Regulator y Guide 1.43 and, ther efore, should not be susceptible to underclad cracking. Vessels fabricated before 1973 m a y have been com p liant as well because the causes of and rem e diati on for underclad cracking wer e widely known before the issuance of the regulatory guide. N e vertheless, t o provide the inform ation needed to support a co m p rehensi v e revision of the PTS Rul e the NRC staf f considered it necess ary to establish PTS screening lim its for vessel s containing underclad cracking for t hos e situations in which co m p liance with Regulator y Guide 1.4 3 cannot be dem onstrated.
As discussed in detail in A ppendix B, u nderclad cracks occur as dense arr a y s 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 a tely 0.0 8 inch (a pproxim a tely 2 m illi meters)). These cracks are oriented norm a l to the direction of welding for c lad deposition, pr oducing axially oriented cr acks in the vessel bel tline. The y a re clustered where the passes of stri p clad contact each other.
Underclad fla w s are m u ch m o r e likely to occur in particular grades of pressure vess el s teels that have chem ical com positions that enhance the likelihood of cracking. Forging grades such as A508 are m o r e 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 lim ited inform ation in the literature concerning underclad crack size and density. This l ack of inform ation on which to base the probabilistic 29 calculations exists because when underclad cracking was discovered in the late 1960 s and early 19 70s t h e understand able focus of the investigations performed at that tim e was to prevent the phenom ena fro m oc curring altogether, not to characteri ze the size and density of the resulting def ects. Because of this lack of infor m ation, the flaw distributio n detailed in Appendix B reflects conserv a tive judgm ents. Hy pothetical m odel s of forged vessels w e re constructed based on the existing m odels of the Beaver V a lle y 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 co m b ined and assigned the following properties, which are cha racteristi c of the forging in Sequo y a h Un it 1 (RVID2)-copper = 0.13 percent, nickel = 0.76 perc ent, phosp hor us = 0.020 percent, manganese
= 0.70 percent, RT NDT(u) = 73 F, upper-sh e lf energy = 72 ft-lbs (this forging was select ed because it has am ong the m o st em b rittlem e nt sen sitive properti es of any f o rging in the current operating fleet).
Using these properties along with the underclad flaw distribution described in Appendix B, FAVOR anal y ses were co nducted at a num b er of different EFPY values to investigate the variation of T W CF with em brittlement level. Becaus e of the extre m ely high density of underclad flaws assu m e d by the Append ix B flaw distribution, a super-com puter cluster was used to perform the se FA V O R analy ses (see (Dickson 07b) for a full de scription of t h e underclad flaw analy s is). 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 em brittlement (as quantified by RT MAX-FO) shown in Fig u re 3.9 for un derclad crack s is m u ch m o re ra pid than shown previously (see Figure 3.4) for plate and weld flaws. The steepness of t h is slope occurs as a direct consequence of the ver y hi gh densit y of underclad cracks assu med in the anal y s is (the mean cr ack-t o-crack spaci ng is on the order of milli m e t e rs). Because of this high density, it is a virtual certainty that an underclad crack will be sim u lated to occur in locations of hi gh f luence and high stress. Thus, once the level of em brittlement has increased to the point that the underclad cracks can initiate, their failure is al m o st cert a i n , and additional sm all incr eases in em brittlement will lead to l a rge increases in TWCF. Beca use of the steepness of the TWCF versus RT MAX-FO relationship, the staff made no attem p t to develop a "best fit" to the results.
Instead, the following bou nding relation s hip (which also appears on Fig u re 3.9) is pr oposed: Eq. 3-8 FO MAX RT FO TWCF185.0 137 95 10 10 3.1 Table 3.2. Re sults of a Sens itivity S t ud y Assessin g the E ffec t of Undercl ad Flaws on the TW CF of Ri ng-F orge d Vessel s A n al ysis ID RT MA X-F O [o F] TWCF 95 from Unde rc la d Fla w s BV 32 187.2 0 (see Note 1)
BV 60 205.8 0 (see Note 1)
BV 100 225.4 5.67E-1 1 BV 200 261.2 2.35E-0 4 Pal 32 193.0 0 (see Note 1)
Pal 60 209.9 0 (see Note 1)
Pal2 00 263.2 3.92E-0 5 Pal 50 0 332.8 2.08E-0 4 Note 1: All T W CF w a s from ci rcumferenti a l w e ld fla w s in thes e ana l y ses 1.E-14 1.E-13 1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 55 0 650 7 50 85 0 Ma x RT FO [R]95 th %ile T W C F fo r U n d e r c la d F la w s F AV O R Re s u l t s B oun d FO MAX RT FO TWCF185.0 137 95 10 10 3.1 Fi gure 3.9. Rel a ti ons h i p betw een T W C F a nd RT for forgings having undercl ad flaws 30 3.4.3 Modification for Thick-Walled Vessels As wa s the ca se for plate-w e lded vessels, the effect of incr eased ves sel wall thickness on the TWCF in ring-forged vessels m u st also be quantified. The sensitivity study presented previously for plate-welde d vessels (se e F i g u r e 3.8) can be used to correct for thickness effects in forgi ngs th at have onl y e m b e dded flaws (no underclad cracking) because of the sim il a rity i n both flaw density and flaw size betw een em bedded flaws in forging s and plates. To investigate the m a gnitude of an appropriate thickness correction for forgings containing underclad cracks, the thickness of the hy pothetical forging based on the Beaver Valley vessel w as increas ed to 11 inches and the analy s is was rerun using s ubclad cracks. Figure 3.10 presents the results of these analy ses and co m p ares the m with the results presente d previously for plate-welde d vessels (se e F i g u r e 3.7) as well a s to the thickness correctio n reco mmended in Section 3.3.3. This co m p arison de m onstrates that the thickness correctio n reco mmended in Section 3.3.3 for plate-welded vessels can al so be applied to ring-forged vessels that have underclad cra c ks. 31 3.5 O p tion s for Regul a tor y Implementation of These Results Any f u ture revision of 10 CFR 50.61 m u st include a procedure by which licensees can dem onstrate com p liance with the 1x 10-6/ry TWCF li m it based on infor m ation that characte rize s a particular plant. Sections 3.5.1 and 3.5.2 des c ribe two com p letely equi valent approaches to achieving this goal, both based on the inform ati on presented so far in this chapter.
The first approach places a lim it on TWCF of 1x10-6/ry, whereas the s eco nd approach places a lim it on the maxima of the various RT values, or co m b inations thereof, which would prod uce a TWCF value at the lim it of 1x10
-6/r y. E quations presented els e where in this report are re peated in these sections for clarity. Adoption of e ither approach in r e gulations wo uld be full y consistent with the technical basis information presented in this report, in NUREG-1806, and i n the other companion docu m ents listed in Section 4.1. It should be n o ted 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 e veloped an alternative em brittlement trend curve of a slightl y sim p lified form (Eason 07). T h e results reported in A ppendix C dem onstrate that the effect of this alternative tre nd curve on the TWCF values esti m at ed by FAVOR i s insignificant.
Thus, the eq uations in Appendix C c ould be adopt ed instead of the equations presented in Step 2 of Sections 3.5.1 and 3.5.2 wit hout t h e need to change an y other part of the pr ocedure.
F F Results from analyses of forge d vessels having subclad cracks
.Th ic knes s correc t i on reco m m ended in Sec t i o n 3.3.3 Fi gure 3.1 0. E ffect o f vesse l w a l l thi c knes s on t he TWCF of for g ings having underclad flaws c o mpar ed with res ults for plate-welded vessels (see Fi gure 3.7)
3.5.1 Limitation on TWCF Step 1. Establish the plant characte r ization pa rameters, which include the following:
RT NDT(u) [ F] The unirradiated value of RT NDT. Needed for e ach weld, plate, and forging in the beltline region of the RPV.
Cu [w eight percent
] Copper content. Needed for each weld, plate, and forging in the beltline region of the RPV.
Ni [w eight perce n t] Nickel co ntent. Needed for each weld, plate, and forging in the beltline region of the RPV.
P [w eight percent]
Phosphor us content. N eeded for each weld, plate, and forging in the beltline region of the RPV.
Mn [w eight perce n t] Manganese content. Needed for eac h weld, plate, and forging in the beltline region of the RPV.
t [s econds] Th e am ount of ti me the RPV has been in o p eration. T RCS [ F] The average tem p erat ure of the RCS inventor y i n the beltline region under norm a l operat ing conditions. t MAX [n/c m 2] The maxi m u m flu e nce on the vessel I D for each plate and forging in the beltline region of the RPV. t FL [n/c m 2/s ec.] The maxi m u m fluenc e oc curring along each axial w e ld and circu m fer e ntial weld fusion line. Th is value is neede d for each axial weld and circum ferential weld fusion li ne in the beltli ne region of t h e RPV. T wall [inches] The thickness of the RPV wall, including the cladding.
Step 2. Esti m a te valu es of RT MAX-AW , RT MA X-PL , RT MAX-FO , and RT MAX-CW using the foll o w ing form ula e and the values of the characteri zation para meters fro m St ep 1: RT MAX-A W characterizes the resistance of the RPV to fracture initiating from flaws found along the axi a l 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 m ul a inside the {-}). The value of RT MAX-AW assign ed to the vessel is the highest of the referenc e te mperature values as sociated with any indivi dual axi a l weld fusion line. In evaluating the T 30 values in t h is form ula the com position properties reported in the R V ID database are used for copper, ni ckel, and pho sphorus.
An independent e s tim a te of the manganese c ontent of each weld and plate evaluated is also neede
- d. FL i pl adj i pl adj u NDT FL i aw adj i aw adj u NDT t T RT t T RT)(30)()()(30)()(AWFL(i)n 1 i AW MAX , MAX RT MAX AWFL where n AW FL 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 n AW F L , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT o f the weld adjacent to the i th axial weld fusion li ne, )()(i aw adj u NDT RT 32 is the unirradiated RT NDT o f the plate adjacent to the i th axial weld fusion li ne, )()(i pl adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th axia l weld fusion line, and
)(30 i aw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axia l weld fusion line. )(30 i pl adj TRT MAX-PL characterizes the resistance of the RPV to fracture initiating from fl aws in plates that are not associate d with welds. It is evaluated using the following form ula for each plate wit h in the beltli ne region of the vessel. The value of RT MAX-PL assi gned to the vessel is the hi ghest of the referenc e te mperature values associ ated with any individual plate. In evaluating the T 30 values in this form ula t h e com positi on properties reported in the RVID datab ase ar e used for copp er, nickel, and ph osphorus. An indepen d ent estim ate of the manganese c ontent of each weld and plate evaluated is also neede
- d. )()(30)()(n 1 i PL MAX MAX PL RT i PL MAX i PL i PL u NDT t T RT where n PL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to n PL , is the m a xi mum fluenc e occurring over the vessel ID occupied by a particular plate, )(i PL MAX t is the unirradiated RT NDT o f a particular plate, and
)()(i PL u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to of a particular plate.
)(30 i PL T)(i PL MAX t RT MAX-FO characterizes the resistance of the RPV to fracture initiating from fl aws in forgings that are not associ ated with wel d s. It is evaluated using the following form ul a for each forging with in the beltline region of the vessel.
The value of RT MAX-FO assi gned to the vessel is the hi ghest of the referenc e te m p erature v a lues as sociat ed with any i ndivid u al plat e. In evaluating the T 30 values in this form ula the co m position pr operties reported in t h e RVID database ar e used for copper, nickel , and phosphorus. An independent esti m ate of the m a nganes e content of each weld and plate evaluated is also needed.
)()(30)()(n 1 i FO MAX MAX FO RT i FO MAX i FO i FO u NDT t T RT where n FO is the num ber of forgings in the beltline region of the vessel, i is a counter that ranges from 1 to n FO , is the m a xi mum fluenc e occurring over the vessel ID occupied by a particular forging, )(i FO MAX t is the unirradiated RT NDT o f a particular forging, and )()(i FO u NDT RT 33 is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to of a particular forging.
)(30 i FO T)(i FO MAX t RT MAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along the circum ferential weld fusion li n es. It is evaluated using the following form ul a for each circu m fer e ntial weld fusion line within the beltline region of the vessel (the part of the form ula in side the {-}). Then the value of RT MAX-CW a s s igned to the vessel is the hi ghest of the referenc e te m p erature v a lues as sociat ed with an y i ndivid u al circum ferential weld fusion line. In evaluating the T 30 value s in this formula the com p osition properties reported in the R V ID databa se are used for copper, nicke l, and phosphorus.
An independe nt esti m ate of the manganese content of each weld, plate, and forging evaluated is als o needed. FL i fo adj i fo adj u NDT FL i pl adj i pl adj u NDT FL i cw adj i cw adj u NDT t T RT t T RT t T RT)(30)()()(30)()()(30)()(CWFL(i)n 1 i CW MAX , , MAX RT MAX CWFL where n CW FL is the num ber of circum ferential weld fusion lines in t h e beltline region of the vessel, i is a counter that ranges from 1 to n CW FL , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular circum ferential weld fusion li ne, is the unirradiated RT NDT o f the weld adjacent to the i th circu m ferential weld fusion line,
)()(i cw adj u NDT RT is the unirradiated RT NDT o f the plate adjacent to the i th circu m fer e ntial weld fusion line (if there is no adjace nt plate this term is ignored),
)()(i pl adj u NDT RT is the unirradiated RT NDT o f the forging adjacent to the i th circu m ferential weld fusion line (if ther e is no adjacent forgi ng this term is ignored),
)()(i fo adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th circ um ferential weld fusion li ne, )(30 i cw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axia l weld fusion line(if there is no adjacent plate this term i s ignored), and
)(30 i pl adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the forging adjacent to the i th a x ial weld fusion line(if ther e is no adjacent forging this term i s ignored).
)(30 i fo adj T 34 The T 30 values in the preceding equations are deter m ined as follows
- CRP MD T30 e RCS t PMn T A MD 471.2 130.6 1 001718.0 1 e e e RCS t Ni Cu g P Cu f T Ni B CRP , , , 1.543 769.3 1 100.1 191.1 for welds 10 x 417.1 plates for 10 x 561.1 forgings for 10 x 140.1 7 7 7 A for welds 0.155 vessels ed manufactur CE in plates for 2.135 vessels ed manufactur CE-non in plates for 5.102 forgings for 3.102 B 10 2595.0 10 10 10 3925.4 for 10 3925.4 10 3925.4 for t t t e Not e: Flux () is estim ated by dividing fluence ( t) by the tim e (in seconds) that the reacto r h as been in o p eration. 6287.0 12025.18 4483.0 1390.1 log tanh 2 1 2 1 , , 10 Ni Cu t t Ni Cu g e e e e 008.0 072.0 for 0.008)-(359.1 072.0 008.0 072.0 for 072.0 072.0 for 0 , 0.6679 0.6679 P and Cu P Cu P and Cu Cu Cu P Cu f e e e wt%072.0 for wt%072.0 for 0 Cu Cu Cu Cu e flux) L1092 with welds (all wt%0.75 Ni for 301.0 wt%0.75 Ni 0.5 for 2435.0 wt%0.5 Ni for 370.0)(e Cu Max Step 3. Esti m a te the 95th percentile TWCF value for each of the axial weld flaw, plate flaw, circu m ferential weld flaw, and forgin g fl aw populatio ns using the RTs fro m Step 2 and the following form ula e. RT m u st be ex pressed in degrees Rankine. The TWCF
Th e resu lts repo rted in App e nd ix C d e m o n s t r ate th at th e altern ativ e fo rm o f th is relatio nsh i p presen ted in Ch ap ter 7 of (Eason 0 7) h a s n o sign if icant effect on the T W CF values es ti m a t e d by FA VOR. T h us, t h e eq uat i o n s i n A p pen d i x C coul d be use d i n st ead o f t h e e quat i o ns p r ese n t e d i n St e p 2 wi t h o u t t h e n e ed t o cha n ge a n y ot her part of t h e p r oc edu r e. 35 contributi on of a particular axial weld, plate flaw, cir c u m ferential weld, or forging is zero if either of the following c onditi ons are me t: (a) if the result of the subtraction from which the natural logarithm i s taken is negative, or (b)if the beltli ne of the RP V being evaluated does not contain the prod uct form in question.
542.40 616 ln 5198.5 exp 95 AW MAX AW RT TWCF 38.162 300 ln 737.23 exp 95 PL MAX PL RT TWCF 066.65 616 ln 1363.9 exp 95 CW MAX CW RT TWCF 38.162 300 ln 737.23 exp 95 FO MAX FO RT TWCF FO MAX RT 185.0 137 10 10 3.1 The factor = 0 if the forg ing is com p liant with Regulator y Guide 1.43; otherwi se = 1. The factor is determ ined as follows:
If T WALL 91/2 -in, th en = 1. If 91/2 < T WALL < 111/2 -in, then = 1+ 8(T WAL L - 91/2) If T WALL 111/2 -in, th en = 17. Step 4. Esti m a te the t o tal 95th percentile TWCF for the vessel using the following form ulae (note that depending on the ty pe of vesse l in question certain ter m s in the following form ula will be zero). TWCF 9 5-TOTAL must be less than or equal t o 1x10-6. FO FO CW CW PL PL AW AW TOTAL TWCF TWCF TWCF TWCF TWCF 95 95 95 95 95 is determined as follows:
If RT MAX-xx 625R, then
= 2.5 If 625R <
RT MAX-xx < 875R then 625 250 5.1 5.2xx MAX RT If RT MAX-xx 875R, then
= 1 Table 3.3 and Table 3.4 pr ovide the RT s and TWCF 95 values esti m ated by this procedure for every currentl y operating P WR. In Tabl e 3.4 TWCF 95 values are r e ported for all ring-forged vessels ba sed on both the assu m p tion that underclad cracking can occur and o n the assu m p tion that underclad cracking cannot occur. No judgm ent regar d ing the incidence (or not) of under c lad cracking in an y operating rin g-forged PWR is m a de in pre senting these values.
However, the se cal culations do dem onst rate that for the em brit tlem e nt leve ls currently expected throug h EOL E the contrib u tion of un derclad cracks to the total TWCF of ring-forged plants is esti m ated to be vanishingly small becau se, even at EOLE, the em brittlement levels expected of the ring for g i ngs is low (at EOLE the hi ghest RT MAX-FO of any ring-forge d plant is 199 F). The graphs in Figure 3.
11 s u mmarize the TWCF values provided in these tables for all currently operating PW Rs. Eight y-o n e percent of plate-welded PWRs (100 percent of ring-f o rg ed PWRs) have esti m ated TWCF 95 values that are 36 two orders of magnitude or m o re below the 1x10-6/r y regulator y lim it (i.e., below 1x10
-8/r y), even after 60 y ears of operation. After 40 y ears of operation t h e highest risk of PTS producing a through-wall crack in any plate-welded PWR is 2.0x 10-7/r y (f or ring-for g ed PWRs this value is 1.5x 10-1 0/r y). After 60 y ears of operation this risk increase s to 4.3x10
-7/r y (3.0 x10-10/r y for ring-forged P WRs). Figur e 3.12 pr ovi d es a perspective on the relative contributi ons to the total TWCF made by the various com p onents (axial welds, circu m fer e ntial welds, plates, and forgings) from which the beltline regions of the operating n u clear RPV fleet are constructed.
This figure com p ar es the histograms depicting the distributi ons of the var ious RT valu es characteristic of beltline m a terials 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 p a r isons show that the level of em brittlement in m o st plants is so low, even when proj ected to EOLE, that the esti m ated TWCF resulting from PTS is very , very sm all. 0 2 4 6 8 10 12 14 B e l o w E-1 3 E-13 t o E-12 E-1 2 t o E-11 E-1 1 t o E-10 E-10 t o E-9 E-9 t o E-8 E-8 t o E-7 E-7 t o E-6 Number of Currently Operating Power Reactors P l at e W e ld e d P l an t s at 48 E F P Y R i n g F o r g e d P l an t s at 48 E F P Y 0 2 4 6 8 10 12 14 B el o w E-1 3 E-1 3 t o E-1 2 E-1 2 t o E-1 1 E-1 1 t o E-1 0 E-1 0 to E-9 E-9 to E-8 E-8 t o E-7 E-7 to E-6 Nu mb er of Cu rr ently Operating Power Reactors P lat e W e ld e d P l an t s at 32 E F P Y R i n g F o r g e d P l an t s at 32 E F P Y Estimated Yearly Through Wall Cracking Frequency All 2E-7 2E-7 to 4E-7 Figure 3.11.
Estimated distributio n of T WCF for curr ently operating P WRs using the pr ocedur e detailed i n Secti o n 3.5.1 37 Table 3.3. RT and T WCF Values for P l ate-Welded P l ants Estim a te d Usin g the Pr ocedure De scr i bed in Sec t ion 3.5.1 Valu es at 32 E F PY (EOL) Valu es at 48 E F PY (EOL E) RT MA X-A W [o F] RT MA X-PL [o F] RT MA X-C W [o F] 95 th Percentile TWCF (/ry) RT MA X-A W [o F] Plant Name RT MA X-PL [o F] RT MA X-C W [o F] 95 th 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 CALLAW AY 1 84.7 84.9 84.9 3.8E-14 92.6 92.8 92.8 8.1E-14 CALVERT CLIF F S 1 196.6 149.8 149.8 4.2E-09 213.5 168.1 168.1 2.7E-08 CALVERT CLIF F S 2 174.1 174.1 174.1 1.1E-10 192.4 192.4 192.4 2.5E-09 CAT A W B A 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 CRYST AL 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 F A RLEY 1 134.8 164.7 164.7 3.1E-11 147.5 183.1 183.1 1.1E-10 F A RLEY 2 153.5 184.4 184.4 1.2E-10 167.1 203.6 203.6 4.2E-10 F O R T 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 MILLST O NE 2 128.1 132.2 132.2 2.5E-12 139.4 144.2 144.2 6.6E-12 MILLST O NE 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 POIN T 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 Valu es at 32 E F PY (EOL) Valu es at 48 E F PY (EOL E) Plant Name RT MA X-A W [o F] RT MA X-PL [o F] 95 th RT MA X-C W RT MA X-A W RT MA X-PL [o F] Percentile
[o F] [o F] TWCF (/ry) RT MA X-C W [o F] 95 th 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 SOUT H T E XAS 1 42.4 47.6 47.6 7.5E-16 49.7 56.0 56.0 1.9E-15 SOUT H T E XAS 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 T M I-1 238.3 67.1 240.2 1.9E-07 247.7 74.3 249.4 3.3E-07 VOGT LE 1 72.5 72.5 72.5 1.1E-14 79.9 79.9 79.9 2.3E-14 VOGT LE 2 97.7 97.7 97.7 1.3E-13 108.4 108.4 108.4 3.4E-13 W A T E RF ORD 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 EF PY th e fluenc e is the value re porte d in (RVID2) at EOL for the vessel ID.
T he 48 EF PY fluenc e is estimated as 1.5 time s the 32 EF PY val ue. Chemistr y val u es are from (RVID2), exc ept that mang an es e of 0.70 an d 1.35 w e i ght perc ent w e re us ed, respective l y , f o r forgin gs an d for w e l d s/pl ate s. T hese defaults represe n t the appr o x imate a v er ag es of the data use d to e s tablis h the un certaint y distri b u tions for F AVOR 06.1 (s ee Appe ndi x A). 39 T a bl e 3.4. RT a nd T W C F V a l u es f o r Ri ng-F orge d Pl ant s Estim a ted Using the Procedure De scribed in Sec t ion 3.5.1 32 EFPY (EOL) 48 EFPY (EOLE) 95 th Percentile TWCF (/ry) 95 th Percentile TWCF (/ry) RT MA X-F O [o F] RT MA X-C W [o F] Plant Name wi t h o u t Unde rc la d Cra ckin g RT MA X-F O [o F] RT MA X-C W [o F] w i t h Un de rc la d Cra ckin g wi t h o u t Unde rc la d Cra ckin g w i t h Un de rc la d Cra ckin g BRAIDW OOD 1 28.4 85.1 7.5E-17 7.5E-17 32.5 95.3 1.2E-16 1.2E-16 BRAIDW OOD 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 CAT A W B A 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 KEW AUNEE 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 NORT H ANNA 1 159.1 159.1 2.0E-11 2.0E-11 168.4 168.4 4.0E-11 4.0E-11 NORT H 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 POIN T 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 T URKEY POINT 3 102.2 215.8 2.2E-12 2.2E-12 108.9 230.1 1.4E-11 1.4E-11 T URKEY POINT 4 92.9 215.8 2.0E-12 2.0E-12 99.7 230.1 1.4E-11 1.4E-11 W A T T S BAR 1 172.2 172.2 5.2E-11 5.2E-11 181.4 181.4 9.8E-11 9.8E-11 At 32 EF PY th e fluenc e is the value re porte d in (RVID2) at EOL for the vessel ID.
T he 48 EF PY fluenc e is estimated as 1.5 time s the 32 EF PY val ue. Chemistr y val u es are from (RVID2), exc ept that mang an es e of 0.70 an d 1.35 w e i ght perc ent w e re us ed, respective l y , f o r forgin gs an d for w e l d s/pl ate s. T hese defaults represe n t the appr o x imate a v er ag es of the data use d to e s tablis h the un certaint y distri b u tions for F AVOR 06.1 (s ee Appe ndi x A). 40 0 2 4 6 8 10475-500525-550 575-600625-650675-700Max. RT CW [R]# of RingForged PWRs 0 2 4 6 8 10475-500525-550 575-600625-650675-700Max. RT FO [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 RT AW [R]95 th %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 RT PL or RT FO [R]95 th %ile TWCF - Plate FlawsBeaverOconeePalisadesFit 0 2 4 6 8 10# of PlateWelded PWRs 0
2 4 6 8 10# of PlateWelded PWRs 0 2 4 6 8 10# 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 RT CW [R]95 th %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 RT FO [R]95 th %ile TWCF for Underclad FlawsFAVORResultsBound 0 2 4 6 8 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 r ization pa rameters, which include the following:
RT NDT(u) [ F] The unirradiated value of RT NDT. Needed for e ach weld, plate, and forging in the beltline region of the RPV.
Cu [w eight percent
] Copper content. Needed for each weld, plate, and forging in the beltline region of the RPV.
Ni [w eight perce n t] Nickel co ntent. Needed for each weld, plate, and forging in the beltline region of the RPV.
P [w eight percent]
Phosphor us content. N eeded for each weld, plate, and forging in the beltline region of the RPV.
Mn [w eight perce n t] Manganese content. Needed for eac h weld, plate, and forging in the beltline region of the RPV.
t [s econds] Th e am ount of ti me the RPV has been in o p eration. T RCS [ F] The average tem p erat ure of the RCS inventor y i n the beltline region under norm a l operat ing conditions. t MAX [n/c m 2] The maxi m u m flu e nce on the vessel I D for each plate and forging in the beltline region of the RPV. t FL [n/c m 2/s ec.] The maxi m u m fluenc e oc curring along each axial w e ld and circu m fer e ntial weld fusion line. Th is value is neede d for each axial weld and circum ferential weld fusion li ne in the beltli ne region of t h e RPV. T wall [inches] The thickness of the RPV wall, including the cladding.
Step 2. Esti m a te valu es of RT MAX-AW , RT MAX-PL , RT MAX-FO , and RT MAX-CW using the foll o w ing form ula e and the values of the characteri zation para meters fro m St ep 1: RT MAX-A W characterizes the resistance of the RPV to fracture initiating from flaws found along the axi a l 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 m ul a inside the {-}). The value of RT MAX-AW assign ed to the vessel is the highest of the referenc e te mperature values as sociated with any indivi dual axi a l weld fusion line. In evaluating the T 30 values in t h is form ula the com position properties reported in the R V ID database are used for copper, ni ckel, and pho sphorus.
An independent e s tim a te of the manganese c ontent of each weld and plate evaluated is also neede
- d. FL i pl adj i pl adj u NDT FL i aw adj i aw adj u NDT t T RT t T RT)(30)()()(30)()(AWFL(i)n 1 i AW MAX , MAX RT MAX AWFL where n AW FL 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 n AW F L , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular axial weld fusion line, is the unirradiated RT NDT o f the weld adjacent to the i th axial weld fusion li ne, )()(i aw adj u NDT RT 42 is the unirradiated RT NDT o f the plate adjacent to the i th axial weld fusion li ne, )()(i pl adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th axia l weld fusion line, and
)(30 i aw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axia l weld fusion line. )(30 i pl adj TRT MAX-PL characterizes the resistance of the RPV to fracture initiating from fl aws in plates that are not associate d with welds. It is evaluated using the following form ula for each plate wit h in the beltli ne region of the vessel. The value of RT MAX-PL assi gned to the vessel is the hi ghest of the referenc e te mperature values associ ated with any individual plate. In evaluating the T 30 values in this form ula t h e com positi on properties reported in the RVID datab ase ar e used for copp er, nickel, and ph osphorus. An indepen d ent estim ate of the manganese c ontent of each weld and plate evaluated is also neede
- d. )()(30)()(n 1 i PL MAX MAX PL RT i PL MAX i PL i PL u NDT t T RT where n PL is the num ber of plates in the beltline region of the ve ssel, i is a counter that ranges from 1 to n PL , is the m a xi mum fluenc e occurring over the vessel ID occupied by a particular plate, )(i PL MAX t is the unirradiated RT NDT o f a particular plate, and
)()(i PL u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to of a particular plate.
)(30 i PL T)(i PL MAX t RT MAX-FO characterizes the resistance of the RPV to fracture initiating from fl aws in forgings that are not associ ated with wel d s. It is evaluated using the following form ul a for each forging with in the beltline region of the vessel.
The value of RT MAX-FO assi gned to the vessel is the hi ghest of the referenc e te m p erature v a lues as sociat ed with any i ndivid u al plat e. In evaluating the T 30 values in this form ula the co m position pr operties reported in t h e RVID database ar e used for copper, nickel , and phosphorus. An independent esti m ate of the m a nganes e content of each weld and plate evaluated is also needed.
)()(30)()(n 1 i FO MAX MAX FO RT i FO MAX i FO i FO u NDT t T RT where n FO is the num ber of forgings in the beltline region of the vessel, i is a counter that ranges from 1 to n FO , is the m a xi mum fluenc e occurring over the vessel ID occupied by a particular forging, )(i FO MAX t is the unirradiated RT NDT o f a particular forging, and )()(i FO u NDT RT 43 is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to of a particular forging.
)(30 i FO T)(i FO MAX t RT MAX-CW characterizes the resistance of the RPV to fracture initiating from flaws found along the circum ferential weld fusion li n es. It is evaluated using the following form ul a for each circu m fer e ntial weld fusion line within the beltline region of the vessel (the part of the form ula in side the {-}). Then the value of RT MAX-CW a s s igned to the vessel is the hi ghest of the referenc e te m p erature v a lues as sociat ed with an y i ndivid u al circum ferential weld fusion line. In evaluating the T 30 value s in this formula the com p osition properties reported in the R V ID databa se are used for copper, nicke l, and phosphorus.
An independe nt esti m ate of the manganese content of each weld, plate, and forging evaluated is als o needed. FL i fo adj i fo adj u NDT FL i pl adj i pl adj u NDT FL i cw adj i cw adj u NDT t T RT t T RT t T RT)(30)()()(30)()()(30)()(CWFL(i)n 1 i CW MAX , , MAX RT MAX CWFL where n CW FL is the num ber of circum ferential weld fusion lines in t h e beltline region of the vessel, i is a counter that ranges from 1 to n CW FL , t FL is the m a xi mum fluence occurring on t h e vessel ID along a particular circum ferential weld fusion li ne, is the unirradiated RT NDT o f the weld adjacent to the i th circu m ferential weld fusion line,
)()(i cw adj u NDT RT is the unirradiated RT NDT o f the plate adjacent to the i th circu m fer e ntial weld fusion line (if there is no adjace nt plate this term is ignored),
)()(i pl adj u NDT RT is the unirradiated RT NDT o f the forging adjacent to the i th circu m ferential weld fusion line (if ther e is no adjacent forgi ng this term is ignored),
)()(i fo adj u NDT RT is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the weld adjacent to the i th circ um ferential weld fusion li ne, )(30 i cw adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the plate adjacent to the i th axia l weld fusion line(if there is no adjacent plate this term i s ignored), and
)(30 i pl adj T is the shift in the Charpy V-Notch 30-foot-pound (ft-l b) energy (estimated using Eq.
3-4) p r oduced b y ir radiation to t FL of the forging adjacent to the i th a x ial weld fusion line(if ther e is no adjacent forging this term i s ignored).
)(30 i fo adj T 44 The T 30 values in the preceding equations are deter m ined as follows
§: CRP MD T30 e RCS t PMn T A MD 471.2 130.6 1 001718.0 1 e e e RCS t Ni Cu g P Cu f T Ni B CRP , , , 1.543 769.3 1 100.1 191.1 for welds 10 x 417.1 plates for 10 x 561.1 forgings for 10 x 140.1 7 7 7 A for welds 0.155 vessels ed manufactur CE in plates for 2.135 vessels ed manufactur CE-non in plates for 5.102 forgings for 3.102 B 10 2595.0 10 10 10 3925.4 for 10 3925.4 10 3925.4 for t t t e Note: Flux () is estim ated by dividing fluence ( t) by the tim e (in seconds) that the reacto r h a s been in o p eration. 6287.0 12025.18 4483.0 1390.1 log tanh 2 1 2 1 , , 10 Ni Cu t t Ni Cu g e e e e 008.0 072.0 for 0.008)-(359.1 072.0 008.0 072.0 for 072.0 072.0 for 0 , 0.6679 0.6679 P and Cu P Cu P and Cu Cu Cu P Cu f e e e wt%072.0 for wt%072.0 for 0 Cu Cu Cu Cu e flux) L1092 with welds (all wt%0.75 Ni for 301.0 wt%0.75 Ni 0.5 for 2435.0 wt%0.5 Ni for 370.0)(e Cu Max Step 3. Co m p are the RTs fro m Step 2 to the limits in Table 3.5. The lim its on RT MAX-CW given in this table correspond to a T W CF 95 lim it of 1x10
-8/r y , not 1 x10-6/r y. This m o re restrictive lim it was i m p o sed to enable a si m p le tw o-dim e nsiona l representati on of the
§ Th e resu lts repo rted in App e nd ix C d e m o n s t r ate th at th e altern ativ e fo rm o f th is relatio nsh i p presen ted in Ch ap ter 7 of (Eason 0 7) h a s n o sign if icant effect on the T W CF values es ti m a t e d by FA VOR. T h us, t h e eq uat i o n s i n A p pen d i x C coul d be use d i n st ead o f t h e e quat i o ns p r ese n t e d i n St e p 2 wi t h o u t t h e n e ed t o cha n ge a n y ot her part of t h e p r oc edu r e. 45 46 m u ltidi m ensi onal relationship between the various RT values and TWCF 95 ill ustrated inFigure 3.
5 while not un d u l y dim i nishing the resulti ng 1 x10-6/ry li m its placed on RT MAX-AW and RT MAX-PL. Adoption of this l o wer lim it for the TWCF produced by circu m fer e ntial welds is not expected to ha ve any practical i m pact b ecause the hi ghest projected values RT MAX-CW at EOLE are 250 F an d 25 8 F for plate-welded and ring-forged plants (respectively
), both of whic h are well bel o w the lim its on RT MAX-CW that appear in Table 3.5. S houl d changes in operations or other unfores een changes that develop in the future increase a value of RT MAX-CW ab ove the Table 3.5 lim its, the licensee could alway s asse ss its plant using the approach that place s a li m it on TWCF described in Section 3.5.1.
T a bl e 3.5. RT L i mi ts for PW Rs Limit on RT v a lue for different v a lues of T WA L L [ F] RT Value 9.5 in. >9.5 in., 10.5 in.
>10.5 in., 11.5 in. RT M AX-A W 269 230 222 RT M AX-PL 356 305 293 RT M AX-A W + R T M A X-PL 538 476 445 RT M AX-C W (se e note belo w) 312 277 269 For RPV s co mplying with RG 1.43 356 305 293 RT M AX-FO For RPV s not complying wi th RG 1.43 246 241 239 Note: The limit on RT M AX-C W co rresp o n d s to a TWCF value of 10
-8/ry. Should these limits on RT M AX-C W be exce ede d, the RT M AX-A W , RT M A X-PL , RT M A X-FO , and RT M AX C W values shoul d be use d , 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 a nd Fig u re 3.1 4 prov ide a gr aphical co m p arison 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) t h e 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 m o re away from the proposed RT screening lim its at EOLE (these num b e rs increas e to 94 percent for plate-welded plants and 10 0 percent for ring-f o rged plants at EOL). At EOLE, 17 F separates the m o st em brittl ed plate-weld ed plant from these screening li mits (this num ber increas es t o 30 F at EOL). For ring-forged plants at EOL E, 47 F separates the m o st em brittl ed plant from the m o st restricti v e screening li m it (the number increase s to 59 F at EOL).
P l a t e W el d ed P l an t s at 48 E F P Y (E O L E)0 50 100 150 200 250 300 350 400 0 50 100 15 0 200 250 3 00 RT MA X-A W [o F]RT MA X-P L [o F]1x10-6/r y T WC F l im i t Simp li fi ed Im p l em e n t a t i o n RT MA X-A W26 9 F, a n d RT MA X-PL356 F, a nd RT MA X-A W+ R T MA X-PL53 8 F.P al o V e r d e 1, 2, a n d 3 at 4 8 E F P Y (E O L E)0 50 100 150 200 250 300 350 400 0 50 100 15 0 200 250 3 00 RT MA X-A W [o F]RT M A X-PL [o F]1x10-6/ry T W CF li mit Simp li fi ed I m pl em e n t at i on RT MA X-A W22 2 F, a n d RT MA X-PL293 F, a nd RT MA X-A W+ RT MA X-P L44 5 F. Fi gure 3.1 3. Grap hi cal c o mpari s on o f t he RT limits fo r pl a t e-welded plants de veloped in Sec t ion 3.5.2 with RT values for plants at E O L E (fr om T a ble 3.3). The top graph is for pl ants h a ving wall thickness of 9.5-in. a nd less, while the bo tto m gr aph i s f o r vessel s h avi ng w a l l thi c k n e sses b e t ween 10.5 a n d 11.5 in. Ri n g F o r g e d P l a n t s at 48 E F P Y (E O L E)0 50 10 0 15 0 20 0 25 0 30 0 35 0 40 0 0 5 0 10 0 15 0 20 0 250 30 0 RT MA X-C W [o F]RT MA X-F O [o F]TWCF = 1x 10-6/r y l imit i f n o t i n co mp li an c e wi th Re g. G u id e 1.4 3 TW CF = 1x10-8/r y l i m it TWCF = 1x 10-6/r y li mi t if in co mpl i ance w i th Reg. G u ide 1.43 Fi gure 3.1 4. Grap hi cal c o mpari s on o f t he RT limits for ring-forge d pl an ts developed in Section 3.
5.2 with RT val ue s f o r pl a n ts at E O L E (f ro m T a bl e 3.3) 3.6 Need for Margin Asi de fro m rely ing on different RT-m etri cs, the PTS screening lim its proposed in Section 3.
5 differ from th e current 10 CFR 50.61 R T PTS screening li mits by the abs e nce of a "
m a rgin term." Use of a m a rgin term i s 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 h ese p r o p o s e d screening lim its are base d. For exam ple , t h e 10 CFR 50.
6 1 m a rgin term accounts for uncertainty in copper, nickel, and initial RT NDT. However, as discussed in detail by (EricksonKir k-PFM), the NRC m odel explicitl y considers uncertainty in all of these variables and represents these uncert a inties as bei ng larger (a conservati ve representat ion) than would be characte ristic of any plant-s p ecific as ses s m ent application.
Consequentl y , use of the 10 CFR 50.61 m a rgin term with the screening lim its proposed in this rep o rt would be inappropriate.
The following additional reasons suggest that use of any m a rgin term wit h the proposed screening li mits is inappropriate:
47 (1) The TWCF values used to establish the screening li mits represent 95th percentile values. (2) Inform ation presented in Chapter 9 of NUREG-1806 (EricksonKirk-Sum) and su mmarized in Section 3.
2.1 herein de m onstrates that the results fro m the three plant-specific analy ses 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 s timate s." On balance, there is a conservative bias to these non-best-esti m ate aspe c ts of the analy s is, as discussed in the following section.
Throug hout t h is project, every effort has been made to perfor m a "best est i m ate" analy s is. Nonetheless, co m p arison of the analy tic al m odel s used to asses s risk with the actual situation being asses sed re veals that cert a in features of that situation h a ve not been represented a s realistic ally as possible. These parts of the model m a y be judged as pro v iding either a conservative representation (i.e., tending to increase the esti m ated T W CF) or a nonconservat ive representation (i.e., tending to decrea se the esti m ated TWCF) relative to the actual situation in service. Table 3.6 su mmarize s these conserva tis m s and nonconservat ism s, 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 m odels do not accurately represent whe n these inacc uracies have been de m onstrated to not significantly influence the TWCF results. This infor m ation dem onstrates that, on balance, m o re conservatisms than nonconservat ism s remain in the m odel, suggesting the appropria teness of apply i ng the proposed screening lim its without an additional margin term
. 3.6.1 Residual Conservatisms I n the reactor vessel failure frequency lim it- The reactor vessel f a ilure frequency lim it of 1x10-6 events/reactor y ear was e s tablished based on the assu m p tion that through-wall cracking of the RPV will produce a large early release i n a l l c i r c u m s t a n ces. As disc ussed in Chapte r 10 of N UREG-1806 through-wall cracking of the RPV is likely to lead to core da m a ge, but large early releas e is unlikely for two reasons: (1) because of re actor safety sy stem s and the m u ltiple barri ers that block radioactive releas e to the environm ent (e.g., containment), and (2) because if a throug h wall crack were to develop it w ould happen when the te m p eratu re and pressure in the prim ary circuit are low, both of w h ich produce a low sy stem ene rgy. Current guidelines on core dam a ge frequency provided b y Regulatory Guide 1.1 74 an d the Option 3 fra mework for risk-inform ing 10 CFR Part 50 suggest a reactor vess el failure frequency lim it of 1x10
-5 events/reacto r y ear (RG1.174). Changing from a 1x10-6 to a 1x 10-5 li mit would increase all of the proposed RT lim its by b etween 50 an d 60 F (between 28 and 33 C). I n 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 i n a conservative manner. Thus, the loading severity has a tendency toward being overest i m ated. I n the PRA model- External initi ating events. As detailed in Section 9.4 of NUREG-1806 and in (Kolaczkowski-Ext), the N RC's analy s is has not considered the potent ial for a PTS transient to be started by a n initiating event external to th e plant (e.g., f ire, earthquake).
The bounding analy ses performed de m onstrate t h at this would increase the TWCF values reported herein b y at m o st a factor of 2.
However, the bou ndin g nat u re of the NRC' s external events analy s is suggests strongl y t h at the actual effect of ignorin g the c ontribut ion of external initiating eve n ts is m u ch smaller than 2 times. The te m p erat ure of water held in the safety injection accum u l a tors was assu med to be 60 F (15.6 C). These ac cu m u lators ar e 48 inside containment and so exist at tem p eratures of 80-90 F (26.7-32.2 C) in the winter and above 1 1 0 F (43.3 C) in the summe
- r. This conservative esti m ate of injection w a ter te m p e rat ure increase s the magnitude of the thermal st resse s that occur during of pipe breaks and reduces the fracture resi st ance of the vessel ste e l. When a main stea mline breaks inside of containment, the releas e of stea m f ro m the break pressurizes the conta inment structure to appro x im ately 50 p oun d s per square inch (psi) (335 kil opascals (kPa). Consequently, the m ini m u m te m p erature for MSLBs is bounded by t h e boiling poi n t of water at approxim a tely 50 psi (33 5 kPa), or approxim a tely 26 0 F (1 26.7 C). However, the NRC's secondar y-side breaks do not account for pressurization of containm ent, so the m i ni mum te mperatu re calculat e d by RELAP for these transient s is 212 F (1 00 C), or appro x imately 50 F (28 C) too cold. This conservative est i m ate of the mini m u m te m p erature a s s o ciated with an MSLB increa ses the magnitude of the ther m a l stre ss es and reduce s the fracture resistanc e of the vessel ste e l. I n the fracture m odel- Once a circumferential crack initiates, it is assu med to instantly propa gate 360 aro und the vessel wa ll. However, full circu m ferential propagatio n is high l y unlikely because of the azim u thal variati on in fluence, which causes al ternating regions of m o re embr ittled and less em brittled materi al to exist circu m ferentiall y around the vessel wa ll. Thus, the NRC m odel t e nds to overestima te the extent of cracking initiated from circu m ferentially oriented defects because it ignores this natural crack arrest mechan is m. Once an axial flaw initiates, it is assu m e d to instantl y become infinitely long. In reality, it onl y pro p agates to the length of an axi a l shell course (approxim a tely 8 to 12 feet (approxim a tely 2.4 to 3.7 meters)), a t w h i c h point, it en co unters tough er material a n d arrests. Even though a shell course is very long, flaws of finite length tend to arrest m o re readily than do flaws of infini te length because of sy ste m atic diffe rences in the throug h-wall variation of c r ack-driving force. Becau se of this approxim a tion, the NRC m odel tends to overe stim ate the likelihoo d of throug h-wall cracking. As detailed in Section 4.2.
3.1.3 of (EricksonKir k-PFM) and i n (English 02), the adopted F AVOR model of how flue nce attenuates through the RPV wall is conservative relative to experi m e ntal 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 k el, phosp hor us, and RT NDT sa m p l e d by FAVOR overesti m at e the degree of uncertainty in these variable s relative to what can actu a lly exist in any particular weld , plate, or forging. While the FAVOR m odel c o rrects (on average) for the sy stem ati c conservative bias in RT NDT , the m odel overe sti m ate s the uncertainty associated with the fracture toughness transition tem p erature m e tri c. I n the flaw model- In the experi mental data u pon which t h e flaw distribution is based, all detected defects w e re m odel e d as being crack-like and, therefore, potentiall y deleterious to the fracture integrity of the vessel. However
, many of these defects a re actually volum etric ra ther than planar, m a king the m either benign or, at a m ini m u m, m u ch l ess of a challenge to the fracture integrity of the vessel. Thus, the NRC m o del overesti m ates the seriousness of the defect population in RPV m a t e rial s, which leads to overly pessi m i stic as sess ments 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 co mment 40 D in Appendi x B of NUREG-1806). The a lternative m odel, with no interdependence between i n itiation and arrest fra cture toughness values, would reduce the est i m ated values of TWCF. As detailed in Section 9.2.
2.1 of NUREG-1806 , the NRC has sim u lated levels of irradiation da mage bey ond those occurring over currently anticipated lifeti m es usin g the m o st conservative available techniques.
3.6.2 Residual Nonconservatisms I n the reactor vessel failure frequency lim it- Air oxidation. The large early release frequency (L ERF) criterion prov ided in Regulatory Guide 1.1 74, w h ich was used to establish the 1x10
-6/r y TWCF li m it, assumes source ter m s that do not re flect sc enarios where fuel co oling has been lost, exposing the fuel rods to air (rather than stea m). Should such a situation arise, so m e portion of the reactor fuel would eventually be oxidized in a n air environ m ent, which would result in relea se fractions f o r ke y fission products (rut h enium 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 environm ents. These larger r e leas e 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 sm all, certainly far smaller than the num ber of scenarios in which only c o re da m a ge (not LERF) is the onl y plausibl e outcom e. Thus, the nonco n servatism introduced b y n o t explicitl y considering the potential for air oxidation is m o r e than com p ensated fo r by the conservatis m of establis hing a TWCF lim it ba sed on LERF when m a ny accident sequences c a n only plausibly result in c o re dam a ge. I n the PRA model- External initi ating events. As detailed in Section 9.4 of NUREG-1806 and in (Kolaczkowski-Ext), the N RC's analy s is has not considered the potent ial for a PTS transient to be started by a n initiating event external to th e plant (e.g., f ire, earthquake).
The bounding analy ses performed de m onstrate t h at this would increase the TWCF values reported herein b y at m o st a factor of 2.
However, the bou ndin g nat u re of the NRC' s external events analy s is suggests strongl y t h at the actual effect of ignorin g the c ontribut ion of external initiating eve n ts is m u ch smaller than 2 times. In the fracture m odel- Through-wall chem istry lay e ring. As detailed in (EricksonKi r k-PFM), FAVOR models the existe nce of a gradient of properties through the thickness of the RPV because of through-w a ll changes in copper content. These copper content changes arise from the fa ct that, given the large volum e of weld metal needed to fill an RPV weld, manufacturers used weld wire from m u ltiple weld wire sp ools (having different am o unts of cop p er coating) to co m p letely fil l the groove.
The m odel adopted in F AVOR resamples the m ean copper content of the weld at the 1/4T, 1/2T, and 3/4T locations through t h e thickness.
This resam p li ng increases t h e probability of crack arre st because it allo ws the si m u la tion of less irradiation-sensitive material s, which could arrest the runni ng cr ack before it fails the vessel. If these weld la y e rs 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 lim it ed sensit i vity studies performed).
Table 3.6.
Non-Bes t-Es t imate As pect s of the Models Used to Devel o p the RT-B ased Scree ning Limits for PTS Situation Poten t ial Co nserv a tism in the An aly t ical Model T he model ass u mes that all fa ilures prod uce a larg e earl y re leas e; ho w e ver, in the accide nt progr essio n eve n t tr ee (APET) (Ch. 10, NUREG-180 6), most seque nces l ead o n l y t o core da mage. An initi a ted a x i a l crack is ass u med to insta n t l y pro p a gate t o infin i te le ngth. In realit y, the crack len g th w i l l be finite a nd li mited to the le ngth of a sin g le shell c ourse b e c ause the crac ks w i ll most lik el y arrest w h en the y enco unter h i gh er tough ness materials i n eit her the ad jac e nt circumfere ntial w e lds or plates. If the vessel fails, w h at hap pe ns ne xt? An initi a ted circ umferenti a l cra ck is assumed to instantl y pro pag ate 36 0 o arou nd the ves s el ID. In reality, t he crack le n g th is limite d b e caus e the azimuth a l flue n c e variati on pl a c es strips of tough er materia l in the pat h of the e x ten d in g crack. Ho w the ma n y possi ble PT S initiators are bi nne d, an d ho w T H transients are selecte d to rep r esent eac h bi n to the PF M anal ysis W hen unc ertai n t y of ho w to bi n e x is ted, co ns istentl y cons er vative decisi ons w e re made. T he minimum temper ature of an MSLB ins i d e contai nme n t is model ed as appr o x imate l y 50 o F (28 C) cold er than it ca n actual l y be b e caus e contai nment pr essuriz e s as a result of the steam esca pin g from the break.
Char acterizati o n of secon dar y-side failur e s Stuck-ope n val v es on the sec ond ar y s i de are conserv a tivel y mod e l ed in Palis ades. T h rough-w a ll a ttenuatio n of n eutron dama ge Attenuatio n is assume d to be more sign ifica n t than meas ur ed in exper iments. Mode l of material u n irra diate d tough ness a n d chemica l com positi on varia b il it y T he statistical distrib u tions sa mple d prod uce more uncerta i n t y tha n cou l d ever occur i n a specific w e ld, plate, or forgi n g. Correction for s y stematic c o nservative bias i n RT NDT Mode l corrects for mean bias, but overrepr es ents uncerta int y in RT NDT. All defects fou nd w e r e assum ed to be p l an ar. Fla w mo de l S y stematic al l y conserv a tive ju dgme n ts w e re made w h en de velo pin g the fla w distri b u tion mo del. Interdep en den c y of bet w e e n i n itiati on tough ness a n d arrest tough ne ss Mode l empl o y e d all o w s al l initi a ted fla w s a c h ance to pro p a g a te into the vessel. Most conservat i ve ap proac h taken (i ncreas in g time vs. incre a sin g unirra di ated R T ND T). Extra pol atio n o f irradiati on da mage Situation Poten t ial No ncons erv a tism in the An aly t ical Mod e l If the vessel fails, w h at hap pe ns ne xt? T he potential f o r air o x i datio n has bee n ig no red. Ex ter nal PT S initiators T he potential f o r ext e rna l eve n ts (e.g., fire s, earthq uak es) initiati ng PT S transi ents has not bee n mod e l ed e x plic itl y. A conservativ e boun di ng an al ysis estim a tes the effect of ext e rna l eve n ts to be at most a factor of 2 increase i n T W CF , but the likel y increas e is expected to be much less than 2 times.
T h rough-w a ll c hemistr y la yeri ng Mode l assume s that the mean leve l of copp er can cha n g e 4 times throug h the vessel w a ll thick ness. If copper la yer i ng is n o t prese n t, the T W CF w o ul d incr eas e. 51 3.7 Su mm ary This report presents the res u lts of FAVOR 06.1 calculations, co m p ares the m to the FAV O R 04.1 results presen ted in NUREG-1806, and uses the new results to propose two options f o r i m ple m enting these findings in a revision of the PTS Rule (10 CFR 50.61).
Changes m a de in FAVOR 06.1 have placed a greater dens ity in the upper tail s of the TWCF distributio n s , resulting in the agency' s adoption of the 95th percentile of the TWCF distribution for use in the analy ses that produced the reco mme nded im plem entation o ptions. Nevertheles s , as was reported prev iousl y in NUREG-1806, t h e NRC again finds that only the most severe tra n sient class es (i.e., mediu m- to large-dia m et er prim ary-side pipe breaks, valves on the prim ary side that stick open an d m a y sudden ly reclose later) contribute significantly to the TWCF. The minor plant-t o-plant variat ion of t h e the r m a l hy draulic 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 t h e United States. Also, the current results reinforce the findin g fr om NUREG-1806 that it is the materi al properties a ssociat ed with axially oriented flaws that dom inate PTS risk.
Thus, the em brittlement properties of axial welds and plates in plate-welded vess els and of forgings in ring-forged vessel s are the m o st i m porta nt indicators of PTS risk. Conversely
, t h e m u ch lower probabi lit y that cracks initiated from circu m ferentially oriented flaws will propagate through wall makes the embrittlement properties of circu m fere ntial welds much less i m portant contributors t o the total PT S risk. T he two recommended implem entation options include either (1) lim iting the TWCF est i m ated for an operati ng plant to a t o tal value no greater than 1x 10-6/r y or (2) l im iting RT values of the various m a t e rials in the RPV beltline so that their total TWCF is not per m itted to exceed 1x10-6/ry. These options are co m p letely equivalent and interchangeable because they are both based on the sa m e for m ul a, 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 in ed from inform ation in the NRC's RVID database, and surveillance program information (to develop an esti m ate for manganese c ontent). Table 3.7 provides the r eco mmended RT lim its (i.e., im plem entation o p tion 2. Assu m i ng that current operating pra c tices are mai n tained, the status of currently ope rating PWRs relative to these li m its is as follows:
For plate-wel d ed 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/r y at EOLE. At EOL the highest risk of PTS at any P W R is 2.0x1 0-7/ry. At EOLE this risk increas es to 4.3 x10-7/r y. Eight y-five p e rcent of all plants are 50 F or m o r e aw ay from the proposed RT scre e n ing lim it s at EOL E (this num ber increas es t o 94 percent at EO L). At EOLE, 17 F separat es t h e m o st em brittled plant from these screening li mits (this num ber increase s to 30 F at EOL).
For ring-for g ed PWRs- The risk of PTS failure of the RPV is very low. All oper a ting PWRs h a ve estimated TWCF values below 1x1 0-8/ry at EOLE.
At EOL the highest risk of PTS at any P W R is 1.5x1 0-1 0/ry. At EOLE this risk increases to 3.0 x10-10/r y. Ninety percent of all plant s are 50 F or m o r e aw ay from the m o st r estrictive of the proposed RT screening li mits at EOLE (this num ber increases to 100 percent at EOL).
At EOLE 47 F separat es t h e m o st em brittled plant from these screening li mits (this num ber increase s to 59 F at EOL).
52 Table 3.7. RT Limits for P WRs Limit on RT v a lue for different v a lues of T WA L L [ F] RT Value 9.5 in. >9.5 in., 10.5 in.
>10.5 in., 11.5 in. RT M AX-A W 269 230 222 RT M AX-PL 356 305 293 RT M AX-A W + R T M A X-PL 538 476 445 RT M AX-C W (se e note belo w) 312 277 269 For RPV s co mplying with RG 1.43 356 305 293 RT M AX-FO For RPV s not complying wi th RG 1.43 246 241 239 Note: The limit on RT M AX-C W co rresp o n d s to a TWCF value of 10
-8/ry. Should these limits on RT M AX-C W be exce ede d the RT M AX-A W , RT M AX-PL , RT M A X-FO , and RT MA X-CW value s sh ould b e u s ed, alo ng wit h Eq. 3-6, to estimate the total TWCF value.
This total TWCF sh ould be limited to 1x10
-6. 53 54 Chapter 4 - Ref e ren ces 4.1 PT S Te chnical B a sis Citations The following three sections provi de the citations that, together wit h this report, co m p rise the technical basi s for risk-infor m e d revision of the PTS R u le. When these reports ar e cited in the text, the citations appear in italicized boldface to di stinguish the m fro m 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 h er m a l Shock (PTS) Screening Lim its in the PTS Rule (10 CFR 50.
6 1): 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 b e r 28, 2004, available in the NRC' s Agency wide Docu m e nts A c c ess and Managem e nt Sy stem (ADAMS) under Accession #ML042880452. Kolaczkowski-Ext Kolaczkowsk i, A. et al., "Esti m ate 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., "Unc ertainty A n alysis a n d Press urized Therm a l Shoc k: A n O p i n i o n ," U.S. Nuclear Reg u latory Commission, 1999, available in ADAMS under Accession
- ML992710066.
Whitehead-PRA Whitehead, D.L. and A.M.
Kolaczkowsk i, "PRA Procedures and Uncertainty f o r 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 h er m a l 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 h er m a l Shock (PTS) Risk Results to Additional Plants," Octo ber 14, 2004, av ailable in ADAMS under Accession
- ML042880482. Whitehead-Pal Whitehead, D.L., et al., "Palisades Pre s s u rized Ther mal Shock (PTS)
Probabilistic Risk Assessment (PRA)," October 6, 2004, availabl e in ADAMS under Accession
- ML042880473.
4.1.3 Thermal-Hydraulics Arcie r i-Base Arcieri, W.C., R.M. Beaton, C.D. Fletcher, and D.E.
Bess ette, "RELAP5 Ther m a l-Hy draulic Analy s is to Support P TS Evaluations for the Oconee-1, Beaver V a lley-1, and Palisades Nucl ear Power 55 Plants," NUREG/CR-6858, U.S. Nuclear Regulator y Co mm ission, Septem ber 30, 200
- 4. Arcie r i-SS Arcieri, W.C., et al., "RELAP5
/MOD3.2.2 Gamma Results for Palisades 1D Downco m e r Sensitivit y St udy ," August 31, 2004, available in ADAMS under Accession
- ML061170401.
Bess ette Bess ette, D.E., "Ther m al-H y d raulic Evaluations of Pressurized Therm a l Shock," NUREG-1809, U.S. Nuclear Regulatory Co mmis sio n , May 30 , 20 05. Chang Chang, Y.H., K. Alm e nas, A. Mosleh, and M. P our-G ol, "Therm al-Hy draulic Uncertainty Analy s is in Press urized Ther mal Shock Risk Assessment: Methodolo g y and Im plementation o n Oconee-1, Beaver Valley , and P a lisades Nuclear Power Plants," NUREG/CR-6899, U.S. Nuclear Regulatory Commission.
Fletche r Fletcher, C.D
., D.A. Prelewicz, and W.C., Arcieri, "RELAP5/M OD3.2.2 Ass essm ent for Pressurize d The r m a l Shock Applicat ions ," NUREG/CR-6857, U.S. N u c l e a r R e g u l a t o r y Co mm ission, Septem ber 30, 200
- 4. Junge "PTS Consistency Effort ," Staff Le tter Report to file, October 1, 2004, available in ADAM S unde r Accession #ML042880480.
Reye s-APE X Rey es, J.N., et al., "Final Report for the OSU APEX-C E Integral Test Facility
," NUREG/CR-6856, U.S.
Nuclear Regulatory Co mm ission, December 16, 200
- 4. Reye s-Scale Rey es, J.N., et al., "Scaling Analy s is for the OSU AP EX-CE Integral Test Facility
," NUREG/CR-6731, U.S.
Nuclear Regulatory Co mm ission, Novem b er 30, 200
- 4. 4.1.4 Probabilis tic Fra c ture Mecha n ics Dickson-Bas e Dickson, T.L., and S. Yin, "Electronic A rchival of the Results of Pressurized T h er m a l Shock Analy ses for Beaver V a lle y, Oconee, and Palisades Reactor Pres sure Ves sels Generat e d with the 04.1 Version of FAVOR," OR NL/NRC/LT R-04/18, October 15, 2004, available in ADAMS under Accession
- ML042960391 Dickson-UG Dickson, T.L., and P.T. William s , "Fr act ure Analy s is of Vessel s Oak Ridge, FAVOR v04.1, Com puter Code:
User's Guide," NUREG/
C R-6855 , U.S. Nuclear Regulator y Comm ission, October 21, 200 4. EricksonKirk-PFM EricksonKirk, M.T., "Probabilistic Fract ure Mechanics: Models, Parameters, and Uncertainty Treat m e nt Used in FAVOR Version 04.1," NUREG-1807, U.S.
Nuclear Reg u lator y Commission, January 26, 2 005. EricksonKirk-SS EricksonKirk, M.T., et al., "Sensitivity S tudies of the Probabilistic Fracture Mec h anics Model Used in FAVOR V e rsion 03.1,"
NUREG-1808, U.S. Nuclear Regulatory Commission, Novem b er 30, 2004. 56 Kirk 12-02 EricksonKirk, M.T., "Technical Basis fo r Revision of the Pressurized T h er m a l Shock (PTS) Screening Lim its in the PTS Rule (10 CFR 50.61)," December 2002, available in ADAMS under Accession #ML030090626. Malik Malik, S.N.M., "FAVOR C ode Versi ons 2.4 and 3.1: Verification and Validation Summary R e port," NUREG-1795, U.
S. Nuclear Regulatory Commission, October 31, 2 004. Simonen Sim onen, F.A., S.R. Doctor, G.J. Schuster, and P.G. Heasl er, "A Generalized Procedure for Genera ting Flaw Related Inputs for t h e FAVOR Code," NURE G/CR-6817, Rev. 1, U.S. Nuclear Regulator y Co mm ission, October 2003, available in ADAMS under Accession
- ML051790410. Williams William s , P.T., and T.L.
Dickson, "Fracture Analy s is of Vessel s Oak Ridge, FAVOR v04.1: C o m puter Code: Theor y and Im plementation of Algorithm s , Methods, and Corre latio ns," 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 e nts for Protection against Pressuri zed Ther m a l Shock Events
," of the Code of Federal Regulati ons, pr o m ulgated June 26, 19
- 84. 10 CFR 50 A pp. H Appendix H to Part 50, "R eactor Vessel Material Surveillance Program Requirem e nts," o f the Code of Federal Regulations, prom ulgated December 31, 200
- 3. ACRS 05 ACRSR-2116, Letter from Graham W a llis to Luis Rey es entitled "Pressurized Ther m a l Shock (PTS) Reevaluation Project: Technical Basis for Rev ision of the P TS Screening Criterion in t h e 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 m ent 4. ASTM E900 ASTM E900-02, "Standard Guide for Pr edicting Radiation-Induced Transition Tem p erature Sh ift in Reactor Vess el Materi als," A m eri can Society for Testing and Mate rials, Philadelphia, Pennsy l vania, 200 2. Becker 02 Becker, L., "Reactor Pressure Vessel Inspection Reliability
," Proceedings of the Joint EC-IAEA Tech nical Meeting on Improvem ents in In-Service Inspection Effectivene s s , Petten, Netherlands, Novem b er 2002. Dickson 07a Dickson, T.L., P. T. Willia ms, and S. Yin, "Fracture Analy s is of Vessels-Oak Ridge FAVOR, v06.1, Com puter Code: User's Guide," ORNL/TM-2007/
0 031, Oak Rid g e Natinoal Laborator y , 2007. Dickson 07b Dickson, T.L., and S. Yin, "Electronic A rchival of the Results of Pressurized T h er m a l Shock Analy ses for Beaver V a lle y, Oconee, and Palisades Reactor Pres sure Ves sels Generat e d with the 06.1 Version of FAVOR," OR NL/NRC/LT R-07/04. Eason 07 Eason, E.D., G.R. Odette, R.K. Nanstad
, and T. Yama m o to, "A Phy s ically Ba sed Correlati on of Irradiati on-Induced Transition Te m p erature Shifts for RPV Steels,"
Oa k Ridge National Laborator y , ORNL/TM-2 006/5 30. 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 a rjorie Eric ksonKirk, "An Upper-Shelf Fracture Toughness Master Curve for Ferritic Steels," International Journal of Pr essure V essel s and Pipi ng 83 (20 06) 57 1-58 3. EricksonKirk 06b EricksonKirk, Marjorie and Mark Erick s onKirk, "Th e Relationship between the Transition and Upper-Shelf Fracture Toughness of Ferritic Steels,"
Fatigue Fr act Engn g M a ter Struct 29 (2006) 67 2-684. Kirk 03 Kirk, Mark, Cay e tano San tos, Ernest Eason, Jo y ce Wright, and G. Robert Odette, "Updated E m brittlem e n t Trend Curve for Reactor Pressure V ess el Steels,"
Transactions of the 17th I n ternation a l 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 e ld Cladding of Low Alloy St eel Co m ponents," May 1973, ADAMS Accession No.
ML003740095. RG 1.162 Regulatory Guide 1.162, "
Ther m al Ann ealing of Reactor Pressure Vess el Steels," U.S. Nuclea r Regulatory Co mm is sion, February 1996. RG 1.154 Regulatory Guide 1.1 54, "Format and Content of P lant-Specific Pressurized T h er m a l Shock Safety Analysis Reports for Pressurized-Water Re acto rs," U.S. Nuc l ear Regulatory Commissi on, Novem b e r 2002. RG 1.174 Re v 1 Regulatory Guide 1.1 74, R e v. 1, "An Ap proach for Using Probabilistic Risk Assessment in Risk-Inform ed Decisions on Pla n t-Specific Cha nges to the Licensing Basis
," U.S. Nucle a r Regulatory Co mm ission, January 1 987. RVID2 Reactor V ess el Integrity Data base, V e rs ion 2.1.1, U.S. Nuclear Regulatory Commission, Jul y 6, 20 00. Schuster 02 Schuster, G.J., "Technical Letter Report-JCN-Y6604-Validated Flaw Density and Distribution within Reactor Pressur e Ves sel Ba se 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 a rdini, 19 98, "Charact eriza tion of Flaws in U.S. React or Pressure V essel s: Density and Distribution of Flaw Indications in PVRUF,"
NUREG/CR-6471 , Vol. 2 , U.S. Nuclear Regulatory Commission, Washington, D.C.
Tregoning 05 Tregoning , R., and P. Scot t , "Estim ating Loss-of-Coolant Accident (LOCA) Freq uencies through the Elicita tion Process," NUREG-1829 , U.S. Nuclear Regulator y Comm ission, June 2 0 05. William s 07 William s , P.T., T.L. Dickson, and S. Yin, "Fracture Analy s is of Vessels-Oak Ridge FAVOR, v06.1, Com puter Code: Theor y and Im plementation of Alg o rit h ms , Methods, and Correlations,"
ORNL/TM-2 007/0 030 , Oak Ridge Natinoal Laborato r y , 20 07. 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 Lam b ros Lois, NRC/NRR cc: B. Richard Bass, OR NL Subj: Changes req uested bet w e e n FAV O R Version 05.1 and FAVOR Ver s ion 06.1 Dear Terry
- As y o u are aware, over the past eight months staff from the N RC's Office of N u clear Re acto r Regulation (NRR) have reviewed the technical basis RES has pro posed for a ri sk-inform e d revision of the pressurized ther m a l shock (PTS) rule (10 CFR 50.61).
As a consequence of this review, I am r e questing that ORNL take the followi ng actions:
- 1. Make certain changes to FAVOR 05.1.
- 2. Issue a new v e rsion of FAVOR, Ve rsion 06.1, in cluding revisions to both the Theory and the Users manual
- s. 3. Re-analy ze the base-c ase f o r the three study plan ts (Oconee Unit 1, Beaver V a lle y Unit 1, and Palisades) using certain new input data and issue the results to the NRC.
- 4. Perfor m sensi tivity studies to asses s the effects of sub c lad cracking on the through wall cracki ng frequency associated with forged vessels and issue the results to the NRC.
The purpose of this m e m o randum 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 chang es made to the FAVO R code) docum ent the technical basi s for the requested changes
. Should y o u have any questions or requir e clarifica tion of any of the points m a de herein, please do not hesitate to contact m e by e m ail addressed to both m t k@nrc.gov and to m a rkericksonkirk
@ve r izon.net , or b y telepho ne to 30 1-41 5-6 015. Many thanks, Mark T EricksonKirk A-1 Acti on 1: Ch ange FAVOR 05.1 Note: Inform ation provided at the beginning of each of the following tasks establishes th e technical basis/m o tivat ion for the requested change to FAVOR. At the end of each task writeup, the specific requested change can be foun d i n a box hig h li ghted, as is th is one, in p in k. Task 1.1 Change in the data basis for RT EPISTEMIC Question 1: Tables 4.1 and 4.2 in NUREG-1807 provide information on materials for which both RT NDT and T o are known. It is only the informat ion in Table 4.2 that is eventually used in FAV O R be cause it is only for this subset of materials for which enou gh K Ic data are av ai lable to establish a RT LB value. There is a discrepancy between the T o value given in these table s for HSST Plate 03 (shaded in gold in the tables). Table 4.1 gi ves a v a lue 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 differ e nt sets of K Jc data, which is the reason they are different. However, the +31 F value in Table 4.2 is n o t considered valid per AS TM E1921 procedures because all of the K Jc values were mea s ured at a te m p erature t h at is m o re than 90 F below T o. The value of
-21 F, which is valid per ASTM E192 1, shoul d therefore be used.
Action: In the FAVOR Theory m a nual (Tab le 10), change the value of T o for HSST Plate 03 to -
21 F, and change the resultant R T NDT-To value to +41 F. A-2 Table 4.1 Summary of U n irradiated RPV Materi als Having Both RT NDT and T o Values Available Author Year Product Form Spec Material Designation T o [°F] RT NDT [°F] RT NDT - T o[°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 H SST 02 -8 0 8 Marston, T.U.
1978 A533B Cl. 1 H SST 02 -17 0 17 Marston, T.U.
1978 A533B Cl. 1 H SST 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 H SST 14A -70 10 80 McCabe, D.E.
1992 A533B Cl. 1 H SST 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 z le -32 27 59 Ramstad, R.K.
1992 HSST 72W 9.4 60 CEOG 1998 -138 -60 78 CEOG 1998 -136 -50 86 William s. 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 William s , J. 1998 Weld -203 -50 153 Table 4.2 Three R e fer e n ce Transitio n Tempe r at ures D e fined Using the ORNL 99/27 K Ic Database A-3 R e fer e n ce Te m p er atur es Uncer t. Ter m s Property Set ID Material Desc ription Product Form Sample Size RT NDT(u) T 0 RT LB RT NDT (u) - T 0 RT LB 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 65 121.4 139 186.4 6 HSST 02 Plate 69 0 2.1 17 2.1 7 A533B Weld 10 151 -187.2 106 142.2 8 A533B Weld/HA Z 6 0 -132 -162.4 132 162.4 9 A508 Cl. 2 Forging 12 50 -124 -97.6 174 147.6 10 A508 Cl. 2 Forging 9 51 -60 0.9 111 50.1 11 A508 Cl. 2 Forging 10 65 -55 10.4 120 54.6 12 HSSI 72W Weld 12 -9.4 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 Noz z le 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 T LB data in Table 4.2 are plotted versus T o (using the corre cte d 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 o r 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 T o (these data are indicated in re d print in Table 4.2 above
), while 11 of the values have RT LB values higher than T o? -2 5 0-2 0 0-1 5 0-1 0 0-5 0 0 50-200-150-10 0-50 0 50 T o [o F]RT LB [o F] D a ta RT LB = T o Answer 2: The figure at the top of the next page, wh ich is taken from the FAVOR 04.1 The o r y Manual, indic a tes that RT LB is established for a particular data set using the foll o w ing procedure:
- 1. Identify a set of ASTM E399 valid K Ic d a ta for which you want to i d entif y RT LB and for which RT NDT is known.
- 2. Plot the K Ic d a ta, and also plot the ASM E K Ic 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 K Ic Curve. 4. Shift the Adj u sted Lower Bound ASM E K Ic Curve leftward until it intersects t h e first mea s ured K Ic value. Call the am ount b y whic h the curve has been translated RT LB. 5. RT LB is now defined as RT LB = RT NDT - RT LB. 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 tem p e ratur es), the RT LB value will alway s exceed the T o value. This is illustrated in the figure at the top of t h e nex t page, where 100 K Jc valu es are randomly sim u lated over the te m p erature ran g e of -15 0 C T-T o +75 C. The 11 a c tual sets of data for which RT LB exceeds T o all have K Ic values measured over a wide range of tem p eratures and so can be expected to have RT LB > T o. We used the Master Curve to sim u late 100 data sets of 100 K Jc values over the tem p erature range of -150 C T-T o +75 C (-270 F T-T o +135 F). The 100 sim u lat e d RT LB values es timated fro m these si m u lat e d data excee ded T o by , on average, 38 F (with a standard deviation of 19 F). This sim u lated am ount b y which RT LB exceeds T o is in good agr e ement with the 11 actual data sets for which RT LB exceeds T o by 41 F (on average). From this analy s is, we draw the following conclusions:
RT LB should exceed T o. For well-populated data se ts where K Ic or K Jc values are m e asured in transition, RT LB will be esti m ated to exceed T
- o. The average am ount b y w h ich RT LB exceeds T o for the 11 data sets shown in bl ack type in T a ble 4.2 is in good agree m ent with our si m u lation based on the Master C u rve. A-6 0 50 10 0 15 0 20 0 25 0-200-1 50-100-5 0 0 5 0 1 00 T-T o [o C]K Jc [M Pa*m 0.5]K J c s i m ul a t e d ba s e d on M C 2.5% M C B oun d Me d i a n MC 9 7.5% M C B o u n d R TLB C ur v e , R T LB = To + 2 5 C The seven data sets shown in red ty p e i n Table 4.2 d o not have m e asured K Ic values distributed over a wide range of tem p eratures. In general, t h e measured K Ic values for all five data sets fall in a range of tem p eratures between
-111 C T-T o -83 C (-200 F T-T o -150 F). As i llustrated by t h e si m u lation shown below, this places all of the m e asur e d K Ic data very close to the lower shelf and causes the esti m at ed 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 y pe, w e used the M aster Curve to sim u late 100 data sets of 20 K Jc values over the tem p erature range of -11 1 C T-T o -83 C (-200 F T-T o -150 F). T h e 100 si m u lated RT LB values esti m ated fro m t h ese si m u lat e d data fell below T o by, on average, 77 F (with a standard deviation of 4 9 F). This sim u lated am ount b y which RT LB falls below T o is well within one standard deviation of the s e ven actual data sets that h a ve onl y K Ic values on the lower shelf. These data sets, shown in red t y pe i n Figure 4.2 , ha ve RT LB values that fall below T o by 43 F (on average). From this analy s is, we draw the following conclusions:
0 50 100 150 200 250-200-150-100-50 0 50 1 00 T-T o [o C]K Jc [M P a*m 0.5]K J c s i m ula t e d ba s e d on M C 2.5% M C B ound Me d i a n MC 9 7.5% M C B ound R TLB C ur v e , R TLB = To -4 5 C RT LB will fall below T o if t h e onl y K Ic data available for analy s is lie on or near the lower shelf.
A-7 The result RT LB < T o 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 captu re the tem p erature dependence inherent to transition fracture. RT LB < T o d o es not reflect any thi ng intrinsic abo u t the m a terial that shoul d be si m u lated in FAVOR. Mo reover, the K Ic values esti m ated when RT LB falls below T o becom e nonconservat ive at higher t e m p eratures.
The data sets shown in red type in Table 4.2 sho u ld t h erefore not be used in the e s tim a tion of the RT EPISTEMIC value sam p led in FAVOR to represent the difference between a known value of RT NDT and a sim u lated value of RT LB. The plot belo w shows the relationship (o r lack thereof) between RT LB and RT NDT for the 11 da ta sets in black t y pe sh own in Table 4.2. For purposes of illustration only, a nonparametric CDF derived from these data is a l so shown on the next page.
Action: Modify the data basis for t h e RT EPISTE MIC distribution used by FAVOR. The data used to establish the RT EPISTEMIC distributio n should include only those data sets fro m Table 4.2 (see pages 4 and 5 of this m e m o randum) for which RT LB > T o. Also, include the three new T o values given for materials 16, 1 7 , and 1 8 in the FAV O R Theory m a nual. The analy s is methodolog y used to establish the RT EPISTEMIC distribution fr om these data should be the same as that used c u rrently. -150-100-5 0 0 50-100-50 0 50 100 RT ND T [o F]RT LB [o F] A-8 0.00 0.25 0.50 0.75 1.00-50 0 50 100 150 200RT EP I S T E M I C = R T NDT - R T LB [o F]C u m u la tiv e P r o b a b ility Task 1.2 Change in where the uncerta i nty in RT NDT (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 assigne d 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 ND T (u) uncertainty is sam p led inside of bot h the flaw and the vessel loops. Because FAVOR si m u lates the ex istence of hundreds of t h ousands of fl aws in a particular m a j o r region in a particular vessel, the curre nt sa m p ling strategy im plies that RT NDT(u) can vary point-wise thr ough out an y one weld, plate, or forgin
- g. This sim u lation 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 m u st be the highest of any value calculat e d from a ll of the Charpy V-notch and nil-ductilit y t e m p erature measurements m a de for the weld, plate, or forgin g in question. Per ASME, RT NDT(u) shoul d th erefore be single-valued for each m a j o r region in each si m u lated vessel. Action: To reconcile this problem , ORNL is req u ested to m o dify the location where the RT NDT(u) uncertainty is sa m p led in FAVOR. RT ND T (u) uncertainty shoul d be s a m p led inside of the vessel loop, but outs i de of the fla w loop. Task 1.3 Change in where RT EPISTEMIC is sa mpled in th e FAVOR looping stru cture The FAVOR program incl udes a series of nested FORT RAN DO-loops that are used to perform a Monte Carlo si m u lat ion. Of these, the outerm o st loop is called the vessel loop. Immed iately inside t h e vessel loop is t h e flaw loop. I n F AVOR Versi on 05.1, a ne w value of RT EPISTEMIC is sam p led from the RT EPISTEMIC distribution for each new flaw si m u lat e d. The sa m p le d RT EPISTEMIC value is used to esti m ate the r e ference temperature for the fractur e toughness transition curve in the following way
- t P Ni Cu RT RT RT RT SHIFT EPISTEMIC u NDT Irradiated , , ,)( For any parti c ular si m u lat e d vessel, hundreds of thousa nds of individual flaws may be sim u l a ted to exist within a particular weld, plate, or forging (i.e., w ithin what FAVOR refers to as a m a jor region). Thus, A-9 the uncertainty sim u lat e d by FAVOR Ve rsion 05.1 in the RT Irradia t e d value will be as large as th e uncertainty in RT EPISTEMIC , which, as shown by the graph at the top of the preceding page, can have a total range exceeding 150 F. This range is m u ch larger than that measured in laboratory tests when fracture toughness sam p les were r e m o v e d from differe nt areas of a weld, plate, or forging.
Action: To reconcile this problem (i.e., that FAVOR 05.1 simulates an uncertainty on RT Irradia t e d that exceeds that mea s ured in laboratory experi m e nts), O R NL is reque sted to m odify the location where the RT EPISTEMIC distribution is sam pl ed in FAVOR. RT EP ISTEMIC shoul d be sam p led inside of the vessel loop, but outside of t h e flaw loop.
No changes to the FAVOR code shoul d be m a de in side the flaw loop t o sim u late the uncertaint y associat ed wi th RT Irra dia t e d. Once the acti ons requested in Tasks 1.2 and 1.3 are ta ken, there will be no uncertainty sim u l a ted within the flaw loop in either of the following variables, RT NDT(u) and RT EPISTEMIC. However, there is uncertaint y within the flaw loop in the RT Shif t value. This unc ertainty arises as a consequence of uncertainties si m u lat e d in the Cu, Ni, P, and fluenc e values. The graph below shows the effect of thes e si m u lated u n certainties on the resultant uncertainty in RT Shift and, consequentl y , the resultant uncertainty in RT I rradia t ed. It can be observed that, except at low mean co pper values, FAVOR si m u lates mo re uncertainty in RT Shif t (an d , consequent ly, in RT Ir radia t ed) than is reflected in either the data from which Eason derived the em brittlement shift m odel or than is characteristic of uncertaint y in the T o referenc e te mperature (AS T M E1921).
If FAVOR sim u l a tes a neg a tive RT Shif t value, it instead sets the RT Shif t used in the calculation to zero, w h ich is why th e si m u lated uncertainty in the low copper shift values is so small. The general overesti m ation by FA VOR of the uncertainty in RT Shif t occurs because inform ation on chem ical co m position uncertainty from many sources had to be co m b ined to obtain enough data to establish a distribution (se e discussion in Appendix D of NUREG-1 807). T h is procedure tends to overestimate the variabilit y in chem ical co mposition t h at would characteriz 0 10 20 30 40 50 60 01 23 45 F l u en ce / 10 19 [n/c m 2]S t an d a r d D evi at i o n o f 100 0 S i m u l at ed S h i ft V a lu e s [o F]M e an C u = 0.0 5 M e an C u = 0.1 0 M e an C u = 0.2 0 M e an C u = 0.3 0 S t a nda r d de v i a t i on of E a s on m ode l f or w e l ds e any individual weld.
Becaus e of these fa ctors, there is no need to add logic insi de the flaw loop to sim u late the uncertainty associated with RT Irradia t e d; this uncertainty is already a ccounted for i n FAVOR by sim u l a ting unc ertainties in the values of Cu, Ni, P, and fluence used in the calculations.
Action: No action is required. The above co mment 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 a ken from Ap pendix D of NUREG-1807. These graphs (and the r e lated text in NUREG-1 807 Appen d i x D) provi de the technical b asis for the standard deviation of bot h copper and nickel within a particular sub-region (i.e., within a par tic ular weld). To be consist e nt with this data basis, FAVOR should sam p le these standard deviations onc e per m a jor weld region in each si m u lat e d vessel.
A-10 This, however, is not what is done in FA VOR 05.1. F AVOR 05.1 si m u lates the Cu and Ni standard deviations ins ide of bot h the flaw and the vessel loops.
The effect of this sam p ling prot ocol is t h at the standard deviation of Cu a nd Ni is m odeled as vary in g poi nt-wise throug hout a p a rticular weld. Action: ORNL is req u ested to m o dify the location wher e the standard deviation on C u and Ni for welds is sam p led in FAVOR. Th e standard deviations for C u 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 (RT Shift equation)
Action: Add the following em brittl em ent trend curve as an opt ion to FAVOR. Note that the units of TTS are F. The technical basis for this equation is c u rrentl y bein g docum ented b y Nanstad, Eason, and Odette and sho u ld be available in April 2 006. CRPterm MDterm TTS e RCS t PMn T A MDterm 471.2 130.6 1 001718.0 1 e e e RCS t Ni Cu g P Cu f T Ni B CRPterm , , , 1.543 769.3 1 100.1 191.1 for welds 10 x 417.1 plates for 10 x 561.1 forgings for 10 x 140.1 7 7 7 A for welds 0.155 vessels ed manufactur CE in plates for 2.135 vessels ed manufactur CE-non in plates for 5.102 forgings for 3.102 B A-11 10 2595.0 10 10 10 3925.4 for 10 3925.4 10 3925.4 for t t t e Note: The relationship for t e is lim ited as f o llows: t e = MA X(3 t). 6287.0 12025.18 4483.0 1390.1 log tanh 2 1 2 1 , , 10 Ni Cu t t Ni Cu g e e e e 008.0 072.0 for 0.008)-(359.1 072.0 008.0 072.0 for 072.0 072.0 for 0 , 0.6679 0.6679 P and Cu P Cu P and Cu Cu Cu P Cu f e e e wt%072.0 for wt%072.0 for 0 Cu Cu Cu Cu e flux) L1092 with welds (all wt%0.75 Ni for 301.0 wt%0.75 Ni 0.5 for 2435.0 wt%0.5 Ni for 370.0)(e Cu Max The followin g items should be noted when im plementing t h is for m ula in FAVOR:
Flux () is estim ated by d iv iding fl uence ( t) by the time (in secon d s) associat ed with the analy s is. Time is c a lculat ed from EFP Y. The effective fluence ( t e) is li m ited to a maxi m u m val u e of three ti mes the fluen ce (i.e., 3 t). When esti m at ing values of TTS for an em b e dded flaw having a crack-tip located z inches from the ID, the values flux () and fluence ( t) at location z should be estim ated as follows before the effective flue nce ( t e) at location z is cal culated:
- 1. ID fluence:
ID , deter m ined from the B N L fluence m a p 2. ID flux: t t ID ID, where t is determ ined from EFP Y 3. Fluence at z:
z t t ID z 24.0 exp 4. Flux at z:
z ID z 24.0 exp 5. Effective flue nce at z: 10 2595.0 10 10)(10 3925.4 for 10 3925.4 10 3925.4 for z z z z z e t t t z z e t t3 MAX)( Task 1.6 Manganese sampling protocols and uncertainty In order to com p l e te Task 1.5, inform ati on 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. Co m bustion Engineering Owners Grou p, "Fracture Toughness Characterization of C-E RPV Materials," Draft Report, Rev. 0, CE NS PD-1118, 19 98. 2. VanDerSluy s, W.A., Seeley, R.R., and Schwabe, J.E
., "An Investigation of Me chanical Properties and Chem i s try within a Thick MnMo Ni S ubm erged Arc Weld m e nt," Electric Power Research Institute Report, EPRI NP-373 , Februar y 19 77. 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 t h e Irradiation Da ta for A302B and A533B Correlation Monitor Materials," NUREG/CR-6413, No vem b er 1995. 5. Fy fitch, S., a nd Pegram , J.W., "Reactor Vessel Weld Metal Chem i cal Co m posit ion Variability Stud y ," B&W Nuclear Technologies Report, BAW-2220, June 1 995. These citatio ns contained enough repea ted measur e ments of Mn to enable esti m ation of the variability i n Mn at both a global and a l o cal level. Globa l and loc a l 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 10 3 square inches. Local variability occurs over an area r e f e rred to as a "sub-region" in FAVOR. A sub-region is co m p letely contained within a re gion and corresponds to an area of the vessel that has within it relatively m inor variation i n fluence. Su b-regions hav e ID areas on the order of 1 0 0 to 1 0 1 square inches. Appendix D of NUREG-1 807 provi des a m o re co m p l e te description of how FAVOR si m u l a t es global and local variability in com position variables.
The data from the se four citations are s u mmari zed in the table and the figure below. Based on this inform ation, the following conclusions can be made: The variability (standard deviation) of Mn is approxi m ately independent of m e an Mn level. The local variability of welds is less than the global variability of w e lds. The global va riability of forgings is less than th at of w e lds and plates. The global and local variabilit y of forgings is approxim a tely equal. Regarding sam pling/res a mpling protocols, the follo wing shall be im pl e m ented in FAVOR for Mn: The distinctio n between region an d sub-region u n certa inty that is currentl y m a de with regard to sam p ling of Cu, Ni, and P shall now also be m a de for Mn. The reco mmendations 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 resa mpled from th e global (or region) uncertainty in the IGA Propagation Sub-Model e ach tim e the propagating crack extends past a 1/4T b oundar y. The se same protocols shall be followed for resam p ling Mn i n welds. Cit a tio n Da ta I D Prod uct Form Gl ob al or Lo ca l Va ri a b ility Number of Mn Measurements Mea n Mn Mn Stand a rd Devi ati o n Pl at e 01-K Pl at e Gl o b al 9 1.35 6 0.09 5 Pl at e 01-M U Pl at e Gl o b al 3 1.40 3 0.03 2 N U R EG/CR-40 92 Pl at e 02-FB Pl at e Gl o b al 3 1.49 0 0.01 0 A-13 Gl ob al or Mn Prod uct Number of Mn Mea n Cit a tio n Da ta I D Form Lo ca l Stand a rd Va ri a b ility Measurements Mn Devi ati o n Pl at e 03-E Pl at e Gl o b al 5 1.34 8 0.05 2 B , OS , F 1 For g i ng Local 4 0.64 8 0.00 5 B , 1/4, F1 For g i ng Local 5 0.64 4 0.00 5 A, 1/2 , F 1 For g i ng Local 5 0.63 6 0.01 1 A, 3/4 , F 1 For g i ng Local 4 0.64 8 0.01 0 A, IS, F 1 For g i ng Local 4 0.65 0 0.00 8 Al l F1 Dat a For g i ng Gl o b al 22 0.64 5 0.00 9 B , OS , F 2 For g i ng Local 2 0.72 0 0.01 4 B , 1/4, F2 For g i ng Local 3 0.73 7 0.00 6 A, 1/2 , F 2 For g i ng Local 3 0.74 0 0.01 7 A, 3/4 , F 2 For g i ng Local 3 0.76 0 0.01 0 Al l F2 Dat a For g i ng Gl o b al 13 0.73 6 0.02 0 Fl ux A Wel d Gl o b al 15 1.41 5 0.02 1 Fl ux B Wel d Gl o b al 11 1.55 4 0.04 8 B , OS , W Wel d Local 10 1.54 8 0.02 8 B , 1/4, W Wel d Local 9 1.49 4 0.01 7 A, 1/2 , W Wel d Local 6 1.44 5 0.01 0 A, 3/4 , W Wel d Local 4 1.42 3 0.02 2 EPRI N P-373 A, IS, W Wel d Local 2 1.39 0 0.01 4 A3 0 2 B Pl at e Gl o b al 4 1.37 5 0.03 7 HSST-01 Pl at e Gl o b al 16 1.39 2 0.09 0 HSST-02 Pl at e Gl o b al 10 1.47 9 0.05 3 N U R EG/CR-64 13 HSST-03 Pl at e Gl o b al 6 1.33 3 0.05 9 27 2 04-B 0 3 Wel d Gl o bal 13 1.29 2 0.03 8 12 0 08/13 2 53-C 08 Wel d Gl o bal 13 1.28 2 0.07 8 3P 73 1 7-T 0 7 Wel d Gl o b al 13 1.45 2 0.04 3 90 1 36-G 1 1 Wel d Gl o bal 13 1.06 7 0.03 4 33 A 27 7-D 08 Wel d Gl o bal 13 1.15 3 0.03 8 83 6 37-N 1 0 Wel d Gl o bal 13 1.50 9 0.05 7 10 1 37-E 08 Wel d Gl o bal 13 1.29 1 0.04 8 33 A 2 7 7-C 1 9 Wel d Gl o b al 13 1.22 0 0.05 5 27 2 0 4-B 0 3 Wel d Local 5 1.26 4 0.01 8 12 0 08/13 2 5 3-C 08 Wel d Local 5 1.26 6 0.01 1 3P 73 1 7-T 0 7 Wel d Local 5 1.44 8 0.01 3 90 1 3 6-G 1 1 Wel d Local 5 1.09 6 0.02 3 33 A 2 7 7-D 08 Wel d Local 5 1.16 2 0.02 4 83 6 3 7-N 1 0 Wel d Local 5 1.49 8 0.00 8 10 1 3 7-E 08 Wel d Local 5 1.27 4 0.01 5 CE N P SD 944-P R e v. 2 33 A 2 7 7-C 1 9 Wel d Local 5 1.18 4 0.01 7 10 1 37 Wel d Gl o bal 20 1.13 2 0.08 9 21 9 35 Wel d Gl o bal 7 1.48 9 0.05 0 20 2 91/12 0 08 Wel d Gl o bal 29 1.25 2 0.07 9 33 A 2 7 7 Wel d Gl o b al 38 1.13 6 0.09 3 10 1 37 Pl at e Gl o b al 12 1.25 9 0.05 7 B A W-2 2 20 21 9 35 Pl at e Gl o b al 7 1.40 4 0.06 7 A-14 Gl ob al or Mn Prod uct Number of Mn Mea n Cit a tio n Da ta I D Form Lo ca l Stand a rd Va ri a b ility Measurements Mn Devi ati o n 20 2 91/12 0 08 Pl at e Gl o b al 17 1.34 1 0.10 1 33 A 2 7 7 Pl at e Gl o b al 24 1.34 8 0.08 8 0.00 0.02 0.04 0.06 0.08 0.10 0.60.8 1.01.2 1.41 M ean M n M n St anda r d Dev i at i on.6 P l at e - G l obal F or gi ng - G l obal F or gi ng - Loc al W e l d - G l obal W el d - Loc al Actions: Model variabilit y in Mn at both t h e global and local level by sam pli ng from distributions as described in the following table. The original data used to generate these values will be supplied to ORNL for further analy s is. Regarding sam pling/res a mpling protocols, the follo wing shall be im pl e m ented in FAVOR for Mn: The distinctio n between region an d sub-region u n certa inty that is currentl y m a de with regard to sam p ling of Cu, Ni, and P shall now also be m a de for Mn. The reco mmendations 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 resa mpled from th e global (or region) uncertainty in the IGA Propagation Sub-Model e ach tim e the propagating cr ack extends past a 1/4T b oundar y. The se same protocols shal l be followed for resam p lin g Mn in welds. Conditi on Value Glo b a l Va riability in Pla t es Glo b a l Va riability in Welds Glo b a l Va riability in Fo rg ing s a n d Lo ca l Va ria b i lity in a ll Pro d uct Fo rms M ean St a nda rd De vi at i on 0.06 1 7 0.05 5 1 0.01 4 1 St anda r d Devi at i on of St anda r d Devi at i ons 0.02 7 8 0.02 1 7 0.00 6 3 A-15 Task 1.7 Change coefficien ts in u pper-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 developm ent work, som e o f the coefficie n ts in th e upper-shelf fract ure toughness m odel i m ple m ented in FAVOR ne ed to be change d, as detailed below.
Eq. 19: The 50.1 and 0.79 4 coefficients used in E
- q. 19 (current version belo w) should be changed to 48.8 43 and 0.7985 , respectively. The da ta supportin g this change are given after the equation.
F i t to A l l S ta ti c Da ta T US = 0.7985*T o + 48.843 R 2 = 0.9812-1 5 0-1 0 0-5 0 0 50 10 0 15 0 20 0-2 00-1 50-1 00-5 0 0 50 1 00 1 50 2 00 T o [o C]T US [o C]A ll S t a t ic Ol d Ne w Li nd e 8 0 Dy n a m i c L in e a r (A ll St a t ic) Eq. 21: The 2.09 coefficient used in Eq.
21 (curr e nt version b e low) should be changed to 1.75. The data supporti ng this chang e are given after the equation.
A-16
-2 5 0 0 25 0 50 0 75 0 10 00-1 50-1 0 0-50 0 50 10 0 1 50 20 0 2 50 3 0 0 T e m p er at ur e [o C]J Ic - J Ic (2 8 8) [k J/m 2]Ol d Ne w Z A F i t to Da ta , a l p h a=1.7 5 Eq. 23: The 62.0 23 a nd -0.004 8 co efficients used in Eq. 23 (current version below) shoul d be changed to 5 1.19 9 and -0.0056 , respectively.
The da ta supportin g this change are given after the equation.
y = 51.1 99e-0.0056x R 2 = 0.862 0 20 40 60 80 10 0-150-100-50 0 50 10 0 150 200 250 300 T e m per at ur e [o C]St andar d D evi at i on of J Ic Val u es [k J/m 2] A-17 Task 1.8 Enhance output Modify FAVOR as nec e s s a ry to enable the user to output the following results for each vesse l iteration:
the RT EPISTE MIC value sampled for that vessel iter a tion for each T-H transient si mulated for th a t vessel for that vessel iter a tion: the num ber of axial cracks that initiated the num ber of circu m ferential cracks that initiated the CPCI for axial cracks the CPCI for circu m fer e ntial cracks the CPTWC for axial cracks the CPTWC for circu m fere ntial cracks the TWCF contribution from ea ch T-H transient for that vessel iter a tion Also, m odify FAVOR to print out values of RT MAX-AW , RT MAX-PL , and RT MAX-CW for each m a jo r 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: RT MAX-A W is evaluated for each of the axial weld fusion lines using the following form ula. In the form ula, the sy m bol t FL refers to the maxim u m fluence occurring along a particular axial weld fusion line, and T 30 is the shif t in the Charpy V-notch 30 ft-lb energ y p r oduced b y ir radiation at t FL. FL axialweld axialweld u NDT FL plate plate u NDT AW MAX t T RT t T RT MAX RT 30)(30)(, RT MAX-CW is evaluated for each of the circu m fer e ntial weld fusion lines using the following form ula. In the form ula, t h e sy m bol t MAX refer s to the maxi m u m fluence occurring ove r the ID in the vessel beltli ne region, and T 30 is the s h ift in t h e Charpy V-n o t c h 30 ft-lb energy prod uced b y irradiati on at t MAX. MAX circweld circweld u NDT MAX plate plate u NDT CW MAX t T RT t T RT MAX RT 30)(30)(, RT MAX-PL is evaluated for each plate using the following form ula. In the form ul a, the sy m bol t MA X refers to the maxi m u m flu e nce occurring over the ID in the vessel beltline region, and T 30 is the shift in t h e Charpy V-notch 30 ft-l b energy produced b y i rradiation at t MAX. MAX plate plate u NDT PL MAX t T RT RT 30)( Task 1.9 Temperature-dependent thermal-elastic properties In FAVOR Version 05.1 (a nd previ ous versions), the therm a l-el asti c m a terial properties (Young's Modulus, P o i sson's Ratio, and the coefficient of th ermal expansion) were m odeled conservatively as being tem p erature-invariant properties. The 06.1 ve r s ion of FAVOR should be m odified to im pl ement te m p erature d e pendencies i n these prope rties as des c ri bed in the following reference:
M. Niffengger, "The Proper Use of Thermal E xpansion Coefficients in Finite El em ent Calculations," Laboratory for Safety and A ccident Resear ch, Paul Scherrer Insti tute, Wurenlingen, Switzerland.
A-18 Also, the clad-base stre ss fr ee refer e nce t e m p erature a nd the through-wall weld residual stress profile m odel s used in FAVOR Ve rsion 05.1 (and previous versions) were esti m ated ass um ing te m p er ature-invariant thermal-el astic material properties (for info rmation on this esti m ation, 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 h e P-T Curve for an RPV," N U REG/CP-01 66, Oak Ri dge National La boratory , Oak Ridge, Tennesse e, Proceedings of the Twenty-Si x th Wate r Reactor Saf e ty Meeting 1, 1999, pp. 47-72). For consistency
, the FAVOR model for the clad-base stress fr ee refer e nce t e m p erature should be rederived using te m p erature-dependent the r m a l-elastic material prop erties. A-19 Acti on 2: Issue FAVOR Versi o n 06.1 Once the task s requested under Action 1 are co m p lete and all consi s tency 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 m a nual , the users m a nual, exam pl e problem s, and the distri bution disks will be issued to the NRC project m onitor for review and comment. All manuals will be prepared in NUREG/CR format.
After the m a n u als have been m odified to address the NRC project m onitor's comment s, they shall be re-issued and di stributed to i n dividuals/or g anizations taking part in the verification and validatio n (V&V) effort. Following V&V, any errors, inc onsistencies, and anom alies id entified will be fixed (s ubject to concurrence of the project m onitor), and the manuals will be revised and re-issued.
A-20 Acti on 3: Reanal yze th e Bas e-C ase f o r th e Three Study Plants Using FAVOR 06.1 Input: Repeat the an aly ses documented in ORNL/NRC/
LTR-04/18 using FAVOR Versi on 06.1. Prior to perform ing this analy s is, the inpu t files should be c h anged onl y i n the followi ng m a nner: 1. Change the initiating event frequencies for prim ary side pipe breaks to be consistent with the inform ation provided i n NUREG-1829.
Alan Ko laskowski of SAIC will provide the necessar y input files.
- 2. Ensure that the global fluence uncertaint y is coded as 11.8%
and l o cal fluence uncertainty is coded as 5.6
% in the inpu t files. 3. The em brittlement trend curve described in Task 1.4 should be selected. Input values of Mn for the various pl ates, forgings, and welds in the thr ee 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 c o rrectly points out that the decisi on to in clude 2% repair flaws in the flaw distribution used in the baseline PTS analy s is was a judgm ent made on the basis that a 2% repair weld volum e exceeded the pro p o r tional 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 g inal fabrication welds was 1.5%).
However, fla w s in welds a re al m o st al w a y s fusion line flaws, whic h suggests that their num b e r scal es in proporti on t o weld fusion li ne area, not in proportion t o weld volum
- e. To address this, RES tasked PNNL to reexam ine the relative proportio n of re pair 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 boun ding. FAVOR mak es the assu m p tion that a sim u l a ted flaw is equally likely to occur at any location through the vessel w a ll thickness. During discussions between RE S and NRR staff regarding the technical basis inform ation developed by RES, NRR questioned th e validity of this assu m p tion for the case of flaws associat ed wi th weld repairs. After further consid erati on, RES has deter m ined that this assu mption is incorrect, as e v idenced by th e following inform ation. The figure be low shows that if a flaw for m s in a weld repair, it is equally likely t o occur any w here with respect to th e depth of the excavation cavit
- y. However, the second figur e below shows weld repair ar eas occur with m u ch higher frequency close to the surface s 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 o r e likely t o be enc ounte red close to the ID or OD surface than it is at the mid-wall thic kness. A-21 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.00 0.20 0.40 0.60 0.8 0 1.00 D e p t h o f F l a w f r o m C avi t y S u r f ace (f r act i o n)C u m m u l a ti v e d i s tr i b u ti o n ( f a c ti o n)R ando m di s t r i b ut i on of f l aw l oc a t i ons Weld Re pa ir M o uth Wel d Repa ir Ro o t N U R E G/C R-6 471, V o l.2 y = 1.10 66e-0.5 5 8 x R 2 = 0.977 3 0%20%40%60%80%100%012 34 56 78 D e pt h of R e pai r E xcavat i o n [i nches]P e r cent of R e pai r Excavat i ons Ext e ndi ng t o t h i s D e pt h or G r eat e r R e p a ir m a d e f r o m ID (2 6 o b s e r v a t io n s)R e pa i r m a de f r o m O D (2 6 o bs e r v a t i ons)C o mb in e d (5 2 O b s e r v a t io n s)E x po n. (C om bi n e d (5 2 O b s e rv a t i o ns)) FAVOR currently uses as input a "blended" flaw distr i bution for w e lds. The flaws placed in the blended distribution are scal ed in proportion to t h e fusion ar ea of the different welding processes used in the vessel. Because of this approach, it is not possible to specify a thr ough thicknes s distribution of repair weld flaws th at is biased toward the surfaces while maintaining a r a ndom 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 o ll owing basis:
In FAVOR, only flaws within 3/8T of the inner diame ter can contribute to the vessel failure probability.
Because PTS transients are dom inated by thermal stresses, flaws buried in the ves sel wall m o re deeply than 3/
8 T do n o t have a high en oug h drivi ng forc e/low enough fracture toughness to i n itiate. A-22 A-23 On the graph above, 3/8T corresponds to 3 in. Th e cu rve 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 h e vessel. The figure above also indicates that 7%
of all repair flaws occur between 5/8T an d 1 T from the outer surface s 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 a ll. FAVOR's cu rrent assu m p t ion of a random through-wall distribution of repair flaws indicates t h at 37.5% of all repair flaws o ccur between the ID and the 3/8T position in the vesse l wall. Thus, FAVOR underesti m ates the 43% valu e based on the data given above.
To account for this underestimation, the 2% ble nd factor for repair welds will be increased to 2.3% (i.e., 2%43/37.5).
Output: Docu m e nt the re sults of the PFM analy ses pe rformed wi th FAVOR 06.1 in the same for m at as that used in O R NL/NRC/LTR-04/18 an d provi de to th e NRC project m onitor for review and co mment. Additionall y , a s soon as it is practicab le after the FAVOR analy ses are co m p let e , and preferably in advance of issuance of the electr onic archive letter report, provide r esults in MS Excel spreads h eets to the NRC project monitor for analy s is.
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] RT NDT(u) Method RT NDT(u) Value (u) Value Cu 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 43 0 0.140.620.0151.4 90C4381-2 INTERMEDIATE SHELL B6607-2 84.3 MTEB 5-2 73 0 0.140.620.0151.4 84C6293-2 LOWER SHELL B7203-2 78.8 MTEB 5-2 20 0 0.140.570.0151.3 84PLATE C6317-1 LOWER SHELL B6903-1 72.7 MTEB 5-2 27 0 0.20.540.011.31 80305414 LOWER SHELL AXIAL WELD 20-714 75.3 Generic -56 17 0.3370.6090.0121.44 98LINDE 1092 WELD 305424 INTER SHELL AXIAL WELD 19-714 79.9 Generic -56 17 0.2730.6290.0131.44 112LINDE 0091 WELD 90136 CIRC WELD 11-714 76.1 Generic -56 17 0.2690.070.0130.964 144Oconee 1, (Designer and Manufacturer: B&W) Coolant Temperature = 556 F, Vessel Thickness = 8.44-in.
FORGING AHR54 (ZV2861) LOWER NOZZLE BELT (4) B&W Generic 3 31 0.160.650.006(5)109C2197-2 INTERMEDIATE SHELL (4) B&W Generic 126.9 0.150.50.0081.28 81C2800-1 LOWER SHELL (4) B&W Generic 126.9 0.110.630.0121.4 81C2800-2 LOWER SHELL 69.9 B&W Generic 126.9 0.110.630.0121.4 119C3265-1 UPPER SHELL 75.8 B&W Generic 126.9 0.10.50.0151.42 108PLATE C3278-1 UPPER SHELL (4) B&W Generic 126.9 0.120.60.011.26 811P0962 INTERMEDIATE SHELL AXIAL WELD SA-1073 79.4 B&W Generic -519.7 0.210.640.0251.38 70299L44 INT./UPPER SHL CIRC WELD (OUTSIDE 39%) WF-25 (4) B&W Generic -720.6 0.340.68(3) 1.573 8161782 NOZZLE BELT/INT. SHELL CIRC WELD SA-1135 (4) B&W Generic -519.7 0.230.520.0111.404 8071249 INT./UPPER SHL CIRC WELD (INSIDE 61%) SA-1229 76.4 ASME NB-2331 10 0 0.230.590.0211.488 6772445 UPPER/LOWER SHELL CIRC WELD SA-1585 (4) B&W Generic -519.7 0.220.540.0161.436 658T1762 LOWER SHELL AXIAL WELDS SA-1430 75.5 B&W Generic -519.7 0.190.570.0171.48 70LINDE 80 WELD 8T1762 UPPER SHELL AXIAL WELDS SA-1493 (4) B&W Generic -519.7 0.190.570.0171.48 70 A-24 A-25 RTNDT(u) [oF] Composition (2) Product Form Heat Beltline flow(u) [ksi] RT NDT(u) Method RT NDT(u) Value (u) Value Cu Ni P Mn USE (u) [ft-lb] 8T1762 LOWER SHELL AXIAL WELDS SA-1426 75.5 B&W Generic -519.7 0.190.570.0171.48 70Palisades, (Designer and Manufacturer: CE) Coolant Temperature = 532 F, Vessel Thickness = 81/2 in.
A-0313 D-3803-2 (4) MTEB 5-2 -30 0 0.240.520.011.35 87B-5294 D-3804-3 (4) MTEB 5-2 -25 0 0.120.550.011.27 73C-1279 D-3803-3 (4) ASME NB-2331 -5 0 0.240.50.0111.293 102C-1279 D-3803-1 74.7 ASME NB-2331 -5 0 0.240.510.0091.293 102C-1308A D-3804-1 (4) ASME NB-2331 0 0 0.190.480.0161.235 72PLATE C-1308B D-3804-2 (4) MTEB 5-2 -30 0 0.190.50.0151.235 76LINDE 0124 WELD 27204 CIRC. WELD 9-112 76.9 Generic -56 17 0.2031.0180.0131.147 9834B009 LOWER SHELL AXIAL WELD 3-112A/C 76.1 Generic -56 17 0.1920.98(3)1.34 111W5214 LOWER SHELL AXIAL WELDS 3-112A/C 72.9 Generic -56 17 0.2131.010.0191.315 118LINDE 1092 WELD W5214 INTERMEDIATE SHELL AXIAL WELDS 2-112 A/C 72.9 Generic -56 17 0.2131.010.0191.315 118 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 m puter cluster. At that time, ORNL is requested to work with the NRC projec t m onitor to define a set of PFM analy s e s 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 s e s (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 perform ed 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 TECHNICAL LETTER REPORT Review of the Literature on Subclad Flaws and a T echnical Basis for Assigning Subclad Flaw D i stributions PNNL Project Num ber: 43565 JCN Y6604 Task 4: Flaw Density and Distribution in RPVs F.A. Si m one n February 2005 W.E. Norris, NRC Project Manager Prepared for Division of Engineering Technology Office of Nuclear Re gulatory Research U.S. Nuclear Regul a t or y Co mmi s s i on 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. Sim onen Pacific North w est N a tional Laboratory Richland, Washington January 3 1 , 2 005 Introduction Pacific North w est N a tional Laboratory (PNNL) has a ssisted the U.
S. Nuclear Re gulatory Com m ission (NRC) in the efforts to revise th e Pressur ized Ther m a l 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 vessel s. These inputs, consisting of com puter files, have been important to probabilistic fracture mechani cs calculations with FAVOR. The flaw inputs have addressed se a m welds, clad ding and base metal materi al s, but had e x cluded subclad flaws as so ciated with the heat-affec ted zone (HA Z) from the w e lding pro ces ses used to deposit stainless steel cl adding to the inner surface of the vessel.
To address concerns expressed by a peer review co mm ittee, ORNL was request ed by NRC to evaluate the potential contribution of subclad flaws t o reactor pres sure vessel f a ilure. Based on inform atio n in available documents, PNN L esti m at ed the num ber an d sizes of subclad flaws in a forged pressure vessel, and provided input files to ORNL for sensitivit y cal culations. The se sensitivity calculations predicted that subclad flaws could contribute significantly to cal culated vessel failure proba bilities. PNNL was then requested to continue its re view of the literatur e for additional inf o r m ation 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 h at PNNL provided t o ORNL for use with the FAVOR code 2. su mmarize results of a literature review performed by PNNL for information on characteristics of subclad flaws
- 3. propose and describe an im proved m e t hod for genera ting distributions for subc lad flaws and present results of exam pl e calculat ions 4. reco mmend future work to im prove the flaw distri bution m odel and the sim u lation of su bclad flaws by the FAVOR code Referen ces (a s listed at the conclusion of this report) provide information on a range of topics, including the metallurgical m e chanis ms that caus e subclad crac ks, measure s that can prevent cracking, and fracture mechanic s ca lculations 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 m o re spe c if ically 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 m ined m a t e rial and has used the data on observed flaws in the different m a t e r ial types to establish statisti cal distributions for the num b ers and siz es of flaws.
However, none of the examined m a terial showed evid ence of subclad flaws. Therefore, the num bers and sizes of subcl a d flaws for a vessel susc e p tible to such cracking wer e esti m ated fr om a preli m i n ary review B-2 of the literature. The primary source was a co m p re hensive paper summari zing European work during the 1970s (A. Dhooge et al., 1978). T h is pa per was ba sed m a inly on e xperience 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 m a y 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 i s cited as a bounding thro ug h-wall depth dimension
- 2. have orientations norm a l to the direction of weld ing fo r clad deposition, gi vin g ax ial cracks in a vessel beltline
- 3. occur as dens e array s of small cra c ks e x tending into the vessel wa ll 4. extend to dep ths lim ited by the depth of t h e 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 x tended perpendicular to the direction of welding and were cluste red where the passes of the strip clad overlapped. Subclad flaws w e re said to be m u ch m o r e likely to oc cur in grades of pressure vessel steels th at have che m i cal co m positi ons that enhance the likelihood of c r acking. For g ing grad es such as A508 are m o re susceptible than p late materi als such as A533. H igh levels of heat inputs during t h e cladding process also enhance the likelihood of subclad crack ing. Other de tails of the cladding process are also i m p o rtant, such as single-lay e r versus t w o-lay e r cladding.
The num ber of cracks per unit area of vessel inner su rface w as e s ti mated fro m F i gure 1, taken from the Dhooge pape
- r. Cracking was shown to occur in ba n d s estim ated to have a width of 4 mm. This dimension was used to estimate the bounding lengths of subclad cracks. The longest indivi d u al cracks in Figure 1 were about 2 mm versus the 4-mm width di mension of th e zone of cracking.
Counti ng the num ber of cr acks pictured in a s m all reg ion of vessel surface gave a crack densit y of 80,512 flaws per square m e t e r. Figure 1 Location and O r ientation of Underclad C r ack; (a) Transverse S ecti o n; (b) Plan View of Cracks B-3 The flaw input files as provide to ORNL were based on the foll owing assum p ti ons: 1. The crack depth dim e nsions were described b y a uni f o rm 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 assu m p tion for flaws in seam welds, the am ount by whi c h flaw lengths exceed their correspondi ng dept h dim e nsion was taken to be a uniform distributio n fr om 0 to 4 mm. Thus, the extrem e length for a flaw with a depth dim e nsion 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). Fla w s with depths of 1 mm h a d 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 m e tal in the vessel wall.
- 4. The file prepared for FAV O R as su m e d that the c ode would sim u la te 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 h e FAVOR calculations.
A very large num ber of flaws (> 130,000) per vessel was predicted based on the photograph of one small area of a vess el surface. T h e im plic ation was that this area was r e presentative of the entire vessel.
Although it is possible that subclad flaws can occur no nuniform ly i n patches of the vessel surf ace, it is generally u n d e rstood that fl aws occur in a widespr ead manner. Large num bers o f flaws have been reported when the proper conditions for subclad crack ing have existed. Based on PNNL' s lim i ted review of docum ents, it was therefore difficult t o justif y redu ctions of the estimated flaw density
. However, sensitivity calculations should be pe rformed to see if refinem e nt of the esti m ated flaw density has a significant effect on the FAVOR c a lculat ions. The estim ated depth dim e nsions of the subclad flaw s were thought to be conserv a tive. The depth of 4 mm was based on statements regarding boundi ng fl aw depths, with no other evidence such as micrographs or data on m e asured de pth dimensions presented. The depth of 4 mm could be an esti m at e for the size of the heat-affe cted zone, which was then taken as a lim i tation on flaw depth. Alter n atively, the 4-mm depth could be th e extreme depth of som e observed subclad flaws. The prelim inary review showed so m e exam ples fro m metallograph y of subclad flaws, whic h showed only flaws of m u ch s m aller depths (< 2 mm). It is therefore suggested that sensitivit y studies a ssu m e d subclad flaws with a bounding depth of 2 mm. The resulting FAVOR calculations include d onl y flaws in the "first bin" corresponding to sizes 0 to 1 percent of the vessel w a ll thickness and pr edicted only s m all 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 m ited 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 a dditional inform ation. PNNL also proposed to review notes from pa st ses s ions with expe rt elicitation panels that have addressed reactor vessel fabrication and flaw distributions for the N RC. The critical need was infor m ation on the depth dimensions of subclad flaws. It was possible that the depth dim e nsion of 4 mm is uncharacteristic of m o st subclad flaws, but is rather a bounding dim e nsion based on consideration of heat-affect ed zones. It was possible that this dept h has also been used in t h e literature for determ inistic fracture mech anics calculations and coul d ther efore reflect the conservativ e nature of i nputs used fo r such calculations.
B-4 Results of Literature Review Individ u al pa pers and reports are su mmarized below.
Welding Research Council Bulletin No. 197 During the early 19 70s, dat a on subclad cracking we re assem bled b y the Task Group on Un derclad Cracking under the Subcommittee on Therm a l and Mechan ical E ffects of the Fabrication Division of t h e Pressure Vessel Research Committee.
T h e following paragraphs from the report of the Task Group are extracted from W e lding Resear ch Council Bulle tin No. 197 (Vinckier and Pense, 1974).
Underclad cr acks wer e def ined as intergranular separ ations 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 a y. Gr ain-boundar y decohesions of sizes less than this were al so included in the inves tigation.
They are generally produc ed during postweld heat treatm e nt. The com b ination of t h ree factors that pro m ote underclad cracking are a susceptible microstructur es, a favorable residual-str ess pattern an d a ther m a l treat ment bringing the steel into a critical te m p erature reg ion, usually between 600 °C (1112 and 1202 °F) where creep ductilit y is low. Weld-overlay claddi ng with high-heat input processes provides the s u sceptible m i crostructure a nd residual-stress pattern, particularly where weld passe s overlap , and postweld heat treat ment provides the critical te m p e rature. High-heat-input weld-over lay techni que s tend to incr ease the incid e nce of underclad cracks. Most underclad cracking was found i n SA508 Class 2 steel forgings with some forged m a t e ri al chem ical com positions found to be m o re sensitive than others. T h ese forgings were clad with one-lay e r submer ged-arc stri p electrodes or m u lti-el ectrode processes. It was not reported in SA533 Grade B plate, nor was it pr oduced when m u ltilay e r overlay processes wer e used. Underclad cr acking can be reduced or eli m inated by a variety of m e ans, but the m o st feasible appears to be by using a two-la y e r cladding technique, controlling welding process variables (e.g., low-heat-input weld processes) or renor malizing the sensitive heat-affe cted-z one region prior to postweld heat treat ment. Control of welding process variables alone m a y not prevent all grain
-boun dar y de cohesions. Another soluti o n would be to use m a t e rials that do not show the co m b ination of a susceptible m icrostruct u re and low creep ductility or, whe re feasible, el i m in ate the ther m a l postweld heat-treat ment cy cle. Other significant findin g s were: Underclad cr acking can include less sev ere manif esta tions of the sa me da mage mechanis ms as underclad cracks, but in th e form of incipient crack s, microcracks, intergranular separations, pores, etc. Underclad cr acks are r estri cted to overlap of the clad passes and occur in the pattern and orientation as indicated in Figure 2. Fracture mechanics evaluations established that subcl a d flaws with dim e nsions of 5 mm by 10 mm are not critical to safe operation. Underclad cr acking was widely reported in an industr y surve y 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 inf o rmation on r e ported depths of u n d e rclad cracks. There was, however , m u ch discussion of the factors that govern t h e susceptibility of m a t e rials t o underclad cracking along with descriptions of the m a terial selecti ons and welding proc edures that can prevent u n d e rclad 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 a bricated for French nuclear power plants. The French evaluation m e thods 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 def ects. These d e fects address different defect locations, different m e c h anis m s 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 m s of occurrence probabilities, the French evaluations have defined the following three defect classes. Envelope def ects-those that have actually been obs erved 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 m ary circuit com ponents (10
-2>P10-4). Conventional defect-covers configura tions of ver y l o w probabilit y (P<10-4). Figure 3 sho w s the full scope of reference defects, with onl y the underclad crack being of in terest to this discussion. F o r the envelo pe category
, t h e undercla d defect has a 3
-mm through-wall dim e nsion and a length of 60 mm. For the exceptional category
, the u nderclad 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 b y EPRI, has issued reports th at provide inf o rmation that is otherwise available only from the French literature. These ASME sources per m itted t h e current review to be co m p leted. The French characterization of flaws was not specifi cally f o rm ulat ed for use in probabilistic f racture mechanic s ca lculations, but has rather been used in F r ance for determ inistic cal culations. The following B-6 discussion nevertheless provides some interpretations in the context of inputs for probabilistic calculations s u ch as with the FAVO R code. The probabili ty values as cited above do not define un its as needed to estim ate flaw frequencies in term s of flaws per unit area or flaws per unit volum
- e. The French public ations im ply t h at that proba bilit y values can be interpreted as the probability of havi ng one or m o re f laws 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 h an in welds.
Howe ver, forged vessels s u ch as those a pplicable to the French experience would have a t m o st two circu m ferential welds in the beltline. It was therefore assu m e d that the probabilities can be treated as flaws per vessel. With this interpretation: A flaw distribution f o r un d e rclad cracks would have a maxim u m flaw depth of 3 mm and maxim u m flaw length of 60 mm. The probabilit y range of 1>P
>10-2 can be interpreted to mean that bet w een 1 percent to 100 percent of a population of vessel we l d s 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 m a xi m u m f law depth of 6 mm. The probabili ty of P<10
-4 c a n be interpreted to m e an that one vessel in 10,000 would have a fabrication surface flaw that extends through t h e entir e clad and then into t h e base metal to give a total flaw depth of 13.5 m
- m. Such a fla w is out side the scope of the present disc ussion of underclad cracking, but has been addressed by ORNL as a low probability surface flaw.
Sensitivit y st udies by ORNL for under c lad flaws were perform ed for maxim u m flaw depths of 2 mm and 4 mm. The 4-mm fla w is c onservative in the contex t of the French work, becau se the French work could onl y support t h e assu m p tion of a 3-mm maxi m u m fl aw de pth. Uncertainty anal y ses could consider flaw depths as great as 6 mm , b u t this flaw d e pth shoul d b e weighted by a factor of 10
-2 to 10-4 i n constructing an uncertainty distribution.
It was noted that the French wo rk used inform ation on fabrication flaws colle cte d from European manufacturer s of vessels.
For the underclad flaws, th e exceptional defect depth of 6 mm c a m e fro m considerations of the repair of un derclad cracks. The French work indicated that the orientations of underclad cracks are expected to be longitudinal and t h at the use of a two-lay e r cladding will minim ize the likelihoo d of un derclad cracking.
Westinghouse Submittals Two topic reports from W estinghouse E lectric were s ubm itted to NRC to address the i m pact of underclad cracks on reactor pressure vessel integrity (Mager et al., 1971; Bamford and Rishel, 2000). The m o st recent report revisits conce rns for underclad crack ing to cover the period of lice n se extension from 40 y ears to 60 y e ars, and concludes that underclad cra c ks are of no concern relative t o structural integrity of the reactor pressure ves sel for a period of 60 y ear s. Both the 1971 and 2000 WCAP reports were reviewed by NRC staf f. A regulatory guide on weld cladding was issued (NRC, 1972). The NRC revie w of WCAP-15338 resulted i n a request for addition inf o rmation (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 m it e d to the 20 00 WCAP report and NRC's response to thi s report. Onl y lim ited inform ation for esti m ating flaw distributions for PTS evaluations was found in the Westinghouse and NRC docum ents. The main focus was on deter m inistic fracture mech anics evalua ti ons that cove red such issues as f a tigue crack growth, with no attention given to PTS e v aluations. The fracture mechanics calculations assumed deter m inistic sizes of underclad cracks, with little doc umentation for the flaw size assu m p tions. The 200 0 W C AP report reviews the history of u nde rclad crackin g, includ ing 1 970 reports o f "reheat cracking" and 1979 experience with "cold cracking."
Ea rly reports of reheat cracks were lim ited in the B-7 United States with vessels fabricated by the Ro tterdam Docky a rd Manufacturing Com p any. Cold cracking was lim it ed to a select group of six U.S. vessel
- s. Reheat cracking has occurred with single-lay e r cladding using high heat input welding onto ASME SA-508 Class 2 forgings. T h e cracks ar e num erous and are confined to a dept h of 0.125 inc h (3 mm) and a width of 0
.4 inch (1 0 mm). Circu m ferential Direction: 1, 2, 8, 1 0 , 1 1 Longitu dinal Direction: 3, 4, 5, 6, 7 , 9, 1 2 Figure 3 Referenc e Def e c ts for Ves sel Beltline fro m Fren ch Evaluations (dimensions in mm) Cold cracking has been reported for ASME SA-508 Class 3 forgings after deposition of the second or third la y e r of cladding. Cr ack depths have varied from 0.007 inch (0.2 mm) to 0.295 i n ch (7.5 mm) and lengths have varied from 0.078 i n ch (2 mm) to 0.59 i n ch (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 m a teri als or for SA-533B, SA-302E, or SA-302B forg ing materials.
B-8 NRC Expert Panels Two expert panels wer e for m ed as part of an N RC project during t h e 1990s t o a ddress concer ns with flaws in rea c tor pressure vessel
- s. The overall objectiv e of this project wa s to review and expand the technical basis of the flaw distributio n m odel of the PRODIGAL co m puter code (Chap m an and Sim onen, 1998) as deve loped in the United Kingd om by Rolls Roy ce and A ssociates. A meeting durin g 19 94 focused on flaws in vessel sea m welds.
A followup meeting during 1996 focus e d on clad region flaws, includin g a di scussion of u nderclad cracking.
Alt hou gh the expert s provided useful and inter esting insights and i n form ation on un derclad cracking, the i nput from the experts was insufficient to provide t h e quantitative i nputs needed to m odel underclad cracking in t h e PRODIGAL com puter code.
The m inutes of the two m e etings (Sim o n en, 19 94; Si m onen, 1996) along with i n formal 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 efr a mes, (1) cracking when the clad is deposited b y we lding an d (2) cracking when a post-weld heat treat me nt 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 sm all depths of about 1 mm th at 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 materi al. There should be no interaction of underc lad cracks with other cracks due to lack of side wall fusion. There is little reason for int e raction between underclad cracks and previous HAZ cracks. Post-weld reheat cracks can also occur along t h e HAZ of the side wall of the weld fill. T h e occurrence of underclad cracks would o f ten be correlated with HAZ along the si dewall. The sa me m e tallurgical cra c king phenomena c a n occur for both underclad crack s and HAZ cr acks with both occurring during stress r e lief post-weld h eat treat m e nt. C racking is likely to occur (if it does occur) both as underc lad and as HAZ, because t h e com positi on of t h e m a t e rial is susceptible. Some heats o f materi al wil l be m o re sus ceptible th an others due to materi al differences. The primary variable is che m ic al co m p osition, and the occurrence of cracking is not m u ch im p acted by heat inputs.
Cracking actually occurs during post-weld heat treatme nt. The locations of cracks are rel a ted to weld beads. The PRODIGAL weld simulation m odel could accoun t for the compositions of f o rgings (5 08), and this inform ati on coul d be used to establish susceptibilities to under c lad cracking. Utilities know forging com position, whic h could be us ed 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 Fra m ato m e 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 h e heat inputs us ed in cladding. This cracking occurs onl y if there is a second la y e r of c lad app lied without preheat. B&W and CE were aware of the potential problem , whi c h can occur in both the 533 and 508 m a terials, but is less likely to occur in weld m e tal. Cracking will also be in the form of a lack of bondi ng of the clad to base metal. B-9 2000 Vessel Flaw Expe rt Judgmen t Elicitation The NRC has funded a n u m b e r of efforts to re-evaluate the guidance and criteria in the Code of Federal Regulatio ns as it relates to reactor vess el integrity
, spe c ifically pressurized therma l shock, whic h challenges the integrity of the reactor pressure ves sel's inner wall. One ele m ent of the re-evaluation required an accurate e s ti mate of fabricat ion flaws, a nd this identified the need for the development of a generalized fl aw distribution for dom e sti c reactor pres sure 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 o r dom estic v essel s, which has been u sed as input int o probabilistic f racture mech anics calculations.
Although underclad cracking was not specifically addr essed by the elicitation, some of the discussions with the experts provided s o me information of i n terest. The following remarks were co m p iled from detailed notes taken durin g inte rviews wi th the experts: Other experts should address underclad cracking. It i s esti m ated that there is a 1 in 50 probabi lit y of conditions for underclad cracking. 508 Class 2 materi als 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 sta y ed with the Class 2 material.
The French changed to 508 Class 3. One expert believed that Babcock and W ilcox had s o me cases of underclad cracking. There can be underclad cracks for single-lay e r clad if the heat input is too hi gh. There can also be underclad cracks with a two-lay e r clad w ithout heat t reatment between lay e rs. One expert had concerns with underclad cracks in 50 8 forgin gs. A n EPRI report on French experience w as mentioned. Only 508 forgings are susceptible to underclad cr ack ing reheat cracks. One of the experts did research and wrote a NUREG for NRC/
ORNL about 7 y ears ago. No reheat underclad crack ing has been r e ported for pl at e m a terials. None of the experts was aware of H 2 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 th e 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 h er than on underclad cracking. T h is report prov ides no specific in form ation on the dim e nsions of cracks observed in nuclear vesse ls. Frederick a nd Hernalsteen Frederick and Hernalsteen (1981) summarize experience with und erclad cracking and evalua tions of the significance of these cra c ks to vessel integrity
. The information provided in this paper does not add to what is available in ot her more co m p rehensiv e review papers such at WRC Bulletin 19
- 7. Dhooge et al.
Dhooge et al. (1978) provi d e an extensive review of experience an d research in the area of reheat cracking in nuclear rea c tor pressure vess els, both unde rclad cracks a nd cracking of structural welds. The paper e m phas izes Europea n experience and research. Topics covered in the review paper are B-10 (1) incidence of cracking, (2) mechanis m of cr acking, (3) detection of reheat cra c king, (4) tests for reheat cracking, (5) control of reh eat cracking, and (6) si gnificance of reh eat cra c king to structural integrity.
Figure 1 from Dhooge et al. (197
- 8) show s the typical locations and orientations o f 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 p erature by the second pass. The following paragraph on the sizes of underclad cracks is quoted:
The underclad cracks range in size fro m the s hort grai n bo undar y s e parations only a few austenitic grains long and deep (0.2 mm) to a m a xim u m 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 h e fusion boundar y being g overn ed b y the depth of the grain coarsened HAZ and thu s principall y b y the particular cladding proced ure. The Dhooge-r eported incid e nce of crack ing is consis t e nt with the conclusions of WRC Bulletin 19
- 7. Dolby and Saunders Dolby and Sa unders note t h at subcla d cracks often refer to conditions such as grain boundar y s e parations or decohesions and in other case s to a ser ies of m i cr o voids. Therefore the ter m "c rack" is subje c t to interpretation. A topical report issued b y Ba bcock and Wilcox (A yres et al., 1972) is cited for inform ation on crack depth dim e nsions. Maxim u m repor ted dept hs of cracking are 4 mm, but depths are usually 2.5 mm or less, being g overned b y the extent of the heat-affected zone.
Other Papers A num ber of other papers are listed as r e ferenc es to the report. These papers we re reviewed, but were found to pr ovide little infor m ation that is im portant to the focus of t h e present report or t o repeat and reinforce inform ation from the other pap e rs that have been discussed above.
Subclad Crack Sensitivity Study Input files for subclad flaw distributio ns were used by Oak Ridge National Labor atory an d NRC staff to perform a sen sitivit y study (EricksonKirk, 2004).
T h i s sensitivity s tudy was for m ul ated as fo llows: 1. One set of forging properties wa s sele c t e d based on the Sequoy a h 1 and Watts Bar 1 RPVs (R VID2). 2. One hypothet ical m odel of a forged vessel was constr ucted based on an existing m odel of the Beaver Valley vessel. The hypothetical forged vessel w as co nstructed by r e m oving the axial welds and co m b ining these regions w ith the surrounding plates to m a ke a forging. This forging was assi gned the properties from Step 1. 3. A FAVO R analy s is of each vessel/forging com b inati on from Steps 1 and 2 were analy zed at three em brittlement levels, 32 EFPYs, 60 EF PYs, and Ext-B. Thus, a total of three FAVOR anal y ses were performed (1 materi al proper ty definition x 1 vessel definition x 3 e m brittlement 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 m u ch higher em brittl em ent level r e presented 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 br itt lem e nt. While these very high em brittlement levels are unlikely to be approached in the foresee able future, these result s indicate that a m o re detail ed assessment of vessel failure proba bilities associat ed wi th subclad cracks would be warranted sh ould a subclad crack ing pr one for g ing ever in t h e future be subjected to very hi gh em brittlem e nt lev e ls. 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 h ickness and the re m a ining fl aws to have depths of 2 percent of the vessel w a ll 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 bo undin g flaw d e pth of 2 percent of the vessel w a ll predicted s m all contribution of s ubclad flaws to vessel f a ilure frequencies.
It is noted her e that the flaw input files used fo r the ORNL/NRC flaw sensitivity calculations had an error that understated the estim ated num ber of subclad flaws b y a factor o f about 2 5. D e tails of this error and the correction of this pr oble m are described below. Th e net effect w ould tend to underesti m at e 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 1.56 E-7 1.60 E-8 0.10 1.40 E-9 2.57 E-12 0.00 1 8 60 5.66 E-7 9.60 E8 0.17 6.15 E-9 1.09 E-9 0.18 Ext-B b 9.00 E-6 1.31 E-5 1.46 3.81 E7 3.95 E-6 10.3 7 The b a s e lin e for all ana l y s es was Beaver Val l e y a s reported b y [E r i cks onKirk, 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 p e r unit area to flaws per unit volum e of vessel material 2. changes to param e ters of the flaw distribution us ing i n sights from the literature review along with a treat ment of the uncertainties in esti m ating these parameter s The proposed m odel has been im plemented into t h e P NNL flaw distributio n algo rithm. The results of exa m ple c a lc ulations are described below. The discussion concludes with reco mmendations for further developm ent of the m odel. Corrections for Flaw Density PNNL determined that flaw input files used fo r the ORNL/NRC flaw sensitivity had an error that understated the num ber of subclad flaw s b y a factor o f about 2 5. A n error was made in conver ting flaw rates fro m fla w s per unit area of vessel s u rface to an equivalent num b e r of flaws per unit volume of forging m a ter ial. The effec t of the underesti m ated flaw densities has not been evaluated b y c o m p arison calculations with the FAVOR code. However, even the incorrect density assigne d 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 m o st cases roughl y pr oporti o n al to the n u m b e r 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 prim ary conclusion dr awn fro m the results of Table 1 should n o t change for a corrected v e rsion of the flaw input fil
- e. That is, subclad flaws can substa ntially increase failure frequencies for em brit tled forged vessels, and m o r e detailed evaluations should be perf or med if such vessels beco me of concer n to fut u re vessel integrity evaluations.
B-12 Flaw Distribution Parameters This section describes a pr oposed m odel for subclad cracks in the beltline regions of reactor pressure vessels. The m odel is based on t h e infor m ation descri b ed above and also addresses uncertaint ies in knowledge of the underclad cracks that could exist in a specific vessel. The m o del includes the following param e t e rs: 1. flaw frequenc y expressed in terms of fla w s per unit area of the vess el inner surface
- 2. the maxim u m (or bo undi ng) throug h-wall depth d im e n s ion of the su bclad flaws
- 3. the conditional distribution of the through-wall depth dim e nsions e xpressed as a fraction of the boun ding dep t h dim e nsion 4. the conditio n a l distributio n of the len g t h dim e nsions of the subclad flaws It is assu med that vessel sp ecific evaluat i ons ha ve been perform ed based on considerations of material/weld ing parameters (and po ssibl y of inspectio n findi ngs) to est ablish whether there is a potential for subclad cracking for the vessel of concern. Fo r purposes of the preli m inary model, this occ u rrence probability ha s been assigned to be one. As the fl aw distribution m odel is furt her refined, expert judgm ent could be applied to better estimate a probabilit y of subcl a d cracking for each given vessel.
Maxim u m Through-Wall D i m e nsions of Cracks
-This param e ter defines the bou nding depth d i m e nsion for the subclad cracks in a given sim u lat e d vessel. As described below, a conditi onal depth di stribution is also defined for the indi vidual cracks. The conditio nal depth distribution is tr unc ated at the bounding crack depth.
The m odel features a bounding flaw depth dim e nsion for each si m u lated vessel.
This bounding depth is assu m e d to be rela ted to details of t h e cladding procedure (e.g., heat inputs f o r the welding proc ess) along with the susceptibilit y of the vessel
's forging m a t e rial to subclad crack ing (e.g., the che m istry 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 lit y for t h e bounding crack depth is a ddr essed by using the French work (Pellissier Tanon et al., 1990; Buchalet et al., 19 90; ASM E, 199 3; Moi n ereau et al., 2001) an d the paper b y Dol b y and Saunders (1977) for guida nce. On this basis, the probabilit y for the m a xim u m d e pth being gr eater 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 a g n itude less (less than 10
-3 for the exceptional defect of Figure 3).
The distribution of bounding flaw depths (Figure 4) is described by uniform dis tribution of the logarithm of the probabilit y over t h e range of 0-6 mm. 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 0.01.0 2.03.0 4.05.0 6.07.0 Bo und ing Fla w De pth , m m Probability G r eate r Than De pt h Figure 4 Probabilities for Bounding Depth of Subclad Flaws B-13 Conditional F law Depth Di stribution
-The conditional distributi on of de pth dim e nsions of subclad flaws for a given ve ssel is a ssu med 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 h is assu m p tion 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 i n form ation on m e asured flaw depth dimensions.
The approach therefore conservatively assigns a large fraction of the flaws to have depth dim e ns ions equal to abou t the bou ndi n g dim e nsion.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Fl a w De pth/Bo undi ng Fl a w D e pt h P rob ab ilit y Great er T h a n Dep th Figure 5 Conditional Depth Distribu tions of Subclad Flaws Maxim u m Length Dim e nsions of Cracks
-The envelope and exceptional defects of Figure 3 w e re first considered the basis for a conditi onal dis tributio n for f law length di mensions. With this appr o ach, the probability of a defect with a 60-mm l e ngth would be assigned as 10
-2 f o r bot h a 3-mm and 6-mm bounding depth of flaw. T h is approach (based on the 60-mm l e ngth) would be significantl y m o r e conservative than that for t h e 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 fl aw l e ngth, whereas other publications s how subclad flaws (s ee Fi gure 1) that have lengths much less than 60 mm. Further m ore, discussions of the mechani s m s of subcla d cracking stat e that flaws a re confined to the overlap region of the heat-affec ted zones of adjacent p asse s of the strips of cladding.
This mechani s tic m odel w ould also give flaw lengths m u ch less than the 60-mm (2.4-inch) flaw of the French public ations. The length di stribution of Figure 6 as adopted f o r th e updated m o del was the same as that assumed for the prior ORNL/NRC sensitiv ity calculations. A unifor m di stribution was used to si m u late the num eri cal differences b e tween the fl aw length and depth dim e nsions. The uniform distribution ranged from 0 mm to 5 mm. For each categor y (or bi n) of t h e flaw depth dim e nsion, the generated input files for FAVOR have a distribution table fo r flaw aspect ratios.
Nu m b er 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 m e ter. Th is 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 u rface with a severe c ase of subclad cracking. This density was treated as a conservative or upper bou ndi n g estim ate of the flaw occurrence fr equency with the lower bound assigned to an order of magnitude less as a lower bound esti m ate. It was a ssu med that the distribution functi on was a uniform distribution for t h e log a rith m of the flaw frequency between these boundi ng values. Figur e 7 shows the resulting dist ribution of fla w frequency. B-14 0.0 0.2 0.4 0.6 0.8 1.0 1.2 012345 Fl a w L e ng th mi nus F l a w De pth, mm Prob ab ilit y Great er T h a n Valu e Figure 6 Conditional Distributions for Flaw Length 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 2 0 , 00 0 40,00 0 60,000 8 0 ,000 100 , 0 0 0 Fl aw s per Squ a re Meter Pr obab i li ty Greater Th an D ensity Figure 7 Flaw Frequen c y 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 u t has results for the first 10 of the 1000 simulated vessels that a re addressed by the full input file for th e FAVO R code. Significa nt differences were s een in the predicted flaw distributions com p ar e d to the pr ior PNNL work. A large part of these differences c a m e from correcting the ori g ina l conversion f r om flaws per unit area to f laws per unit volum
- e. Table 2 summarizes results fro m both t h e prior m ode l (Tables 2a throug h 2 d) and the u pdated m odel (Tables 2e and 2f). Results are pres ente d both in te r m s of flaw density (flaws per cubic foot) and total num ber of flaws in a vessel considering only the be ltline region (assum ing a surfa ce area of 627 square feet correspo nding to a ves sel in a typical FAVOR c a l c ulation). The flaws a re further categorized in term s of their throu gh-wall depth dim e nsions (0-2 m m , 2-4 mm , and 4-6 mm). Table 2 sho w s very large num bers for subclad flaws, ranging up to a few m illion 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 m e insensitive to flaw density. Failure frequency will the n become m o r e sensitiv e to the sim u l a ted 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 m odel. For exa m ple, only vessel #8 of the first 10 sim u l a ted vess el s has any flaws with depth dim e nsions greater than 2 mm. The sensitivity calculations perfor m ed by OR NL with FAVOR predicted zero failure probability for a 2-mm flaw depth, even though m a ny 2-mm flaws were present in the beltline regions. The r efore, 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 u lat e d vessels w e re predicted to fail.
B-16 Table 2 Summary of R esults for Su bclad Flaws-Prior Model Versus Proposed Mod e l T o ta l 0-2 m m 2-4 m m 4-6 m m 456 233 223 0 T o ta l 0-2 m m 2-4 m m 4-6 m m 1 90, 60 8 9 7, 3 94 93 , 2 14 0 T o ta l 0-2 m m 2-4 m m 4-6 m m 10 , 95 8 5, 599 5, 3 59 0 T o ta l 0-2 m m 2-4 m m 4-6 m m 4 , 5 80, 31 0 2 , 3 40, 37 8 2 , 2 39, 93 2 0 T o ta l 0-2 m m 2-4 m m 4-6 m m A v er ag e o f 1 00 0 V es sel s 6, 329 5, 444 850 3 5 V es se l #1 5, 580 5, 580 0 0 Ve ss el #2 1 0,7 01 10 ,70 1 0 0 V es se l #3 4, 272 4, 272 0 0 V es se l #4 8, 312 8, 312 0 0 V es se l #5 2, 554 2, 554 0 0 Ve ss el #6 1 0,6 15 10 ,61 5 0 0 V es se l #7 6, 351 6, 351 0 0 V es se l #8 1, 784 1, 606 178 0 V es se l #9 1, 190 1, 190 0 0 V ess el #10 7, 718 7, 718 0 0 T o ta l 0-2 m m 2-4 m m 4-6 m m A v er ag e o f 1 00 0 V es sel s 2 , 6 45, 52 2 2 , 2 75, 59 2 3 55, 30 0 14 , 6 30 V es se l #1 2 , 3 32, 44 0 2 , 3 32, 44 0 0 0 V es se l #2 4 , 4 73, 01 8 4 , 4 73, 01 8 0 0 V es se l #3 1 , 7 85, 69 6 1 , 7 85, 69 6 0 0 V es se l #4 3 , 4 74, 41 6 3 , 4 74, 41 6 0 0 V es se l #5 1 , 0 67, 57 2 1 , 0 67, 57 2 0 0 V es se l #6 4 , 4 37, 07 0 4 , 4 37, 07 0 0 0 V es se l #7 2 , 6 54, 71 8 2 , 6 54, 71 8 0 0 V es se l #8 7 45, 71 2 6 71, 30 8 74 , 4 04 0 V es se l #9 4 97, 42 0 4 97, 42 0 0 0 V ess el #10 3 , 2 26, 12 4 3 , 2 26, 12 4 0 0 Flaw D e p t h D i me nsion (c) Prior M o d el - C o rre ct e d Va l u e s (Fl a w s pe r C u bi c F oot)(a) P r i o r M o d el - Un co r r ect ed V al u e s (Fl a w s pe r C u bi c F oot)(b) P r io r Mo d e l - U n c o r r e c t e d V a lu e s (F l a w s p er V ess el)Flaw D e p t h D i me nsion Flaw D e p t h D i me nsion (d) P r i o r M o d el - Co rr e cte d V a l u es (F l a w s p er V ess el)Flaw D e p t h D i me nsion (f) Propos e d M ode l (F l a w s p er V ess el)Flaw D e p t h D i me nsion (e) P r opos ed M ode l (Fl a w s pe r C u bi c F oot)Flaw D e p t h D i me nsion B-17 Referen ces ASME. 1993.
White Paper on Reactor Vessel Integri ty Requirements for Level A and B Conditions , EPRI TR-100251, prepared by ASME Se ction XI T ask Group on Reactor Pressur e Vessel Integrit y Requirem e nts, prepared for ASME Section XI Worki ng Group on Operating Plant Criteria, pu blished b y Electric Power Research Institute.
Ay res, P.S., e t al. 197
- 2. B a bcock and W ilcox, Topi cal Report, BAW-10012-A , October 197
- 2. Bam f ord, W., and R.D. Rishel. 20
- 00. A Review of Cracking Associated with W e ld Deposited Claddin g in Operating PWR Plants , WCAP-1533 8, Westingho use Electric Co m p any , P it tsburgh, Pen n s y lvania, March 2000.
Buchalet, C., W.L. Server, and T.J. Griesbach. 1990. "U.S. and French Approaches to Reacto r Vessel Integrity ," prepared for the 1990 ASME Pressure V essel and Piping Conference, Nashville, Tennessee, June 1990. Canonico, D.
A. 1977. Significance of Reheat Cracks to the In tegrity of Pressure Vessel s for Light-Water Reactors , ORNL/NUREG-15, prepared b y Oak Ridge National Laborator y for t h e NRC. Canonico, D.A. 1979. "Si gnificance of Reheat Cr ack s to the Integr ity of Pressure Vessels for Light-Water Reacto r s," Welding Research Supplem ent to th e Welding Jo urnal, Ma y 1 979. Chap m a n, O.J.V., and F.A. Sim onen. 1998.
RR-PR ODIGAL-A Model for Estimating the P r obabilities of Defects in Reactor Pres sure Ves sel Welds , NUREG/CR-5505, prepared b y Pacific North w est Laborator y th e NRC, October 1998. Dhooge, A., R.E. Dolby
, J. Sebille, R. S teinmetz, and A.G. Vinckier. 1978. "A Review of Work Related to Reheat Cra c king in Nuclear Re actor Pressure V ess e l Steels,"
Inte rnational Journal of Pressure Vess els and Pi ping , Vol. 6, 1 978 , pp. 3 29-409. Dolb y , R.E., and G.G. Saunders. 197
- 7. "Underc lad Cracking in Nuclear Vessel Steels-Part 1 Occurrenc e a nd Mechanism of Cr acking," Metal Construction , Vol. 9, No. 12 , pp. 5 62-566 , December 1977. Dolb y , R.E., and G.G. Saunders. 197
- 8. "Underclad Cracking in Nuclear Vessel Steels-Part 2 Detection and Control o f Underclad Cracking,"
Metal Construction , Vol. 9, No.
12, pp. 2 0-24 , January 19 78. Du m ont, P., M. Bieth, and J.P. Launa
- y. 198 7. "F rench Develop m ents in the Ultrasonic Examination of Pressure V ess els," International Journal of Pressure V essel s and Pi ping , Vol. 28 , pp. 19-23. EricksonKirk, M., et al. 2 0 04. Technical Basis for Revision of the Pressuri zed Thermal Shock (PTS)
Screening Limit in the PTS Rule (10 CFR 50.61): Summary Report , NUREG-1 806. EricksonKirk, M., T. Dick son, T. Mintz , and F. Sim onen. 20 04. Sensitivity Studies of the Probabil istic Fracture Mechanics Model Used in FAVOR , NUREG-1808 (availa ble Febuary 2 010). Frederick, G., and P. Hernalsteen. 1981.
"U nderclad Cracking in P W R Reactor Vessels,"
AIM International Meeting: Mo dern Electric Power Stations, Liege, Paper 20.
Gonnet, B. 1 982. "How Fram ato m e Has Dealt with the Cracking Problem
," Nuclear Engineering Internationa l , Vol. 27, No. 322, Januar y 1982 , pp. 21-24. Horiy a , T., T. Takeda, and K. Yama ta. 1985.
"Study of Underclad Cracking in Nuclear Reactor Vessel Steels," ASME Journal of Pressure Vessel Technology , Vol. 107, F e bruary 198 5, pp. 30-35. Jackson, D.A
., and L. Abra mson. 2000.
Report on t h e Preliminary Results of th e Expert Judgment Process for t h e Development of a Methodology for a Ge neralized Flaw Size and Density Distribution for Domestic R e actor Pres sure Vessel s , MEB-00-01, PR AB-00-01, N RC, Septem b e r 2000. B-18 B-19 Lauerova, D., M. Brum ovsk y , P. Sim p anen, and J Ko hopaa. 20
- 03. "Problems of Underclad Type Defe cts in Re actor Pressur e Ves sel Inte grity Evaluation," Transactions of the 17 th I n ternationa l Conference on Structural Mechanics in Reactor Technology (SMIT 17), Paper
- G02-2, Prague, Czech Republic, August 17
-22, 2 003. Lopez, H.F.
1987. "Underclad Crackin g of Pressu re Vessel Steels for Light-Wat er Reactors,"
Scripta Metallurgica , Vol. 21, pp. 753-758. Mager, T.R., B. Landerm an, and Kubi
- t. 197 1. React o r Vessel s and Weld Cladding , Westinghouse Electric, WCAP-7733, Jul y 19 71. Moinereau, D., G. Bezdikian, and C. Fai d y. 200 1. "M ethodology for the Pressurized Ther mal Shock Evaluation:
Recent I m pro v em ents in French RPV PTS Assessment,"
International Journal of Pressur e Vessel s and P iping , Vol. 7 8 , pp. 69-83. Pellissier Tan on, A., J. Grandemange, B. Houssin, and C. Buchalet. 1990.
French Verification of PWR Vessel Integri t y , EPRI NP-6713, prepared by Fram ato m e, Pa ris, France, for Electric Power Research Institute, February 1990. Sim onen, F.A. 1994. M eeting M inutes-NRC Flaw Distribution W o rkshop-December 7
-8, 19 94, Rockville, Ma ryland , prepa red for the NRC by Pacific Northwest National Laboratory
. Sim onen, F.A. 1996. M eeting M i nutes-NRC M e eting o n Clad R e gion Flaws
-July 29-3 0, 199 6, Rockville, Ma ryland , prepa red for the NRC by Pacific Northwest National Laboratory
. NRC. 2002a.
Information Supporting W OG Request for Modification of NRC Safety Evaluation of W C AP-15338 , NRC, June 2002. NRC. 2002b.
Safety Evalu a tion of the O ffice of Nuclear Reactor Regulatio n To pical Report W C AP-15338-A Re view of Cracking Associated with Weld Deposited Cladding in Operating Pressurized Water Reactor (PWR) Plants Westinghouse O w ners Group
, NRC, Septem b e r 25, 20 0 2. NRC. 1972.
Control of St ainless Steel Weld Cladding of Low-All o y Steel Components , Regul atory Gu ide 1.43. NRC. 2002.
Information Supporting WOG Request for M odification of NRC Safety Evaluation of W C AP-15338 , NRC, June 2002. NRC. 2002.
Safety Evalua tion of the Office of Nuclear Reactor Regulati on To pi cal Report W C AP-15338-A Re view of Cracking Associated with Weld Deposited Cladding in Operating Pressurized Water Reactor (PWR) Plants Westinghouse O w ners Group
, NRC, Septem b e r 25, 20 0 2. Vinckier, A.G., and A.W.
Pense. 1974.
A Review of Underclad Cracking in Pressure-V e s sel Components , Welding Research Council Bulletin No.
197, Weldi n g Research Council, New York, August 19 74. Wilkie, T. 1980. "Cracks in French Pressure Ves sels Pose no Danger,"
Nuclear Engineering Internationa l , Vol. 25, No. 294, Januar y 1982 , pp. 27-29.
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 .
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000 .000 .000 37 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 38 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 39 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 40 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 41 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 42 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 43 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 44 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 45 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 46 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 47 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 48 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 49 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 50 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 51 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 52 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 53 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 54 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 55 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 56 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 57 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 58 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 59 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 60 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 61 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 62 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 63 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 64 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 65 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 66 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 67 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 68 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 69 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 70 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 71 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 72 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 73 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 74 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 75 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 76 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 77 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 79 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 80 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 82 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 83 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 84 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 85 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 86 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 87 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 88 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 89 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 90 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 92 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 93 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 94 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 95 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 97 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 98 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 99 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 100 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
000 .000 .000 B-30 LARGEST OF EACH ELEMENT FOR 1000 SIMULATIONS N FLAWS/FT**3 1.0-1.25 1.25-1.5 1.5-2.0 2.0-3.0 3.0-4.0 4.0-5.0 5.0-6.0 6.0-8.0 8.0-1 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 .
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000 .000 .000 78 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
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000 .000 .000 81 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
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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 .
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000 .000 .000 91 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
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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 .
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000 .000 .000 96 .00000E+00 100.000 .000 .000 .000 .000 .000 .000 .000 .
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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 .
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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 m ent of FAVOR Version 0 6.1 as per the change specif ication in Appendix A, Eason developed an alternative em br ittl em ent trend curve of a slightl y sim p lified form (Easo n 07). This alternative rel a tionship is very sim ilar in form to th at which appears as Eq. 3-4 in the m a in te xt of this report, and is provided belo w for referen ce. Eq. C-1 CRP MD T30 e RCS t PMn T A MD 47.2 13.6 1 001718.0 1 e e e t Ni Cu g P Cu f Ni B CRP , , , 77.3 1 191.1 for welds 10 x 417.1 plates for 10 x 561.1 forgings for 10 x 140.1 7 7 7 A for welds 0.155 vessels ed manufactur CE in plates for 2.135 vessels ed manufactur CE-non in plates for 5.102 forgings for 3.102 B 10 2595.0 10 10 10 39.4 for 10 39.4 10 39.4 for t t t e Note: Flux () is estim ated by dividing fluence ( t) by the tim e (in seconds) that the reacto r h as been in o p eration. 629.0 120.18 448.0 139.1 log tanh 2 1 2 1 , , 10 Ni Cu t t Ni Cu g e e e e 008.0 072.0 for 0.008)-(359.1 072.0 008.0 072.0 for 072.0 072.0 for 0 , 0.668 0.668 P and Cu P Cu P and Cu Cu Cu P Cu f e e e wt%072.0 for , min wt%072.0 for 0 Cu Cu Max Cu Cu Cu e e )(e Cu Max 0.243 for Linde 80 welds, and 0.301 for all other m a terials. Since FAVOR 06.1 had be en coded and the throu gh-wall cracking frequency (T WCF) values reported in Table 3.1 had been calculat e d before the developm ent of Eq. C-1 there wa s a nee d to assess the effect, if any , of using Eq. C-1 inste a d of Eq. 3-4 in the FAVOR calculations. Eq. C-1 w as therefore c oded into C-1 C-2 FAVOR, and four different em brittlement conditi ons, as su mmarized in Table C.1 , were anal y zed. In Figure C.1 , the TWCF and referenc e te mperature (RT) values from Table C.1 are com p a red to the baseline resul t s from F A V O R 06.1 (Figure 3.4). This co m p arison shows that changing from the Eq. 3-4 to the Eq. C-1 trend curve does not produce any sign ificant effect o n the TWCF values esti m a t ed 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 TW CF Results Us ing Eq. F-1 for the Embrittlement Tre nd Cur v e RT Values [
o F] % T W CF due to -
95 th Percentil e TWCF Con d itio n RT AW-MA X RT PL-MA X RT CW-MA X Ax ial We ld Fla w s Plate Fla w s Circ We ld Fla w s To t a l Ax ial We ld Plate Circ Weld BV200 251 339 339 21.77 66.79 11.44 2.82E-0 6 6.14E-0 7 1.88E-0 6 3.23E-0 7 PAL 500 421 391 397 97.42 2.35 0.23 9.09E-0 5 8.86E-0 5 2.14E-0 6 2.09E-0 7 OCO32 160 74 179 100.0 0 0.00 0.00 2.16E-1 5 2.16E-1 5 0 0 OCO1000 294 205 322 99.12 0.28 0.60 3.69E-0 7 3.66E-0 7 1.03E-0 9 2.21E-0 9 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. RT AW [R]95 th %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. RT PL [R]95 th %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 RT CW [R]95 th %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 Fla w s in Vessel Forgings F.A. Sim onen Pacific North w est N a tional Laboratory Richland, Washington July 28, 20 04 Pacific North w est National Laborator y (PNNL) has been funded b y the U.S. Nu clear Regulator y Co mm is sion (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 m e t a l re gions. Data fro m vessel examinat ions, along with insights from an expert judgm ent elicitation (MEB-00-01) and from applications of the P R ODIGAL flaw sim u latio n m odel (NUREG/CR-5505, Chapm a n et al., 199 8), have been used to generate input files (see NUREG/CR-6817, Si m onen et al., 2003) f o r probabilistic fracture mech anics cal culations perform e d with th e FA VOR code by Oak Ridge National Labor atory. NUREG/CR-6817 addresses onl y flaws in plate m a t e r ials and provi ded no guida nce for esti m ating the num bers and sizes of flaw s in forging m a terials.
Mor e recent studies have exa m ined forging materi al, which has provided data on flaws that were detected and sized in the exa m ined mate ri al. At the request of NRC staf f, PNNL has used these m o re recent data to supplem ent i n sights from the expert judgment elicitation to generate FAVOR code input files for f o rging flaws. The discussion below des c ribes the technical basi s and results for the forging flaw m odel. Nature of Base Metal F l aw s PNNL exa m i n ed m a t e rial f r om so me for g ing m a te rial from a Midland vessel as described by Schuster (2002). The f o rging was made during 19 69 b y Ladish. Exam ined material included onl y part o f the forging that had been re m oved from the top of the fo rged ring as scrap not intended for the vessel. This materi al was expected to have m o re tha n the aver age flaw density , and as such may contribute to the conservatism of an y derive d flaw distribution.
Figures 1 and 2 show m icr ographs of s m all flaw s in plate and forging m a teri als. These flaws are inclusions rather than por o s ity or voi ds. They are al s o not planar cracks. Theref ore, their cate gorization as si m p le pla n ar or volumetric flaw s is subject to ju dgment. The plate flaw of F i gure 1 has many sharp and crack-like features, wh ereas such fe atures are not r eadily identified for the particular forging flaw seen in Figure 2. It should, however, be e m phasiz e d that the PNNL exa m ined only a lim ited volum e of both plate and forgin g m a terial and foun d ver y few fl aws in exa m in ed material. I t is not possible to generalize fro m such a s m a ll sa m p le of flaws. Ac co rdingly , the flaw m odel makes assu m p tions that may be somewhat conservative, due to the lim ited data on the flaw chara c teristic s. Flaw Model for Forgin g Flaw s The m odel fo r generating distributions of forging fl aws for the FAVOR code uses the sa m e approach as that for m odeling plate fla w s as describ e d in NUREG
/CR-6817.
The quantitati ve results of the expert elicitation are used along w ith available data fro m obser ved forging flaws. The flaw data were used as a "sanity check" on the results of the expert elicitati on. Figure 3 sum m ariz es re sults of the expert elicitation. Each expert wa s asked to estimate r a tios between fla w densities in base metal co m p ared to the corresponding flaw densities observed in the weld me tal of the PVRUF vessel. Separate ratio s were requested for plate m a teri al and forging materi al. D-1 As indicated in Figure 3, the parameters for forging fl aws ar e si m i l a r to those for plate flaws.
The forging and plate m o dels 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 materi al is so mewhat gre a t e r than the density of flaws in plate m a t e rial. 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 us e d for both plate and forging flaws. As described in the next section, the data from forging exa m inations show that these factors are consistent with the available data. It is noted that the assu m p tion for the 0.07 factor is supported b y onl y a sing le data point cor r esponding to the largest observed forgi ng flaw (with a depth dimension of 4 mm). The factors of 0.1 and 0.07 ca me fro m the reco mmend ations from t h e expert elicitation on vessel flaw
- s. As noted below, the very limited data fr om PN NL's exa m inations of forging m a terial show that these factors are consistent with the data, although the 0.07 factor is supported b y onl y one data po int for an observed forg ing flaw with a 4-mm depth dim e nsion. Comparison w i th Data on Observed Flaw s The PNNL e x a m inations of vessel m a t e rials included both plate materi als and forging m a t e rials. For plate flaws less than 4 mm in thro ugh-w a ll depth dim e nsion, Figur e 4 shows data fro m NUREG/CR-6817 that show frequencies for plate flaws.
Also shown for com p ari s on are the flaw frequencies f o r the welds of the PVRUF and Shoreh am vessels.
This plot co n f irm e d results of the expert judgm ent elicitation (Figure 4) and indicated (1) there are fe wer flaw s in pl ate m a teri al than in weld materi al, 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 pr eparation of NUREG/CR-6817. For g in g 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 a tes that (1) plate and forging m a terials have sim i lar frequencie s for sm all (2 mm) flaws, and (2) f o rging m a t e rial 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 rgin gs tha t were provid e d to ORNL as input files for the FAVOR code. This plot shows mean frequen c ies fro m an uncertainty distribution as described by the flaw input files. It is seen that the cu rves for plate and forgin g fl aws are identical for sm all flaws, but show differences for the fla w s 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 (a bout 5% of t h e 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 h e Development of a Methodology for a Ge neralized Flaw Size and Density Distribution for Domestic R e actor Pres sure Vessel , MED-00-01, PRAB-00-01, U.S. Nuclear Reg u lator y Commission.
Schuster, G.J., 200
- 2. "Technical Letter Report-JC N-Y6604-Validated Flaw Density and Distribution Within Reactor Pressure V essel B a s e Metal Forged Rings," prepared by Pacific Northwest Na tional Laborator y fo r U.S. Nuclear Regulator y Co mm ission, December 20, 200
- 2. Sim onen, F.A., S.R. Doctor, G.J. Schuster, and P.G. Heasl er, 2003.
A Generalized Procedure for Generating Flaw-Related Inputs for t h e FAVOR Code , NUREG/CR-6817, Rev. 1 , prepared b y Pacific Northwest National Labora tor y for U.S.
Nuclear Regulatory Commission.
Figure 1 Small F l aw in Plate Material Figure 2 Small F l aw 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) 1 10 10 0 1, 00 0 10 ,0 0 0 1 0 0, 00 0 0 2 4 6 8 10 12 1 4 Fl a w De p t h , mm Fl a w Ra te- p e r c ubi c m e te r Shore h a m W e l d PV R U F W e l d C:\F L A W D A T A\O RNL-F L A W-0 0 2.X L S S h o r eh am Ba se M e ta l Ri ve r B e n d Ba s e M e t a l Ho p e C r eek PVR U F Ba se M e t a l Aver age o f Ba se Met a l Figure 4 Flaw Frequencies fo r Plate Material s w i th Comparisons to D ata for Weld Flaw s D-4 1.E+0 2 1.E+0 3 1.E+0 4 01 2 3 4 T h r oug h-w a l l si z e (m m)Cu m u l a t i v e De n s i t y (p er cu b i c m e t e r) 5 P V R U F pl at e 10 9-1, 2 , 5 10 9-1, 2 Figure 5 V (cumulative flaw density is the w s per cubi c meter of equal or greater siz e) alidated Fla w Density and Si z e Distribution for Three Forging Specimens number of fla 1.E+02 1.E+03 1.E+04 01 2 34 5 T hr o ugh-w a l l s i z e (m m)Cu m u l a t i v e De n s i t y (p e r cu b i c m et e r)6 P V R U F pl at e 109-5 109-1 1 09-2 Figure 6 Average of V alidated Cumulative Flaw Density for Forging Material, A508 D-5 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 0123456 F l aw Depth Dimens i on , Percen t of Wall F l a ws pe r Cu bi c Fo ot Fo rging Pl ate Figure 7 Comparison of Flaw Di s t ributions for Forging and Plate D-6 D-7
- 1. REPORT NUMBER (A ssigned b y NRC, A d d Vol., Supp., Rev
., and A ddendum Num b ers, if an y.) NUREG-18 74 3. DATE REPORT PUBLI S HED MONT H Y EAR 2. TITLE AND SUBTITLE Recomme nd ed Screeni ng L i mits for Pressurized T hermal Shock (PT S) 4. FI N OR GRANT NUMBER 6. TY PE OF REPO RT T e chnical 5. AUTHOR(S)
M.T. EricksonKirk 1 and T.L. Di ckson 2 7. P ERIOD COVER ED (Inclusive Da tes) 1-20 05 to 2-2 0 0 7 8. PERFORMI NG ORGANI ZATI ON - NAME AND ADDRESS (If NRC, provide Division, Office or Regi on, U.S. N u clear Re g u latory Com m issio n , a nd m a iling ad dress; if c o ntract or, pr ovi de nam e and m a i l i ng a ddr ess.) 1 Division of Fuel, Enginee ring, and Radiologi cal Research, Office of Nucl ear Regulatory Research, U.S. N u c l ear R eg u l at or y C o mmi ss i o n , W a shin gton, D C 205 55-0 0 0 1 2 Oak Ridge National Labor a tor y , P.O. Box 2008, Oak Ridge, T N 37831-6075 NRC F O RM 335 (9-2004) NRCMD 3.7 U.S. NUCLE A R R E GUL A T O R Y C O M M I SSI O N BIBLIO GR A P HIC D A T A SHEET (See i n str u c t i ons on th e r e ver s e) March2010 9. SPONSORI NG ORGANI ZATI ON - NAME AND ADDRESS (If NRC, type "Sa m e as above
"; if con t ra ctor, provid e NRC Divisi on, Of fice or R e gion , U.S. Nucle a r Reg u lato ry Commission, and m a iling a ddress.) Di vi sion o f Fuel, Eng ineering , an d Rad iologi c a l R esea r ch , Office o f Nuclea r Regula t o r y Re sea r ch , U.S. N uc l e ar R e gu l at or y Co m m is sion, W a shin gton, D C 205 55-0 0 0 1 10. SUPP LEMENTARY NOTES 11. AB STRACT (20 0 words or l e ss) Durin g pl ant op eratio n, the w a l l s of reactor pr essure vess els (RPVs) are e x pose d to neutr on rad i atio n, re sultin g in loc a li zed embrittlem ent of the vessel steel a nd w e ld m a teria l s in the c o re are a. If an e m brittle d RPV had a fla w of critical size and ce r tain severe s y stem transie nts w e re to occur, the fla w c o u l d ver y r api dl y pro p a g a t e t h rough th e vessel, resu lting in a throug h-w a ll crack and ch all eng ing th e inte grit y of the RP V. T he severe trans ie nts of conce r n, kno w n a s pressuriz ed thermal s hock (P T S), are char acteriz ed b y a rap i d c ooli ng (i.e., the rmal shock) of the intern al RP V surface in co mbin ation w i t h repress u rizati o n of the RPV. Advance m ents in our u ndersta ndi ng a nd kno w l e dg e of materi als b e havi o r, ou r ab ili t y to real istical l y mod e l p l ant s y stems and o per ation a l character i stic s, and our a b il ity to better eva l uate PT S transie nts to estimat e loa d s on ves s el w a l l s le d the U.S. Nucle a r Re gul ator y C o mmiss ion (NR C) to re alize th at the e a rlier a n a l ysis, cond u c ted i n th e course of d e v elo p in g the P T S Rule in the 19 80s, c ontai ne d si gn ifi cant conserv a ti sms. T h is report provides t w o o p tio n s for using th e upd ated tech ni cal basis d e s c ribe d here i n to deve l o p PT S screeni ng lim its. Calcu l ati ons re ported h e re in s h o w that t he ris k of through-w a ll cracki n is lo w i n all oper ati ng press u rize d-w a t e r reactors , and current PT S re gul ations i n cl u de cons der ble i m plicit marg in. 12. KEY WORDS/DESCRIPT ORS (L ist w o rd s o r ph ra se s t h a t w ill a ssist re sea r ch e r s in lo ca ting t h e rep o r t.) Pressuriz ed th ermal sh ock, reactor press u r e vessel, pro b a b ilistic fractur e mecha n ics 13. AVAI LAB I LI T Y S T ATEM EN T unlim ited 1 4. S E CURIT Y CL ASS IFICAT ION (T hi s Page) unclassified (Th is Re p o rt) unclassified
- 15. NUMBER OF P A GES 16. PRICE NRC FORM 335 (9-20