ML20149D729
| ML20149D729 | |
| Person / Time | |
|---|---|
| Site: | Yankee Rowe |
| Issue date: | 08/31/1993 |
| From: | Bass B, Bryson J, Cheverton R, Dickson T, Keeney J, Shum D OAK RIDGE NATIONAL LABORATORY |
| To: | NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| References | |
| CON-FIN-B-0119, CON-FIN-B-119 NUREG-CR-5782, ORNL-TM-11945, NUDOCS 9309210205 | |
| Download: ML20149D729 (114) | |
Text
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NUREG/CR-5782 ORNL/TM-11945 I
Pressurizec Thermal Shock ProbaJilistic Frac ~:ure Mechanics Sensitiviv Analysis for Yankee Rowe Reac~:or Pressure Vessel
^l I)i k Tn, R. D. Cheverton, J. W. Inrywn, H. R. Bass, D. K. M. Shum, J. A. Keeney
. Oak Ridge National Laboratory Prepared for U.S. Nuclear Regulatory Commission l
- .. )
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I NUREG/CR-5782 ORNL/TM-11945 l
Pressurizec Taermal Shock l
Pro 3abiLis~:ic Fracture ;
I Mechanics Sensitiviy Ana:ysis for Yan <cee Rowe l Reac':or Pressure Vessel 1
Prepared by T. I _ Ik kun, it I). Cheverton, J. W. Hryson,11. H.
I L K. hl. Shurn, .I. A. Kecocy Oak Ridge National I.almratory Prepared for l'.% Nuclear Regulatory Commission 9309210205 930831 PDR ADOCK 05000029 P PDR L------------------------------------------- ---- - - - - - - - - --- - - - --
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AVAllABluTY NOTICE Avas!abeltty of Reference Materials Crted in NRC Pubhcations t
4 Most documents etted in NRC publicatk>ns will be available from one of the fouowing sources: L t The NRC Public Document Room, 2120 L Street. NW. Lower Level, Washington, DC 20555-0001
- 2. The Superintendent of Documents. U.S. Govere. ment Printing Office, Mall Stop SSOP, Washington, 1 DC 70402-9328
{
3 The National Technical information Service. Springfield. VA 22161 '
1 Although the listing that fosows represents the majority of documents cited in NRC pubilcations, it is not
[
] Intended to be exhaustive. I i
5 Referenced documents avallable for inspection and copying for a fee from the NRC Pubhc Document Room include NRC correspondence and internal NRC memcranda; NRC Office of inspection and Enforcement bulletins, circulats, information notices hspection and investigation notices; Ucensee Event Reports; ven-dor reports and correspondence; Commtsdon papers; and applicant and licensee documents and corre- !
spondence.
The fonowing documents in the NUREG series are avaliable for purchase from the GPO Sales Program; format NRC staff and contractor reports, NRC-sponsored conference proceedings, and NRC booHets and ,
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- Documents avaEable from the National Techrucal information Service include NUREG series reports and technical reporte prepared by other fecoral agencies and reports prepared by the Atomic Energy Commis-e6on, forerunner egency to the Nuclear Regulatory Commission.
I Documents avadable from public and special technical librarles include all open literature items, such as books, journal and periodical articles, and transactions. I ederal Register notices, federal and state legisia- l t6on, and congressional reports can usualty be obtained from these librarles.
Documents such as theses, dissertat6cna, foreign reports and translations, and non-NRC conference pro-ceedings are available for purchase from the organization sponsoring the publication cited.
4 Single copies of NRC draft reports are available free, to the extent of suppfy. Upon written request to the l Office of Information Resources Management. Distribution Section, U S. Nuclear Regulatory Commission. l j Wabhangton. DC 20555-0001 ij Copies of industry codes and standards used in a substanttve manner in the NRC regulatory process are 3
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NUREG/CR-5782 ORNIJTM-11945 l' RF Pressurized Therma Shock Probabilistic Fracture Mechanics Sensitivity Analysis for Yankee Rowe Reactor Pressure Vessel l
( hianusenpt Completed: June 1993 f Date Published: August 1993 i
Prepared by T. L Dickson, R. D. Cheverton, J. W. Bryson, B. R. Bass,
+ D. K. h1. Shum, J. A. Keeney Oak Ridge Nati onal laboratory hianaged by h1artin h1arietta Energy Systems, Inc.
~; Oak Ridge National Laboratory Oak Ridge, TN 37831-6285
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,$ Prepared for i Division of Engineering i Office of Nuclear Regulatory Research j U.S. Nuclear Regulatory Commission i Washington, DC 20555-0001 i NRC FIN B0119 I Under NRC Contract No. DE-AC05-840R21400 L _
Abstract The Nuclear Regulatory Commission (NRC) requested code, which was developed during the Integrated Pressur-Oak Ridge National Laboratory (ORNL) to perform a ized Thermal Shock (IPTS) Program. The NRC request pressurized-thermal-shock (PTS) probabilistic fracture specified that the OCA-P code be enhanced for this study mechanics (PFM) sensitivity analysis for the Yankee to also calculate the conditional probabilities of failure Rowe reactor pressure vessel for the fluences corre- for subclad flaws and embedded flaws. The results of sponding to the end of operating cycle 22, using a spe- this sensitivity analysis provide the NRC with (1) data ,
cific small-break-loss-of-coolant transient as the loading that could be used to assess tt: relative influence of a cor.dition. Regions of the vessel with distinguishing number of key input parameters in the Yankee Rowe features were to be treated individually-upper axial PTS analysis and (2) data that can te used for readily de-weld, lower axial weld, circumferential weld, upper plate termining the probability of vesel failure once a more spot welds, upper plate regions between the spot welds, accurate indication of vessel embrittlement becomes lower plate spot welds, and the lower plate regions be- available, tween the spot welds. The fracture analysis methods used in the analysis of through-clad surface flaws were This report is designated as HSST report No. I17.
those contained in the established OCA-P computer
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Contents Pse Abstract.. iii List of Figures.. vii List of Tables. ix 1 Introduction . I 2 Scope and Basic Ground Rules 2 3 Methods of Analy sis 3 3.1 Probabilistic Methodology 3 3.2 Combining Probabilities of Failure for Individual Regions of the Vessel 3 3.3 Overestimation of P(FIE) Because of" Double Counting" 4 3.4 Fracture Analysis Methods 4 3.4.1 Basic Methodology . 4 3.4.2 Types of Flaws 5 3.4.3 Fracture Analysis Method for Surface Flaws 5 3.4.4 Fracture Analysis Method for Subclad Flaws 5 3.4.5 Fracture Analysis Method for Embedded Flaws 6 3.5 Methodologies for Estimating Fracture Toughness 6 3.5.1 Basic Approach 6 3.5.2 ARTNDT Correlations for Welds 6 3.5.3 ARTNDT Correlations for Plates 6 3.6 Residual-Stress Considerations 7 3.7 Method of Analysis to include Dynamic Fracture 7 3.8 Method of Analysis for laclud2ng Cladding Rupture for Subclad Flaws . 7 3.9 Method of Analysis for including Noncontinuous Clad / Base Interface 7 4 Results 8 4.1 Temperatur~., Stresses, and Kl 's 8 4.2 Values of ['(FIE) 8 5 Example Problems for Calculating P(FiE) and h u,=ncy of Failure [?(F)] 9 5.1 Example Problem 1 (Surface Flaws) 9 5.2 Example Problem 2 (Subclad Flaws) 10 6 Discussion of Results 11 7 Conclusions 12 References 13 Appendix A: Transient Definition and Resulting Loads . A.1 Appendix B: Surf ace Flaw hkxlel and PFM Methodology . B.1 Appendix C: Subclad-Flaw Model and PFM Methodology .. C.1 l Appenda D: Embedded-Flaw Model and PFM Methodology . . D.1 l l '
l v Nl.iREG/CR-5782 l l -
- Appendix E: Methodology for Simulating Fracture Toughness for. Welds . .. . . . . ... . . . . . . . E.1 Appendix F: Methodology for Simulating Fracture Toughness for Plates .. . . . . .. F.1 1 i
Appendix G: Residual-Stress Considerations . . . . . . . . . . . G.1 Appendix H: Dynamic-Frxture Considerations .. . . . . . . . . . . H.1 ,
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Appendix 1: Cladding-Rupture Studies for Subclad Flaws . . . .. . . . . . . 1.1
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Appendix J: Analysis of Noncontinuous Clad / Base Interface . . . . . . . . J.1 ;
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List of Figures Pac 1 Unadjusted best-estimate condidonal probability of failure. Upper Axial Weld 20 2 Unadjusted test-estimate condidonal probability of failure. Lower Axial Weld 21 3 Unadjusted best-estimate conditional probability of failure. Circumferential Weld 22 4 Unadjusted best-estimate conditional probability of failure. Upper Plate 23 5 Unadjusted best-estimate conditional probability of failure. Lower Plate 24 A.] Yankee Rowe SBLOCA7 thermal and pressure transient A.3 A.2 Thermal response of vessel to SBLOCA7 transient (time = 20 min) A.4 A.3 Hoop stress distributions (dme = 20 min) A.5 A.4 Axial stress distribution (time = 20 min) A.6 A.5 KI distributions for axial surface naws (time = 20 min) . A.7 A.6 K 1distnbutions for circumferential surface flaws (tirne = 20 min) . A.8 A.7 K 1for embedded flaws kcated in welds (time = 20 min) A.9 A.8 K 1for embedded flaws k)cated in plate (time = 20 min) A.10 B.1 Surface-flaw model B.3 B.2 Surface-fbw PFM methodology B.4 C.1 Subclad-fbw model C.3 C.2 Subclad. flaw PFM methodology C.5 D.1 Endedded-fbw model D.3 D.2 Embedded-flaw PFM methodology D.5 G. ! Hoop-stress distribudor s for axial welds (at time = 20 min) for three residual stress cases G.3 G.2 K ldistributions for axial welds (at time = 20 min) for three residual stress cases G.4 G.3 Best-estimate unadjusted conditional probability of failure for upper axial weld for three residual-stress cases G.5 H.1 Expenmental dynamic fracture toughness data H.3 IL2 K Id ower-bound l curve approximation . H.4 H.3 Ratio of mean dynamic fracture initiation toughncss to IPTS mean K ci curve . H.5 L1 Stress / strain curve for 7th irradiation series three-wire cladding material (T = 550*F) 1.6 L2 Finite-element model employed for cladding-rupture studies .. L7 1.3 Enlargement of crack-tip region I8 1.4 Further enlargement of crack tip region L9 1.5 J integral values at each crack tip for a 2-in. subclad fbw, SBLOCA7 transient. 0.25-in. cladding 1.10 1.6 J-values near clad / base interface,0.25 in. cladding . L11 1.7 A 1.65-in. subclad fbw ruptures a 0.25-in. claddmg I.12 1.8 J-values near clad / base interface,0.109-in, cladding L13 1.9 Jo-Block specimen for measuring fracture properties of cladding over a subclad flaw . Ll4 1.10 Mises stress in 0.25-in. cladding, t = 21 min L15 1.11 Mises stress in 0.109-in. cladding, t = 21 min 1.16 J.1 Schematic showing a portion of an RPV with a flaw that is modeled using finite-element techniques J.2 J.2 Detail of the finite-element model showing the gap interface J.3 J.3 Hoop stress dist.ibution for OCA-P and ADINA analyses (SBLOCA7 transient, t = 20 min) 3.4 J.4 Distribution of K1 values for finite-element models with and without interface gap J.5 vii NUREG/CR-5782
List of Tables BIEC 1 Input data for the Yankee Rowe FFS PFM sensitivity analysis... . . . .. . 14 2- Best-estimate unadjusted conditional probabilities of failure [h(F1E)] for welds .. . . .. . . 16 3 Best-estimate unadjusted conditional probabilities of failure [h(FIE)] for plate (between spot welds).. .. 17 4 Best< stimate unadjusted conditional probabilities of failure [P(F1E)] for plate (at spot welds).. . .. I8 ;
5 Summary of results of Example Problem 1. . . . . . . . 19 I.1 Parameters used in subclad-flaw rupture studies. .. . . . . .. . . . I.3 1.2 Comparison of J-values near clad / base interface for two different clad penetration models.
1/32 in. and 1/16 in.. ., .. . . . . . . 1.4 1.3 Results of cladding-rupture studies... . . .. .. . . . . I.5 i i
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NUREG/CR.5782 viii s
i 1 Introduction i Following the Oak Ridge National Laboratory (ORNL) The objective of this study was two fold: (1) provide the review! of the Yankee Atomic Electric Company reactor NRC with results that could be used to assess the rela- ,
pressure vessel evaluation report for the Yankee Rowe tive influence of a number of key input parameters in the reactor,2 the Nuclear Regulatory Commission (NRC) Yankee Rowe PTS analysis and (2) provide data that can l requested ORNL to perfomi a pressurized-thermal-shock be used for readily estimating the probability of vessel i probabilistic fracture mechanics (PFM) sensitivity anal- failure once a more accurate indication of vessel embrit- ;
ysis for the vessel, using a specific small-break loss-of- tlement becomes available, i coolant transient (SBLOCAose 7) as the loading con.
dition.' Subsequent discussions regarding the details of This repon discusses the scope, ground rules, analytical the methodologies to be used in performing the specified methodologies applied, and the results. j analyses were held between members of the NRC staff and ORNL staff in meetings at Rockville, Maryland, on March 22 and May 14, 1991.
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- Mavfield, M. E., NRC. personel communication to W. E. Penneti, ORNI., February 15,1991.
1 NUREG/CR-5782 !
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2 Scope and-Basic Ground Rules The initial NRC request specified that tr A-P com- the Integrated Pressurized Hermal Shock (IPTS) puter codc3 be enhanced to calculate the s Jonal Program.4 Fracture-analysis methodology for subclad
. probability of failure for subclad and embeoced flaws as and embedded flaws were not available in OCA-P, and well as for through-clad (surface) flaws. The NRC also thus they had to be developed for the present study.
rpecified that the spatial varianon of fluence be consid- Because of the tight schedule,less precise methods than cred to the extent practical, and ORNL modified OCA-P used for the surface flaws were considered acceptable.
to enhance this capability, All calculations were to be performed for fluences corresponding to the end of oper- The PFM sensitivity analyses for weld regions were to ating cycle 22 (-21 EFPY'). be performed with copper concentration as the indepen-dent variable (0.15 to 0.35 wt% in increments of 0.05),
Regions of the vessel with distinguishing features were while the analyses for plates were to be performed with -
to be treated individually; they are the upper axial weld, surface RTNDT as the independent variable. The upper- j lower axial weld, circumferential weld, upper-plate spot plate surface RTNDT values were to range from 250 to l welds, upper plate regions between the spot welds, 325 F in increments of 25'F,and the lower-plate surface lower-plate spot welds, and lower-plate regions between RTNDT values were to range from 250 to 400*F in ;
the spot welds. (Spot welds attach the cladding to the increments of 25 F.
base material, except over the vessel welds, w here the cladding is weld deposited.) These and other specified input data for the Yankee Rowe ,
PTS PFM sensitivity analysis are included in Table 1.
The fracture-analysis methods to be used in the analysis of the surface flaws were those represented by the estalw lished OCA-P methodology, which was developed during i
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- Effecuve full power yem (EFPY).
3 Methods of Analysis 3.1 Probabilistic Methodology P(FlE) = lP,(FlE) = E(N,
- Vj
- l)
- fj(FlE) ,(2)
J J The probabihstic fracture mechanics analyses were per-formed using an enhanced version of OCA-P, which is where P(RE) = total conditional probability of failure for based on Monte Carlo techniques; i.e., a large number of the vessel.
s essels is generated, and each vessel is subjected to a deternunisuc fracture mecharucs analysis to determine The Marshall probability-of-nondetecuon funcdon really whether the vessel will fail in each determinisuc analy- can not be applied to the untended-claddmg region sis, the region of the vessel being analyzed contains one tccause ultrasonic detection could not have penetrated the flaw. Each vesselis defined by probabilisucally select- gap between the cladding and base material. The func-ing values of several parameters that are judged to have bon w as included for consisterry with the previous I
significant uncertainues associated with them, primarily ORNL analysis of Yankee Rowe.1 The effect on '
the flaw size and the parameters that determine the degree Pj (EE) is less than a factor of two.
of embrittlement (Appendices E and F). The conditional probability of failure (" conditional" in the sense that the transient is assumed to occur), based on one flaw per region (referred to herein as the unadj,usted condiconal 3.2 Combining Probabilitles of probability of failure)is simply the number of vessels f, allure for IndlVidHal that fail divided by the total number of vessels simu- Regions of Vessel bted. The conditional probbility of failure for each vessel region based on the " actual" number of flaws per When addmg the probabilides of failure for the individ-region is obtained by muldplymg the unadjusted vjdue ual regions of the vessel,it is necessary to make sure l by the number of flaws that exist in the vessel region- that the individual values constitute a consistent set with Thus, i
regard to plant operadng dme and the spatial dis:ribution
_ (zg)* of the fluence. The reason for the concern is that P' (FlE) = (N ' *V ' ' I)
- P ' (FlE) . for this pardcular study the elfect of fluence spatial dis-d ,I tribudon on the potential for crack initiadon was consid-cred, and fluence values correspondmg to 21 EFPY were used for calculaung E(HE) for the welds, while a range
/RE) = condidonal probability of of values of RTNDT was used, without reference to spe-failure for the jth region cific values of fluence, for calculating P(RE) for the plate regions. Calculated values of E(FIE) for the welds Ej(EE) = unadjusted condidonal (Table 2, Figs.1-3) are consistent and cocespond to 21 probal. ly of failure for the ji EFPY: they can be added as indicated in Eq. (2).
region (failures / flaw)
N. = flaw density of the j;h region The calculated valees of E(RE)in Tables 3 and 4 and Figs. 4 and 5 for the two plate regions are not consistent (flaws / unit solume) with each other and are not necessarily consistent with
~
V= values for the welds. They can not be added to exh J
solume of the jth region other or to values for the welds m the manner indicated by Eq. (2). Instead, the process described below must le I= { f(a)
- B(a) da = used.
0.587 for these studies The independent vanable used in calculating E(FIE) for h a) = Marshall flaw-size distribution the plates is RINDT at the inner surface of the vessel at funcdon3 the k> canon of the maximum value of the fluence within the specific plate region. Because the maximum Bia ! = Marshall probability-of- fluences and the chemistries are not the same in the two nondetection funcdon (fraction plate regions, maximum values of RTNDT for the two of flaws remaining af ter regions will not be the same. To obtain consistent max-mspecdon and repair) imum valuc s for the two plate regions, the correspond-ine fluence values, and, of course, chemistries, must be
'lhe condit/ 1al probabihty of failure for the entire add.
vessel is ca$ulated by summing the Py TIE) values over all regions of the vessel. Thus,
- tengnudmal (z) and anmuthal(c) 3 NUREG/CR-5782
As indicated in Sect. 3.5 and Appendix F. Odette where zmand 9nare axial and azimuthal coordinates.
recommends the following correlations between fluence Thus, even if Eq. (6) is not used to obtain the necessary and ARTNDT for the upper and lower plate regions: relation between the upper and lower plate regions, the Odette correlations [Eqs. (3) and (4)], with the excepdon B of the value of A, are used in the analysis (used to con-(ARTM)UP =AG CP '
(3) struct the map of ARTNDT).
(ART")"' = AC" + C . (4) 3.3 Overestimation of P(FjE)
Thus, Because of " Double
' c y, '" _ (ARTY)t P Counting"
( @ty j (ARTY )u, - C ' (5)
In the present version of OCA P, the number of flaws in the vessel is accounted for as indicated in Eq. (2). If y INjVjl is less than unity for regions of the vessel that 38 contribute significantly to P(FIE), Eq. (2) is appropriate.
f @lP If not, there is the possibility of overestimating P(FIE)
(ARTY ),, = (ARTY)t e + C ,(6) because only one flaw can result in failure of the vessel.
W>
A More than a single flaw does increase P(FIE) because it increases the chances of having a flaw of critical size, where but the increase in P(FIE) is less than indicated by (ARTNDT)UP = ARTNDT in upper plate Eq. (2). However,if P(FIE) 1,INjVjl can be (ARTNDT)Lp = ARTNDT in lower plate substantially greater than unity without Eq. (2) being c up= maximum value of fluence in significantly in error.4 upper plate = 2.74E19 n/cm 2 (21 EFPY)
- LP = maximum valuc of fluence in 3.4 Fracture Analysis Methods lower plate = 2.439E19 n/cm?
(21 EFPY) 3.4.1 Basic Methodology A= 183 l fmmOdette B= 0.315 > correlations for All fracture analyses were performed in accordance with C= 80 J T in *F linear elastic fracture mechanics (LEFM) theory. Based on this methodology, flaws are predicted to commence Thus, if a maxinmm value of RTNDT conesponding to propagation (initiate) when the stress intensity factor 21 EFPY is somehow obtained for the upper or lower (KI) is equal to the static crack-initiation fracture tough-plate region, the conesponding value in the other plate ness (Kic) or the dynamic-loading fracture toughness can be estimated. (Kid). Arrest of a fast running crack is predicted when K1 = Kla, the crack-arrest toughness. Dynamic loading Equations (3) and (4) were used to account for the spatial is introduced when one portion of a crack front initiates distribution (z,9) of the fluence in the calculation of under static loading conditions, thereby subjecting the Pj (FIE). For mstance, for the upper plate, ARTNDT remainder stationary part of the crack front to dynamic (zm.9n) was obtained from loadmg.
B la the fracture analysis of flaws residing in welds, the ARTsn7(z m 9n) =
$(zm 9n) Kl's corresponding to crack tips that reside in the first
' (7) inch of base metal include the effect of a 6-ksi tensile ART *(max) - C(max) - -
residual stress. The Kl's for crack tips in the cladding and the remainder of the base material do not include the and for the lower plate' effect of residual stresses. (See Sect. 3.6 and Appen-3 dix G for a more detailed discussion regarding the
_G(z,,9,) inclusion of residual stresses in the fracture-mechanics ART,(z ,9,)= x analyses.)
(mn) ;
In the fracture analyses of subclad and embedded flaws, (ART,,(max)- C] + C, (8) dynamic effects have been included to the extent of including the dynamic-loading fracture toughness (Kid) for specific crack-initiation events. The Kid curve was approximated by shifting the KIc curve 33 F, and it was
- Odene, G. R., College of Engineenng. Univ. of Cahfonda. Santa Basara. personal communicauan to A. Taboda, NRC, July 30,1990.
used in the prediction of crack initiation in the base ma- 3.4.3 Fracture Analysis Methad for terial at the time step for which the cladding was pre- Surface Flaws dicted to fail. (See Sect. 3.7 and Appendix H for details of how dynamic effects were included in the analyses.) Surface flaws are flaws that penetrate the cladding and base metal from the inner surface of the vessel. The 3.4,2 Types of F1awS stress intensity factors (KI) used in the PFM analyses of I surface flaws were calculated in the usual OCA.P man-As indicated in Sect. 2, the basic types of flaws con- ner, i.e., a superposition technique that applies a large sidered am surface flaws and embedded fla ws, of which a number of K1 influence coefficients (calculated by a 2-D subclad flaw is a special category. All flaws analyzed finite-element method) and the stresses induced in the were considered to be normal to the surface and oriented uncracked vessel as a function of time and radial position in either an axial (longitudinal) or azimuthal (circum- in the pressure vessel wall (calculated by a 1-D finite-ferential) direction. All other flaws that might exist element thermal and stress analysis).3 It should be noted were ignored. that all surface-flaw KI's used in these analyses are for The length of an initial flaw in the axial or circumferen-tial direction is more likely to be short than long, but It is of interest to note that the ASME Sect. XI
\
upon propagation, short flaws have a tendency to procedure for calculating K I's for surface flaws 6 was also become long flaws.5,* Previous studies have indicated included in the speciahzed code for perfonning the I that under thermal-shock loading, a semicircular surface Yankee Analysis. The values calculated by the ASME flaw has a greater potential for surface extension than methodology are very close to those calculated by the other short flaws and about the same potential for surface OCA-P methodology (discussed above) for very shallow propagation as that for radial propagation of a long sur- flaws; however, they diverge for greater depths, with the l face flaw of tiie same initial depth. Thus, the assump- ASME values being higher. Probabilities of failure for l
tion was made that all initial surface flaws were semicir- surface flaws, calculated using the ASME K1 cular, in which case the spatial distribution (z,9) of the methodology, are higher than those using the OCA-P K1 fluence could be considered for the first initiation event, methodology by approximately a factor of 2.
but the K Ivalues used were those for a very long flaw.
Details of the surface-flaw model and the flow-chart logic Initial embedded flaws were also assumed to be short so for performing the deterministic fracture mechanics anal-that the spatial distribution of the fluence could be con- vsis of each of the probabilistically simulated embrittled sidered. Even though the shoner embedded flaws have vessels containing a surface flaw are included in l less potential for propagating, the embedded-flaw K1 Appendix B.
values used were for long flaws. In any subsequent studies, the more realistic shorter flaw should be 3.4.4 Fracture Analvsis Method for considered. Subclad Flaws As indicated above, when flaws propagate, they tend i A subclad flaw is a flaw that has its inner crack tip at the extend in length to become long flaws. However, the clad / base interface, and thus its outer crack tip is in the length can be limited by increases in toughness base metal. The outer flaw tip is checked for initiation (decreasing fluence and/or changes in chemistry). For according to LEFM principles.
T ankee Rowe, the decrease in toughness appears to be rather large for both the plate and welds, and thus the if the subclad-flaw size reaches the critical size for which length of axial flaws would be hmited only by the steep cladding is predicted to fail, the subclad flaw is converted attenuauon of the fluence at the ends of the core. It to a surface flaw, and the Kl's for surface flaws are then appears that for this length (~100 in.) there will be sig- used to predict imtial initiation, crack arrest, and subse-mficant finite-length-flaw cf fects on K1 for deep flaws quent reinitiation of the outer crack tip. At the time step that should be taken advantage of for crack arrest and corresponding to cladding failure, dynamic effects were reinitiation. Tlus effect was not considered but should s mulated by using a value of KJd, instead of Kic, to be in an extension of the study. (The effect is negligib!c for the very shallow imual flaws.)
di pynamic fracture considerations are included in Sect. 3.7 and Appendix H).
Propagating circumferential flaws may also be limited in If the cladding does not fail, the probability of initiation length, although variations in chemistry (in a circumfer-ential weld) and in fluence tend to be relatively small.
o % h hmh sh h Analysis of thermal-shock experiments performed at ORNL indicate that at times of maximum loading, the KI for a subclad flaw is approximately 34% less than that for a surface flaw.7 Based on these experimenta!
'where the ci,33m, ,s not bonded between the s results, the stress intensity factors for predicting the be a small range of shatlow flaw depthssurf forace whick,ai extension w eidsinitial thereinitiation may of subCritical (Cladding has not failed) e base matenal will not take place. This has not been considered subclad flaws were Calculated by reducing K1for a surface 5 NUREG/CR-5782
. . ~ -
flaw (with the crack tip at the same radial wa!! location) analysis of each of the simulated vessels containing an by 35E emtedded flaw are included in Appendix D.
Subclad flaws that exist in the plate regions between the :
spot welds are treated differently than the subclad flaws 3.5 Methodologies for Esti- l analyzed for welds and plate regions in the spot welds.
niat.ing Fracture Toughness These subclad flaws are treated like surface flaws i.e., l the K I's are not reduced by 35% because a gap (assumed l; to be 3-mils) exists between the cladding and base 3.3.1 Bas.ic Approach material. ADINA-T,8 a general purpose multidimen-sional finite-element thermal analysis program, was used The mean fracture toughness for all regions of the vessel to calculate the thermal response of the plate region was obtained from the ASME lower-bound relations between the spot welds assuming the 3-mil gap to be with a modification to convert from lower-bound to filled with water. The insulating effect of the gap mean.4 The relations are slightly reduces the severity of the thermal shock [ lower _
thermal stresses, and high fracture toughness (Figs. A.2, K u= 1.43 * {33.2 + 2.806
- exp[0.02
- A.3, and A.5)]. (T-RTNDT + 100))),
Details of the subclad-flaw model and the flowchart logic for performing the detenninistic fracture mechanics = 1.43 * {33.2 + 2.806
- cxpl0.02
- analysis of each of the probabilistically simulated (T-RTNDT + 67))),
vessels contai ting a subid flaw are included in _
Appendix C K n= 1.25 * [26.80 + 1.223
- cxp[0.01449
( " +
3.4.5 Fracture-Analysis Method for whm '
Embedded Flaws
= mean values of Kl e, K Id, Kl a (ksiE),
An embedded flaw is considered to be a flaw that resides entirely in the base metal. In the probabilistic analysis, T= temperature at tip of flaw ( F).
the kicauon of the inner tip of the embedded flaw is probabilistically simulated, i.e., located randamly along Details of the methodolocies used for determining the the mesh between the clad / base interface and the vessel fracture toughness for weids and plates are included in outer wall. The flaw has equal probability of being Appendices E and F, respectnely.
h>cated at any one of the mesh points in the base metal. '
11 should be noted that the calculated probability of 3.5J failure is sensitive to the mesh size, presumably because ARTNDT Correlations for Welds ;
of its effect on the minimum distance be: ween inner For the case of welds, the sensitivity analyses were crack tip and clad / base mterface. Mesh convergence oM with copper as the independent variable; and '
analyses were performed, and it was detennmed that a Reg. Guide 1.99 Revision 2 (welds),10 plus a 50 F low-mesh spacing of 0.005 m. is converged with respect t '
temperature-irradiation correction factor, were used to the probability of failure.
calculate ARTNIYr. The correction factor was added The ASME Sect. XI procedure for subsurface flaws 6 was imately 500eF mstead of 550 F, for which Reg. Guide used to calculate Krs for the embedded flaws. The 1.99 is most appropriate.
mathemaucal representation of the ASME cur.es was taken from Ref. 9.
3.5.3 ARTNDT Correlations for Plates The inner tip of the embedded flaw is checked for initia-For the case of plates, the sensitivity analyses were per-tion according to LEFM principles. If the inner tip initiates,it is assumed that the flaw propagates all the formed with RTNDT at the inner surface of the vessel as the mdependent variable, and values of ARTNITT were way through the cladding, because the flaw is propagat-ing into a region of higher embrittlement and higher calculated using Odette's correlations. The correlations thermal stress. Therefore,an emtedded flaw that are as follows:
initiates at the inner tip is converted to a surface flaw. I 4) #"
Surface-flaw K 's I are then used to predict subsequent Upper Plate: ARTNDT( F) = 183 * ,
initiation and arrest events. Dynamic effects (as described Aove for subclad flaws) are included for the # 4) #
time step a; which the flaw breaks through the cladding. L werPlate: ARTNDT (*Fj = 183 * + 80 ,
Details of the embedded-flaw model and the flow chart where o = neutron fluence (E> 1.0 MeV, n/cm2) t logic for performing the deterministic fracture mechanics t
l l 3.6 Residual-Stress 3.8 Method of Analysis for l Considerations Including Clad Rupture for Before selecting rs residual stress distribution for the Subclad Flaws Yankee Rowe sensidvity study, the cffect of three Analyses were performed to determine the minimum ,
different residual-stress assumpdons was evaluated. The flaw size and corresponding time during the sBLOCA7 assumptons were transient for which the cladding would fail. The results '
of these analyses indicated that for welds, with 0.25-in,
- 1. N.o residual stresses. cladding, a subclad flaw with a 21.65 in. vauld result in
. . cladding failure at a time of 21 min into the transient.
- 2. A 6 ksi tensile residual stress acting across the For the case of plates, with 0.109-in. cladding, a subclad entire pressure vessel wall thickness. In this case, Haw with a 20.75 in, would result in cladding failure at the residual stress enhances the probability of a time of 21 min into the transient.
initiation and dimmishes the probabihty of a stable crack arrest.
The details of these studies are presented in Appendix I.
- 3. A 6 ksi tensile residual stress across the first inch of base metal. In this case, the residual stress enhances the probability of miual crack imtiauon 3.9 Method of Anal 3' sis for but has little or no effect on crack arrest and Including Noncontinuous reiniuatim. Clad / Base Interface ,
Case 1 is considered to be nonconservative; case 2 is The plate regions between the spot welds were specified considered to be unnecessarily conservatis e; and case 3 is as having a water-filled gap of ~3 mils between the considered to be a more realistic method because residual cladding and the base metal. As explained below, the stresses are self equihbrating; as the crack propagates, noncontinuous interface reduces the probaility of crack the residual stress is reheved. '
propagation for flaws that exist in the plate regions between the spot welds and increases the probability of Figure G.1 shows the hoop stresses at a time of 20 min crack propagation for flaws that exist in the plate spot "
for the above three cases and Fig. G.2 shows the welds
- co responding K1distributions for axial surface flaws.
A f Figure G.3 shows that P(FIE) for case 2 is higher by a Flaws that exist in the plate regions between the spot factor of approximately 2 than that for case 1, and case 3 welds do not penetrate the cladding and are subjected to is bracketed by case 1 and case 2. lower thermal stresses and reside in a region of higher fracture toughness (deeper flaw for same flaw size), and The models used in this report to calculate probabilities higher temperatures. This reduction in the probability of of failure for welds incorporated method 3. No residual flaw propagation was included in the analysis. ;
stresses were included in the analysis of the plate regions. Flaws that exist in the plate region spot welds are subjected to higher loads because of load transfer resulting from the existence of the adjacent 3-mil gap.
3.7 Method of Ana1ysis ~
to However, as indicated below, the effect on P(FIE) is Inelude Dynamic Fraeture sm 11 and im thaucason was not included in the sensitivity study.
In the analysis of subclad and embedded flaws, rapid Three-dimensional thennoclastic fmite-element analyses loading effects caused by cladding failure w cre included
_ were performed to determine the variation in KI along a by using K id, mstead of k le, to predict crack imuation straight axial flaw that connects two or more spot welds.
m the base metal (outer crack tip) for the time step at which the cladding fails. Figure H.1 shows The sBLOCA7 transient (time = 20 min) was used for the mechanical and thermal loadirigs, and a cladding expenmeatal dynamic fracture imuauon toughness thickness of 0.109 in, and a flaw depth of 0.25 in. were datall as a function ofloading rate and temperature.
used. The calculated K1 value was higher by only 5% at Values of K Id or f a loading rate of 10 5 ksiE/s and the spot weld than at the center of the unbonded region .
various temperatures are plotted in Fig. H.2, which The details of the three-dimensional finite-element shows that the lower-bound Klc curve shifted by 33*F is analyses are included in Appendix J.
a reasonable lower-bound approximation for the kid experimental data. Figure H.3 shows that for T-RTNDT = 0 F, which corresponds to many of the j initiation events, the value of Kid is ~75% of K le.
4 Results 4.1 Temperatures, Stresses, and 4.2 Values of 5(FlE)
KI's Best-estimate values of i'(FIE) for each flaw type and -
Plots of the thermal response and loads for the different region of the vessel are presented in Tables 2-4 and vessel regions are included in Appendix A. It suffices to Figs.1-5, and two example problems are included in say here that the maximum load occurs at ~20 min into Sect. 5 to demonstrate the methodology for obtaining the transient. values of P(FIE) and $(F) from these results.
l NUREG,CR-5782 8 l
5 Example Problems for Calculating P(FlE) and j Frequency of Failure [Q(F)]
5.1 Example Problem 1 (Surface E,(FlE) = Pj(FIE)/NjVjl F1aws) Vuaw = volume of upper axial weld in beltline region = 0.675 ft3 (from Assumed conditions: Flaws are surface flaws Table 1)
Flaw Density for welds = Vlaw = Volume oflower axial weld in I flaw /m3 = 0.028 flaw /ft3 beltline region = 0.30 ft3 Flaw Density for plates = Vew = Volume of circumferential weld in I flaw /m3= 0.028 flaw /ft 3
beltline region = 2.73 ft3 Weld Copper Content =
0.30 wWC Obtaining values of E(FIE) from Table 2 Upper Plate Surface RThTrr
= 280*F P(FE) welds = (0.028)(0.587)[(0.675)(0.074)
Lower Plate Surface RTNUT + (0.30)(0.049) +
= 35 l'F.* (2.73)(0.0024)]
As discussed in Sect. 3.1, the contribution of each = 0.00117.
region must be included in the calculation of P(FIE) total:
Plates P(FIE) total = E P3 (FlE) ,
To obtain P(FlE) for the plates, values of RTNDT at specific locations in the plates must be known, and they where j = all regions of the vessel.
must be consistent with the fluence spatial distribution,
.p ,f ,' including that in the welds (see Sect. 3.2). Consistent values are given for this sample problem; for the more j general c se, see Sect. 3.2.
P(FIE) total = P(FlE)uaw + P(FIE) law +
P(FIE)cw + P(FiE)up + P(FIE)lp , Surface flaws in the plates are assumed to exist only in the cladding-attachment spot welds, which occupy ~52%
when: of the plate surface area: multipling the total plate uaw = upper axial weld volume by 0.52 and considering that consistent values of law = lower axial weld RTN17r are given, cw = circumferential weld up = upp:rplate P(FIE)P l ates= 0.52 E(N,V,1)xp,(FIE) 3 P = 1 wer P lam.
= 0.52N1 V,f(FlE), + V,5(FjE) ,
A convenient grouping is as follows:
P(FIE) total = P(FIE) welds + P(FIE) plates .
Vip = total volume of upper plate in beltline W.lds e region e 144 ft3 (Table 1)
E" P(FIE)weldscan be obtained by simply adding values from Tables 2-4 (Figs.1-5) because these values are -
g "[ft 3 properly normalized with regard to the fluence spatial P(FlE),,, and P(FIE)3p co!Tespond to surface flaws distribution. Thus, in the spot welds (Table 4).
Thus, P(FIE)we133 = E(N,V,1) x p,(FlE) l P(BE) plates = (0.52)(0.028)(0.587)
= bl {Vuaw E(FIE)uaw + VlawE(FIE) law l
{(144)(0.017) + (64)(0.068)] = 0.0581, I
+ Vcw P(FIE)cw} , !
wtm P(FIE) total = 0.00117 + 0.0581 = 0.059.
'See Sect. 3.2. l 9 NUREG/CR-5782 ,
I l
The mean value of P(FIE) is estimated roughly by P(FIE) welds = (0.028)(0.587)[(0.675)
- multiplying the best-estimate value by the ratio of mean (0.0053) + (0.30) (0.0031) +
flaw density to best-estimate flaw density. For this (2.73)(0.0)).
study that ratio is 45. Thus,
= 0.000074.
P(FIE)mean = 0.059 x 45 = 2.7.
Plates.
Of courae, P(FIE) can not actually exceed unity but does
' in this case because of double counting. In the absence Subclad flaws in plates exist in the spot welds (52% of of a proper correction for double counting,let plate surface area) and in the area between the spot welds P(FIE)mean 51.0. With this conservative simplifying (48% of plate surface area); therefore, the method for assumption made, and taking the event frequency to be combining P(FIE) for the upper and lower plates is as 2 x 1&3/yr, the frequency of failure is follows:
c(F)mean = 1.0(0.0020) = 2.0E-3 failures /yr.
P(FIE) plates = 0.52 [ (N,V;I)P(FIE)],, + 0.48 3
in a previous ORNL study of the Yankee Rowe reactor i pressure vessel,1 only the upper axial weld was cal- N1 ER, culated in detail. The n: ported value of P(FIE) = 8E-4 compares well with the value calculated here for the P(FIE) plates =
' (0.52,)(0.028)(0.587) upper axial weld,[(0.028)(0.587)(0.675)(0.074) = 8E 4), ,
even though there are some slight differences in the two IY=PP(FIE),, + V,,P(FlE),,},, + ;
analyses. In the earlier study, the contribution of the (0.48)(0.028)(0.587) e other regions and the effect of double counting were I estimated by doubling the value of P(F1E) calculated for {V "PP(FIE)"P + V'PP(FI E)i, } 6'*
the upper axial weld. In this example, each region was treated in detail, and double counting was accounted for where-
}
in a different way, leading to larger values of P(FIE) and c(F). 'Ihe actual effect of double counting has yet to be Vup,Vlp = Volume of upper and lower l
determined. plates (Table 1)
E(FlE) = appropriate values for subclad flawsin the upper and lower '
3.2 Example Problem 2 (Subclad plates for regions in the spot Flaws) welds (Table 4)and regions :
hetween the spot welds Assumed conditions: Flaws are assumed to be subclad (Table 3) flaws isw = designates plate regionsin the Flaw density for welds = spot welds bsw = designates plate regions between 1 flaw /m3 = 0.028 flaw /ft3 the spot welds. .
Flaw density for plates =
I flaw /m3 = 0.028 flaw /ft3 Obtaining values of P(FlE) for subclad flaws from Weld copper content = 0.25% Table 3 and 4, Upper-plate surface RTNDT =
250#F P(FIE) plates = 0.00855[(144)(0.00051)+ (M) I lower. plate surface RTNDT =
(0.0033)) + 0.00789 [(144) [
322 *F., '
(0.001) + (M) (0.011))
Following the same methodology demonstrated in = 0.00243 + 0.00669 = 0.00912 Example 1:
P(FIE) total = 0.000074 + 0.00912 = 0.00919 Welds-aal .
E).gs = . -
P(FIE)mean =0.00919 x 45 = 0.41.
NI V.P(FjE)_ + V 3P(FlE)3 + V,P(FlE), ;
Taking the event frequency to be 2 x 10-3 /yr, c(F)mean = (041)(0.002) = 8.2E-4
- see sect. 3.2. j NUREG/CR-5782 10
I 1
6 Discussion of Results The sensitivity of P(FIE) to variations in the several RTNIJr values and thus 5(RE) values for the upper and parameters considered depends on the values of P(FiE) lower plates are nearly identical even though the fluences and RTNDT. As P(EE) approaches unity the sensihvity for the upper plate are considerably higher than those for decreases, and when RTN17r corresponds to the lower the lower plate (the average fluence for upper plate is shelf of the fracture-toughness curve, P(FIE)is not 1.689 x 1019; for lower plate it is 1.074 x 1019) sensitive to RTNDT and thus chemistry and c.
because the Odette ARTNDT correlation for the lower
, pbte adds 80*F to that for the upper plate to account for Values of Pj(ME), NjVjl and Pj(EE) for Example the higher nickel concentration in the lower plate..
Problem 1 are summarized in Table 5. It is ofinterest 4 to note that the upper and lower plate regions are the For the upper and lower axial welds, h(RE) values for dominant regions [ contribute the most to P(FIE)mtal]. subclad and embedded ibws are approximately 1 and 3 Also, the total number of flaws in the 1:citline is orders of magnitude lower than those for surface fbws, substantially greater than unity, indicating a double respectively, counting problem. He extent of the problem depends on the total number of flaws and the value of For upper and lower plates in the spot weld regions, P(FIE) total; for this case, if P(RE) total <10-2, double counting is probably not sigmficant. Obviously, there P(RE) values for subclad ibws and emtedded ibws are approximately 1 and 2 orders of magnitude lower than is a senous problem because P(FIE) total >1.0. For the those for surface flaws, respectively. The reason that best-estimate case (flaw density = 1 flaw /m3) double there is only 1 order of magnitude difference in the counting is not a significant problem because subclad flaws and the embedded flaws for the plates in the spot-weld region (relative to 2 orders of magnitude Z(N,V,I) = 1.8 and P(RE) total = 0 06. difference in the case of welds) is because KI values for J
, embedded flaws are very sensitive to the location of the For a given vahie of copper, values of P(FIE) for the inner flaw tip (see Figs. A.7 and A.8). For the case of upper axial wcid are higher than those for the lower axial plates (clad thickness of 0.109 in.), the embedded flaw weld by approximately a factor of 2. This is attributed inner tip locations reside in a higher stress field, which to the higher fluences used for the upper axial welds. results in more initiations and failures.
The average surface fluence in the upper axial weld is 0.914 x 1019, whereas for the lower axial weld, the The fact that E(EE) values for the subclad fhws for the average surface fluence is 0.605 x 1019. Also, the upper and lower plate regions between the spot welds are volume of the upper axial weld in the beltline region is higher than for the plate at the spot-weld regions at first over double that of the lower axial weld; therefore, the seems surprising since these flaws are subjected to a less upper axial weld will contribute to the total vessel severe thermalload because of the insulating effect of the probability of failure more than the lower axial weld by 3-mil gap between the clad and base. Another difference, approximately a factor of 4, assuming the same value of however,is that the subclad flaws between the spot-weld copper and flaw density. regions are treated as surface flaws instead of subclad flaws. This competing effect more than offsets the effect f(FIE) values for circumferential ibws, w hich exist in of the reduced thermalload.
the circumferential weld, are lower than those in the upper axial weld by tetween I and 2 orders of mag- P(RE) values for the embedded flaws in the plate region nitude; therefore, the circumferential flaws are relatively between the spot welds are considerably lower than those small contributors to the overall value of vessel failure. for embedded flaws in the plate region at the spot weld The probability of initial initiation for flaws in the because of the insulating effect of the 3-mil gap between circumferential weld is approximately the same as for the the cladding and base metal. This results in a reduced upper axial weld; however, the smaller ter. ding effect for thermal shock to the base metal, lower thermal stresses, circumferential flaws (Fig. A_6), results in considerably and higher fracture toughness.
more stable anests and subsequently less failures for the circumferentialibws.
4 11 NUREG/CR-5782 i
7 Conclusions A. 'Ihe results of this sensitivity analysis provides C. Double counting may have to be accounted for, -
the NRC with data (Tables 2-4, Figs.1-5) and a depending on the total number o ^ flaws and the methodology (Sect. 5) to assess the relative value of P(FE) tota). If the total number of flaws influence of key input parameters on the con- is less than unity, there is no double-counting i ditional probability of failure [P(FE)] and the fre- effect.
quency of failure [9(F)] for the Yankee Rowe reactor pressure vessel D. The consideration of finite flaw length for arrest and reinitiation of surface flaws and initial initia- J B. When using the above data to estimate P(FE) and tion of embedded flaws could reduce the values of 9(F), one must be careful to use values of P(FE) P(FIE) substantially.
that are consistent with the overall fluence spatial ,
distribution and the time of reactor operation.
- 1 5
i i
I NUREG/CR-5782 12
i 8 References
- 1. R. D. Cheverton et al., Martin Marietta Energy 7. W.J. Mc Afee et al.."A Specimen and Method for Systems, Inc., Oak Ridge National Lab., Review of Evaluating the Effect of Cladding on the Behavior of Reactor Pressure Vessel Evaluation Reportfor Subclad Flaws," ASME Pressure Vessel and Piping Yankee Nuclear Power Station (YAEC No.1735). Pressure Yessel and Piping, PVP Vol. 213/MPC NUREG/CR 5799 (ORNl/TM-11982), March Vol. 32-Pressure Vessel Integrity, June 1991.d 1992.8
- 8. K. J. Bathe,"ADINAT - A Finite Element Program
- 2. Yankee Atomic Electric Company, Reactor For Automatic Dynamic incrementalNonlinear Pressure Yessel Evaluation Reportfor Yankee Analysis of Temperatures," Massachusetts Institute Nuclear Power Station, YAEC-1735, July of Technology, Cambridge, Mass., December 9,1990.6 1978.c
- 3. R. D. Cheverton and D. G. Ball, Union Carbide 9. R. C. Cipola et al., Failure Analysis Associates, Corp., Nuclear Division, Oak Ridge National Lab., ComPu'atim Vethad to Perform the Flaw Oak Ridge, Tenn.,0CA P, A Deterministic and Evaluatior Frw, ' arc as Specifiedin the ASME Probabilistic Fracture Mechanics Codefor Code, Sect. . .spendix A, EPRI Report NP-Application to Pressure Vessels, NUREGICR- 1181, September 1979.c 3618 (ORNL-5991), May 1984.8
- 10. U.S. Nuclear Regulatory Commission. Regulatory
- 4. D. L. Selby et al., Martin Marietta Energy Guide 1.99, Revision 2," Radiation Embrittlement Syctems. Inc., Oak Ridge National Lab., of Reactor Vessel Materials," May 1988.8 Pressurized Thermal Shock Evaluation of the H.B.
Robinson Nuclear Power Plant, NUREGICR-4183 11. W. O. Shabbits, Dynamic Fracture Toughness (ORNLfTM-9567), September 1985.a Properties ofHeavy Sect. A333 Grade B Class 1 Steel Plate, Westinghouse R&D Center, December
- 5. R. D. Cheverton et al., Martin Marietta Energy 1970.6 Systems, Inc., Oak Ridge National Lab., Pressure Vessel Fracture Studies Pertaining to the Pl\ R Thermal Shock issue: Experiment TSE-7, NUREG/CR-4304 (ORNL-6177), July 1985.8
- 6. The American Society of Mechanical Engineers Boiler and Pressure Vessel Code, Sect. XI, Rules for Inservice Inspection of Nuclear Power Plant Components, Appendix A," Analysis of Flaws,"
Article A-3000, Method For K IDetermination, 1989.c i
8 Available for purchase from Government Printing Office Sales Program.
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"Available for purchase from Govemmen: Prinung Office Saks C Program Available for purchase from organizanon sponsoring publicadon b caed. and/or authors, and/or recipients (documented letters).
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Available for purchase from organizanon sponsonng pubbcation csted, and/or authors, anNor recipients (documented leners)-
. . . . ,l
Table 1. Input data for the Yankee Rowe PTS PFM sensitivity analysis Vessel Geometry:
Inner vessel radius = 54.5 in.
Wall thickness = 7.875 in.
Cladding Thickness:
Weld regions = 0.250 in.
Plate regions = 0.109 in.
Cladding Thermal Elastic Material Properties:*
Modulus of elasticity (E) = 27,000 ksi Poisson's ratio (v) = 0.3 Thermal expansion coefficient (ac lad) = 9.9E-6 /"F Thermal conductivity (k) = 10 BTU /h-ft *F "
Specific heat (cp) = 0.12 B7U/lb *F Density (p) = 488 lb/ft3 Ilase Metal Thermal-Elastic Material Properties:'
Modulus of clasticity (E) = 28,000 ksi Poisson's ratio (v) = 0.3 Thermal expansion coefficient (abase) = 7.85E-6 / F Thermal conductivity (k) = 24 BTU /h.ft *F Specific heat (cp) = 0.l' BTU /ib *F Density (p) = 488 lb/ft3 Plate Regions lietween Spot Welds:
Gap between clad and base metal = 3 mils
'fhermal conductivity of water (L)= 0.32 BTU /h-ft- F Specific heat of water = 1.00 BTU /lb *F Density of water = 62A lb/ft 3 Operating Conditions:
Initial vessel temperature = 515 F Initial water temperature = 515'F Coefficient of Convective IIcat Transfer = 504 BTU /h ft2.op Fluence Map Corresponding to the End of Cycle 22 Volume of Vessel Regions in lleltline:
Upper-axial weld: 0.675 ft3 Lower-axial w eld: 0.300 ft3 Circumferential weld: 2.73 ft3 Lower plate: 64 ft3 Upper plate: 144 ft3 See footnotes at end of table.
NUREG.CR-5782 ' 14
Table 1 (Continued) i Fracture Properties:
Initial (uninadiated) RTNDTo for weld material = 10*F
, initial (unirradiated) RTNIJro for plate material = 30'F Maximum K l a = 200 kSid Flow stress = 80.0 ksi -
Kic and Klamean curves were same as those used in the original IPTS studies,i.e.:
Kla mean = 1.25
- ASME lower bound K al curve {
K!c mean = 1.43
- ASME lower bound K el curve ;
Kid mean = 1.43
- ASME lower bound K el curve shifted by 33 F
+
RTNDT Correlations: :
Weld material:
Regulatory Guide 1.99 Revision 2 (welds) + 50 F for a low operating temperature correction factor. ;
Plate material: i Upper Plate - Odette correlation: ARTNDT ( F) = 183
- fluence 0315 +
Lower Plate - Odette correlation: ARTNDT (*F) = (183
- fluence 0315) + 80 t Probabilistic Parameters:
ARTNIyr standard deviation (welds) = 24'F ARTNDT standard deviation (plates) = 37*F s RTNDTo standard deviation = 17"F l K ls a tandard deviation = 0.15 ;
K is c tandard deviation = 0.10 ARTNDT truncation = + or - 3a '
K ic truncation = + or - 3a K la truncation = + or - 30 Fluence standard deviation (fraction of mean) = 0.1 :
Fluence variability truncation = + or - 3o ;
Mean nickel = 0.6 wt% ;
Copper standard deviation = 0.07 wt%
Marshall flaw size distribution function used Marshall flaw nondctcction function used (simulates preservice inspection) i All flaws were assumed to be infinite length.**
'No temperature dependence of matenal properues indaded an analysts.
- *See Sect. 3.4.2, 1
1 1
15 -- NUREG/CR-5782
'l
- i
l Table 2. Best-estimate unadjusted conditional probabilities of failure [P(FIE)] for welds Sensitivity with respect to copper Upper Axial Weld Cu = 0.15 Cu = 0.20 Cu = 0.25 Cu = 0.30 Cu = 035 j Surfxe flaw 1.3E-2 2.5E-2 4.5E-2 7.4E-2 1.0E-1 Sutdad flaw 7.3E-4 2.0E-3 5.3E-3 1.1E-2 2.0E-2 Emtedded fbw 7.0E-6 2.5E-5 7.4E-5 1.5E-4 2.2E-4 Lower Axial Weld Surfre flaw 8.7E-3 1.7E-2 3.0E-2 4.9E-2 7.lE-2 Subclad flaw 3.SE-4 1.2E-3 3.lE-3 7. l E-3 1.2E-2 Emtedded flaw 3.0E-6 1.0E-5 3.0E-5 6.9E-5 1.2E-4 Circumferential Weld Surface flaw 9.lE-5 3.8E-4 1.0E-3 2.4E-3 4.7E-3 Subclad flaw < l .0E-6 <l.0E-6 <l.0E-6 < l .0E-6 < 1.0E-6 Emtxxided fbw < 1.0E-6 <l.0E-6 2.0E-6 4.5E-6 1.5E-5 NUREGCR-5782 16
.. )
<$t
$+$bh',
- g SO t9 IMAGE EVALUATION gq,(p
\O
\ ////p Y *a*pthff* TEST TARGET (MT-3) </
(S @f g,
\ tkh' ll s / h
+
i 4 6" >
r.,4 p% **+f,
,/ - - --
4+ a ;;p///A r
Ao o
w%jo gy x. s 8,4 g Oy [ ,,g#
t e
Q-;' l
~
y
$+
+ ,
,,s ;lj')
S' M$ ...m .J-- -MU--i<SM ISN Ob5 N , _,. ., .y . .- . . M_n . r
- 4 9
["' ?
Q Q ', IMAGE EVALUATION /
//'/f f%
'A TEST TARGET (MT-3) 4/ /f ' ?> de s\['f/
)f< $* (p, g[,
I.0 i
- ,i t lg23
!s! ts w=
l.25 1.4 i'l I.6 am= i!be=4 4 _ _ _ _ . _ .__..- 1 5 0 m m >
__._._._6" -
w Sj'L. /
y g..
e #8 -
ffh Ib v
byXa .
+tW4% -
O ,
p \. [...
,p
_ _ JJ
~- . , ,. k ,
y i e a 9s Oh?
ilto g/ O ' 9e' gI IMAGE EVALUATION g//j Q d[hg
'$ TEST TARGET (MT-3) g 0 ,
- +
t>
r4 4
'2B y 2.5 l*0 .,,
~
g u-:
,. l 2.0
- ==
1.1 .
llll 1.8 ap._.
l.25 ijl.4 4 1.6 p==
tj 4__....____.-- 150mm >
4 _._ _ . _ _ _ _ .
6" - >
Jp 'f'?(p g g q 4 4 4
- Nf77 ,
(y{s,g,7 p
/
s<A;,.g[.4 <u* m 4, #~
Oy/
[ (& l
! ii i L m . = . . . - . . . . . . ,.
A . :.0% Mis . _ . _ .
/
1 1
Table 3. Best< stimate unadjusted conditional probabilities of failure [P(FIE)] for plate l (between spot welds) .
l 4
Sensitivity with respect to surface RTNDT l Upper Plate RTNUrsa = 250 275 300 325 1
1 Subclad flaw
- 1.0E-3 2.7E-3 6.2E-3 1.2E-2 Embedded flaw 1.5E-5 4.0E-5 9.0E-5 1.8E-4 Lower Plate l
RTNUT'= 3 250 275 300 325 350 375 400 Subclad flaw 6 1.1E-3 2.8E-3 5.7E-3 1.1E-2 1.7E-2 2.5E-2 . 3.3E-2 Dnbedded flaw 1.6E -6 3.5E-5 7.6E-5 1.6E4 2.7E--4 4.2E-4 5.7E4 1
8Maumum value in region bSubclad flaws treated as surface flaws.
1 l
1 l
l j
i-e 17 NUREG/CR-5782
, l l
l Table 4. Best-estimate unadjusted conditional probabilities of failure [P(FIE)) for plate (at spot welds)
Sensitivity with respect to surface RTN DT Upper Plate RTNar sa = 250 275 300 325 i
Surface flaw 6.9 E-3 1.7E-2 3.0E-2 5.2E-2 Subclad flaw 5.lE-4 1.lE-3 2.0E-3 3.6E-3 Embedded flaw 1.0E-4 2.2E-4 4.2E-4 6.9E-4 Lower Plate RTNur? = 250 275 300 325 350 375 400 ;
Surface flaw 7.4E-3 1.5E-2 2.8E-2 4.5E-2 6.8E-2 9.lE-2 1.lE-1 :
Subclad flaw 5.3E-4 1.lE-3 2.0E-3 3.3E-3 5.2E-3 7.3E-3 1.0E-2 Embedixiflaw 1.2E 4 2.3E-4 3.9E 4 6.4E-4 9.lE-4 1.2E-3 1.5E-3 8Maumum value m regiort ;
l
)
e t
NlREG/CR-5782 18
l i Table 5. Summary of results of Example Problem 1 Number of flaws Region pg) Nj*Vj*I Pj(FIE)
UAW 0.074 0.011 0.0008 LAW 0.049 0.005 0.0003 CW 0.0024 0.045 0.0001 UP 0.017 1.231 0.0209 LP 0.068 0.547 0.0372
, Totals (best estimate) 1.839 0.0593 t
Totals (mean) 82.755 2.669 i
P 1
)
+
i i
19 NUREG/CR-5782 l
1 !
.1 - Surface Flaw ig j 1 -
~ .
~ .....,,,,,,, .
.07 .
' SUbC/gg N/asy \ ,,,,,," "*" " '
- f m
.. ~ ~........
% *007 j h :
'Q.
~0007 .
lap; \>.~~~.~,,,,,~ :
/ ,
~ .
f 0099 ,_~
~ /
t 4
.000001 i
- i !
0.1 0.2 0.3 0.4 j i
% COPPER !
=
l Fig.1. Unadjusted best-estimate conditional probability of failure. Upper Atial Weld.
i
.l d
t l
l NUREG/CR-5782 20 l
.1
' l l Surface Flaw ,
s .
)
i
.01 .
9..'...-
)
~
Subclad Flaw
.001 .
m C)
,,****,s* :
v N 000y
"~""~~"
- . ~~ :
OWdeq p ~~~~"~"~~ .
. l
?
0001 d " "" :
5
.000001 . i -
0.1 0.2 0.3 0.4
% COPPER Fig. 2. Unadjusted best-estimate conditional probability of failure. Lower Axial Weld.
1 i
21 NUREG/CR-5782 i
i
.01 :
Surface Flaw w -
.001 .
n o .0001 ' .
v .
<CL
,~
'00001 .
,e :
Embedded F!aw ,/ ,#,* -
.000001 , '
0.1 0.2 0.3 O.4
% COPPER vig. 3. unaajusica dest-estimate c "di'i "^' P'"" "" "'""' ' 'ir'"*f t "ti l l' NUREG/CR-5782 22
_ _ _ _ _ ~ .
l l
l NOTE: ISW = Flaws existing in spot welds ,
BSW = Flaws existing between spot welds l
.1 -
- I i
- Surface Flaw ISW -
N :
.Oy /
- 0 Fla;y g s ....,....... .... l
.~
- ~ '
00y
......',, g- .
~~~~~
,q .
- J Cladp,is'/Sm
?
~~~~~~~
COOy '
.. ~~~~ '
- Onbeg, VISty
. ;5
,,.. bedge4 /dlyc% ;y . .
_,,,,, 6
.00001 , .
200 250 300 350 SURFACE RTng7 ( F)
Fig. 4. Unadjusted best-estimate conditional probability of failure. Upper Plate.
l l
4 23 NUREG/CR-5782
_- I
7 i , '
i NO75. 'ISW
- Platyg existing - 5 BSW ~ Play ling fgg,of0 tygjggspot sygjg, .
j l ,I 1 ' Surface y,g l I ~
l
~
~ ~~~~~~~~~~~ ~
01 . " . , " _
- lSubcla# flBW BSW
~.~~~"**"-* l ,
- 14. ; *
< q' ,
g-
. coy
. ~ .............
. / ..... ....... ~"
l l
llSubclayp,g w .
,,.. ******* " " " ~~
.0001 1Embodded p,oW ISty 5
- "........4*l
! i
- ... Embedded pIBW BSW .
b f
0000y '
l .
1 200 250 300 350 400 450 SURFACE RTNDT ( Fi e Fig. 5. Unadjusted best-estimate conditional probability of failur : Lower Plate. :
l l
1 l
l NUREG/CR-5782 24 i
i 1
1 Appendix A: Transient Definition and Resulting Loads l l
Figure A.1. Yankee Rowe SBLOCA7 Thermal and Pressure Transient.
Figure A.2. Thermal Response of Yankee Rowe Vessel to SBLOCA7 Transient (time = 20 min). l 1
Figure A.3. Hoop Stress Distributions (time = 20 min). j Figure A.4. Axial Stress Distribution (time = 20 min).
Figure A.5. K Distributions 1 for Axial Surface Flaws (time = 20 min).
Figure A.6. K Distribution I for Circumferential Surface Flaws (time = 20 min).
i Figure A.7. K for 1 Embedded Flaws Located in Welds (time = 20 min).
Figure A.8. K for I Embedded Flaws Located in Plate (time = 20 min).
l b
?
l 2
1 9
A.1 NUREG/CR-5782 a l
600 3 Water Temp (*F) ,
Pressure (ksi) l 500
^
IL L
W -2 C ^
-> 400 -- ._
VJ ,
F 6
<C '
C W W C .
D- -3 '
2 300 W W -1 m
1-- W
- W L, C W CL ;
g %,, f
.m ,
200 - --
~
I 100 i , i m 0 O 20 40 60 80 100 >
TIME (min) ;
i i
Fig. A.] Yankee Rowe SBLOCA7 thermal and pressure transient.
i
)
i I
I A.3 NUREG/CR-5782
l 500 WELDS: 0.25 inch clad 450 , l a
,/ .
h J
v 400 w ,/
T 2
F
< ,- \
m 350 g w / \ *
- 0. <
- s / PLATE: 0.109 " clad at Spot Weld -
w ,9 300 g[ .
}?
PLATE: 0.109 " clad between Spot Weld
~
I i l l l l 1 250 . .
O 1 2 3 4 5 6 7 8 R (in.)
Fig. A.2. Thennal response of Yankee Rowe vessel to SBLOCA7 transient (time = 20 min).
80 ,
3 WELD: 0.25 " Clad -includes effect of 6 ksi ,
residual stress in 1st inch of base metal 6
f ,
]Y PLATE: 0.109 " Clad - At spot Weld m
g . 'j.
x \
U) m 40
\s\\ .
Lu C
\s . .
I- '
U) 20 PLATE: 0.109 " clad - between sp$t weld -
fl. hs 3 '.
C)
's -
N O '
I 0 x-
-20 .
a O 1 2 3 4 5 6 7 8 R (in.)
Fig. A.3. Hoop stress distributions (time = 20 min).
l 1
A.5 NUREG/CR-5782 i
I
\
1 1
l i
80 7
60 ,
Effect of 6 ksi tensile residual stress m 'i* in the 1st 1 inch of base metal .
- = 3 g u o
$ 40 w
in ."
(4 %*
LLJ . '
CC .
l- .
y) 20 -
.J
~
X
'+.****. .
4 **.,~~..**
0
= .*%
,,,,*==...
-20 .
c 0 1 2 3 4 5 6 7 8 R (in.)
Fig. A.4. Axial stress distribution (time = 20 min).
t i
k
?
NUREG/CR-5782 A.6
4 l
l J
300 WELD: .25" clad-include effect of 6 ksi '
tensile residual stress in 1st inch of base !ly ' \ s i
/ \
\
/
/
/
(/
200 -
/
7 e' c s'
.=;- -
g ,
x
<< l
-)
,--h M 100 ,
/<p' PLATE: 0.109 " CLAD - between spot weld i
,/,
.?; s -
/ PLATE: 6.109" CLAD- at spot weld l t i i 0 .
0 1 2 3 4 5 6 7 8 R (in.)
i Fig. A.5. K distributions 1 for axial surface fiaws (time = 20 min).
i 1
i l
l l
l A.7 NUREGER-5782 I
120 , ; , ,
Effect of 6 ksi tenaile residual stress in 1st1 inch of base <
~~"~"""~ "~"'~~""'-
100 ~
,. /
~
\' ~
1 i
,x/ \
'iB /
X l
N l
M 60 l l .
I 40 *i
- l)'
20 . . .
i ...
8 0 1 2 3 4 5 6 7 R (in.)
t Fig. A.6. K1 distributions for circumferential surface flawv (time = 20 min).
1 4
NUREG/CR-5782 A.8
l 1
120 inner crack tip located at clad / base interface 4 100 -
N. i 80 inner crack tiplocated t depth of 0.77 inches ,
C l
QW 60
~~
.x
" s',,,,,, '
M- gnner crack tiplocated 40 s " **,,f: tdepth of 2.27 inches
,, / , ...
,e s
0 . -
0.0 1.0 2.0 CRACK SIZE 2a (in.)
Fig. A.7. K for 1 embedded flaws located in welds (time = 20 min).
l l
A.9 NUREG/CR-5782
l 100 i i :
Inner crack tip located at clad / base interface 80
\
4 !
Inner crack tip located .
at depth of a.53 Inches 7 ,
60
.5 y
.~
U) ~
X v ,,,,
_ 40 y ,,,.~~ +
Inner crack tip located .
,./ at depth of 2.63 inches 20 ,/
~ ,,,,, ...............................,,,,
0 .
0.0 1.0 2.0 CRACK SIZE 2a (in.) .
Fig. A.8. K for I embedded flaws located in plate (time = 20 min).
NUREG/CR-5782 A.10
Appendix B: Surface Flaw Model l and PFM Methodology l
-)
l Figure B.l. Surface-Flaw Model. ;
Figure B.2. Surface-Flaw PFM Methodology. l l
l l
i i
i l
l i
i B.1 NUREG/CR-5782
SURFACE FLAW MODEL:
Initial Flaw Sue
- P(a)* *
(in.) %
- "~ 0.085 69.12 I
N 0.262 22.30 S i 0.457 6.44 1.65 0.671 m
0.904 0.37 '
Initial Flaw Size
- l.158 0.01 A Mesh Points 1.437 <0.01 -
( 3 Located at 1/4" 1.742 <0.01
" '* ** nts 2.076 <0.01 J
k
- Defauh values from OCA-P
- Probability of Occurance - Determined from the integration of the product of ,
the Marshall flaw size and probability of nondetection function.
[asize]- Array of nine possible initial crack sizes.
I
[a]- Array of discrete mesh points where surface flaw tip can be located.
Note: For surface flaws [asize] = [a] for first nine discrete mesh points.
T(a,t) - Temperature for each surface flaw mesh point for each transient time step. Used for calculating fracture toughness of surface flaw tip.
Ki(a,t)- SIF for each surface flaw mesh point for each transient time step.
Used for predicting initiation / arrest of surface flaws. Calculated using K* superposition method.
Fig. B.1. surface-flaw model.
PFM METHODOLOGY FOR SURFACE FLAWS
@ t VESSEL = VESSEL + 1 l l
V l Simulate Flaw Size (a): Marshall l Y
l Simulate Amount of Embrittlement Plate y Weld Y 1) Randomly Select Surface Fluence (Fo)
- 1) Randomly Select ARTNDTs from 2D Array from 1D Array
- 2) Simulate Suriace Fluence (SFID)
- 3) Sirnulate Copper (SCu)
I I
T Simulate RTNDT Error (ERRTN)
Finished Calculate h P(F;E)
--> Simulate Kic Error (ERKIC)
@ +
Y A O increment Transient Time N \.C
_/ 4 t=1 + at l Enough Vessels?
A h Simulate Fracture inrtation Toughness (Swk):
- 1) RTNDT (a)
Add 1 Nontailure
- 2) TADJ = T(a.t)- RTNDT (a)
A 3) (Ke)m.an - f(TADJ)
- 4) Swie = (Kehn
- ERKIC y @
k V Transient Over, Check for initiaton (Initial /Reinitiaton)
Ki(a.t) > Swic(aj)?
Y v
h h-> Propagate Flaw; a = a + aa t +
Add 1 Failure d Vesse! Failure?
yN Simulate Fracture Arrest Toughness (Swia)
- 1) RTNDT(a): Use Maximum Fluence
- 2) Taca-T(a.t)-RTNDT(a)
- 3) (Kia)m.an - f(TADJ)
- 4) Simulate Kia Error (ERKla) ,
- 5) Swia = ERKla * (Kia)mean
- 6) Impose Upper Shelf Lirnit: Swia S USKla v +
+
Continue Flaw Propagation d K a t) (a )?
Fig. B 2. Surface-flaw PFM methodology.
NUREG/CR-5782 B.4
Appendix C: Subclad Flaw Model and PFM Methodology Figure C.I. Subclad-Fbw Model.
Figure C.2. Subclad-Flaw PFM Methodology.
i 1
I C.1 NUREG/CR-5782
1 SUBCLAD FLAWS MODEL:
> CLADE 4--
INTERPOLATE
. ...n ... . .
\ J Y SURFACE MESH Flaw will propagate along
's size.:,. Subclad mesh.
Initial flaw sizes and probability of occurrance are
,- the same as for surface flaws
- (from Marshall).
SUBCgD MESH r ,
[asize]- Array of nine possible initial crack si7es
[a] - Array of discrete mesh points where subclad crack tip may be located.
a = asize + cladth
.KI(a,1)- SIF for surface flaws with crack tip located at [a] for each transient time step. Calculated using K* superposition method.
NOTE: Subclad flaws which are considered as surface flaws have a different location for crack outer tip than regular surface flaws. The crack outer tip is located at (a + Cladth). To obtain K 1for surface flaw located at a + Cladth, interpolate between two surface KI's for the two surface mesh points which bracket (a + Cladth).
acrit - Critical flaw size for determining cladding failure.
Fig. C.1. Subclad-Daw model.
C.3 NUREG/CR-5782 i .
i l
terit - Critical time at which cladding will fail if flaw size exceeds acrit. i
- T(a,t) - Temperature for each subclad mesh point [a] for each transient time Step. Used for calculating fracture toughness of subclad flaw.
Criteria for cladding failure: ;
a 2 acrit and t 2 terit ,
l Dynamic effects (via Kid) is included for only that time step at which the cladding !
has failed. !
Positive Effect of Unbroken Cladding Simulated as: f KI(a,t) = [K1(a,t)] surface flaw
- 0.65 !
I P
1
. 1 I
l t
i f
I 1
- i Fig. C.1. (Continued)
NUREG/CR-5782 C.4 [
f
PFM METHODOLOGY FOR SUBCLAD FLAWS VESSEL - VESSEL + 1 I
Y Simulate Flaw Size (a): Marshall Y
Simulate Amount of Embrit*Jement Plate Y Weld
- 1) Randomly Select Surface Fluence (Fo)
- 1) Randomly Select ARTNOT.from 2-D Array from 1D Array
- 2) Simulate Surface Fluence (SFID)
- 3) Simulate Copper (SCu)
I Y
Simulate RTNDT Error (ERRTN)
+
Simulate Kc Error (ERKlC)
I Y
increment Transient Time 1 = t + At V
Simulate Fracture initiation Toughness (SMKIC)
Calculate: 1) RTNDT (a)
- 2) TADJ - T(a t)- RTNDT (a)
- 3) (Kc)=n - f(TAIM)
- 4) Surc - ERKlC'(Kc)maan l
i 3r N is Current Crack Size (a) 2 Critical Crack S:ze a 2 acnt?
Y AK = Ki(a,t)*0.65 Y is time (t) < Critcal Time l SuKc = Enkc"Kc), san t < tearr?
y N Y
is time (t) - Critcal Time t = tCRfT?
Y N v y Claad ng Failure: Include Dyname Effect Crrtical Time Exceeded; Subclad Flaw Became Surface Flaw on Earlier
- 1) Subclad Flaw Becomes Surface Flaw Time Step:
- 2) Calculate (K:D)mean
- 3) SuKc = ERKc'(kid)maa' 1) Calculate (Kc)maan
- 4) AKI = Kga,t)
- 2) Sukic = ERKlC'(Kc)mean 5,) ICFLAG 1 3) AKi - Ki(a,1) l l i
6 Fig. C.2. Subclad-flaw PFM methodology.
C.5 NUREG/CR-5782
hh D i N y N Check for initiation (Initial.Beinitiation) i Transient Over? 4 AKi > SuKc? )
.Y Y T y i
Add 1 Nontailure Propagate Flaw; a - a + aa
- V y i Enough Vessels? 1 h h Check for Failure?
N y y 3r 1r 1r Q Finished:
Calculate P(FiE)
- Add 1 Failure V
Simulate Fracture Crack Arrest Toughness (Suxia)
Calculate:
- 1) RTNDT(a): Use Maximum Fluence ,
- 2) TAoj - T(a.t)- RTNDT(a)
- 3) Km Error (ERKla)
- 4) (Kin)~ man - f(TAal)
- 5) SuKm - ERKla * (Km)mean
- 6) Impose Upper Shelf Limit: Suca s USKla y :
N Has Cladding Fai;ed 2 (CFLAG - 1?
Y 3r 1r Still A Subchd Flaw: Treat as Surface Flaw AKI - 0.65*Ki(a,t) AKi - Ki(a,t)
@h O h y
Y Check for Crack Arrest N Check for Reinitiation 1 AK! < SMKla Continue Flaw Propagation ,
Fig. C.2. (Continued)
NUREG/CR-5782 C.6 i
l l
l l :
I Appendix D: Embedded Flaw Model and PFM Methodology 1
Figure D.1. Embedded-Flaw Model. l Figure D.2. Embedded Flaw PFM Methodology. !
1 l
l l
l 1
l i
l D.1 NUREG/CR-5782
I EMBEDDED FLAW MODEL: !
l i
)
L J l i y
! SURFACE FLAW MESH (a) Inner Crack Tip Location Chosen l Randomly From Uniform Distribu- l tion of Equal Spaced Points. '
~
i
.. .D Initial Flaw Sizes (2a) and the Proba-(-XINb ER-> 2a <- bility of Occurance are the Same as Applied to Surface Flaws (from rshaH)
EMBEDDED FLAW MESH (XINNER)
A T .
.T . ........ .
[asize]- Array of nine possible initial crack sizes
[XINNER]- Array of discrete mesh points where embedded flaw inner crack tip may be located. Used for claculating fracture toughness of embedded inner flaw tip.
T(XINNER,1)- Temperature at each mesh point for each time step in ,
K1(XINNER,2a,t)- SIF for each combination of XINNER and flaw size (2a) for each transient time step. Used for checking for initial initiation of embedded flaw inner tip. Calculated using ASME rnethodology for subsurface flaws.
[a]- Array of discrete points where surface flaw tip can be located.
KI(a,1)- SIF for each surface flaw mesh point for each transient time step.
Used for checking initiation / arrest of surface flaws.
T(a.t)- Temperature for each surface flaw mesh point for each transient time step. Used for calculating fracture toughness of surface flaw tip.
Fig. D.1. Embedded-fbw model.
If entbedded flaw inner tip initiates, cladding is assumed to fail and embedded flaw becomes surface flaw. Surface flaw propagates along surface flaw mesh.
D namic effect (via Kid) is included for only the time step at which cladding Fig. D.I. (Continued) i NUREG/CR-5782 DA
PFM METHODOLOGY FOR EMBEDDED FLAWS d VESSEL = VESSEL + 1 l V
Locate Embedded Flaw inner Tip (XINNER): '
Randomly Chosen From Uniform Distribution l Y
Add 1 Nontaih:re L ' XINNER > 3.0 inches l 4N Simulate Flaw Size (2a): Marshall Y
imulate Amount of Embrittlement y Weld fPlate l
- 1) Randomfy Select Surface Fluence (Fo)
- 1) Randomly Select ARTNDT.from 2-D Array from 1D Array
- 2) Simulate Surface Fluence (SFID)
- 3) Simulate Copper (SCv) i Simulate RTect Error (ERRTN)
Simulate Ke Error (ERKlC)
+
increment Transient Time OB 4 1 = 1 + At Finished Calculate P(FlE) v 4 Check for Tensile instabil:ty of y inner Ligament Unstable?
t Enough Vesselt? 4-.-
v Simulate Fracture initiation (Swe) at g
Embedded Flaw Inner Tip (XiNNER):
A
- 1) RTNDT (XINNER)
Add 1 Nontailure 2) TAD; = T(XINNER.t)- RTNDT (XiNNER)
- 3) (Ke)mean = 1(TAD;)
A 4) Swe = ERKIC * (Kic)m an Y A I N T N Check for Initiation of Flaw inner Tip:
Transient Over? 1 Ki(XINNER.2a,t) > Sme?
y Y Cladding Assumed to Fail:
Embedded Flaw Becomes Surface Flaw with Outer Crack Tip at a = X1NNER + 2a V !
O Fig. D.2. Embedded-flaw PFM methodology.
D.5 NUREG/CR-5782 l
@ l Y
tetai = t
+
Decrement Transient Time t = t - at
+
h% Simulate Kic Error (ERK!C) l 4
Increment Transier't Time OG A t = 1 + .st Y
Calculate: RTNOT (a)
TAca T(a.t)-RTNDT(a)
Y is This The Time Step at Which N Cladd:ng Failed: ! = tetaii?
Y y Indude Dynamic Effect: Do Not Indude Dynamic Effect:
- 1) Calculate: (Km)=an = f(Taos) 1) (K-c)m.an = f(Taos)
- 2) Swie = ERKlC * (Km)m.an 2) Swie = ERKlC * (Kic)mean l
@ V A
N N Check for initiaton (Initial /Reinitiation)
Trans4ent Over? 4- of Surface Flaw
- Kr(a.t) > Swe(a.t)?
Y Add 1 Nontailure y Propagate Sur' ace Flaw A H a = a + ba
~
V Y
Md 1 Failure h Check tor Failure?
3_.
/b G oimulate Fracture Arrest Toughness (Swra):
- 1) RTNot (a): Use Maximum Fluence
- 2) Tro; = T(a.t)- RTNOT (a) ;
- 3) Calculate Kia Error (ERKla)
- 4) (Kia)m.an = f(Taos)
- 5) Smia - ERKla
- Sw:a
- 6) Impose Upper Shelf Umit: Swis s USKla V i Y Check for Crack Arrest N Continue Flaw l Check for Reinitiation % Kr(a.t) < Swia? Propagation Fig. D.2. (Continued)
NUREG/CR-5782 D.6
Appendix E: Methodology for Simulating Fracture Toughness for Welds i
E.1 hWG/CR 5782
~. . __ .. _
METHODOLOGY USED FOR SIMULATING FRACTURE
. TOUGHNESS FOR WELDS: }
Specified: Fluence Map (1-D) l Nickel 1 ARTNDT: RG 1.99 Rev. 2 f
a SENSITIVITY WRT COPPER !
.{
t i
z l
) Fmax Crack Tip: ,
Q Surface flaw l
> ll :
- .2 Subclad flaw I ;
u t E 5 %
g / mbedded flaw I !
h M Fo C C 3 f Randomly Selected lf }
1 Step 1: Simulate Fluence :
a) Fo - Value af mean surface fluence is randomly chosen from l unifo m distribution, i.e., each fluence value has equal !'
prob ability of being chosen.
Fmax - Maximum value of surface fluence in fluence variation map. j i
b) Probabilistically Simulate Surface Fluence: .;
i Simulated surface fluence (SFID) chosen from normal distribution l about randomly selected mean fluence Fo. i E.3 NUREG/CR-5782 1
Mean = Fo 1o=0.1*Fo i i Limit: Fo > 0 I
l I
l FID(I) i I
I I
=
IJo SURFACE FLUENCE c) Different attenuated fluence curves are used to predict initial crack initiation [SFID(I)], crack arrest (s), and subsequent reinitiation(s)
[SFID(A)].
A "
SFID(A) = Fmax
- e SFID( Predict A+rrest/Reinitiation 5
+
Predict Initial Initiation R (in.)
NUREGER-5782 E.4
Step 2: Probabilistically simulate copper (SCu):
Randomly chosen from nonnal distribution about mean Cu.
n 1 MEAN = Cu I 10 = 0.07 i LIMIT: SCus0.40 1
I I
I ,.
0 l %-
0.40 Step 3: Probabilistically simulate RTNDT Error (ERRTN):
Randomly chosen from normal distribution about mean = 0.
Note: ERRTN is calculated once per vessel.
I MEAN = 0 I lo = 1 i LIMIT: -3 s ERRTN s 3 I
I I
I I
I m .
1 0
E.5 NUREG/CR-5782
_ - _)
Step 4: Compute ARTNDT Per RG 1.99 Rev. 2. i
[0.28 - 0.1 log (SFID)]
ARTNDT(a) = CF
- SFID where: -)
for initiation: SFID = SFID(I)
- exp(-0.24
- a) j arrest /reinitiation: SFID = SFID(A)
- exp(-0.24
- a) I CF = chemistry factor = f(SCu, Ni)'
Step 5: Calculate embrittlement (RTNDT) ;
'RTNDT = RTNDTO + ARTNDT + ERRTN
- ho[TNDT0 + UbTf where: ,
RTNDT = value of RTNDT used in fracture toughness calculations RTNDTo = initial (unirradiated) value of RTNDT ,
= 10 F for welds ;
= 30 F for plate j t
ARTNDT = shift in RTNDT due to irradiation as a function of simulated i fluence (attenuated to wall depth location corresponding to l crack tip location) and simulated copper as predicted by '
RG 1.99 Rev. 2 for welds. (Nickel = 0.6 = constant) >
i hohTNDT0+Ub7NDT= square root of the sum of the square of la variability for RTNDT and ARTNDT (10 for RTNDTo = 17 F and la for ARTNDT = 24 C). This represents the lo uncertainty for the specified value of RTNDTo and the 10 uncertainty in the predictive correlation used ;
to caluclate ARTNDT.
ERRTN = Random number between -3 and +3 chosen from uniform -
distribution. The product of ERRTN and 1, ,
joRTNDTO +U RTNDT essentially increases the uncer tainty of RTNDT from 1o to 30. :
LTCF = Low temperature correction factor = 50 F. This accounts. ;
for the lack of self-annealing due to the fact that Yankee Rowe i t
NUREGER-5782 E.6 f i
l r - -
operates at ~500 F. The ARTNDT values predicted by RG 1.99 Rev.
2 are based on an opemting temperature of 550 F.
Step 6: Calculate TA DJ = T(a.t)- RTNDT(a) i Step 7: Calculate fracture toughness error (ERKlc and ERIKa):
These terms account for the scatter of the fracture toughness about '
the mean. These terms are recalculated for each crack tip position.
Randomly chosen from nomial distribution about mean = 1.0 A
I I
I I
Error Tenn I ,
I :
I I
I I t ,
1.0 Initiation lc = 0.15 .. 0.55 s ERKIC s 1.45 Arrest 10 = 0.10 . . 0.70 s ERKIA s 1.30 i
, Step 8: Calculate mean fracture toughness = f(TADJ) >
(K Ic)mean = 1.43
- ASME Lower Bound Klc Curve ,
(Kla)mean = 1.25
- ASME Lower Bound Kla Curve l Step 9: Calculate simulated fracture toughness used in predicting initial initiation / arrest /reinitiation.
SMKIC = ERKIC * (K c)mean i ~
SMKIA = ERKIA * (Kla)mean SMKIA s 200 ksidiri E.7 NL' REG /CR-5782
l l
l l
Appendix F: Methodology for Simulating Fracture Toughness for Plates l
1 i
l i
l l
h 9
F.I NUREG/CR-5782
l i
METHODOLOGY USED FOR SIMULATING FRACTURE TOUGHNESS FOR PLATES:
l Specified: 2-D Fluence Map ARTNDT Correlations (Odette)
Upper Plate - ARTNDT ( F) = 183 FO.315 Lower Plate - ART NDT ( F) = 183 FO.315 + 80 l
SENSITIVITY WRT RT NDTS - VALUE OF RTNDT AT VESSEL :
INNER SURFACE l Problem: Specified Fluence Map not Necessarily Consistent with Specified !
Value of RTNDTs and Odette Correlation i Prior to performing PFM analysis, the 2-D fluence map is first normalized WRT f specified value of RTNDTs and then transformed to a ARTNDTs map:
Step 1: Value of RTNDTs specified i
Step 2: Calculate value of surface ARTNDT ARTNDTs = RTNDTs - RTNDTo 1
Step 3: Calculate value of surface fluence Fo which produces ARTNDTs when ;
using appropriate Odette correlation:
(a) Upper Plate: Fo* = (ARTNDTs/l83)1/0.315 ,
(b) Lower Plate: Fo* = [(ARTNDTs - 80)/l83)1/0.315 Step 4: Normalize the entire 2-D fluence map by (Fo*/Fmax) where Fmax is the !
maximum value of surface fluence in the 2-D map. This implicitly !
assumes that the specified value of RTNDTs corresponds to the location of maximum fluence. <
F.3 NUREG/CR-5782 l
Step 5: Transfomi the normalized 2-D surface fluence map to a ARTNDTs map using the appropriate Odette correlation.
~ Normalized -
ARTNDTs op
~
r Odette Map
_ Fluence Map _ Correlation _ _
During the PFM Analysis:
Step 1: For each simulated vessel, a value of ARTNDTs is randomly selected from a uniform distribution.
z e - - - - - - - - - - - - - + ARTNDTs
< A a.
I O Randomly Selecte I l $ Value of ARTNDTs l l F i 1 < g x
y - - - *(ARTNDTs)nax !
J I A
$ I i
< l I AZIMUTHAL VARIATION OF ARTNDTs Step 2: Calculate radiation induced damage (ARTNDT) attenuated to specific wall depth (a):
for initiation: ARTNDT(a) = (ARTNDTs - B)exp(-0.315 *0.24*a) + B for reinitiation and arrest: ARTNDT(a) = [(ARTNDTs) max - B]exp(-0.315*0.24*a) + B NUREG/CR-5782 FA
. . _ _ - _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ h
where:
ARTNDTs = value of ARTNDTs randomly selected from map (ARTNDTs) max = maximum value of ARTNDTs in 2-D map B = 0 for upper plate B = 80 for lower plate.
A (ARTNDTs) max g ' ARTNDTs Used in Pre iction of Arrest and e
< Subsequent Reinitiation A
Used in Prediction of Initial Initiation
=
R (in.)
Step 3: Probabilistically simulate RTNDT error (ERRTN):
Randomly chosen from normal distribution about mean = 0. ERRTN is calculated only once for each vessel.
4 F.5 NUREG/CR 5782
il MEAN = 0 lo = 1 LIMIT: -3 s ERRTN s 3 m
0 ERRTN .;
Step 4: Calculate embrittlement (RTNDT)
RTNDT(a) = RTNDT0 + ARTNDT(a)+ ERRTN o[TNDT0 + UbTNDT Step 5: Calculate TA DJ = T(a,t)- RTNDT(a)
Step 6: Calculate fracture toughness error (ERKIc and ERIKa):
These terms account for the scatter of the fracture toughness about the mean. These terms are calculated for each crack tip po:;ition.
ERKIc and ERKla are randomly selected from a normal distribution about a mean = 1.0.
t E
+
k NUREG/CR-5782 F.6 i
A i
I I
i I
Error Term i
I I
I I
I s 1.0 Initiation lc = 0.15 c. 0.55 s ERKIC s 1.45 Arrest 10 = 0.10 c. 0.70 s ERKIA s 1.30 Step 7: Calculate mean fracture toughness = f(TADJ)
(KIc)mean = 1.43
SMKIC = ERKIC * (KIc)mean SMKIA = ERKIA * (Kla)mean SMKIA 5 200 ksid F.7 NUREGER-5782
Appendix G: Residual Stress Considerations Figure G.I. Hoop-stress distributions for axial welds (at time = 20 min) for three residual-stress cases.
Figure G.2. K distributions I for axial welds (at time = 20 min) for three residual-stress cases.
Figure G.3. Best-estimate unadjusted conditional probability of failure for upper axial weld for three residual-stress cases.
l l
I G.1 NUREG,CR-5782 i
__-.--__ ._ _ - --- _ -------- -- - -- ---------------------------------J
80 6 ksi residual stress through 60 -
m entire wall thickness . <
m j l l -
x ; , ;
f o No Residual Stress v
g e 40 -b 'i--
W 111 bs g + 6 ksi residual stress in 1st -
F- -
I inch of base metal only
@ 20 r-D.
O .
0 l
l
- ; ;; +
-20 . , , .
i .
0 1 2 3 4 5 6 7 8 R (in.)
Fig. G.I. Hoop-stress distributions for axial welds (at time = 20 min) for three residual-stress cases.
1 1
G.3 NUREG/CR-5782 m-_____________________ .
. . .. _ _ d
500 3 ksi tensile residual stress through entire wall thickness x [N 400 g f n
300 g.gF4, _
- g %+
4 +.x 5 #
_ 200
/ 4 y .+,gn I
- o No residual stress
.'q9
- q++ , ,
l 100 '
+ 6ksi residual stress in 1st inch of base metal only .
1 0 .
i s
. , s 0 1 2 3 4 5 6 7 8 l
l R (in.)
Fig. G.2. K distributions 1 for axial welds (at time = 20 min) for three residual-stress cases.
NUREG/CR-5782 G.4
_ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ - . _ - . _ I
1 .
D l ~
With 6 ksi tensila residual stress
(
across entire wallthickness
/
x 1 ;
g,~ ~,,*~ . .
~ , , , , , , ,...... , , .,_,
, , , , , , ,,,,,,,j t
a.
~...
sj Of .
.. ...... ...... IV#b no 'OSigy #I!es,
- With 6 ksi tensile residual stress -
in the 1st 1 inch of base metal .
.001 .
0.1 0.2 0.3 0.4 COPPER Fig. G.3. Best-estimate unadjusted conditional probability of failure for upper axial weld for three residual-stress cases. ,
l l
1 1
G.5 NUREG/CR-5782 l
Appendix H: Dynamic Fracture Considerations Figure H.1. Experimental dynamic fracture toughness data.
Figure H.2. kid ower-bound l curve approximation.
Figure H.3. Ratio of mean dynamic fracture toughness to IFTS mean K el cune.
1 i
H.1 NUREG/CR-5782 l
t l
260 j i j i l 24 0 A533 Gr. B Class 1 Plate -
- ITCT Spec.imen Steel Plate 12" Thick (HSST Plate 02) 220 -
o 2TCT Specimen -
c men _
200 -
o STCT Specimen 125 F 180 160l-50 F 100 F
~
)
g 140 a 75 F j 120 -
a 9 *
"c, 3 100 80 -
- 50of .
~
60 g & _c- _
q p ,
$g 6 v 40 3 6 .{ --
20 -
I I I I O
I 5 1 10 10 10 10 10 K ksi/in./s l Fig. H.l. Experimental dynamic facture toughness data.
l H.3 NUREG/CR-5782 l I
l I
300 .
a KID
~ LB KIC (SH -33) '
LB KIC i
, i i
.6 200 -
l
> l (n l x
v #
u -
/
Z /
o A 2 100 -
.d' -
< /e
- o ,-
x -
0
-200 -100 0 100 200 (T-RTng7) ( F) l Fig. H.2. kid ower-bound curve approximation.
I i
a H.4 NUREG/CR 5782
1 1
s.o- ,r >
s r \ \ , ,
T
~ .
s ,-
\ 39 -
s, s ,'
)
- s
.,, s. ;
\
.,c 93 - -
4 j .
s, .
o,' . .
Y o3 - -
's , ,
4.
. s ob '
.~
I 0.5 o o o o o o o o o ;
o to o to to o to o ;
- . - - a
- m. . a
\
(T-RTgg7) ( F) i Fig. H.3. Ratio of mean dynamic fracture toughness to IFTS mean K cl curve.
l i
l I
H.5 NUREG/CR-5782 -
l i
Appendix I: Clad-Rupture Studies for Subclad Flaws Finite-element fracture analyses were conducted in order Two failure criteria were employed in the studies, one to determine the minimum subclad flaw depths and tneir based on J and another based on a critical level of stress ,
corresponding times in the transient for which rupture of in the cladding. The first accounts for failure by fracture '
the cladding is predicted. Two cladding thicknesses were while the second considers failure by necking or tensile considered; one with 0.109-in.-clad thickness for plate instability. In order to produce initial results in a timely material and another with 0.25-in.-clad thickness for manner, it was decided to apply a simplified and conser- )
weld material. Table 1.1 shows the relevant geometry vative criteria for tearing instability based on JIe using I and material parameters employed in the study. A non- data from the 7th irradiated series 1 (Ji c = 538 in.-lb/in.2 linear material description (Fig.1.1) was utilized for the at T = 200'F). The need for more refmed analyses would stainless steel cladding while elastic-only properties were then be judged by the effect of the initial results on the employed for base material. The cladding properties overall failure probability. A complication, however,in shown simulate irradiated propertics1 (-2 x 10 19 applying the small specimen data to the present studies n/cm2). The pressure-thermal transient (SBLOCA7), is that there is a back-free surface effect in the clad cylin-shown in Fig. A.1, Appendix A, represents the loading der with subclad flaw that is not present in the small condition for the studies. specimens. Thus, it was decided to use a slightly more conservative value of Jic = 500 for the J failure criteria.
Elastic-plastic stress and J. integral calculations were performed using the ABAQUS2 finite-element structural Figure 1.6 gives the computed J-values throughout the analysis program executing on an IBM RISC/6000 transient "near" the clad / base interface for a range of sub-workstation. Figures 1.2-1.4 show a typical finite clad flaws under 0.25 in. cladding. Each flaw depth has a element mesh that was utilized to analyze various depths maximum J.value at t ~21-22 min. Figure I.7 shows of subclad flaws under 0.25 in. cladding. A similar the J-values from Fig. I.6 at 21 min pioned against sub-mesh was used for 0.109 in. cladding. A generalized clad flaw depth and indicates that the critical subclad flaw plane strain (2-D flaw) model was employed with crack depth for 0.25 in cladding is acrit = 1.65 in.
collapsed eight-noded isoparametric elements at the crack Figure 1.8 gives 3-values near the clad / base interface for tip to create a singularity and simulate blunting. subclad flawe under 0.109 in. cladding. As will be dis-cussed below, subclad flaws in 0.109 in cladding reach a Figure 1.5 shows J integral calculations at various times l critical level of stress before J exceeds Jl c.
in the transient for each end of a 2-in. subclad flaw under 0.25 in. cladding. nroughout the transient, J values are The Jo-Block specimen3 shown in Fig. I.9 has been higher near the cladtbase interface than at the deepest used for measuring strength properties of cladding over a point of the flaw, indicating that a subclad flaw has a. subclad flaw. This specimen is basically a tensile har greater propensity to rupture the cladding than to run in that simulates the basic geometry, deformation, and the other direction tiuough the vessel wall. Accurate failure behavior teatures of cladding over a subclad flaw J-mtegral calculations at the clad / base interface are in a vessel wall. It consists of two machined steel comphcated by the fact that the J-contours must blocks with the ends butted together to form a " crack."
necessarily pass through two dissimdar materials. State-Opposite edges are clad such that subclad flaw tips are of-the-art computational techniques, such as the virtual generated where the cladding is laid across tie interface of crack extension algorithm in ABAQUS, require that the two blocks. He " rupture stress and strain" in the J-contours pass through a single homogeneous material" cladding can be determined from a simple tensile test in In order to ngorously satisfy this condition it was conjunction with posttest cross-section measurements.
necessary to consider subclad flaws that slightly penetrate the cladding so that J-contours could be taken Tests3at ORNL show that the rupture stress in the cladding is -90% of the flow stress, where flow stress is through small elements m cladding material only. A k average of yield and ultimate. Hence, rupture of the penetration depth of 182 of the cladding thickness (see cladding is assumed to occur in the present studies if the Fig.1.4) was utilized in the computauons reported here.
" average" stress in the cladding at any time in the tran-This penetration depth is consistent with fractographic sient exceeds 0.9 flow stress, results for Jo-Block specimens 3 m which cracks can be observed to penetrate the cladding by about that amount. g ,g gg g g, gg Addiuonal calculations were perfonned at the outset of cladding reaches a maximum value at t -21 min into the study using a 1/16 clad thickness penetration model to invesugate the sensitivity with respect to small the transient for each subclad flaw depth analyzed.
Figure 1.10 shows " average" Mises stresses in a 0.25 in.
peretration depths. These results are presented in Table 1.2 and indicate only a slight sensitivity for a wide cladding at t ~21 min for the range of flaws studied. As g g gg f,;3 g range of subclad flaw depths. Hence,it was decided that stress; however, as shown earlier, a 1.65-m.. subclad flaw a 1S2 penetration model would suffice for the present Sl" * * ' does fail based on J. For a 0.109 art. cladding, however, a critical level of stress is reached in the cladding before a critical value of J is reached. Figure 1.11 shows Mises stresses in the cladding for subclad flaws ranging from 1.1 NUREG/CR-5782 l
0.33 in. to 0.78 in. deep. It is observed that a 0.78-in. in the transient,it was decided to take a conservative subclad flaw has a stress level that very nearly exceeds approach and declare failure by critical stress for a 0.9 flow stress and, indeed, convergent stress solutions subclad flaw depth of 0.75 in. under 0.109 in. cladding.
were not able to be obtained for flaws deeper than
-0.8 in. (see Table 1.2). Extrapolating the curve in Table 1.3 summarizes the results of the clad rupture Fig.1.11 to 0.9 flow stress indicates that the critical studies. A 0.75-in. subclad flaw ruptures a 0.109 in.
subclad flaw depth is -0.85 in, for 0.109 in. cladding. cladding at t ~21 min into the transient while a 1.65-in.
In light of the fact that the 0.78 in. subclad flaw took subclad flaw ruptures a 0.25 in. cladding at i ~21 min many iterations for convergence and that a slightly into the transient.
deeper flaw doesn't converge at all for times much earlier References
- 1. F. M. Haggag, W. R. Corwin, and R. K. Nanstad, 3. W, J. McAfee, J. W. Bryson, R. D. Cheverton, and -
Irradiation Efects on Strength and Toughness of G. C. Robinson, " A Specimen and Method ior.
Three-Wire Series-Arc Stainless Steel Weld Evaluating the Eifect of Cladding on the Behavior of Overlay Cladding, NUREG/CR-5511 (ORNL/FM- Subclad Flaws", PVP-Vol. 213/MPC-Vol. 32, -
11439), Oak Ridge National Laboratory, Oak R?.dge, Pressure VesselIntegrity, ASME 1991.b Tennessee (February 1990).8
- 2. ABAQUS User Manual, Version 4-8, Hibbit, Karlsson & Sorensen, Inc., Providence, Rhode !
Island (1989).b e
a I
y i
i I
1 A
r i
a i
i l
?
- Available for purchase from GPO Sales Program. :
bAvailable for purchase from organiza'io a c'xmsoring '
publication cited, and/or authors, and/or ,ecip?cnts ,
(documented letters).
NUREG/CR-5782 1.2 l i<
?
l 1
I Table 1.1. Parameters used in subclad-flaw rupture studies Yankee-Rowe Vessel:
Inner vessel radius = 54.5 in.
Wall thickness = 7.875 in. ,
1 Claa thickness = 0.109 in.,0.25 in.
Stainless Steel Cladding:
Modulus of Ecasticity = 27.000 ksi Poisson's ratio = 0.3 Coefficient of thermal expansion = 9.9 x 10-6/*F Thermal conductivity = 10 Btu /h-ft- F Specific heat = 0.12 Btu /lb *F Density = 488 lb/ft3 A5338 Base Metal:
Modulus of clasticity = 28,000 ksi Poisson's ratio = 0.3 Coefficient of thermal expansion = 7.85 x 10-6/"F Thermal conductivity = 24 Btu /h-ft *F Specific heat = 0.12 Btu /lb *F Density = 488 lb/ft3 No temperature dg.endence of matenal properues included in analyses, frutial vessel temperature = $15'F trunal water temperature = 515'F Coefficient of cmvecuve heat transfer = 504 Btu,h-ft2 *F 1.3 NUREG/CR-5782
Table 1.2. Comparison of J-values near clad / base interface for two different clad penetradon models: 1/32 in. and 1/16 in.
Subclad flaw Clad penetradon dcpth J-value (in,_lb/in.2) Time (in.) (s) 0.250 in. cladding 1/32 2.00* 664 1298 1.50 426 1297 1.00 245 1290 l 0.50 105 1267 j 1/16 2.00* 601 1301 1.50 403 1304 1.00 250 1307 0.50 113 1290 '
I 0.109 in. cladding I 1/32 0.78* 250 1290 h 0.55 160 1307 0.33 85 1272 r 1/16 0.78* 228 1290 ~
0.55 155 1309 0.33 88 1276
- NOTE: Not able to get a convergent stress solution for larger subclad flam s. ,
f l
r t
.'F
[
t h
i I
NUREG/CR-5782 1.4 i
Table 1.3. Results of cladding-rupture studies Cladding Thickness acrit Time Failure +
(in.) (in.) (min) by 0.109 0.75 = 21 Stress 0.25 1.65 = 21 J
- Failure Cntena:
- 1. Clad stress > 0.9 flow stress
- 2. J > J Ie
-1 1.5 NUREG/CR-5782 I
80 - - - -
s 7
~~"'
70 - ' ~ ~ ~ - " ' ' ~ ~ " - ~ ~ ~ "'-
- i :
60 - - " ' ~ " -
c
.O : :
=
. . . . . . - . ...a... . . . . . . . . . . . . . . . - . . . . . . ~ . . .
rx .
~
_ . . . . . ~ . . . . . - . . ...m. ....;... . . . . .
i-- :
z -
7
+
..-... woe. .w.s.- see..a ...e.a Y
r f
20
~~
E = 27,000 ksi .
Yiehl stress = 35 ksi .
Ultimate stress = 75 ksi -'"
+
10
~
0 0 0.05 0.1 0.15 0.2 TRUE STRAIN (in./in.)
Fig. I.l. Stress / strain curve for 7th irradiation series three-wire cladding material (T = 5507).
NUREG/CR-5782 1.6
}
I l
l l
l
. _ _ . _ _ _ _. . _ . ABA_QUS 1
/ #dE~ BiE EffE hN #'
'N N f ,
%' b#
'k g
/'8
[/,f/ kih'\ ;
wg?
kf '
i w
l '
I s% \ }s I.'sl' lla l1 1{;. -\-\
.,,a Ti
~\
f lllll' \ \
as!! ' lll!!!.
I Fig. I.2. Finite-element model employed for cladding-rupture studies.
I.7 NUREG/CR-5782 1
~
ABAQUS
\\\ \'\ \
\
s \
-m___p \ \ -r, Dase ,
-l " t Material t-l Claddinh k ,
' ~~ l I I_.__.__
r ;
} }
l I
}
~ __ - --
~~~~ ~
~ ~
\ ~l :) C/
/d-t ; :_..... ___
n l
Fig. I.3. Enlargement of crack tip region.
NUREG/CR-5782 1.g
l l
l ABAQUS 1
N
\
\
l
[ Clad /Dase Interface
\ l 1 i Cladding Base Material N_ _/ N /
T/N_ _/
" ' / N_
\
/ /'7ilGii~7N r N Fig. IA. Further enlargement of crack tip region.
B 1.9 NUREG/CR-5782
800_ - - -
i s
i u
~
n Clad / Base Interface :
700 7 !
- Max Depth Location
}
R 600 [- -
[ ;
.s
~
1
\
m 300 _ _
=
-- r .
J 400 - -"
r '
C '
F 300 .
'g
~ ~
L ,
- O -
m z - ,
200 . _
( :
w= Z ~ ~' [
100h _ : i F
3 - -
t e i I i r I i t t I 1 ! 1 I e a 0 5 10 15 20 25 TIME (min) l Fig.1.5. J-integral values at cach crad tip for a 2-in. subclad flaw, SBLOCA7 transient,0.25-in. cladding.
e b
NUREG/CR-5782 1.10
1 i
r .
l l
800p i L - - 0.50" Subclad Flaw 0.25-in. cladding L - - - - 1.00" Subclad Flaw 700g'
+ --
- 1.50" Subclad Flaw .
- - - - - - ~
600 2.00" Subclad Flaw ----
C -
.5
~
F
+
- S 502 I
. L JIc= 500 ,
.=
1
< - 4 -
3 -
/
p 300 . y
_____+ -
z / -
...v- ...+.wm=.....
w.4.
100 7" , ;;-"" , , ,~;", _ . _ . -: "*" ~-- ~ ~ " " ' - -
g'_,- 'T' , l ;
0 5 10 15 20 25 :
t TIME (min) i Fig I.6 J-values near clad / base interface. 0.25-in. cladding i
i 1
l 1
1 I
I l
1 I
1.11 NUREG/CR-5782 i i
l l
800 !
i !
0.250 in. cladding '
700 -~~
t = 21 min
, t "7c 600 _ [ l
~
C
.c:
JIc= 500 .
i l
T 500 _
.E - -
... ....u j -
p 300 _
Z . .
7 .
e.. . . . . ,e, .a egee...
100 --- -
ac ,1 = 1.65 -
0 O 0.5 1 1.5 2 2.5 SUBCLAD FLAW DEPTII (in.)
Fig. I.7. A 1.65-in. subclad flaw ruptures a 0.25-in. cladding.
NUREG/CR-5782 1.12
800 -
i g !
i .
~
- - 0.33" Subclad Flaw 0.109-in. cladding
~
4-700 -
- - - - 0.55" Subclad Flaw _
i
- 0.78" Subclad Flaw ,
i
- a. 600 ---
l
\
.=
~
2 -
. 500 :
i
- : Jp-= 500 l E-t -
f w ~-
H 300'- -
z-
- ~% :
00 -
-- - ' ~ ' - -
--~~--;'--'-~
'='
+-
100 r .-
=
,- ~,___ _._i.
r---- -
y",
p .**
0~"' , ,
0 5 10 15 20 25 TIME (min)
Fig. I.8. J-values near clad /oase interface,0.109-in. cladding.
1.13 NUREG/CR-5782 l
DIMENSIONS IN INCHES
+ 2.0 + ->- 1.0 . . . . . . . .
)[
1.0D h
CLADDING l BUTTED END h FLAW 3.0 -------.
6.0 8.0 Y
0.10 to 0.30 + +
Y Y
(a) Front (b) Side Fig.1.9. Jo-Block specimen for measuring fracture properties of clading over a subclad flaw.
N1.;' REG /CR-5782 1.14
i l
i 80 ; ; ! !
~
Ultimate stress = 75 ksi _
-+
70 _
0.25 in. cladding l -
t = 21 min I l
$ 60 - - ----
x
~ .
~
if
= 0.9 Flow stress = 49.5 ksi 5 0 [- --' ~ ' ~~ -
U .
C .
40 ~~
~- C ~ ~ ~ - ~' ~~ -~+ "- - - - +--
Yield stress = 35 ksi _
30 '
0 0.5 1 1.5 2 2.5 SUBCLAD FLAW DEPTII (in.)
Fig.1.10. Mises stress in 0.25-in. cladding, t = 21 min.
1.15 NUREG/CR-5782
80 '
Ultimate stress = 75 ksi ;
i d... d .... .u 0.109 in. cladding -
m -
t = 21 min -
6 .
m 60
~ ~ ~ '~~~
j r -
p - .
rr' I 0.9 Flow stress = 49.5 ksi
_ f
- 50 ~ ~
w 9 -
r - -
h 6
-~ ~~
40 Yield stress = 35 ksi! [
30 0 0.5 1 1.5 2 2.5 SUBCLAD FLAW DEPTH (in.)
Fig.1.11. Mises stress in 0.109-in. cladding, t = 21 min.
NUREG/CR-5782 1.16
Appendix J. Analysis of Noncontinous Clad / Base Interface Three-dimensional (3-D) thennoelastic analyses were per- methodology permits the use ofincreased mesh refine-formed to determine the variation in KI values for a ment in the crack-tip region of the model. Loadmg due straight axial flaw in an RPV due to the clad / base inter- to internal pressure was applied on these surfaces in the face gap between the spot welds in the upper plate form of resultant forces derived from a Pr/t stress region, as described in Section 2. The vessel geometry distribution in the hoop direction and Pr/2t stress distri-and material propenies are reponed in Table 1. The load- bution in the axial direction, as shown in Fig. J.l. The ing condition used in these analyses is taken from the through-wall temperature profile (at time = 20 min) from pressure-thennal transient, SBLOCA7, at a time of Fig. A.2, Appendix A, was used to interpolate 20 min from initiation into the transient; the transient is temperatures for the 3-D model.
shown in Fig. A.1, Appendix A.
' Thermoclastic analyses were performed for the 3-D The 3-D finite-element model of a cubic element from a model using the ADINA/ORVIRT2.3 system and the cylinder is shown in Figs. J.1 and J.2. The model con- material properties from Table 1. Three different models sists of 6060 nodes,1148 twenty-nodej isoparametric were analyzed, one containing no flaw (model 1), and the brick elements, and 56 wedge elements at the crack front. second and third containing a 0.25-in.-deep flaw with and
'Ihe gap thickness in Fig. J.2 is taken to be 10 mils. without interface gaps (models 2 and 3 respectively).
Mesh convergence studies in Ref. I for RPV cylinders The through-wall hoop stress distributions from models containing shallow flaws demonstrated that meshes on 1 and 2 are compared with corresponding results from the order of 8700 degrees of fmedom produced converged OCA.P in Fig. J.3. The far-field stresses (away from the crack) for the two models compare well with OCA-P KI values within l'7c. The finite-element model of the cylinder employed in this study has >15,000 degrees of results.
freedom and is estimated to pre"ide comparable accuracy in K 1values. The calculated K1 for model 3 (no interface gap) had a uniform value of 39.3 ksi6 This value is compared Generalized planc-strain boundary conditions were with the K Ivalues generated for model 2 (with interface imposed on the venical surfaces of the model to simulate gap) in Fig. J.4, When the gap was included, the peak deformation restraint consistent with that found in an KI value increased by 0.5% at the spot weld and RPV shell.1.c., plane surfaces remain planc. This decreased by 137c between the spot welds.
References
- 1. D. G. Ball et al., Martin Marietta Energy Systems, 3. B. R. Bass and J. W. Bryson, Union Carbide Corp.,
Inc.. Oak Ridge National Lab., Stress Intensity Nuclear Div., Oak Ridge National Lab.,
Factor Influence Coefficientsfor Surface Flaws in Applications of Energy Release Rate Technique to Pressure Vessels, NUREG/CR-3723 (ORNL. Part-Through Cracks in Plates and Cylinders, Volume 2. OR17RT: A Finite Element Programfor CSDfTM-216), Oak Ridge, Tenn., February 1985.a Energy Release Rate Calculationsfor 2- <
Dimensional and 3-Dimensional Crack Mcdels,
- 2. K. J. Bathe, ADINA - A Finite Element Program for Automatic Dynamic Incremental Nonlinear NUREGICR-2997/ Volume 2 (ORNLfrM-Analysis, Report A-1, Massachusetts Institute of 8527/V2), February 1983.b Technology, Cambridge,1984.b aAvailable for purchase from GPO Sales Program.
bAvailable for purchase from orFanization sponsoring publication cited. and/or authors and/or recipients (documented letters).
J.1 NUREG/CR-5782 l
Pr/2t (AXIAL)
A i
Pr/t 7 ' s_
i (HOOP) y\ h_ _
^
i i
SN s
l 1
,_._ s\ _ _.- - - __1
' s s N ~
LJ u 7.875
'l l (l %. m t b-- ~w==---
=- --'____ _ ; = .- - x ~
- - ~
i O*8
,o $h;'55 l l%,w ~= ! l l l .__-
l J l
ui k I zngn am i 7; , r e, ! !
1 .
i w l_ -
Q ]
__ i_
~
.V-h' ,,'?l$llY I
'%s
- l ,ll$
mm, ,
0.665 (dimensions in inches)
Fig. J.1 Schematic showing a portion of an RPV with a flaw which is modeled using finite-element techniques.
i f
y -fl
/
o., d{
f N ' \ I f 0.ss i >
j l
7 Y y,^gCK
\ '
\/E D '
\
\
\hdf\\
i b
\ \ \
\
\ '\ \ l'N \ l
\\\\\\ \
\\\\ \ \\\\d . ,Il (dimensions in inches)
Fig. J.2. Detail of the finite-element model showing the gap interface.
J.3 NUREG/CR-5782
9 O-e 9 OCA-P i C- i t.O !
- ~~ ADINA (NO CRACK) .!
- -- ADINA (CR ACK, GAP) 9 .
s.
. ., *o - ', ..
- - ; '.. t
.x. .
~. .
~.
u, en a.
'N s ,
r,,j a _ s, ,
e2r ,
f** '.,
tn ,
c_ ,
R we
~.
-d~ ' ,,,~*~, .,,.,
o.
R,-
k o
a 1
? , e , i i 6 5 0.0 1.0 2.0 3.0 4.0 5.0 5.0 7.0 R (Ln) t 5
6 Fig.13. Hoop stress distribution for OCA-P and ADINA analyses (SBLOCA7 tmnsient, t = 20 min).
t NUREGER-5782 J.4
i l
i, l
! l CLAD LAYER I SPOT '
i -
WELD ! i ! ! I i L I i ! ! l l l I l 1 l
( GAP CRACK TIP t
j i l
el ! j , .
01 ! i l I i
- J
_ql (NO GAP) q ;n -
x...,.... . ........... .... .......................... ......
j
.a .j ; -
(WITH GAP)
L) lo 6-x r i
9i E 1 c
Fj i
- .c :. c.2 :i.3 0.4 c.s c.s c'.7 d.e x t . r. )
Fig.J.4. Distribution of K values 1 for finite-element models with and without interface gap.
J.5 NUREG/CR.5782 l
NUREG/CR-5782 i ORNL/TM-11945 I Dist. Category RF Internal Distribution
- 1. B. R. Bass 51. R. K. Nanstad 9-16. J. W. Bryson 52. D. J. Naus l-
- 17. E. W. Carver 53. C. B. Oland 18-25. R. D. Cheverton 54-58. W. E. Pennell '
- 26. J. A. Clinard 59. C. E. Pugh
- 27. J, M. Corum _60-67. D. K. M. Shum
- 28. W. R. Corwin 68. Cynthia Southmayd 29-38. T. L. Dickson 69. T. J. Theiss ;
- 39. J. E. Jones Jr. 70. ORNL Patent Section 40-17. J. A. Keeney 71. Central Research Library
- 48. W.J. McAfee 72. Document Reference Section
- 49. D. E. McCabe 73-74 Laboratory Records
- 50. J. G. Merkte 75. Laboratory Records (RC)
External Distribution
- 76. L. C. Shao, Director, Division of Engineering, U.S. Nuclear Regulatory Commission
- 77. C. Z. Serpan, Jr., Division of Engineering, U.S. Nuclear Regulatory Commission 78-79. S. N. M. Malik, Division of Engineering, U.S. Nuclear Regulatory Commission
- 80. M. E. Mayfield, Division of Engineering, U.S. Nuclear Regulatory Commission
- 81. A. Taboada, Division of Engincenng, U.S. Nuclear Regulatory Commission l
- 82. D. P. Bozarth, Science Applications International Corporation. 708 S. Illmois Ave., Oak Ridge, TN 37830
- 83. J. W. Minarick, Science Applications Intemational Corporation,708 S. Illinois Ave., Oak Ridge, TN 37830
- 84. F. A. Simonen, Pacific Northwest Laboratories, P. O. Box 999, Richland, WA 99352
Rockville, MD 20852
- 86. K. A. Williams, Science Applications International Corporation, 2109 Air Park Rd., SE, Albuquerque, NM 87106 *
- 87. Commander and Director, US AE Waterways Experiment Station, Attn: CEWES-lM-MI-R, Alfrieda S. Clark, CD '
Dept /#1072,3909 Halls Ferry Road Vicksburg, MS 39180-6199
- 88. Office of Assistant Manager for Energy Research and Development, DOE-ORO, Oak Ridge,TN 37831 89-90. Office of ScientiGc and TechnicalInformation, P. O. Box 62, Oak Ridge, TN 37831 l
t I
L i
I
?
I l
)
U.S. NUCLE AR REGULATORY CoMMISSloN 1, REPORT NUMBER NRC Fonu 335 (Assigned try NRC. Add Vol., Supp., Rev.,
(249, and Addendum Numters,if any.)
NRCfA 1102, m:232 BIBLIOGRAPHIC DATA SHEET NUREG/CR-5782 (se, m,m,a.cns on ene enese! ORNL/TM-11945 2, TITLE At o SUbTIT LE Pressurized Thermal Shock Probabilistic Fracture Mechanics Sensitivity Analysis for Yankee Rowe 3. DATE REPORT PueL SHED uom vtan Reactor Pressure Vessel l August 1993
- 4. FIN oR GRANT NUMBER B0119
- 5. AUTHOR (Si 6. TYPE OF REPORT T. L. Dickson, R. D. Cheverton, J. W. Bryson, B. R. Bass, D. K. M. Shum, J. A. Keeney Technical
- 6. ,,.me .mnaMING
,oomaoRGANIZ AT loN - N AME AND ADDR ESS tar n,RC. prorror Dornoon. orr t or nenson. v.1 Nuciear eepurotary commussion. enst maarme m Oak Ridge National Laboratory Oak Ridge, TN 37831-6285 EspoNsoRxNG ORGANnzrTuoN - N AMe ANo soonEss iir nec evve s.me s uv ez aconrrector orova unc o,,>soon. orreca er neeson. v s. nacie.o eeousarorv comm-on.
ana mawn, aweso Division of EngineerinF Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001
- 10. SUPPLEME NT ARY NOTES
mechanics (PFM) sensitivity analysis for the Yankee Rowe reactor pressure vessel, for l the fluences correspondin;; to the end of operating cycle 22, using a specific snall- !
break-loss-of-coolant transient as the loading condition. Regions of the vessel with distinguishing features uere to be treated individually - upper axial weld, lower axial weld. circumferential weld, upper plate spot uelds. upper plate regions betueen the spot !
welds, lower plate spot welds, and the lower plate regions between the spot velds. The i fracture analysis methods used in the analysis of through-clad surface flaws were those contained in the established OCA-P computer code, which was developed during the Inte-grated Pressurized Thermal Shock (IPTS) Program. The NRC request specified that the OCA-P code be enahneed for this study to also calculate the conditional probabilities of failure for subclad flaws and embedded flaws. The results of this sensitivity analysis provide the NRC with (1) data that could be used to assess the relative influence of a number of key input parameters in the Yankee Rowe PTS analysis and (2) data that can be used for readily deternining the probability of vessel failure once a more accurate in-dication of vessel embrittlement becomes available. This report is designated as HSST report No. 117.
- u. n t v woRos, oEsum ors a., oros o,,a, e. ,n,r .m ,uor m-cam ioc.ne, rne ,c,ma u avan.uma o o anuoa Pressurized Ther=al Shock Unlimited
- 14. $k CUMI T r LL A%t F 8LA f turw Integrated Pressurized Thermal Shock (This Paget Keactor Pressure Vessels Unclassified iankee Rowe m . eas,ani Probabilistic Fracture Mechanics Unclassified 1b. NUMBER of PAGEL
- 16. FRICE NRC FORu 335 Q49)
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- WASHINGTON, D.C. - 20555-0001 ussac FTRMIT NO. G 67 ,
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