ML19249C498

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Octavia Computer Code:Pwr Reactor Pressure Vessel Failure Probabilities Due to Operationally Caused Pressure Transients
ML19249C498
Person / Time
Issue date: 03/31/1978
From: Goldberg F, Lynn E, Vesely W
NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
To:
References
NUREG-0258, NUREG-258, NUDOCS 7909120305
Download: ML19249C498 (49)
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{{#Wiki_filter:NUREG-0258 THE OCTAVIA COMPUTER CODE: PWR REACTOR PRESSURE VESSEL FAILURE PROBABILITIES DUE TO OPERATIONALLY CAUSED PRESSURE TRANSIENTS I W. E. Vesely E. K. Lynn F. F. Goldberg ec p oq, ~ i,,, I'} ~5)},,v{.I tT (m / r ry p na p p,q p r ,ohn Office of Nuclear Regulatory Research U. S. Nuclear Regulatory Commission ~/ 29 0Ci , x ' ',

Available from National Technical Information Service Springfield, Virginia 22161 Price: Printed Copy $4.50, Microfiche $3.00 The price of this document for requesters outside of the North American Continent can be obtained fron the National Technical Information Service. ,ac'Q ., 5 k, i emi \\ J '~ i s ) - 3 s l L w? l.

NUREG-0258 R1 THE OCTAVIA COMPUTER CODE: PWR REACTOR PRESSURE VESSEL FAILURE PROBABILITES DUE TO OPERATIONALLY CAUSED PRESSURE TRANSIENTS W. E. Vesely E.K.Lynn F. F. Goldberg Manuscript Completed: March 1978 Date Published: March 1978 Probabilistic Analysis Staff and Metallurgy & Materials Research Branch Office of Nuclear Regulatory Research U. S. Nuclear Regulatory Commission Washington, D. C. 20555 ~j ; O nn! /L / ULJ

ABSTR/CT The 1.T AVI A computer code tias been developed to calculate the prcbability of pressure vessel faii from operationally caused pressure-transients which can occur in Pressurized Water Reactors. The analysis approach involves calculation of vessel failure reessures using frac-ture mechanics methods and estim3 tion of pressure-t ransient characteristics using historical nt. clear data. Any of the parameters in the code can t>e modified f or sensitivity analyses. The Surry 1 pressure vessel is analyzed as an (xample problem to demcastrate the code's capabilities. .s I 3 l 1 I f i L. / UU' i

TABLE OF CONTENTS Page Chapter I A. CALCULATIONAL TECHNIQUES. 1 1. GENERAL APPRCACH. 1 2. FAILURE PRESSURE CALCULATIONS. 2 3. FAILURE PROBABILITY EVALUATIONS. 4 B. INPUT ')ESCRIPTION. I 1. !NTRODUCTION. 4 2.

ASES.

4 3. DATA GROUPS. 4 3.1 Data Group 1: TITLE. 5

3. 2 Data Group 2: CCNSTANTS.

6

3. 3 Data Group 3: TEMPERATURES.

8 3.4 Data Group 4: FLUENCES. 8 3.5 Data Group 5: FLAW SIZES. 3.6 Data Group 6: TCUGHNESS (Optional). 10 10 3.7 Data Group 7: RUN. 13 4. CHANGE CASES. 14 C. SAMPLE PR09LEM. 14 1. INPUT. 15 2. PRINTED CUTPUT. 18 3. GRAPHIC OUTPUT. 35 APPENDIX I - FAILURE PRESSURE ANALYlICAL METHODCLOGY. 39 APPENDIX II - STATISTICAL EVALUATIONS. l -/ Q 9 iii

LIST OF TABLES Table Number Page 8-1 Data Group 1 - TITLE. 5 8-2 Data Group 2 - CONSTANTS. 6 B-3 Data Group 3 - TEMPERATURES. 7 B-4 Data Group 4 - FLUENCES. 8 8-5 Data Group 5 - FLAW SIZES. 9 B-6 Data Group 6 - TOUGHNESS. 10 B-7 Description of Output Tables. 11 B-8 Data Group 7 - RUN. 13 II-1 Major Pressure Transient incidents. 40 II-2 Empirical Distribution Tabulations. 41 o, c '. U 6 / ,s iv

LIST OF FIGURES Page Fiqure Number 14 C-1 Listing of nput for Sample Run. 16 C-2 Output Listing of OCTAVIA Input. C-3 Run Data Group - Outcome Pequest 1. 15 17 C-4 Failurc Pressures for a Half Inch Flaw. 18 C-5 Run Data Group - Output Request 2. C-6 Failure Probabilities for Best Estimate Occurrence 19 Rates Summed Over All F'aw 5izes. C-7 Failure Probabilities for Best Estimate Occurrence 20 Rates for a Half Intn Flaw. C-8 Failure Proabilities for 95% Upper Bound Occurrence Rates Summed Over All Flaw Sizes. 21 C-9 Failure Probabilities for 95% Upper Bound 22 Occurrence Rates for a Half Inch Flaw. 24 C-10 Failure Pressure vs. Temperature. C-11 Failure Pressure vs. Fluence. 25 C-12 Best Estimate failure Probability vs. Temperature. 26 C-13 Best Estimate Failure Probability vs. Fluence. 27 C-14 Best Ectimate Failure Probability vs. Temperature. 28 C-15 Best Estimate Failure Probability vs. Fluence. 29 30 C-16 95% Bound failure Probability vs. Temperature. 31 C-17 95% Bound Failure Probability vs. Fluence. C-18 95% Bound failure Probability vs. Temperature. 32 C-19 95% Bound Failure Probability vs. Fluence. 33 I-l The Four Regimes for Pressure vs Temperature. 35 36 I-2 Stress vs. Strain Relationship. 39 11-1 Empirical Probability Plot. V< / v

1 A. CALCULATICN TECHNIQUES 1. GENERAL APPROACH The OCTAVIA computer code has bean developed to calculate the probability of pressure vessel failure from operationally caused pressure-transients which can occur in a Pressurized Water A given PWR pressure vessel is first described by inputting the vessel char-Reactor (PWR). acteristic, and operating environment characteristics. For the given vessel and environment, for different-sized OCT AVI A then computes the f ailure pressure at which the vessel will f ail flaws axisting in the beltlin-Only axially oriented flaws in the vessel beltline are considered. Having calculated the vessel failure pressure fnr a given flaw size, the OCTAVIA code then The prob-calculates the probability of vessel failure per reactor year due to the flaw. ability of vessel failure is the product of two factors; the probability that the maximum-sized flaw in the beltline is of the given size, and the probability that the transient will occur and will have a pressure exceeding the vessel failure pressure associated with the flaw sizes to obtain The orobabilities of vessel failure are summed over the various flaw size. the total vessel failure probability. The vesse' failure probabilities can be printed or plotted for different fluences and tempera-The failure pressures for the different flaw sizes can also be cutput and the relative tures. importan e of the flaws can be obtained. The user can override any parameter values used in ilities. Sensitivity studies the code, such as the values for the different flaw size prob can also be easily performed to investigate difterent vessel or sperating characteristics in the same computer run. 2. FAILUf PRES 5URE CALCULATIONS The pressure vessel is first described by inputting a set of vessel and ope ating characteris-characteristics include the vessel wall thickress, inside radius, copper tics. The vessel Additional failure characteristics which are input include content, and phosphorus content initial RTgg7, yield strength, the residual stress, flaw sizes, the flaw depth-to-length rati_, ultimate strength, and stable crack growth percentage. An upper limit on the toughness attainable by the vessel material may also be input. The operating characteristics include the fluence and actual temperature. IOCTAVIA is an acronym for Operationally Caused Transit :ts And vessel Integrity Analysis. 72) OUS

2 j.. jo jo The flaw sizes (flaw depths) considered are ",, d 3", and failure pressures 8'4'2, are computed for flaws of each size existing in the vessel beltline. For a given flaw, the failure pressure is computed using linear-clastic and elastic plastic methods. The failure pressure calculation can lie in one of four regions depending on the temperature: a linear-elastic regime, a gross yield plateau, an elastic plastic regime, and tne upper shelf plastic instability regir.e. The failure pressure calculations are essential'y those of ORNL-TM-5090 [1] and are further describet. in Appendix I. In the failure pressure calculations, a best fit curve is ustd for tough e n g g ) versus temperature; the basic data for this fit are cbtained from tne HSST program [2]. At the user's request, the OCTAVIA code will print or plot a two-dimensional table of failure pressure versus temperature and fluence for a given flaw size. Using the change case options in OCTAVIA, the u,er can also analyze one or more vessels or dif ferent vessel characteristics in the same computer run. 3. FAILURE PROBABILITY EVALUATIONS Having calculated the failure pressure for a given flaw size, the probability evaluation is next performed. First a probability P is assigned that the maximum-sized flaw in the vessel S is of the given size; only discrete flaw sizes are considered. The probability P is then T computed that an operational transient will occur, per reactor year, and have a pressure exceeding the failure pressure essociated with the flaw, e product of probabilities P xP g T is then the probability per reactor year that the pressure vessel will f ail from the particular size flaw. The probabilities for the different flaw sizes are then summed to cbtain the total probability of pressure vessel failure from the various flaws which might exist in the vessel. Based on operational information and discuss'ons with metallurgical person.el, the OCTAVIA code uses the following values of P ; g Flaw size 5 (inches) P g 1 g .25 1 4 .125 f .025 I .0025 2 .00025 3 .000025 y I ' ; ; '- l j dv e

3 Since the flaw size probabilities P are discrete, they apply to a range of flaw sizes g about the given reference point, i.e., P f r S = 1" is the probability that a flaw between S 3,. j. ju y and 1 y exists. The flaw size probabilitv for g applies to sizes from approximately 0 to T6 and the flaw size probability for 3" applies to sizes larger than approximately jo jn Evaluations have shown that flaw sizes smaller than approximately I6 '"9'" 2 7 than approximately 3 y make insignificant contributions to the vessel failure probability. The flaw size probabilities P aprly to vessels at the end of their life (s 40 yrs) and c are conservative for new vesself If the user feels he has more appropriate values of and input his own values. P, he can override the code's values of Pg g The probability P that a transient will occur and have a pressure exceeding the faiiure T pressure is computed using the formula P * ^ **P (~IP -800)/P) T i where A is the occurrence rate, per reactor year, of pressure-transients having pressures exceeding 800 psi; p, is the failure pressure for the given flaw size; and P+800 is the average maximum pressure associated with the transient. The above formula is based on statistical analyses of historical transient data as described in Appendix II. The formula is limited to failure pressures above 800 psi. Based on these statistical analyses, the OCTAVIA code uses values of A = 0.080 per year and P = 440 psi for best estimate (median) evaluations. The upper 95% confidence bound for is 0.136 per year and the upper 95% confidence bound for P is 806 psi. These 95% A values are used to obtain approximate 951, bounds on the vessel f ailure probability. The user can override these values of A and P and input his own if he so desires; different functions fo,- P can also be incorporated into the code if deemed more appropriate. T The formula for P is based on recorded transient pressures which range fron 8C0 psi to T 3326 psi. When the failure pressure p is much larger than 3000 psi, say 4000 psi or g greater, there will be large uncertainties in the failure probabilities due to the large extrapolations of pressure involved. Examination of the tables of tailure pressures cf the contributing flaw sizes is useful in determinirq the amount of pressure extrapolation involved The 95% confidence bounds incorporate the extrapolation ncertaint'es and hence also reflect the " hardness" of the calculated probabilities. tiigh confidence bounds do not necessarily mean that the actual probability is high but only that the evaluation technig s is highly uncertain. T, summed over the different flaw sizes, are finally printed x P The failure probabilities P g or plotted as the total vessel failure probability. The individail flow size contribut:,ns are also printed or plotted if desired. The code will terriinate the run unless change cases are irput, whereupon the cnde will repea; all the calculations for the different vessel and operating characteristics input. 2The PS values can also be interpreted as the expected numter of maximum-sized flaws of the given size. Because the P values are small, expected values and probabilities of one q flaw existing are, within the accuracies of the estimates, numerically the same. [ d

4 B. INPUT DESCRIPTION 1. INTRODUCTION The input to DCTAVIA consists of data describing the particular vessels and operating environ-me.its to be studied and the output options to be exercised. The data are subdivided into cases, several of which may be executed in a single OCTAVIA run. 2. CASES An OCTAVIA run consists of one or more cases. A case is descriFed by the following data: Constants describing the physical t tracteristics of the pressure vessel. Temperstures at whic;. failure pressures are to be computed. Fluences at which failure pressures,re to be computed. Flaw sizes at wh':h failure pressures are to be computed. Titles, prirt, and plot options. The data input schtme o,.uws a simple method for running multiple cases whereby only those data which dif fer from the previous case need be er.tered. The program terminates when no further cases are detected in the input stream. 3. DATA GROUPS Cases are described by 7 sets of data cards which we will call " data groups." Each data group consists of a kervord card which identifies the data group, and 1 or more additional cards. Only the first four characters of the keyward need be entered for proper identification of the data group. The seven data groups are described below. 3.1 Data Group 1: TITLE This data group specifies the title for the case to be run. It consists of a keyword card beginr:ing wi tl: the characters "IITL" followed by 2 cards of text (one or both may be blank) to appear as a header on ? printed and/or plotted output for the case. The TITLE data group is depicted in Table B-1. i, nj*1 /G-U,

5 C U tL tMtstd, 1976 B LASL 1 - FM AY POWER PLA.4T [TilLE A CARD PROGRAM TYPE COLUMNS VARIABLE FORMAT DESCRIPTION A 1-4 AKEY A4 Keyword "TITL" B l-80 TITLEl 20A4 First title card C 1-80 TITLE 2 20A4 Second title card TABLE B-1. Data Group 1 - TITLE 3.2 Data Group 2: CONSTANTS It This data group describes the physical characteristics of the reactor pressure vessel. consists of a keyword card beginning with the characters " CONS" followed by 2 cards containing the following constants: - ASP Flaw depth to length natio - TH Reactor pressure vessel (RPV) wall thickness (inches) - RI RPV inside radius (inches) RI Initial RT OT (F ) - CU Percent copper content - PH Percent phosphorous content - Su Ultimate strength (ksi~j - SCC Stable cr ack growth (%/100) - TUFLIM An upper limit on the toughress attainable by the vessel (ksi) (leave t, lank if no limit) The CONSTANTS data group is depict ' in Table B-2. q o 3,, - i

6 6 0.106o7 /. >$ 7 3 73.5 9.0 U.2b U.Ull d7.0 U.2 A Le%I Aa b CARD PROC 4M TiPE LOLUMNS VARIABLE FORMAT DESCRIPTION A 1-4 AKEY A4 Keyword " CON 5" B l-10 ASP F10.0 Flaw depth to length ratio 11-20 TH FlC ' RPV wall thickness (inches) 21-30 RI F10.0 RPV inside radius (inches) 31-40 RT F10.0 Initial RTNDT (F ) 41-30 CU F10.0 % copper ccntent 51-60 PH F10.0 % phosphorous content 61-70 SU F10.0 Ultimate strength (ksi) 71-FD SCG F10.00 Stable crack growth (%I00) C 1-10 TUFLIM F10.0 Upper limit on the tough-ness attainable of the vessel (leave blank if no limit) TABLE B-2. D a '. Group 2 - CCNSTANTS

3. 3 Data Group 3: TEP?ERATURES This data group specifie. the temperatures at which failure pressures are to be computed.

The iEMFERATURE, data group is identified by a xeyword card beginning with the characters "lEMP.' This cird must be followed by a card containing the following data: - NT Tre number of temperatares - T5 TART The startir a temperature - TINC The te%oratur e increment - TMM The maximtli temperature If NT is less than zero, T5TARI. TINC, and IMAX are icnored; a^d the program uses the 95% Icwer beund, median, and 951 upper Lound i Mperatures. No further teTperature cards are required in this case. 3 The 95% lower baund, median, and 95% upper bound teneratures were computed based on a statistical an31; sis of recorded operating vessel temperatures. See NRC internal memorandum from James W. Johnson to W. E. Vesely- "fhe W Test for Narmality of the Logarithms of Vessel Tempe ra tures,' May 26, 19/l. / t : j) J I e/ t i

7 If NT is zero, the program generates temperatures at increments of TINC beginning at T5 TART and ending with the first temperature to equal or exceed TMAX (up to 100 temperatures are allowed). No further temperature cards are required in this case. If P- ~. 5 greater than zero, TSTART, TINC, and TMAX are ignored; and the pronram expects NT temperatures to be input on the succeading card (s), 16 temperatures per card, up to a maximum of 100 emperatures. All temperatures are in degrees Fahrenheit. The TEMPERATURES data group is depicted in Table B-3. C 'Ivu. 11u. 125. 135. d 4 A I L.iPE R AT JR E S CARD PROGRAM TYPE COLUMNS VARIABLE FCRMAT DESCRIPTION A 1-4 AKEY A4 Keyword " TEMP" B l-5 NT* 15 Number of temperatures (ma=imum=100) 6-10 TSTART F5.0 5 tarting temperature 11-15 TINC F5.0 Temperature increment 16-20 TMAX FS.C Maximum temperature C 1-80 T(K) 16F5.0 Temperatures (use as many cards as required when NT > 0)

  • if NT =

-1, the 95% lower cound, median, and 95% upper bound temperatures are used, and TSTART, TINC, and TMAX 6re ignored. If NT = 0, the program generates temperatures at increments of TINC, start ng at TSTART, ~ up to TMAX. If NT 0, TST ART, TINC, and TMAX are ig:ored, and NT temperatures (T(K), K = 1 tu NT) are read from the Tyne "C" card;(s). TABLE B-3 O sta Group 3 - TEMPERATURES O.

8 3.4 Data Group 4: FLUENCES This data group specifies the fluences for which failure pressures are to be computed. It is identified by a keyword card beginning with the characters " FLUE." Af ter the keyword cird, a card with the number of fluences, NFL, is required. This card may also contain the fluence to reactor age conversion factor AGECON. After the NFL card, the program expects NFL fluences in units of neutrons per certimeter squared (n/cm ) to te input on the succeeding card (s), 8 fluences per card, up to a maxieum of 12 fluences. If a non-zero value is entered for the constant AGECON, fluence is converted to t5e age of the vessel on all of the output according to the fo mula: vessel age (years) = AGECON

  • fluence The FLUENCES data group is depicted in Table B-4.

C %.JJE13 o 00Ela 3 4 A ELUE' ICES CARD PROGRA4 TYPE COLUMN 5 VARIABLE FORMAT DESCRIPTICN A l-4 AREY A4 keyword " FLUE" B l-5 NFL IS Numter of fluences (maximum = 12) 6-15 ACECOs F10.0 fluence to age con-version factor (opticnal) C l-80 ft(J) 8F10.0 Fluences (use 1 or 2 cards as required) TABLE E _4 Data G cup 4 - FLUENCES 3.5 Data Group 5: FLAW SilE5 This data group specifies the flaw sizes for which failure pressures are to Le computed. It is identified by a keyword card Leg)nnin.j uith tt" . ha r.!c t er: " FLAW After the keyword card, a card with the number of flaw sizes, NA, i s rec,ui red. If NA is zero the program uses th> follo ing defaalt data: ') j i, L) e .)

9 SQUARE ROOT OF THE RESIDUAL FLAW FLAW SIZE SIZE (INCHES) PRCBABILITY MODULUS RATIO STRESS I A(I) EF(I) ER(I) RESID(I) 1 0.125 .25 .116

0. s 2

0.25 .125 .222 0.0 3 0.50 .025 .430 0.0 4 1.00 .0025 .840 0.0 5 2.00 .00025 1.550 0.0 6 3.00 .000025 2.130 0.0 The number of flaw sizes, NA, is set to 6. If NA is greater than zero, the program expects NA additional cards. Each of these cards must contain a flaw size in inches and corresponding EF, ER, and RESID (flaw size probability, square roct of the modulus ratio, and residual stress). If EF and/or ER are left blank and the flaw si2e is or,e of the 6 listed above, the program will supply the corresponding EF and/or ER. If no residual stress is input, zero stress is assumed. The FLAW SIZE data group is depicted in Table B-5. 2.0 C 1.5 U.U50 1.25 3 4 A FLAW SIZE 5 CARD FROGRAM TYPE COLUMNS VARIABLE FORMAT DESCRIPTION A 1-4 A%EY A4 Ke yword "F LAW" B l-5 NA IS Number of flaw sizes (maximum =8) if NA-0, 6 default flaw sizes are used and no additional cards are needed C 1-10 A(I) F10.0 Flaw size 11-20 EF(I) F10.0 Flaw size probability 21-30 ER(I) F10.0 Square root of tF. modulus ratio 31-40 RESID(I) F10.0 Residual stress (ksi) Note: If EF(I) and/or ER(I) are left blank on card type C, and A(I) is one of the 6 default flaw sizes (.125,.25, .5, 1.0, 2.0, or 3.0), then the EF(I) and/or ER(I) are set to the default values for the given flaw size. TABLE B-5 l- [)' '\\ v Data Group 5 - FLAW SIZE 5 ,^ I' i-o

10 3.6 Data Group 6: TOUGi; NESS (Optional) This data group specifies the toughness fur mtion to be used. It is ideitified by a keyword card beginning with the characters "TOUG." After the keyword card, a (ard with the toughness function identifier, ITOUGH, is required. The value of ITOUGH specif.es the toughness func-tion to be used as indicated in the table below. ITOUGH Toughness Function 0 best estimate toughness I lower 95% bound on toughness 2 upper 95% bound on toughness If the TOUGHNESS data group is omitted entirely, the best estimate toughness function is used. The TOUGHNESS data group is depicted in Table B-6. B / fT00GitNESS A CARD PROGRAM TYPE COLUMNS VARIABLE FORMAT DESCRIPTION A 1-4 AKEY A4 keyword "TOUG" B l-5 ITOUGH* IS Toughness function identifier a If ITOUGH = 0, best estimate toughness is used. If ITOUGH = 1, lower 95% bound on toughness is used. If ITOUGH = 2, upper 95% bound on toughness is used. TABLE B-6 Data Group 6 - TOUGHNESS

3. 7 Data Group 7: RUN This data group defines the parameters of the failure probability function (s), A exp[-(p-800)/p],

selects the output to be printed and/or plotted, and causes the case to be executed. The other 6 data groups must be input (in any order) before the RUN data group. The RUN data group is identified by a keyword card beginning with the characters "RUN." After the keyword card, a card containing the number of output requests NREQ, must be input. The program then expects NREQ cards, each containing the following data: - FREQ Failure occurrence rate, A (per.2ar) - SCALE Average pressure minus 800, p (rsi) - ICUT Output set type (see Table B-7' r V!/

ll 0 - An output ,le containing the som of the icilure probabilities over all flaw sizes will be computed, 1 - Output tables containing the failure probabilities fc# individual flaw sizes will be computed. These failure prcbabilities include the flaw size probability. 2 - Same as 1 except the flaw size probability is not included. 3 - Output table containing the percent contributions of individual flaw sizes to the sum of prcbabilities over all fla sizes wilI be computed. 4 - Output tables containing the f3ilure pr ssures for individual flaw sizes w!ll be ccmputed 5 - An cutput table showing the shift in RT e o NDT fluerce for each flaw size and fluence is ccmputed. Output Number of Number of NuTLer of value of Table. E-try Set Tables Rows ir Cel e s in Type Computed Each Table Each T3ble 0 1 1 per temperature I cer faiture probability at a part cu;ar temperature and i until upper shelt fluence or toughness limit fluence summed over all flaw sizes is reached in all columns for all fla. sizes 1 1 per 1 per temperature 1 per Failure probabilitj for a flaw until upper shelf fluence p3rticular terperatare, flLence size or toughness limit and flaw size (including flaw is rached in all prehaLility) columns 2 1 per 1 per semperature 1 per Failuro probability (nct includ-flew until upper shelf fluence inq flaw probability) for a size cr tou';hnest limit particular temperature, fluence, is reacted in ai, and flaw size columns 3 1 per 1 per temperature I per Percent contribution of a single flaw until upper shelf fluenca flaw size to the total failure size or tcur;hness limit prcrability far a particular is reached in all temperature and flucoce Columns 4 1 per 1 per temperature 1 per failuro pressure for a particulir flaw until upper shelf or fluence temperature, fluence, and flaw size size toughness is reached in all columns 5 1 1 per flaw size 1 per Shift in RINDT due to fluence fluence ll N -TABLE E-i-t_ U i v Cescription of Output Tables

12 - IPRINT Printed output option 0 - The tables computed for this output set are printed 1 - Printed output is suppressed - IPLOT Graphic output option 0 - Plots are suppressed 1 - The columns of the output tables are plotted (one plot per table) 2 - The rows nf the output tables are plotted (one plot per table) 3 - Both the rows and columns of the output tables are plotted (two plots per table) Options 2 and 3 for IPLOT are invalid when a single fluence is run; and pl-ts may not be produced when 10UT=5 - TITLE 3 Title describing the failure probability function (optional). In terms of the mnemonic symobls FREQ and SCALE, the failure probability is computed according to the form la: PROB = FREQ

  • e(-(p-800)/ SCALE) where PRCB is the probability of exceeding the failure pressure p.

Three "special" values for FREQ have the following meaning: FREQ = 0.0 Failure pressures only are computed and output. FREQ =-1.0 The code's best estimate values for FREQ and SCALE are used (FREQ =.08, SCALE = 440). FREQ =-2.0 The code's 95% upper bound values for FREQ and SCALE are used (FREQ = 1.36, SCALE = 806). When pressures only (FREQ = 0) are compu.ed, the output set type (IOUT) is always set to 4. When probabilities are computed (FREQ / 0.0), the cutput set type may be 0, 1, 2, or 3. When the output set type is 5, FREQ and SCALE are ignored. TITIE3 is automatically set by the program when the special values (0.0, -1.0, or -2.0) are input for FREQ. The RUN data group is depicted in Table B-8. '. j' i L - V l /

13 -2.0 0 0 1 C r.1.0 0 0 1 0.0 4 0 0 B 3 A R"" CARD PROGRAM TYPE COLUMNS VARIABLE FORK' T DESCRIPTION A 1-4 AKEY A4 Keyword "RUN" B l-5 NREQ IS Number of output requests C 1-5 FREQ F 5. 0 Frequency (G) 6-10 SCALE F5.0 Scale (P) 11-15 IOUT IS Output request type (0, 1, 2, 3, 4, or 5) 16-20 IPRINT 15 Print option (0 print, 1-suppress) 21-25 IPLOT 15 Plot option (0-no plots, 1-temperature, 2-fluence, 3-both) 26-80 TITLE 3 13A4, A3 Notes: If FRE0=0, pressures only are computed, SCALE and TITLE 3 should be left blank, and 10VT-4. If FREQ=-1, best estimate parameters are supplied by the program, SCALE and TITLE 3 should be left blank, and 100T=0, 1, 2, or 3. If FREQ=-2, 95% upper bound parameters are suppl ied by the program, SCALE and TITLE 3 should be left blank, and 10UT=0, 1, 2, or 3. If 10VT=5, FREQ, SCALE, and IPLOT are ignored. TABLE B-8 Data G.oup 7 - RUN 4. CHA';E CASES All data groups (except RUN) remain in effect until they are changed. To run change cases, simply mou'fy the data by re-inputting the appropriate data groups and follow these modifica-tions by another RUN data group. .s /_ vJ

14 C. SAMPLE PROBLEM This section discusses the use of the OCTAVIA code to run a sample problem. The sample problem involves an example analysis of the Surry 1 pressure vessel. 1 INPUT The following characteristics will be used to describe the pressure vessel: flaw depth-to-length ratio 1/6 (.16667) wall thickness (inches) 7.875 inside radius (inches) 78.5 initial RTNDT ( ) 9.0 % copper content .25 % phosphorous content .011 ultimate strength (ksi) 87.0 stable crack growth (%/100)

0. 2 upper limit on the toughness attainable blank (unlimited) by the vessel beltline material For this prcblem failure probabilities and fail re pressures are desired for temperatures from 40 to 200 at 10 intervals and for 11 input fluences using the 6 default flaw sizes.

A listing of the OCTAVI A input required to run this problem is shown in Figure C-1. TITL. J'J CL EA ? .Azr), i' i ~ ? F.- vo' -?nt- 's I Ty Lys!; qL 's N a ^J r' I C -~ 3; J C L t. ' " , _a" ny W E,.1 .t A 72 CO C T.\\ :.T ; .16667 7.;73 n_

.?t

_111 27_s T r3: e f o A! L 4 _ 4u.

10. 2 5LUL7 5 11 0.1 1.1172-1; - -

.41 .'f' -1' n. '?- 1_ ; 7 c - 1 '- 3. 7 5 '.1 ' 7,55 1 1.5;f17 3.0CE11

1 )

FLAW lIZES 3 rJ1 5 0.0 4 -1.7 0 -1.0 1 3 -2.0 1 -2.0 i - '.J w Figure C-1 I P 0 0 R B1 R15 L Listing of Input for Sample Run II i

15 2. PRINTED OUTPUT The printed output produced by the OCTAVIA program has two parts: a printout of the input data and a printout of output requests from data group RUN. Figure C-2 shows the first page of output produced by running the sample input. This output echos Dack the input up to the first RUN card so that the user can check his di.ta. The names of the constants a e printed as a checking aid. Also, the default flaw sizes with corres-ponding detection ineffi-iencies, square roots of the Julus ratio, and residual stresses are prcvided when the user inputs NA = 0. The next page of output, Figure C-3, shows the parameters of the first outpJt request of the RUN data group.

    • l55frN twt CCiagia (CCE a(%[$Y

'A5 s.5. ,.tF14 Eis.Laf'Ry ^ t s.t; 4's T a daEsar v- 'tt f allva! Par *arittfy asatv5ls sa*PLE CaTa 'ft !.C if N,~Li d .E ' L a T ;GV 9t5taaC" JhNs 1779 (* (f A+ '* T s[NT DL JT TITLI LCi e

97 3

WE5 EL Taitt O! 02T'. a', fwS!) Figure C-3 Run Data Croup - Output Request i Since FREQ = 0.0, only the failure pressures are to be computed. Figure C-4 shows one page of the output resulting frcm this request. It shows the failure pressures for the third flaw size (0.5 in) at each of the input temperatures and fluences. At the bottom, several addi-tional pieces of information are printed for each fluence. They are: P(GY) The gross yield pressure. T(Gf-tB) The temperature at the beginning of the gross yield plateau. KlC(GY-LB) The toughness required at the beginning of the grass yield plateau. !(GY-UB) The temperature at the end of the gress y eld piateau. i AlC(GV-UB) The tougbress required at the end of the gross yield plateau. P00DRIGlWL T"

CASF 1 U.S. NUC! EAR REGULATORY CL* MISSION - THE CCTAv!A CODE TITLE NUCLEA* REACTOR PR655URF VES%EL FAILU4E PROdA6tlITY ANALYSIS SAMPLE DATA PFFICE OF NUCLEAR REGULATORY R25EARCH JtN. 1978 CONSTANTS ASPFCT THICK c2E 5 5 1N5!0f RADIU5 IN!T[AL COPPER PHOSPHORUS ULT STRENGTH STABLE r1ACK KIC L'0?ER ttMIT RATIO t!NCH:56 (INCHES: RTNOT IF) tti iti (K51) C#DmTH It) (K51/5Cititill 7.le67 7.6753 78.5003 9.0300 0.253C 0.0410 87.000C G.2000 5000.000* TEMP *R ATURE (J4BFR OF START TE*P MAX h)[)l T IMP S T i. MP INCREMENT TEMP 17 40.3 10.0 200.0 FLUEN:c5 mummme 11 0.0 g j",",) C.C 1.17E+17 2.36E+17 4.69E*17 9.33E+17 1.ePE+1e 1.7SE+18 7.5Cr+18 1.5]E+19 3.CCE*19 6.00i+t9 FLAm 5!ZE5 r-- " e FLAW FLAW SQR T I MCDUL U S RiSIOUAL 5!ZE PR0dA91LITV RATIC) STRESS 3.1250 0.250000 0.!!60 C.C 0.250C 3.12130C 0.2220 C.0 C.500* 0.*25300 0.4300 0.0 1.3000 0.002230 0.84CC C.0 2.000 ; 0.000250 1.35CO C.0 3.C03 3.CC0025 2.13rc 0,0 ~j ix) s g, OUN 5 C7-. Figure C-2 f' Output Listing of OCTAVIA Input t~

8 17 E. N e 16 '3 O a P C O O O O O O O O O O O O O O O O Ce4PN OWN w O O O O O O O O O O e e e o o e e O. O. O. O. m O O O O e e e e e e e e o e=cmO

    • N 4

e e e e e w w w w w w w w w w w w w w w w w w wPNmP who O 4 4 4 4 f + t + 4 4 N m w O N m 4 74% O O O O O O O O O O O-O O O O m a m N P e e e e e e e e e e e o e e e e e 4 m m m m e m m m e e e m i e e e m 4 N P O O O O O O O O O O O O O C O O O ONeON OPN O O O O O u O O O O n O O O O O O O e e - e O e o "e e e e e o e edemo eEN w w w w w w w w w w w w 6 w w w w w weNe@ wNm N O W k m* P4N O P e e 4 4 N 7 O N m +m N N N N P 4# Q O L O O Q O O O Oe e m e e e e m m 4 N e e e e e e e o e e e e e e e e e e m e m m e e m m 4@ m Om P O O O O O O O O O O O O O O O O O OP4mW OmN w O O O O O O O O O O O O O O O O O O *

  • e
  • O e *

%7 e o e o e o e o e e e4+EO e 4N 14 w w w w w w w w w w w w w w w w w w w#NN P vom N N PmN 4 9 O O= m o m m o N e P 4 O c 4 N 4 N mN P = N 4 4 N N N m 4 4 + 4 N C m d e m m m A m e e m m m e 4 4 N m m m e e e e e e e e e e a e e e e o w Q f G O O O O O O O O O O O O C O O O O 0440m OeN v m O O O O O O O O O O O O O O O O O O ^ e

  • O
  • e e

e e e e o e e e e e o e +

  • e e
    1. e40
  • PN 4

e w w m w w m# 4 N C mN 4 h O 4 P m wm webOP wem w w w 6 w w w w w w w m m O h N m m w w N 4 m 4 4 m N N N P mm N CNN N c D W N m 4 4 e e e e o o e e e w w N e m me 4 4 4 4 e c 4 4 4 A U M Q 2 4 E O O O O O O C O O O O O O C O O O C044* ONN O. N O. C. O. O. O. O. O. O. O. O. O O O O O O O - e e y-v e e e e e e ememo z > e e w w w w mW@@ wem i.. e N w w w w w w w w w w w w* w w wm N O ONN f m ~ 4 N a o N < ~ ~ f P N e f 4 4 0 7 4 i m C e e 4 4 4 4 f f 4: N N m o N P m ~ e w e e e O e e e e e 3 e o e G O A W 4 4 4 4 4 4 4 N O m 4 e W Z t e G O e O O O O O O O O C O O O O G O O C OP@NN OON Gm 6 = e e e e + e e e e e e e e e e o e e e #c40

  • DN m

O O O O O O O O O O O O C O O O O O e e - e O e v w a w w w w m w. w ~w w w w w w w w w w w?>m? wem w w ~ m r 4 e m w A w G m m O 4 7 N N N 4 4 4 m T y = ~ emN O 4 N P P T N ? E m a e e e w S DZ= ^ O su w m 4 4 4 e e c 4 4 4 4 4 N A N 4 me 1 q O w44w v Y Z F C O O C 0 0 0 O O C O O O C O O O C44CM OT N U' ww t m m O O O O O L 0 0 0 0 O O O O O O O O - e - O

  • b 2

V O m e e e o e e ePcmo

    • N O

wC wwe 4 w N m C N Nm m .o N P a ~ N Nw w w w w w 4b er wem w

  1. > E

~ e o e e e a e 4 C O P 7 C -e N wmV + O N w w w 6 w w w w 7 c e w w w b w t-N C N N N E O e O > wD A m 4 ? r 4 O 4 4 4 4 ~ N M ~ N ~e e o e C G e 3 wms D L w e W 3 x w40 1 aw2 N O O O O O O O O O O O O O C O O O OO4th ONN e m DJs a = G O O O J O O O O G O O O O O O O O e e e O 4 +0m e o e e o e e e e e o e e e e e e e emt&O erN w

  1. w e w

w w w wm w* w w w u-w w w w w w w w w w#N GC wem L 4 4 c e r N 4 2 2 ? w J P 7 m ?mN e w w ww 7 4 m N N r N 3 N T ? 7 ? ? ? e ? J m 4 4 e 4 4o 4 h h N N N N N he y 3 O as e e e e N N 4 N g E qw = 4 4 4 4 ,3 M wY M e Gat N e N uw

  • N O

O O O G O C O O O C O O C O O O Oc4NN OmN L e e e e e o e e + e o e e e e e e ek- - e O O O C O O C O O O O O O O O O O O O e 00m o "e w V. m m f w N f m 4 e

  • ?

O ? 9 9 ?- Ww O w

  • P40 e te N 4Z E

N r* _Nm Nw % 4 u w e a w V w w b, m VmN m 4 w P c N (: 2e N N N 4 4 r e m m 4 o w a 4 4 N N N A N N N N m N h 4 A 4 m su C am m A O O O O O O O O O O O O r) O O O O O 44ON (> zN oa 3w a=* G G J r O O C O O re r> O G A O O O O e e 7L 1.n + e + e e e eF rNO e ee A a w wNN 4& .s-** @ k a O u a ~.A a 4 w w u Ow w a O ? m emN u w w J N ~ N 4 4 E = 4 P 7 P F ? e N e S 4 D e m P ? L' m N >m c C 4 4 4 h P A N h N Ne A N N 4 h N w 4 A O O O O O J O O O O O O O O w O O Om eek O*N ur (~ O O O O O O O O O O O O P O O O O e O e o e e e e o e e e e e

  • +

e e e e ce40

  • ON wJO 4

4 7 re e C T w* c u. ua u. 'u N NP w C -e 2 m w w w w w w w ci w LJ w c N c .s t-c N c T T C C C T T N 7 a e 4 0 g g 4 A h N N b b A N e N A A A h d N M A w a wa 2 m L U O O O O O O O O O O O O t O ce e e u L 4 4 O O O O O O O O O 7 O O A - w>7> ~ ~ # O O O O e e e e e e e t O e O 7 2 E-P O m N 4 4 E P > > m >m evm d w m m m m m = m N OOQOQ mDJG g w h N b & M &>m m m mmmm h U [ e e w s ,4 i

18 P(US) The upper shelf plast:c inst 3bility pressure T(US) The temperature at the beginning of the upper shelf plastic instability region. KlC(US) The toughness required at the beginning of the upper shelf plastic instability region. These data are printed only wnen pressures are printed. The rest of it output request (not shown) coqsists of a similar i ye for each of the cther 5 flaw sizes. Note that the last temperaturt printed is 200.0, the salue input f or TMM. If the upper shelf prtssure or input tcughness limit had been reached for all input fluences at a temperature lower than IMAX, say at 180, the output would hase stopped at 180" Figure C-5 shows the first page of output for the second request. r r, ci-a. o ,,r'.y ..is e s - rm <:ra,ta as avu t d ' i[ .I db g, ( p-4j[ ,.( DJ"G4%lLj{V {\\1(y}l5 $3W@([ [&(( . '1 v } -ad d il4' 41 erta: Ja%, 1978 E I ',1 if 5, ']'t.

(-

2 r- ..stran a a air s figure C-5 Run Jata Grotp - Output Request 2 In this request, ikEQ -1.0, so test estimate par--rneters were used in computing the probabilities. figure C-6 shans the output produced by the sectrd request. Sir.ce the output type requested was zero, the probabilities are suwd over all the 'nput flaw sizes. F igure C-l shows one pa ;e of the third cutput request. FREQ was set to -1.0 as in the second

request,

>t this time s' cutput set type was I, so the probabilities are printed with each flaw size on a separate px;o and with the flaw size prouability, EF(I), included. The rest of tho outpit (not shown) consists of a,imilar page for each of the other 5 flaw sizes. Figures C-3 and C-9 are similar to C-6 wd C-7, but they shnw the 95% tound probibilities. The printed output ends with the message "[ND CF CCTA41 A RUN. ' 3. GDANIC GUIPUT in addition to the printed output, OCIAv!A will produte, if requested, CALCOPP plots of the rcws and/or colua.ns of the output t mles. $ N'

19 N s.- e s* > C0 6 C to e er o en in ers ie e ne c w cr. -e LA O ( O O 63 O O C.> (* (J O C O O C O e e e I e 4 0 e 4 e f 8 9 e B t 6 I tas ha ua +as tas est ue up w w te W tsJ w k' tu to - W D E' b 6f4 4 r* 42 de M P ( O 4 P* f* O e tA e3 + e to C O O O O O O O O CP f* ea e o e e e e e e o e e e e e 4 e m m re ew N N N N N N N N N te to er% ers iss art to an O C f e e to Cs O ry a c) g3 o n o ti o g 3 o o J v 4 1 9 6 1 6 0 0 f a 9 0 0 0 I 1 w w as4 w aan w taJ g.s taJ taJ 448 taJ nas lA8 haJ t 4 tad w eJ ee O @= O -e SS 4=% OJ N e e e l (* 4 8m N O P-8@ O O C' (* O gi su e= P= J en 4-e e o e e o e e e e e e e e e-r~ e m e tw re eJ N N N ce N ce N rw rw .-e -e wg d' & m .N O8 f f f er' nh f er f f + f en 4 4 4 4 D eu = O o O O O O O O L O O O O O O O O m 4 7 I O t e B e e t i e a e 8 0 4 I I .4 w t.d LJ .ad g X 4 p. w

  • W w

su us tu u' W tad w ta4 na.s W cP 4 O O e O e O P c O 4 o o o o -. P 4 4 en 4 N e t' 9 4J 4e o e e e M. N O 4 F~ Q f v. e o e e e ee -e -e .-* m D 4 N e a e -e N N re ce N N N "Y he K ln er so f en 4 4 4 4 4 F P~

  • '= >=

K L G i O O O O C' O O O O O G C O O G O O 5 e i I I t 4 0 t t e p I e 6 4 I a b u e w w w w un W w u' a' w w u-w w w w w W N. O O c e o r-(- 4 o e e-e e CP er m C Q rs v h O - -* e P 4 N O. P. D e e e P. e .s

  • ==

m2 4 4 me 99 F-4 N .* c e 4 w e o e e e T3 W O ed 4 4 e e e 4 4 4 4

  • =

P-O si E E e (* E3 'J z a nt i

== r o C D o y r O O e ( O O O y e O g 3 I O e f 4 i e i 9 i e i t 4 6 e 4 6 6 us w kJ has w aeJ w i, is w w as is w ue uJ t., w w ir* ee c O N r. -e N e o-Ia eri 2 tra-4 4 4 4 A (_,e c er N P-4 se p e= Le D O N Fw Em C en e o e o g .e W@ P-W et% e e e e e 1 Ew e e 4 e N

  • e 4

e4 et 3 a.a e er g

  • E O **

(* (* P 7 C OM t,'_ O O w. 4 ( P-e- e to co e c o e c o O g C* w 3

== O O rs e o O O O o o iM d 4 e e e e e i I e e e s e I i e e s U w w e w us u.e C e e= a w w us ua us w us tea w w w n.a=* N re ar' O .) N. G

== w

  • E w e'

7 4 O N O N tr l' "e b t N >=* k nr c 4 4 m 4 4 O. O. e e o o e e 8 b e 3 et k. to 3. 3 I ** e-- -s A N m e.e ace 4 N -e co e re ew N e U I u e s i a= J V V - cr 4 a V f* P CP (* 4 *E ta 2 t'."o I" O w of a P= 4 P-A h 4 K G3 dr C* 9 ( O O u V Q G ) e5 G O C O O r-O C O O (J .d i e e4 J 9 e d f e 5 8 e e e e t t i e t 9 e C W s .u 4 4 w w 4 u u w o. u 'er 'LAI' +M ra me rv c 4 e et e s-W& wW w w t_ w ud 4 e 44 w m O O 4 a O N e' J e f* .e E. 7 e.4 7 F. => > J O .a 7 h -e P=

  • n e

O eg e4 N .s e --e .e .J M> m O EC O 4 r-2 w cr a a e d in 'u s-es. > et e# P-P- N ee e T 9 e Cr (* P /* CP 6.aJ er Lu 4 C O O C O t.' O tJ 2 D C.3 e O O O O O O O O O a e') s.3 C u e+ e e e e t ) e e e i e a e s s a p tt nas t#- ' u Cr 3 hu u* I t'J aJ tu nu tJ ur a eu nu nas W b w s p 4 s WWhk U O 4 N e s N 4 4 w M N ae E e g M =* O O f'P FP (P g (* P-P4 s F rw @o e e e e 6b 7 v C*e -e (* 4 r4 e* @e 4 N N N re

== a e 4 g e e e e J (L S sas B e F s g I es er -= et nai 3 p-a n e e. r-2 at. e e CP (> em r* fP t* rP rm N C J.Je u34 e.* O O O O O O O Q O O ( t3 O O (s () O i#5 5 ( f e f 4 0 t 6 e e e e 4 0 4 e 1

t. I 4

u ur s t iJ a. t_ t t1 L s se r O 4 #u O e m m v e N J n. O.-s ww % 4 - + c e 4 N m 4 u.s O F 4*' f* fP

  • F

.) y e 6" O 8M tr O 89 P= P-Pe e rw

  • e IL 4

N N N N e e e e - e D af au Oe M its n P. A 'r' O O fP f'P (* 8> P r* (= CS r> m D J a,e i) O O 1 O O t> O O J ') O m O O O O O tyA 8 6 f 8 f f ^$ e I 4 8 1 8 l 1 ') w t 8 as J (sJ _1 u./ A.1 J f 'E-iu u J =J 7[ u 4 1 r%d 1 E O CIJ 'O 41 W'lf ' 8J N.* am.8 4 (* N f4 L-O C fP CP >= C N=* N C g O e e e,nJ p.e e e o e e .e g., .e. e .n N ew ev e e N ) e O ew m,,,.

  • "f m

T> W 'P to t' n m f* ro n rP

  • P t*

W r* id C. O O O r O (> O O O rs O C O O O O g I t 5 i i 4 7 p 6 4 4 e e I e yg t) a tJ EnJ w ta w w u: ua t ta a t in ei P-c .s 4 d c' e' a. a to er a o o / T 2 r~ N =-n a t' ? lt V CP Ve e u 3O f N P-o e e o -4 e em = e e e W e wC Aa =* 4 se re N N N -= ,e t n th t O ) O tI tb c n s) rb rJ f w a e e e o e e C O O t) O r1 O C L r-4 () {b (- O E) O (l .O P-2 t* c P= ss] m-= r m 4*

== e es, 3 4 e a ee w / >= e" L P00R ORGM a

C A 5e 1 U.S. iJCLEAR WE LLL A f 0p v C L P1!$5!:;N - THF CCTAVIA LOC: GEOUFST 1

  • m C t : 4 '4 a f AC TUR PRE 55uof vES$f t F Alt u2E PirRA'Ittiv ANaty515
  • Apple CATA PfFI;t CF
4. CLEAR m ' ",U L A I L R Y RLSTAR:H
JAN, 1976 iAlLU9E DECM5 'Od 61 57 E 5 f lM A fi PCCUNPtNC 44TES FLAm SilE ( I NC s' i l
500, FLAW p? Lea?lt!TV q.c?seco 2

FLLEN;E AI V f S ,5 L 1C (N/Cr**2) C.C 1.17; + 17 1.54r+17 4.b ar

  • l r 1.19:+1T 1.d4E+1a 1.75:+1a T.30F+1H 1.505+19 3.CCE*19 6.00F+11 TLwe (F)
  • S.'
5. 91 E - n )

7.*6t-0) n.36--Ja 1.11 E ^ 8

1. F F - i l 4.f?t-11

$.19 ' ' 6

7. 3 3 r.06 1.CPf-C$

1.21f-05 1.23f I5 23 3.jsr.39 g,63t-c) 9.c.r-Og a it-ca f rtr-Ca , 7tr-77 ,.44E-et 6.t0F-06 4.e$r.cs 3,7; g,7,t_rc s o LO " 1.9CT-01 S.11. - ; ) 8.*$

  • 1 1.0$f-Ci

,. P 4. - ( ? /. 796 -?7

1. 7 7 t ~ e S.Hli-06 1.r2t-Os 1.17E 5

1.22 -15 C3 70 7.69 -10 1.77;-07

3. 7 7. - J 7 1.lef-09
1. n o - 01 1.32c-?7 1.

l f ' t, $.02E et

9. a c.' - C 6 1.487-:%

1.?2'-C$ uma um a)."

4. 3 4 r _ g 9 j.1 :,c - ; )

5.64r_+9 c.3ct.24 i.T6f-r# 5.41r_P 7.6 4 r -0 7 4.29t-C6

7. 3 5 E - 0 6 1.17I-L5 1.11:-r5 10
1. 6 T r - t g g, tog _ c a p,;g;_pg 4,fsr_ g 3,94: _cq g,an[_;"

4.*25-07 1.17 -Ct P.A45-06 1.ltr.,$ g,y,r_et h li'. l.S*'-10 5.11t-13 1.lb -C) '.S2f-C9 .1/L t7 e. C t.1 ^ 't + - ' 7.64: 8.?*t-76 1.14 J - 15 .20E-93 t- ~ N r 1:3. 1.3 -10 2.14 : - 1 ) 5.>6.-10 '.47t- ?) Ci 1.7t- 'l C*! n 7 1.92 r3 7,ege-26 1.' v' l. l 'er O wm l h 12' 1.6Cc-13 1.Mt-10 1.31 -1)

  • 56'-10 c. 32

-( 9 T.*S -C9 4.C V r F 1.34f-C6 f..q?'-06 1.105 u' t.191-0% mummmmum WW 3 l')." 1,*Cf-10 1.6]L-1, 1.6? -10 '.7Ct-1" 1.14r- '3 5.4 5f-U9 1.14 ! ^ a

6. o6 E - C F 6.1FC-06
1. 0 T E - C 1.17E-C5

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1. o D ' - ! C
1. t C T - l :

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tC '.

S.11f-07 5.97I-C6 1.04 -C* 1.l'i-C5 lf" 15'.C L. t 7 - 10 1.;3 -1) 1.>J.-10 1.60'-10 /.?S -13 1.4P'-09 9.CS' 17

2. 7 9 '- 0 T 4.5sr-C6
1.
  • C E - r. 5 1.14!-05 It? ~

1.t:E-lc 1.6? -1) 1.2 -1; 1.60'-10 1, t - - ' '3. 4 f i - 10 7.0ti "9 1.9E-07

4. 74 E -C 6 1.57E-C6 1.12:-?5 1 ??

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1. s n' - 1 :

1.6' -10 1.t -1: 4.24'-It 4.tFi-^1

s. ? 7[-re 2.9tt-Ce 9.

9:-Ce. 1.01E 3 19 ?. 1.t:_-10

1. t. :

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pt.c3 n.3st ce g, met _-5 11; 1.

-10 1.+. 13 '.00 -l? 1.

r- '
1. t "

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1. r. J 5 -lJ 1.60 -1C
1. t, C i - l C

!.oC!-l' !.ees-la F.t S t - 11 7.f6'-(9

1. rte-06 7./t;-C*

9.qsr_re r T. F igure C- / Failure Probabilities for Best Estimate Cc:

e Rates for a Half Inch flaw C T~ ^

t

j '. m-I 5 E W 1 4 4 4 4 4 4 4 4 4 4 R 1 G ^~ 9 0 1 ^ ? ^ 0

  • ^

0 C ^ * - ^ - - - a f E 7 4 I t 1 r E f f E E [ C C A 1 4 / e 0 8 t '5 "5 4 9 3 5 5 2 I 1 C 9 5 5 5 0 6 5 5 5 5 5 5 5 5 6 5 5 5 5 4 4 4 4 4 4 4 4 5 4 9 4 4 C 1 3 4 4 4 4 A C 0 0 ( C C L 1 0 U 0 f E f E C r r c C E t 't I 3 2 E 5 E E. A 7 O. 5 4 4 46 6 9 C 2 2 C 2 0I 7 4 5 4 1 41 3 9 6 S 3 1 e l. ? 1 A 9 1 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 a D1 s p -d. 4 4 4 4 4 4 4 e 9 4 4 4 4 4 4 4 F 1 0 C C 0 0 C 7 0 0 r n C C C 0 iz 1 + p A i E ' h F 5 t 5[ E1 4 4 2' 6 3 7 S a 71 E E f f f A J G 7 R 5 9 w 9 2 5 2 9 f 4 e 5 1 a 1 5 5 4 4 4 6 1 9 S 2 2 1 1 l f F C C'> l 5 5 O 9 4 4 4 4 4 4 4 4 4 4 5 5 5 C 0 C 1 3 I ') r 3 C 0 r 3 0 C 0 C l A 5 f f r f f 4 1 t 7 7f r '6 1 C 7 5 1 E l S 7 A 5 e f l l f c, I f r E 5 2 r A Y f I 9 6 4 1 1 ? 7 B 0 4 d 4 0 e A v C AL 4 y 4 5 1 3 5 4 / 2 1 i 1 9 e 5 4 i ' T O C N d f N g 0 O ^ C ^ r-5 5 O e A C a 4 4 4 4 4 5 5 5 5 5 e C J m H V I 'S h f f f M F t '5 f m r f 7 T 7 6 i R s 7E 2 7 u ) 9 7 e 8 8 1 P 6 0 S t U$ T 6 4 9 A C 1 t 9 7 4 - i C [ 4 2 1 1 1 1 P 5 3 6 1 I 1 9 F s R Mf e A j t N B 0 C J f d 4 4 5 5 s 5 5 5 4 5 6 6 t. 6 6 a G' 2 1 J N. l ) 0 0 ^ J O' 0 G J 3 C 3 C 3 0 R F 'I A m( t t l t f f 4 S 2 5 t I E e F 1 F l T P f S P ?" 1 le 'e 'P> 9 S f. 1 1 45 P 6 c 5 5 5 4 1 n W UUd T e C l RP P 1 1 1 8 7 5 4 1 L 1 1 3' 7 t' 6 6 r U lC' U 8 r A A P N 6 6 u 6 6 6 V UI / s 5 5 5 i r r r a I' C c R f $' 1 O 0 0 ( 2 0 0 n e c IU t. r 8 t e O t G ) 7 ^ 9' o f t'. 6' c 6 r 4 5 9At f8 1 5' F F9'

5. i 5

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== -e O -e O t' Oe t' O O O O P O CP 8' o e e e e e a 4 N N rv N N N N N N N N N rw

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23 In the sa+ple input, notice that in subgroup RUN, IPLOT = 3 in each output reouest. Therefore, both the rows and columns cf the output tables are to be plotted. Figures C-10 and C-Il show the pressure plots for flaw size 0.5 in. Figure C-10 is a pressure vs. temperature plot for the 11 input fluences (i.e., the colurr. s of Figure C-4 have teen plotted). Figure C-il is a pressure vs. fluence plot for a series of temperatures (i.e., selected rows of Figure C-4 have been plotted). Figures C-12 and C-13 are the plots of the columns and rows, respectively, of the output table shown in Figure C-7. Two plots are produced for all the other flaw sizes, and another Complete set of plots is proddCed for the 95% bound tables. Figures C-16 and C-17 correspond to Figure C-8 for the 95% bounds; figures C-18 and C-19 correspond to the table in Figure C-9. l' ~> VJd i e

24 NUCLEAR REACTOR PRESSURE VESSEL FAILURE PROBASILITY ANALYSIS SAMPLE DATA CASE 1 OFFICE OF kUCLEAR REOULATORY RESEARCH JAN. 1978 REQUEST 1 VESSEL FAILURE PRESSURES (KS!! 8 FLAW S!!E 0.600 cn o FLUENCE MEY i O'# 4 [C ' 72E17. 0 /O c / A 2.344E17. + 4.688E17. [ X 9 376E17. o / / e 1.675E16. j / + 3.750E10. o X 7.500E18. if / Z 1 500E19. ~ I g Y 3.000E19. ,,/ X 6 000E19. O 7 e 1 [ 5"_ Y/ / V d "a / W f %n y / / a / / o / in ( / / W V/ / n Ve r r n /= p - rn-on l 8 ci 8 l 8 I %.00 40.00 80.00 120.00 l'0.00 2'0 00 2'40.00 280.00 6 0 TEMPERATURE (DEGREES FARENHEIT) l~{ @ (( f h j)~ k '.I. ! !! i ! !l l L C' Figure C-10 [ r? i @ U [q Failure Pressure vs. Temperature F jl j (J]lj hU b bb.h g q 'i ). / U-1

25 NUCLEAR REACTOR PRESSURE VESSEL FAILURE PROBASILITY ANALYSIS SAMPLE DATA CASE 1 0FFICE OF NUCLEAR REOULATORf RESEARCH J A'd. 1978 REQUEST 1 VESSEL F RILURE PRE SSL'RE5 (MSI) g FLAW SIZE : 0.500 og i i i l l t \\ l \\ f f TEMPERATURE KEY i g j j f --;i >-- j - - - - - - - - + - - - - \\ t A 80 0 l 'N \\sI l + 100.0 I K';N lN i s X 120.0 I l \\ s : A k f 0 _g. -- 4 _ N_-w_._ N p\\.__\\ _ f -- X 180.0 l Z 200 0 N N \\ \\' \\ l \\ -{\\ jq \\ A Q 1, xl f l Nx A _. N' S- %;N j l l k \\'7_i_ J\\1 _ ___.._.__._.4_ O C S. \\

\\

t .N t I M

x s

i (n s N '\\ s r s s \\ l, i \\ n i i x's \\ \\ \\ t\\ j { i o g .\\ \\ \\ .\\ _1 \\ \\ i O W r k '% \\[\\ \\ s l I h 's \\ \\ \\ g \\ A (k l \\x 's i t W t f \\ \\4.' \\i i [O _._[_ . _ _ _ _ _ _ ',.1 % _ A g _4

  • _ _____L

\\('s\\ ! i i \\l N ' 1 \\ \\ 4 w [a '!('(' l s d h I 2 l co l =wM_, 5 +i o

u.,

7-- l l O i g. _t l l I 6 l f i i O i i r. _---_-_._.L__. L_L \\ i l I i I o J_.. _$-.--.~- i -r__ O 10 " 10 ' 10 10f0 L tFE AI INNER WALL (N/CHs=2) 0, [ EtM. i l u !i j> '( u, l Il i., il i .s figurP C*Il f } "~ ~ wh.I W t W e tr+85u~ vs v ~, ! !._u in' il Iu a ' ') ,_,,uf _;a i k'

26 NUCLEAR REACT 09 PRESSUFC VESSEL FAILUPE FROBASILITY AN4 LYSIS SAMPLE CATA CASE 1 0FFICE OF NUCLEAR AE?;LATORY RESEARCH JAN. 1978 PEGUEST 2 FA!LUPE PROSS FOR 8EST ESTIMATE OCCUPPENCE RATES PROBa9!LITY OF EXCEE0!h9 FA! LUCE FrE SSUPE SUMED DVf R ALL FLGW SIZES 10-4 I --i M,"% 7-7-* + - GW-*-s FLUENCE KEY L7 00 O 1 172E17. A 2.344E17. 10-5 'A + 4.E88E17. \\ 'A. X 9 375E17. ~~ \\ e

1. 8"7 5 E I P.

N h g x + 3.750E18. - X 7.500E18. T Z 1 500E19. \\. Y 3.000E19. g N x 6 000E19. g 6 \\ \\ 'A (_ A s o \\ \\ k 5 x i \\ \\ r .,1 .x. x \\ s a 10 .t 3 g g - - -. - _ x. -S \\s D "x '1 'I

  • {

x 9 \\ N = I w s x x NQx.r-4 -% g _ _ q N _ N D\\ \\ __\\_ "Q%Y Nh ;. uo 10.e W ,~. O co T co O gg-10 i tr CL. 10-11.; 1 0 00 40.00 80.00 120 00 160.00 200.00 240.00 280.00 TEMPERATURE (D GREES FARENHEIT) 7 1 D q; D 't Fiqure C-12 -'s 'a ; i a Best Estimate failure Probability vs. Tecperature C']bO] / Y U1u h 3 Llik.a 7'a p 7 /L ' y .J

27 NUCLEri R^ ACTOR PRESSURE VESSEL FAILURE PFCBA8!LITY ANALYSIS SAMPLE CATA CASr_ 1 0FFICE OF NUCLEAR REOULATORY PESEAPCH

JAN, 1979 REQUEST 2 FAILLRE PR0d$ FOR BEST EST! MATE CCCURRENCE RATES PP08A91L1TY OF EXCEE0!NG FAILURE PRESSURE SUMME0 OVER ALL FLAW $!!ES I

i i l f T d '~' ~ TEMPERATURE KEY 10-8 1 IF <// //7// + 100.0 ).,,/ /f/ / jf /

M

\\ t x 120.0 _f'/y /#/ i j j lljij i t i l I w ) 1 -7 l l Z 200 0 I / l I m 10-e g Ly -/ /y ? !! e

/ _j_.

4_. / !. / / i i / / I i A r l 10'7 I ) ?$ L - ___ / y . [__ _ J / / l i o _ _. -l. 7. l... /.. _ f .+-_ f! { c -y _._ [ /_..! I1. .;.... _. _ _d _ _ [ _ h__d / f e m o s 10-s _.._.[..._ _ p. 4_. [ _ _ L_. _1_ f ___.__7_- qw d _ _ _ _ _ _ _ _.... _, _ _. ~. I m l' i c

  • i l

l m l ____._'_g'.. _.t--~-- o 10-10 = --f -M 10-11 i 1017 gate 1018 t 10 o FLUENCE AT INNER WALL [N/CMas2) 0 9b

  • i ij j fl)

Figure C-13

s. ) v ua

,-, B est ,cimate Failure Probability vs. Fluence 9I ' h 1))Uda I l [i l di 'ti _ u 7 _. / u _, d. m

28 f& D g hULOdLiblia kUCLEAR REACTOR PRESSURE VESSEL FAILURE PROBA81LITT ANALYSIS SAMPLE ORid CASE 1 0FFICE OF NUCLEAR REGULRT3RY RESEARCH JAN. 1978 REQUEST 3 FAILURE PROSS FOR BEST ESTIMATE OCCURRENCE RATES FLAd SIZE = 0.500 FLUENCE KL' O 0.0 -4~-h =H-M - w - C - 2. 10-8 i ' * ~' h + 4.68ta_.i. g% X 9 37FE17. 4 4 1.875E18. h b + 3.750E18. \\ X 7.500E18. \\ \\ \\, ? i:888li": m 4 5 X 6 0 PSF.19. g x A g + N \\ \\ eW '\\ \\ \\ y m \\ w M h IU-7 3 k ~ \\ \\ \\ \\ t \\ \\ E \\ \\ \\ \\ \\ E h10-e ,_ w %y a x SN N w N N D\\ \\ \\ \\, w .\\\\ a I \\ 10-8 g xg \\ \\ g g \\ k\\ \\ k '\\ ~ \\\\ \\ \\ \\ ~ (- = BA= _ N \\

= = = h-64B g o 10-10 i s I i I i 0 00 10. 40.00 83.03 120.00 160.00 200.00 240.00 200.00 TEMPERATURE (DEGREES FARENHEIT) Figure C-14 Best Estimate Failure Probability vs. Temperature ~i . s

29 Qljij@(Jj!Tl J f.u{ m r T-3 q b .idLC j NUCLEAR REACTOR FALSSURE YESSEL FAILURE PROBASILITY ANALYSIS SAMPLE DATA CASE 1 0FFICE OF NUCLERR RE00LAT'.AY RESEARCH JAN. 1978 REQUEST 3 FAILbn PROBS FOR BEST ESTIMATE OCCURRENCE RATES FLAW SIZE = 0.S00 l . TEMPERATURE MEY O 40.0 10-5 i A - <- - .0 VWWAW' + 100.0 /f////' ///~ X 120=0 .//P'/M // in:8 I in:8 ///[f// i m g o-e / J/~i; / x 5 M / / ' / / ll w / / / 1 ll 0 / / / /7 / // 4 i,0.. / ////// # I / / f I ll ) ll a / / d i IJ/ li E / - / / /# // / h,0-e j / / w / /" A /2 / f w / /' / /) d s' / / / /] / 10-8 / i / / / 7 / / 2 / / 9 // / d / / / // \\ E )_ -l -l m o 10-18 o_ Y t i 10-81 i 1087 10 e 1018 10 0 t 2 FLUENCE AT INNER HALL (N/CMus2) Figure C-15 Best Estimate Failure Probability vs. Fluence e 4 w / v

30 C O{ O D o e JL D 3 ~ T 19 I ~ % D Al L UG_ NUCLEAR REACTOR PRESSURE YESSEL FAILbAE PROBABILITY ANALYSIS SAMPLE OR'A CASE 1 0FFICE OF NUCLEAR REDULATORY RESEARLH JAN. 1978 REQUEST 4 FAILURE PRO 3S FOR 95% UPPER SOUND OCCU:'RENCE RATES PROSASILITY OF EXCEEDING FAILURE PRESSURE SUMM*0 OVER ALL F AW SIZES [-. r r FLUENCE REY C 0.0 0 1.172E17. A 2.344E17. 4 + 4.688E17. A \\ + 3.760E18. 8 8. A N N h\\ \\ \\ \\ I i'.ID0!!!'. e yN

i
888lll:

10-s, 4 M E ABnEALA n. w E 1 J m 1L 10-8 i c3 Z maww U X 10-7 wa n .I J m cz) $ 10-8 i o E Q. t 10-s, 40.00 80.00 120 00 160 00 200.00 240.00 280 00 0.00 TEMPERATURE (DEGREES FARENHEIT) Figure C-16 95% Bound failure Probability vs. Temperature T~- p,, u,

31 o- ~c's ~l O k [kk[,/~Q'5Iba l NUCLERA REACTOR PRESSURE YESSEL FAILURE PROBABILITY 61ALYS!$ SAMPLE DATA CASE 1 0FFICE OF NUCLEAR REOULATORY RESEARCH JAN. 1978 REQUEST 4 FAILURE PROSS FOR 95% UPPER BOUNO OCCURRENCE RATES PR08 ABILITY OF EXCEEDING FAILURE *RESSURE SUMME0 OVER ALL FLAW SIZES { = /8kPb TEnPERATuRE KEY [ '/[ O 40.0 / [ O S0.0 // // $00!O t o-. /// // / ///__ i li8'8 y / // / / // ! + ISO.0 20////jl!!/ N $00'0 f / // /# // ]/ /// w / / 10-s / W / 4 a. ,&/ f/ / N S E u. go-a c3 e i_ d 5 10-7 i . _.. g - C d a -e ca 10 o N 10-e t 1017 101s 1010 1028 FLUENCE AT INNER WALL (N/CMus2) Figure C-17 95% Bound Failure Probability vs. Fluence 76 03B

) 0$@NS NUCLEAR REACTOR PRESSURE VESSEL FRILURE PROBABILITY ANALYSIS SAMPLE ORTR CASE 1 0FFICE OF HUCLEAR REGULRTORY RESERRCH JRN. 1973 REQUEST S FRILURE PROSS FOR 95% UPPER SOUND OCCURRENCE RATES FLRW $1ZE = 0 500 r FLUENCE KEY O 00 10, X 9.375E17. '\\ + 1 875E18. -\\ g Z 1 500E19 y s Y 3.000E19. X 6.000E19. m 10-8 3___ ._.\\ t_ I .I T(S N \\

  • \\

N c a u. go-e h \\'A '\\ \\ \\ e 5 \\=bhhh U b d 10-7. o 5 ~ 2 cn $ 10-e i a. 1 t o-o 2'0.00 2'40.00 2'80.00 O'.00 4b.00 8b.00 th0 00 l'0.00 0 8 TEMPERATURE (DEGREES FARENHEIT) Figure C-18 95% Bound Failure Probability vs. Temperature j s, v.l

33 b Qs L a n cr q re n. T, T ' ~ t Li i . i [ [! U v L' d huCLEAR REACTOR PRESSURE VESSEL FAILURE PROSABILITY ANALYSIS SAMPLE DATA CASE 1 0FFICE OF NUCLEAR REOULATORY RESEARCH JAN. 1978 REQUEST 5 F AILURE PROSS FOR 95% UPPER BOUNO CCCURRENCE RATES FLAW SIZE = 0.500 l TEMPERATURE MEY O 40.0 "e-- m O 60.0 0 s 10., [ i !!a:8 ////V/// / y / // //l / / A % go.s A i / / i/ HJ // 0- . _.//_ - /-. ~ N _ M S ./ { l \\ ~c t I j ' 10-s e J [__]_1_. ~ y ______.y U 5 10-1 y L C ] E $ 10 e O n. 10.e 1017 1018 101s 10 " CLUENCE AT INNER WALL (N/CMus2) Figure C-19 95% Bound failure Probability vs. Fluence i;'l' t.. 'd ' i d / /_

34 REFERENCES 1. J. G. Merkle, G. D. Whitman, R. H. Bryan, "An Evaluation of the HSST Program Intermediate Pressure Vessel Tests in Terms of Light-Water-Reactor Pressure Vessel Safety," ORNL-TM-5090, November 1975. Available for purchase from NTis. 2. HSST Quarterly Progress Report, ORNL-TM-4914, March 1975. Available for purchase from NTIS. /1 v ~i :

N N-35 APPENDIX I - FAILURE PRESSURE ANALYTICAL METHODOLOGY The fracture mechanics methods that are used in this program are essentially those used in ORNL-TM-5090, "An Evaluation of the H5ST Program Intermediate Pressure l'essel Tests in Terms of Light-Water-Reactor Pressure Vessel Safety," by J. G. Merkle, G. D. Whitman, and R. H. Bryan, November 1975. In relating RPV failure pressure to temperature for various flaw sizes, there are four distinct regimes, as depicted in Figure I-1. In terms of increasing predicted failure pressure, these regimes are linear elastic fracture mechanics (LEFM); gross yield plateau, elastic plastic fracture mechanics (EPFM), and the upper shelf plastic instability pressure. The LEFM regime is the most important, in that it is the governing regime for pressures up to the gross yield pressure of the vessel. This regime is the best characterized because of the significant advances in LEFM in recent years. The equations used, though not as exact as those that might be obtained frcm spicific finite element analyses, are close approximations for describing the imposed stress intensity factor at the deepest point in a semi elliptical flaw, and most importantly, they do contain the importent variables that must be considered, such as front and back free-face correction factors and flaw aspect ratio consideration.

1. Linear Elastic Fracture Mechanics (L E FM)
2. Gross Yield Plateau
3. Elastic Plastic Fracture Mechanics
4. Upper Shelf Plastic l

Instability b I O O l l l win l Tlll I C M O n r p 73 p i I c l l n l( I l i. l 3 l 1 l b dbd b dtJL[lY d E l l l l l 1 1 2l 3 4 I I I I I i TEMPERATURE Figure I-l The Four Regimes for Pressure vs. Temperature 7M 042

36 The gross yield plateau regime exists because of the yield plateau in the stress versus strain relationship for RPV matPrials, as depicted in figure 1-2. As seen from the figure, until strain hardening occurs, there can be no increase in the failure pressure over the gross yield pressure. w a-Os STR AIN Figure 1-2 Stress vs. Strain Relationship The EPFM regime relects the additional toughress available if the material has the capability of straining into the strain hardening region. The method of analyzing this regime was devel-oped daring the testing of the intermediate test vessels in the HSST program, and is described in det3ii in Appendix H of ORNL-5059, "Te't of Six-Inch-Thick Pressure Vessels, Series 2: Intermediate Test Vessels V-3, V-4, and V-6," by R. H. Bryan, J. G. Merkle, M. N. Raftenberg, G. C. Robinson, and J. E. Smi'.h, November 1975. The upper shelf plastic instability pressure reoime is determined by estimating the pres 3ure dt whiCh plastic instability occurs in the reginr. surrounding the flaw. This estimation procedure was developed during the testing of tre intermediate test vessels in the HSSI pro-gram, and is described in ORNL-4895, " Test of Six-inch-Thick Pressure Vessels, Series 1: Intermediate Test Vessels VI ar.d V2," by R. W. Derby, et.al., February 1975. Although most of the procedures used in the CCTAVIA program are the same as those reported in ORNL-TH-5090, there are two significant changes made that affect the results, lhe first of these is the modeling used for the degradation caused by irradiation, ard the sec,.K! is the relationship used for fracture touchness versus terparature. '~

37 In the OCf*"IA program, irradiation degradation caused by fluence is evaluated in the manner recommendu. U.S. NRC Regulatory Guide 1.99, revision 1. In general this evaluation results in more degradation than that reported in ORdL-TM-5090, particularly with hijh residual ele-ments in the steel. Furthermore, only internal surface flaws are considered for they are far more critical in the presence of irradiction than are external flaws. The basic fracture toughness data versus temperature for RPV steel wa; developed by the HSST program and presented in HSST Quarterly Progress Report, ORNL-TM-4914 for January-March 1915. These data are a closer representation of the average of the fracture toughness data than that used in ORNL-TM-5090. The best est*nate o,f toughness (Kk) versus temperature is based on a regression analysis of the HSST data. If K is the best estimate and t is the temperature ( F), then OCTAVIA uses g the formula KIc = a + ce where: a = 36.94 (; 1.011) b = 0.01794 (+ 0.002179) c 40.73 (! 3.655) The numbers in parentheses are the estimated standard deviations.4 The calculated f ailure pressures are based up'an nominal or average f racture toughness as exhibited by HSST-02 plate material. Fracture toughness values exhibit spread as do other mechanical procerties, and variation occurs from heat-to-heat and among welds. The results of the code should therefore be interpreted with this nominal toughness model in mind. The value of the yield strength and the constants used to describe the stress versus strain relationship are internal parts of the program. These values and constants can be changed at a later time to reflect the chaages induced by irradiation. These changes have not been put into the program to date because of the difficulty of defining the irradiated material stress versos strain relationships; the failure pressures, as calculated, are conservative, that is, lower than if the irradiatic, effects aere censidered. It is generally consider od that surface flaws are most likely to reside in weld regions. For this reason, this program has been oriented in fasor of mater.als that have not been quench and tempered. That is, a fixed value of the initial RT irput fm use with vaHous flaw NOT 4 The regression analysis is described in more detail in the letter frcm W. E. Vesely to E. K. Lynn, " Statistical Analysis of the HSST Basic Fracture Toughross Cata Versus Temperatures," dated May 20, 19/7. Y qt

38 depths. The quench and tempering that occurs with plates and forgings causes a significant decrease in the initial RT near the surface, which in turn, causes an increase in the NOT fracture toughness, above that of the weld region, to approximately one fourth of the way from each surfaca. ^ ,G G i VTJ

39 APelNDIX II - STATISTICAL EVALUATIONS Listed in Table 11-1 are the major transients incidents which have been reported, where " major" is defined as a transient having a maximum pressure exceeding 800 psi. The transient incidents which cccurred before criticality are denoted with an asterisk. Since the vessel failure pressure is generally larger than 800 psi, the " minor" transient inci-dents (<800 psi) are not consicered here. The statistical fitting techniques which are used are somewhat insensitive to the possibility that one or more transients have not been reported. Only the 'ransients which occurred af ter criticality will be used since, as shown later, the transients occurring before criticality are marginal in the similarit, of distribu-tions. Figure II-l is the empirical probability distribution of the maximum pressurri of the transients occurring after ;riticality. 5 F 0 f f 1 l> D 08A > J }] o r k* h i ] 1'Op os 9 0 i,1 h Jb 1 M L U e a 03 w 5 02 1 i 5 [ 01 en-08 - 01 (A t, 05 04 f 03 PH()r, ABiLIT Y VE RSU$ phi SSURE F OH ObSi HVF() TRANSif N TS LHE All R TH AN 800 PSIG i 01 1 1 L--- L-L 1 0 300 600 900 1200 1%0 1H00 ?R E SSU R E HOO) PSIG [jsure II-1 Empi.-ical Probability Plot 7,, (i / /_ V '10

40 PRESSURE VESSEL TECH SPEC LOCATIONS TRANSIENT TtMPERATURE PRESSilRE LIMITING RTND[ Oi INCIDENTS DATE FROM (PSIG) TO (*F) LIMIT (PSIG) (*F)

1. Beaver Valley 2/24/76 400 1000 130 440 75 Unit No.

1*

2. Oconee NJclear 11/15/73 800 1860 300 1600 60 Station Unit 2
3. Palisades 9/1/74 960 150 65
4. Point Beach 12/10/74 345 1400 170 615 110 Unit No. 2
5. Point Beach 2/28/76 400 830 16e 615 125 Unit No. 2
6. Prairie Island
  • 10/31/73 420 1100 132 720 15 Unit No. 1
7. Prairie Island 1/16/74 395 840 90 610 15 Unit No. 1
8. Prairie Island
  • 11/27/74

?90 155 800 5 Unit No. 2 9. Trojan

  • 7/22/75 400 3326 100 52U 40
10. Turkey Point 12/3/74 50 800 105 510 75 Unit No. 3
11. Zion Unit 6/13/73 110 1290 105 460 40 No.

1*

12. Zion Unit 6/3/75 100 1100 115 480 75 No. I
13. Zion ~ nit 9/18/75 95 1300 88 450 60 u

No. 2

14. Ginna*

1969 2485 100-150 600 45

15. Beaver Valley 3/5/76 400 1150 150 440 75 Unit No. la
16. O. C. Cook 4/14/76 1040 110 110 40 Unit No. 1
17. St. Lucie 6/17/76 435 815 100 520 20 Unit No. I
18. Indian Point 9/30/76 50 2250 185 740 75 Unit No. 3 The limiting RTNDT value is based on the fluence at the time of the incident.

Incidents occurring before criticality. TABLE 11-1 Major Pressure Transient Incidents O?7 i UM/

41 The ordinate is the probability that the maximum pressure of the transient will exceed a given value. A value of 800 psi nas been used as the origin (location) and the abscissa is the recorded maximum pressure minus 800 psi. Table 11-2 gives the tabulations used for the figure. I Pressure p p - 800 N I IN 1 (PSIG) (PSIG) 0 800 0 1. 815 15 .091 .909 2. 830 30 .182 .818 3. 840 40 .273 .727 4. 960 160 .364 .636 5. 1040 240 .455 .545 6. 1100 300 .545 .455 7. 1300 500 .636 .364 8. 1400 600 .727 .273 9. 1860 1060 .818 .182 10. 2250 1450 .909 .091 Average (p'800) = 440 TABLE 11-2 Empirical Distribution Tabulations The exponential distribution was initially assumed (giving rise to the semi-log plot in Figure II-1) because of its simplicity ar.d its ger.eral adequacy of describing extreme phenomena. A formal Lilliefors statistical test does not reject the exponential as being inadequate, having an observed significance level cf 0.75. Figure 11-1 should only be taken as a rough indication of the probability distribution and more f3rmal technipes need to be used to obtain the actual distribution. Maximum likelihood techniques are used here which allowed Lilliefors test to be performed. If P is the prob-g mbisity of exceeding a pressure p (psi) given a transient, then from maximum likelihood, the forma h for P is detennined to be g -(p 0) P exp [ ], > 800 = g Since there have been 10 transients exceeding 800 psi, the best estimate of the occurrence rate A far these transients is 10 A = g = 0.08 per reactor year ['s -G / y,v w <

42 where 125 reactor years is used as the approximate PWR experience. The best estimate prob-ability P f r a transient occurring and exceeding a given pressure is thus T -(p

0) ],

> 80L PT = 0.08 exp [ which is the formula used in OCTAVIA. This best estimate is also an approximate 50% confi-dence value (" median" value). is obtained by using upper 95% confidence bound values The upper 95% confidence bound for PT for A and the maximum pressure (scale factor). P (95%) = 0.135 exp -(p-800) , p > 800 7 806 The bound is not a precise 95% bound, but it is g, eater than 90% (using Bonferonni's inequality) and should be near 95% because the upper bound (800 psi) on P dominates the upper bound 7n the vessel failure probability. It is of interest to compare the abcve probabilities with those cbtained from the transients which occurred before criticality. Using the asterisked data in Table 11-1 and using the same is determined to be techniques as before, the best estimate for PT T (bef re criticality) = 0.06 exp -(p-800) P 807 The exponential is again found not to be inadequate with a significance level of 0.73 observed for Lilliefors test. f r before and af ter criticality, in particular, Comparison of the two best estimates of PT comparing the scale parameters 440 versus 807, results in enou0h statistical difference so as to be possibly significant.6 It is interesting to note that the best estimate of PT f r the f r transients after transients before criticality is approximately the 95% value for PT criticality. 6The observed F statistic value (fl=14, f2=20) is 1.83 whi h is near the 10% significance level (1.85).

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