ML031110242

E-mail from P. Williams to Rlt, Regarding DB Analysis Status Report for November 8, 2002

ML031110242
Person / Time
Site:	Davis Besse
Issue date:	11/08/2002
From:	Williams P Oak Ridge
To:	Robert Tregoning Office of Nuclear Reactor Regulation
References
FOIA/PA-2003-0018
Download: ML031110242 (21)

Text

MODeF efi regoning -_ub naiysis biatus report tor Novemoer b, 2uuz Page From:

"Paul T. Williams" <williamspt ornl.gov>

To:

<RLT@ nrc.gov>

Date:

11/8/02 11:10AM

Subject:

DB Analysis Status report for November 8, 2002 Rob:

Attached is a brief status report for the week ending November 8, 2002, on the Task 9.1 stress analysis of the Davis-Besse problem. This status report describes the work done on the short-term uncertainty analysis comparing two failure modes: (1) onset of ductile tearing and (2) plastic collapse.

Please let me know if you have any questions regarding this material.

Thanks Paul Paul T. Williams, Ph.D., P.E.

Computational Sciences and Engineering Div.

Oak Ridge National Laboratory P.O. Box 2009,Bldg. 9204-1,MS-8056,Rm.213A Oak Ridge, Tennessee 37831-8056 USA lnternet:williamspt @ ornl.gov FAX: (865) 574-0651 Phone:(865) 574-0649 CC:

mark Kirk <MTK@nrc.gov>, <NCC1 @nrc.gov>, <bassbr~ornl.gov>,

<williamspt @ ornl.gov>

'4Q

! jeaniette I orres - t-wd: LU Analysis status report tor November 8, 2002 Page 1, From:

Robert Tregoning / /CtS To:

Jeannette Torres Date:

11/27/02 8:30AM

Subject:

Fwd: DB Analysis Status report for November 8, 2002

• i jeannene Iorres - Lsd Analysis btatus report tor Novemner 8, 2()U2 Page 1 i

• ,jeanneue I orres - Ub natys:s btatus repon br Novemter 8, 2002 Page 1 From:

"Paul T. Williams" <williamspt9ornl.gov>

To:

<RLT@nrc.gov>

Date:

11/8/02 11:10AM

Subject:

DB Analysis Status report for November 8, 2002 Rob:

Attached is a brief status report for the week ending November 8, 2002, on the Task 9.1 stress analysis of the Davis-Besse problem. This status report describes the work done on the short-term uncertainty analysis comparing two failure modes: (1) onset of ductile tearing and (2) plastic collapse.

Please let me know if you have any questions regarding this material.

Thanks Paul Paul T. Williams, Ph.D., P.E.

Computational Sciences and Engineering Div.

Oak Ridge National Laboratory P.O. Box 2009,Bldg. 9204-1,MS-8056,Rm.213A Oak Ridge, Tennessee 37831-8056 USA lnternet:williamspt@ ornl.gov FAX: (865) 574-0651 Phone:(865) 574-0649 CC:

mark Kirk <MTK@nrc.gov>, <NCC1 @nrc.gov>, <bassbr~ornl.gov>,

<williamspt@ ornl.gov>

i Jeannette I orres - ()RNL D B status 1 08.doc Page I Jeannette I orres - ORNL 0 B status 11 08.doc Page I

MEMO DATE:

TO:

08 November 2002 R. L. Tregoning and M. T. Kirk FROM:

P. T. Williams and B. R. Bass

SUBJECT:

Status Report on Davis-Besse Analyses The attached Figs. 1-9 provide a summary of the Davis-Besse analyses performed to date under the new Task 9 of JCN Y6533. In Fig. 1, the cladding properties used in the current study are presented:

(a) true stress versus true strain and (b) thermal expansion coefficient versus temperature. The remaining figures address a specific sub-task described in the workscope for Task 9.

Sub-task 9.1D requires an estimate for crack driving forces as a function of flaw size and applied membrane stress in cladding. Table I shows the Case Matrix developed for this subtask.

Figure 2 depicts the first step carried out in preparation for the J-integral analyses, i.e.,

calculation of an updated estimate of the exposed cladding "footprint" based on the recent "dental mold" cast from the D-B cavity. That footprint area was estimated to be 28.23 in2.

Comparisons of the latest "footprint" statistics with previous ORNL interpretations are given in the table of Fig. 2(b). The newly calculated "footprint" area was used to define a burst disk having the same lateral surface area under load.

Table 2 presents ductile tearing data for three-wire series-arc stainless steel weld overlay cladding published in NUREG/CR-551 1 [1]. Table 3 presents additional ductile tearing data for stainless steel cladding [2]. The ductile-tearing data in Tables 2 and 3 are plotted as a function of temperature in Fig. 3. The J1, data at 288 'C (550.'F) has been extrapolated to 318.33 'C (605 °F) using a curve fit developed from Table 2. The extrapolated Jio data are also shown in Table 3.

The ExpertFit0 statistical software [3] was used to fit a statistical distribution to the data in Table 3 for 318.33 'C (605 'F). The resulting fit is a log-logistic cumulative distribution of the form CDF = F(Jiaxjy) =

I

\\* MERGEFORMAT

- \\* MERGEFORMAT where a 9.12897 f=79.46842 kj/m2 and T 0 ;-The corresponding percentile function is

\\* MERGEFORMAT Figure 4 shows a density/histogram overplot and the CDF of the log-logistic distribution.

I

Ijeannene i orres - UHNL U-b status 11 08.doc p ng ri

- - I _
. _Z'_ -

Figure 5 presents three finite-element models developed for this phase of the analysis. Surface-breaking flaws were centrally located in each burst disk with the three relative flaw depths: alt =

0.5, 0.25, and 0.05 for a flaw length of 2.0 inches (50.8 mm).

Each model was loaded with an increasing lateral pressure. The calculated J-integral loading paths for the three models are shown in Fig. 6a. The TableCurves 3D [4] software was then used to fit a surface of critical pressure for ductile tearing as a function of Jj, and relative flaw depth, alt, (see Fig. 6b). The resulting surface was ln(PD,) = -2.409372112829741 - 0.9619997646244488[ln(a It)] -

1.674757970053341 x 1 0 [jJ2 + 0.8312894992181433[ln(J, )] \\

MERGEFORMAT where PDT is MPa and Ja, is in kJ/m2. Equation \\* MERGEFORMAT (4) can be interpreted as given a value for relative flaw depth (2L = 2.0 inches) and J,¢ for the cladding, PDT is the lateral pressure required for the onset of ductile tearing of the flaw in the burst disk (radius = 3.0 inches, thickness = 0.25 inches).

An estimated cumulative distribution function for relative flaw depths in cladding [51 is shown in Fig. 7a. The CDF of Fig. 7a was sampled (N = 1000) to produce the histogram shown in Fig. 7b.

The plastic collapse curve shown in Fig. 8a was developed using the models in Fig. 5. The curve in Fig. 8a represents the pressure at numerical instability, PNI, that can be applied to the scaled log-Laplace statistical distribution described in [6].

Q,(P 0J1. 1057 x P,, 11.45441) =

exp[ln(I.1057xpl)+ l2454p41]

p* 0.5 BP, =

In [2(I - p)]

for (0 < p < 1) exp In(I.1057x PNI)- 11.45441

p>0.5 MERGEFORMAT where from Fig. 8a, PNI =52.739-39.656(a/t)-57.659(a/t) 2

\\* MERGEFORMAT A Monte Carlo code (see Exhibit I for a listing) was developed to simulate a large number of possible flaw configurations (single flaw located in the middle of the representative burst disk) with sampled relative flaw depths (flaw length = 2.0 inches for all realizations, see Fig. 7),

sampled uncertainties in plastic collapse burst pressure (Eqs. \\* MERGEFORMAT (5) and \\*

MERGEFORMAT (6)), and sampled uncertainties in the required pressure for the onset of ductile tearing (Eqs. \\* MERGEFORMAT (3) and \\* MERGEFORMAT (4). The results from 5000 simulations are shown in Fig. 9. From Fig. 9, it is clear that, for the relative flaw depth CDF assumed in the analysis, plastic collapse is the dominant failure mode compared to the onset of ductile tearing with a cumulative probability for plastic collapse of 0.996 at a median 2

• E jeannene 1s Orres - UHNL U _B status 1 1 - 08.doc Pag(

eannetie orres - UHNL U I status 11 08.doc Pag

pressure of 8.4 ksi. Additional calculations will be carried out to check the sensitivity of the results to the number of simulations used in the analysis.

3

I jeanneue " orres - uHJNL U b statusii iut.doc PagE References 4

. dIoctUItLw I or reb - UrINLLubstaus_-i iw.aoc Page E Table 1. Case Matrix for Task 9.1D 9.1DI 0.1250 2

0.50 16 9.1D2 0.0625 2

0.25 32 9.1D3 0.0125 2

0.05 160 9.1D4 0.1250 1

0.50 8

9.1D5 0.0625 1

0.25 16 9.1D6 0.0125 1

0.05 80 9.1D7 0.1250 0.375 0.50 3

9.1D8 0.0625 0.375 0.25 6

9.1D9 0.0125 0.375 0.05 30 Table 2. Ductile Tearing Data Extracted from Table 13 of NUREG/CR-5511.

+ iSpclmenX Temperature ^

f

'Jt. <>~dlo Unirradiated Specimens A13G H2 A15Ba Al 3D Al OG Al OE H5 H3 A13Fa H6 H4 Al 5D Al 3C HI

-75

-75 20 20 20 120 120 120 120 200 200 288 288 288 117 137 165 134 171 128 119 120 159 90 111 77 66 82 64 49 270 209 176 246 229 232 359 240 231 267 170 192 Irradiated Specimens A15F

-75 78 40 Al5G

-75 56 36 A13A 30 144 177 A15C 50 124 146 AlOF 120 94 175 A15A 288 25 191 aSpecimen was not side-grooved, while all other specimens in table were side-grooved 20%.

5

I Jeannette i orres - UhNL_ ub-status-l_uw.coc Pac I

eannetie orres - Ul-INLUbstatus 11 Ub.OOC Pr Table 3. Ductile Tearing Data Used in Development of Ji, Statistical Distribution SOecfTeamp',stJemp A15D 288 78 NUREG/CR-5511 Three-Wire Cladding Study 1

31833 7407 Al13C 288 68 NUR~EG/CR-551 1 Three-Wire Cladding Study 2

318 33 64 57 H13 288 79 NUREGICR-5511 Three-Wire Cladding Study 3

318 33 75 01 H1O 288 85 NUREGICR-6363 Aged 3-wire cladding @ 288C for 1605 hours0.0186 days <br />0.446 hours <br />0.00265 weeks <br />6.107025e-4 months <br /> 4

31833 8071 AA04 288 93 NUREGICR-6363 Aged 3-wire cladding 0 288C for 1605 hours0.0186 days <br />0.446 hours <br />0.00265 weeks <br />6.107025e-4 months <br /> 5

318 33 8831 AA02 288 59 NUREG/CR-6363 Aged 3-wire cladding 0 288C for 1605 hours0.0186 days <br />0.446 hours <br />0.00265 weeks <br />6.107025e-4 months <br /> 6

318 33 58 02 AA 3 288 91 NUREGICR-6363 Aged 3-wire cladding 0 288C for 20,000 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> 7

31833 8641 AA15 288 77 NUREGtCR-6363 Aged3-wirecladding 0 288Cfor20,000hours 8

31833 7312 H15 288 il1 NUREGICR-6363 Aged3-wirecladding 0 343Cfor20,000hours 9

31833 10540 H16 288 110 NUREGtCR-6363 Aged 3-wire cladding 0 343C for 20,000 hours0 days <br />0 hours <br />0 weeks <br />0 months <br /> 10 31833 10445 Data extrapolated to 318.33 °C (605 °F).

6

-i Jeannette I orres - LWhNL u b- -status-i 1-ub.aoc Page 7

.Jeannette I orres - UMNL u bsTatusiI LUb.aoc Page 7 I-80 -

• 500 70 -

- b-en 50-40 4

LU oi 30 l-cy= 94.36 sG, "(ksi)

- 400 E Cn

-- 300 vi C

- 200 t

- 1 L0

--100 20 f1 E = 25570.85 ksi v= 0.295 10 0

(a) 0 1.510 0.05 0.1 Total Strain (-)

0.15 0.2

- O9I272002 K3 pt,&'

tL 1.4 10 i

0 5

C.) 1.3 10'5 -

U' Cw

a.

1.2104 L w

.0 1.110 L I

1 1 04 1 0

500 1000 1500

. 2000 2500 3000 09'2712002 K2 ptw Temperature ('F)

(b)

Fig. 1. Cladding properties used in the current study: (a) true stress vs true strain and (b) thermal expansion coefficient.

7 l

I jeannene I orres - UHNL D B status 11 08.doc 0-tn a

rajw o

O I-

.~.

\\)

(3

~,

Footprint 9/23/2002 Area = 28.23 in.2 (a)

K, "

0-0 I-,

.¢ 1 1j R31.712 l

=

&ff

Fhla, e1. Pelwdd f Kd D ft.

S3=43 FPk r

'ik,

Am 0 BA P Am F-I _Ah4 X, ^

'I t

, I t_

J. '

7,

-~~;

I,,t

£ 4e _ -^v tI

• hw.

I If.I if.^ I I fb l

I t-

-,,I A, Fo.d Fa. m I

35 36 30.36 164122 401194 9t19 969933 -11716 7326 197 41

<09f04.04351

<04351 0904 AMJ..adFooln 0.253.

4006 3178 164301 40 12U5 12902 11031t1 -14135 9903 24571 601943,04476>

04476.08943, 1~ B-dfli CaWAL~

A4F.dFf pn I

23 23 2455 15332 401t 9356 670f363 50.32 5401 11307 10.55t.O.M1 I0.13M0 531 91792(02 GI,.bW C-dna*.ywm a

U. Z. -.a iWpg4 ah fth wnK~.1 rnwi. th..3,e.L The.-y pbn. d IhC p1.6 ooadla., su.,

U a hAtl pl-aC (b) h thC -

ft II-0 tII Ito fhC tatot.t d No 3 Yf II Fig. 2. Latest footprint estimated from "dental mold".

8

I Jeannette I orres - ORNLDB_status_1 1_08.doc Page 9 Temperature (°F) 0 200 400 600

'12U r 160 N

1-U 140 120 S0 a

SI

'I I

I

• N 100 I 1 0N^

-i 0.8 e

I 0.7

'.CL

.E

-0.6

.o

- 0.5 0.4 0.3 400

)02 K2 pth 80 -

60 !-

40L

-100 300 101/4'2C 0

100 200 (a)

Temperature (°C)

Temperature (°F) 0 200 400 600 A^^

YUU 350 1-Data from Table 13 (unirradiated)

NUREGtCR-551 1 U

300 O

250 0

m 200 C

L._

M 150 I.

L-Applied Tearing Modulus S

/

at 6 4 MPa (0.928 ksi)

/

2L a 50.8 mm (2.0 inches) t - 6.35 mm (0.25 Inches)

Applied Tearing Modulus

->8 at 8.2 MPa (1.19 ksl) 2L = 25 4 mm (1.0 inches) 0 t = 6.35 mm (0.25 inches) 100 I 50 nL

-100 0

100 200 300 10 25J2002 K2 phw 400 (b)

Temperature (°C)

Fig. 3. Ductile tearing data for stainless steel weld overlay cladding: (a) J1, data from unirradiated specimens and (b) tearing modulus data from unirradiated specimens 9

I judi it iette i orres - UHNL u t-slatus-1 1 08.doc M___ne If, I JtdfIIIejtLe I orres - UMNLUbsTatus 11 O8.doc lr'U Density/Histogram Overplot I

j 02 1 0I IV 6.A!

(a)

Jk (kJ/M2)

I 0

I-._

a.

03 E

M 0.8 0.6 0.4 Log-logistic Distribution Location = 0 Scale = 79.46482 kJ/m2 Shape = 9.12897 0.2 j 0 L 40 60 80 100 (kJ/m2) 120 10/24,12002 K3 ptW 140 Jc (b)

Fig. 4. Statistical distribution for J1, at 318.33 'C (605 °F): (a) histogram of data with fitted log-logistic density overplot and (b) log-logistic cumulative distribution function compared to cumulative probabilities of J,¢ data estimated by median rank order statistic p =

(i-0.3)I(n+0.4).

10

I eannetteI orres - ORNL D-B status-1 1 08.doc eanete s -

L__Bstatus__0.d Page' Fixed-Grip Boundary on Outer Edge (a)

(b)

Fixed-Grip Boundary on Outer Edge Fixed-Crip Boundary on Outer Edge (C)

Fig. 5. Finite-element models used in calculating applied J-integrals produced by pressure loading of burst disk: (a) Model 9.1D1 (aft = 0.5, 2La = 16) (b) Model 9.1D2 (alt = 0.25, 2LIa = 32), and (c) Model 9.1D3 (a/f = 0.05, 2I~a = 160) (Task 9.1D) 11

Lotcir I ii itmiurreb.- uJI'JL u__status_ Ii_uu.aoc pnalg 19 1- -tnc~

Pressure (ksi) 600° 1

2 3

4 5

6 7

8

owu, 3

3 e

U cL ma.

A ol 5 a/t = 0.25 50o [-

2La = 32 A

4.)

E 400 300 c) I,

i rn a/t = 0.5 2L/a = 16 I-4:'-

3.2 2.8 N

2.4 0.2 2

c.

1.6 W

0) 1.2 a

0.8 0.4 0

zuuI i

t C;

O.0 2L = 2.0 in. (54.8 mm) 2L/a = 160 aft = 0.05

.*me O. a"

,e

-a dow 100 n

(a) 200 180 z 60' aZ 140 60 40 20 0

(b) 0 10 20 30 40 50 6C Pressure (MPa) 11108,2002 K5 ptw In(Press) =a

• b In(a?)+cJ,-+d In(J,)

e2=0 99019297 DF Aq r-2=0 99004151 FKS1dEt 4433544 Fstat=8750 5319 a-2 4093721 b-5 96199976 c.1 674758.Q-d-0 8312895 to inP EL Fig. 6. Surface fit of J-integral driving forces - applied pressure as a function of J., and alt for a 2-inch long flaw: (a) driving forces, (b) fitted surface.

12

I Octrll MtUM I UI Itdb -

.JruML_.u_bsiatusl 1_ub.aoc Page 13:

Based on PVRUF Flaw Data i

0.8 !

LIL a

0.6 a/t= 62294 0 125045'CDF+ 62752 0-CDF2 aft( 0.01 677CDF PVRUF-CLAD-DEPTHrtbvvjds OA 0.2 O.

0.2 0.4 0.6 08 a/f 1.42W2 K1 fx (a) ouu soo Histogram of Relative Flaw Depths for i 000 sampled flaws 400 C

V 300 200 100 It-0 0 00400012 016 0.2 0.214C."0.32 0344 0444"0052006 06 064 06072 (b) aft 1VO4I2002K3pW Fig. 7. Relative flaw depth cumulative distribution function: (a) curve fit to CDF and (b) histogram resulting from random sampling (1000 sampled flaws) of CDF.

13

11 Jeawiaeue Iorres - UNL _U_tssTatus_11 ub.aoc Page 14 60 t

6.35 mm (0.25 inches) c~ 50?

'~,

Plastic Collapse 2

2L 2.0 in.

en 6

a. 30 a

0 MO52.739 L

0 Y=3M9+M*x+M2*x*2 l

Ml

-39.656 v

10j 0 L M21

-57.659 1

R 1 0.99993 I

0 0

0.1 0.2 0.3 0.4 0.5 0.6 (a) alt 1012412002 K2 ptw 0.9 P = 52.739 - 39.656(al0 -

2

=

0.8 LL.

4-0.7 0

0.6

.0 0.5 Log-Laplace 0

0.

0.4 -

Median = 1.1057 o

Mean

= 1.1142 0.3 Variance = 0.01959 Std Dev = 0.13998 E

0.2/

0.1 0.8 1

1.2 1.4 1.6 (b)

Burst Pressure/ PNI, a 11/08/2002 Ki ptw Fig. 8. (a) Plastic collapse curve of pressure at numerical instability, PNi, as a function of alt for a 2.0 inch flaw centered in the representative burst disk and (b) Log-Laplace CDF generated from previous study.

14

I JeaHrnetle j orres - U1NLU t3bstatus_11 _U.doc Page E1 U

I 08a 06 OA CDF = (1-.3)1(n+0.4) n = 5000

/ Failure Mode. Plastic Collapse l

Mean a85416ks1 Std Dev e 10739 ksl Median

• 84036ksl 02 o

(a) u0 1 r 4

a 12 Critical Pressure (ksl) 16 t1 ID!240 K2 K

CDF = (1-0.3)I(n+0A) n = 5000 0.8 n,

a.Ie 0 6 IL E

04 U

02 0

Failure Mode Ductile Tearing Mean

- 2306 ksl Std Dev Y 2508 2 ksl Median = 49 01 ksl 0

SO 10W 150 200 Critical Pressure (kslI) 1,1'OO2K3 At, (b) a

.0 3

U 1

08B 0 6 0 4 0.2 I

0.9 I CDF = (i-0.3

!/n - 5000 96

/'

Fail-Mode Pleaft C

_e/eeI tictile T -. rr Mav,.8146 Sld u.rS tSSS Median - e 1703 Ductile Tearing COUapse 1)1(n+OA) o*

0 0.5 I

I 1tS 2

Ratio of Plastic Collapse I Ductil Tearing Critical Pressures (-)

(c) tt&2,Z'2 K4 pt.

Fig. 9. Results of Monte Carlo sampling of 5000 flaws (2.0 inches in length) comparing (a) plastic collapse critical pressures (burst pressures), (b) onset of ductile tearing critical pressures, and (c) ratio of plastic collapse to ductile tearing critical pressures for each simulation.

I 15

IL I JdI nII ILLtU i orres - UMNL U b StsIJS 11 (IX tlnto

~

,age Exhibit 1. Listing of Monte Carlo Code Simulating Flaws in Cladding program monte-carlo implicit none C

==

==

-======================

integer iseed, i double precision P1, P2, P3, BP, PDT double precision JIc, at, PNI double precision, parameter

one=1.

integer, parameter

Ntrials=5000 double precisiondimension(Ntrials):: P-Order double precision,dimension(Ntrials):: BPI, PDTI, JIcI double precision,dimension(Ntrials):: atI, Ratio, RB integer,dimension(Ntrials)

iperml,iperm2,iperm3 integer,dimension(Ntrials)

iperm4,ipermS C=======

=

===================

c rnset - set random number generator see c

drnunf -

random number generator c

dsvrgp - sort vector in ascending order external RNSET I IMSL Routines double precision, external :: drnunf, DSVRGP I IMSL Routines open (unit=10,file='Monte.DAT',status='UNKNOWN')

iseed = 123457 call RNSET(iseed) I IMSL Routine: set seed write (10,1000) do i=1,Ntrials ipermC=i) = i iperm2(i) = i iperm3(i) = i iperm4(i) = i iperm5(i) = i c

prSi

= i POrder(i) = (REAL(i)-0.3dO)/(REAL(Ntrials)+0.4dO)

C=

=

I==

== = =

P1 = DRNUNF() I IMSL Function: Random Number Generator P2 = DRNUNF() I IMSL Function: Random Number Generator P3 = DRNUNF() I IMSL Function: Random Number Generator if ( P1 <= 0.99585dO ) then at = 0.0167dO*P1 else at = 62294.OdO - 125045.OdO*Pl + 62752.OdO*P1**2 endif C

Plastic collapse C=============== =

=========

PNI = 52.739dO -

39.656dO*at - 57.659dO*(at**2)

PNI = MAX(PNI,0.0001dO) if ( P2.LE. 0.5dO ) then BP = exp( LOG(1.1057dO*PNI) + (LOG(2.OdO*p2)/

11.45441d0) )

else BP = exp( LOG(1.1057dO*PNI) -

(LOG(2.0dO*(one-P2))/

11.45441dO) )

endif C

Ductile Tearing c = -

=

==

=

=

=

=

=

==

=

=

=

=

=

=

-L

__=====-

==

JIc = 79.46482d0*EXPC -LOG(

(one-P3)/P3 )/9.12897dO )

16

jeannete I orres - OHNL_D_B_status_11 _08.doc Page 1 7 CALL Driving.Force(at,JIc,PDT)

BPI(i)

= BP/6.894757dO PDTICi)

= PDT/6.894757d0 Ratio(i) = BPI(i)/PDTI(i) atI~i)

= at JICi)

= JIC enddo C

Ductile Tearing C

Sort by increasing magnitude CALL DSVRGP(Ntrials~atI, RB.iperml)

CALL DSVRGP(Ntrials,BPI, RB,iperm2)

CALL DSVRGP(Ntrials,PDTI. RBiperm3)

CALL DSVRGP(NtrialsRatioRB~iperm4)

CALL DSVRGP(Ntrials, 3IcI,RB,iperm5)

DO i=1,Ntrials write (10,1100) atI(iperml(i)),BPI(iperm2(i)),

PDTI(iperm3(i)),Ratio(iperm4(i)),

3lcI(iperm5(i)),POrder(i)

ENDDO C=============

=

=======

C 1000 FORMAT('

a/t BP(ksi)

PDT(ksi),

BP/PDT 3Ic P-Order')

1100 FORMAT(6ES14.6) end program monte.carlo SUBROUTINE Driving..Force(at,3I,Press)

• TableCurve 3D

• X = a/t

• Y = 31

• Z = Press

• Eqn#= 151240781 Eqn

=

lnz = a + b*ln(x) + C*yA2 + d*ln(y)

• r2

=

0.9901929705470828

• r2adj = 0.990041510632752

• StdErr= 1.443354380463457

• Fstat = 8750.531904291727

• a

= -2.409372112829741 b

= -0.9619997646244488 c

= -1.674757970053341E-06

• d

= 0.8312894992181433 DOUBLE PRECISION at,JI,Press DOUBLE PRECISION x,y,z DOUBLE PRECISION fl,f2,f3 x = MAX(at,0.0000000ldO) y

= MAX(JI,0.OOOOOOOldO) f1 = LOG(x) f2 = y*y f3 = LOG(y) z

= -2.409372f12829741DO-0.9619997646244488DO*fI

-1.674757970053341D-06*f2+0.8312894992181433D0*f3 z

= EXP(Z)

Press = z RETURN 17

E

,Ijiali i

11 a

tUIItb

- VrilIL

_L JStatus1 iuo.aoc PagelE END

[1] F. M. Haggag, W. R. Corwin, and R. K. Nanstad, Irradiation Effects on Strength and Toughness of Three-Wire Series-Arc Stainless Steel Weld Overlay Cladding, NUREG/CR-551 1 (ORNL/TM-l 1439), Oak Ridge National Laboratory, February 1990.

[2] Personal communication from R. L. Tregoning, November 4, 2002.

[3] A. M. Law, ExpertFit0 User's Guide, Avenill M. Law and Associates, 2002.

[4] TableCurve 3D - Automated Surface Fitting and Equation Discover, Version 3.0 for Windows NT, User's Manual, SPSS Software, 1997.

15] Personal communication from R. L Tregoning, November 4, 2002.

[6] P. T. Williams and B. R. Bass, "Stochastic Failure Model for the Davis-Besse RPV Head," USNRC Letter Report ORNL/NRC/LTR-02/10 (under review).

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