ML032600980

E-mail from Hackett to DB Lltf, Failure Model for DB

ML032600980
Person / Time
Site:	Davis Besse
Issue date:	07/03/2002
From:	Hackett E Office of Nuclear Reactor Regulation
To:	- No Known Affiliation
References
FOIA/PA-2003-0018
Download: ML032600980 (32)

Text

Je Sta fos-Fwd: Failure ModelforDB Pa_

From:

Edwin Hackett To:

DB LLTF Date:

7/3/02 4:33PM

Subject:

Fwd: Failure Model for DB -

FYI - update on RES contractor efforts

I Joelle Stare=s - Fwd; Failure Model for Pan Page

From:

Mark Kirk Cez To:

Steven Long,

Date:

7/3/02 4:13PM

Subject:

Fwd: Failure Model for DB Steve -

Attached please find a report from ORNL regarding the state of their model of DB in the "as found" condition. Paul is currently putting the finishing touches on this report (please consider the attached only a draft).

The short summary of this report is as follows:

1. If we use a Weibull cumulative probability function to represent the uncertainty associated with the failure criteria we arrive at a predicted lower bound burst pressure of 6.65 ksi. Because the 3 parameter Weibull function has a finite lower bound value there is - according to this model - zero probability of failure at pressures below 6.65 ksi

2. If instead we adopt a Normal cumulative probability function to represent the uncertainty associated with the failure criteria we arrive at a cumulative probability of failure of 8.4E-10 at the operating pressure of 2.165 ksi. At a slight overpressure (2.5 ksi) the probability of failure goes up by about an order of magnitude to 8.9E-9.

In either event, these are very small numbers.

Next week we will begin calculations on larger footprints for the wastage area Mark CC:

Bass, Richard - ORNL; Edwin Hackett Nilesh Chokshi; Wallace Norris; Williams, Paul - ORNL

I Joelle Starefoa - Failure Model for DB Paue1 1 I Jell Starefo.3 Fa oe o DB Paoe II From:

"Paul T. Williams" cwilliamspt~oml.gov>

To:

mark Kirk <MTK~nrc.gov>

Date:

7/3/02 3:10PM

Subject:

Failure Model for DB Mark:

Attached is a summary with figures and tables of a letter report that I am still working on for the Davis-Besse failure criterion. I hope to have a draft of a more detailed report up to you by early next week.

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

Oak Ridge National Laboratory P.O. Box 2009,Bldg.9204-1,MS-8056,Rm.213A Oak Ridge, Tennessee 37831-8056 USA Intemetwilliamspteoml.gov FAX: (865) 574-0651 Phone:(865) 574-0649 http:/hvww.cped.oml.gov/bio/ptw.html CC:

<bassbr~oml.gov>, cWilliamspt~oml.gov>

Lileviui qtnrla n I JVz__V--r

. CUUC c.ll rs--- X Mora ragei i DRAFT NOT FR ATTRIBUTION 7/3/2002 ORNIUN RCILTR-Contract Program or Project

Title:

Subject of this Docu ment Type of Docu ment:

Authors:

Date of Docu Mnt Heay -Section Steel Technology (HSST) Program Engineering Technology Division Statistical Failure Model for the Davis-B esse RPV Head Letter Report P. T. Williamns B. R. Bass July 2002 Responsible NRC Individual and NRC Office or Division M. T. Kirk Division of Engineering Technolog y Office of Nuclear Regulatory Research Prepared for the U. S. Nuclear Regulatory Commission Washington, D.C. 20555-0001 Under iteragency Areement DOE 186-NOI-9B NRC CN NoY6533 OAK RIDE NATION AL LABOR ATORY Oak Ridge, Tennessee 37S31-8056 managed and operated by UT-Battell e, LLC fr the U. S. DEPAR TMENT OF ENERGY under Contra ct No. DE-AC05-000R22 725

- IJoelle Staretos - ORNL Failure Cntenon.pdt Page 21 DRAFr NOT FDR ARIBUTION 7/3/2002 ORNJN RCILTR -

Statistical Failure Model for the Davis-BesseRPV Head P. T. Willinms B. R. Bass Oak Ridge National Labor story Oak Ridge, Tennessee Manuscript Corn pleted - July 2002 Date Published -

Prepared for the US. Nuclear Regul atory Comnmi ssion Office of Nuclear Regulatory Research Under Interagency Agrean ent DOE 1886-NO1I-9B NRC JCN No. Y6533 OAK RIDE NATION AL LABOR ATORY Oak Ridge, Tennessee 37831-4063 managed and operated by UT-Battell e, LLC for the U. S. DEPAR TMENT OF ENERGY under Contra ct No. DE-AC054000R22 725 2

- I Joelle Starefos - ORNL Failure Citerion.pdf Page 31 DRAFT NOT FOR ATTRIBUTION 7/3/2002 CAUTION This document ha not be rn aven fial patent docurn ent Isla be ven pubi reas a. It must be hnae t

oeT 3

0 MQ whthilo

$ IQ the proper patent d

tedmW el Information rev lws mm axnpl ted Mcord nce with the poides of Oak Ridge National Laboratory and UT-Satteale tLC This repot was prepared s n account of work sponsored by an agency of the Le d States gover nment. Neither the Unied States government nor any agency there of, nor nyo thelir employees.

makes any warranty, express or Implf ad, or assumes any legal flabily or responsibily, for he accsrac y, complete ness, or usefui ness of any hIfrrma on, appar atus, pro duct. or proces dbcos ad. or repress nts tat It use would not kfdnge privately owned ightb. Refere nce herein to ny spec We commercla I product process, or service by ade name, udemar K manamsctre r or other wise. does not necess arily constitute or inply Ks endorsement, reconme ndast on. or favorin g by the. Unite d States gover nment or any agency there.

The views and ophions of aors expressed here I do not necessar ly state or refect those of the Unite d States government or any agency theref.

- I Joelle Starefoc - ORNL Failure Criterion.ocif PanpA I Jofl St ef-

_QNL aiur Citrio.Df

-;n4 DRAFT NOT FOR ATTRIBUTION 7/3/2002 Statistical Failure Model for the Davis-BesseRPV Head P. T. Williams and B. R. Bass Oak Ridge National Labor atory P. O. Box 2009 Oak Ridge, TN, 3783 140 56 Summary This report describes the development of a statistical model of failure for the cladding in the wastage area of the damaged head of the Davis-B esse reactor pressure vessel (RPV). The technical bases for the statistical model are (1) the experimental data developed during disk burst tests reported by Riccardell a Il with geom etries and material proper ties relevant to the Davis-Besse cladding condition, (2) nonlinear finite-strain elastic-plastic finite-element analy ses (perfor med for the current study) of the nine disk burst test specimens reported in [

and (3) a theoret ical continuum-mechanics treatment of plastic instabilit y due to Hill [2] (as cited in [31) applied to the disk burst tests.

In the early 1970s, constrained-disk burst tests were carried out under the sponsorship of the ASME PVRC Suboommittee on Effective Utlization of Yield Strength [4] This test program employ ed a range of materials and specimen geometries that were relevant to components in a nuclear power plant steam supply system. The geometries of the three test specimens analyzed in [] are shown in Fig. 1, and the properties of the three materials are presented in Table 1. The nine disk burst tests produced three center failures and six edge failures over a range of burst pressures from 3.75 to 15 ksi as shown in Table 2. Also presented in Table 2 are the results of a computational study reported In 1] with a comparison to the experim ents quantified by the param eter,

, defined as the ratio of the experimental to predi cted burst pressures for each test.

In the current study, three axisy mmetr c finite-element models (see Fig. 2) were developed to simulate the nine disk burst tests by applying the ABAQUS code with a nonli near finite-strain elastic-pi astic analy sis of each test speci men geo metry and material. The materi al properties provided in 11 ] were used to fit a power-law model for each materi al. The resulting power4aw parameter s are given in Table 1, and the true stress vs. true strain curves are shown in Fig. 3. Also shown in Fig. 3 is the stress-strain curve provided b y

Framatome for simulations of the SS308 cladding In the Davis-Besse bead. Comparison of the curves in Fig. 3 indicates that the ABS-C carbon steel provides reasonably close agreement with the SS308 curve, although SS308 has a yield-strength lower than the three test materials.

Figure 4 presents effective plastic strain contours for the deformed condition of the Geometry A (ABS-C)

J

Joelle Starefos - ORNL Failure Criterion.pgf Page 51 DRAFT NOT rR ATTRIBUTION 7/3/2002 analy sis at the point in the load path just before the onset of a state of numerical instability that aborted the ABAQUS execution.

This state of numerical instability served as the condition for defining a predicted burst pressure for the test specimens. The highly localized plastic straining evident in the region near the fillet at the edge of the disk signals a necessary precondit ion for the onset of plastic collapse (in the form of a numerical breakdown of the solution procedure) in the specimen. This transition from uniform to localized plastic yielding is analogous to the onset of necking n a round-bar tensile specimen.

Figure 5 provides a comparison of the predicted centerline vertical deflection histories with the experim ental deflections at failure for the nine tests.

It is important to note that this nalysis does not attempt to simulate the detailed continuum damage mechanic s associated with this mode of failure. The goal of the analysis Is to simulate the stress-strain state of the specimen along the load path up to the point of Incipient tensile plastic instability. The material is assumed to be homogeneous with no significant defects, where Its elastic-plastic deformation response to multiaxial stress states can be characte rized by the application of increm ental plasticity. J2 flow theory ith Its assoc iated flow rule and Isotropic strain hardening.

Table 3 compares the results of three sets of predicted burst pressures with the experimentally determined burst pressures. The parameter

(- experimental burst pressure/pr edicted burst pressure) is shown as the third colum n for each group of predictions in the table. The predictions based on Hill's theory of plastic instability for pressurized circular diaphrag ms were deve loped by apply ing Hill's failure criterion [2,3] to the materials and geometries of the nine tests. Hill's criterion is valid only for failure at the centerline of the disk and assumes that the deformed geometry of the disk in this region can be treated analy tically as a thin spherical shell under an equiblaxial state of srss. Moving away from the centerline towards the edge of the disk, the stress state becomes more complex (triaxiall and the assumptions of the theory no longer pertain. In Table 3, it can be observed that the predictions using Hill's nstabilit y criterion are in close agree ment with the ABA QUS solutions, even for the cases with edge failures which are not addressed by the theory. This result suggests that, even though six of the nine disks failed at their edges, an of the disks were near a conditi on of the theoretical center line plastic Instability at the point of failure.

Table 4 provides descripti ve statistics for the three sample sets of burst-pressure predictions, using the param eter as the relevant metric. The three samples are also collected together in Table 4 to provide a combined sample size of 26. The Normal and 3-pra. meter Weibull models were investigated to describe the statistical distributions of the FEM solutions (sample size equal to 9) and the combined sample (sample size equal to 26). The results of these analyses are presented in Tables and 6 and Figs. 6 through 9. Given a computational failure prediction for a specific condition of the Davis-Besse wastage area, the resulting Normal and Weibull models can be scaled to provide a statistical distribution for the cumulative probability of failure as a function of pressure loading.

S

Joelle Starefo - ORNL Failure Criterion. f Page 6 DRAFT NOT FOR ATTRIBUTION 7/3/2002 A bounding calculation was carried out for the as-found' condition of the wastage area in the Davis-Besse head. The finite-element model used in the analysis is shown in Fig. 10. An adjusted stress-strain curve (see Fig. 11) was constructed to lower-bound the available data for the cladding material. The geom etry of the wastage area footprint (taken from Fig. 13 in the Root Cause Analysis Report [5D was extended by approxim ately 025 inches (see Fig. 12 and Table 7 for a geometric description of the adjusted footprint).

A uniform cladding thickness of 0.24 inches (the minimum cladding thickness value shown in Fig. 14 of ref. [5]) was assum ed in the model. The model was then loaded with increasing pressure until the point of numerical instability at an internal pressure of 6.65 ksi (see Fig. 13).

For the predicted burst pressure of 6.65 hi the Norm al and Weibull statistical failure models can be scaled to provided estim ates of cumulative probability of failure as a function of internal pressure for the specific conditi on of the wastage area simulated by the analysis. Exarnples of the scaled Weibull model are shown in Figs. 14 and 15 for normalized internal pressure and direct internal pressure, respectively.

As discussed

above, the bounding calculation predicted a burst pressure of 6.65 Wi. For pressures below 5A86 Jai (at the position of the location param eter), the Weibull model pred icts a zero probability of failure. The model based on a normal distribution estimates a cumulative probability of failure of 8.43-10 at the operating pressure of 2.165 ksi and 8.89-10' at 2.5 Wi. (See the table below for additiona I estim ates).

2.155 7.84E-10 0

2.165 S.43E-10 0

2.200 1.09E-09 0

2.225 1.30E-09 0

2.250 1.55E-09 0

2.275 I.86E-09 0

2.300 2.22E.09 a

2.325 2.65E 09 0

2.350 3.15E-09 0

2.375 3.76E-09 0

2.400 4.47E-09 0

2.425 5.32E -09 0

2.450 6.32E-09 0

2.475 7.50E.09 0

2.500 8.89E-09 0

6

joelle Wareos - UKNL -ailure Urnterlon.Ddt Pan 71

• I DRAFT NOT FOR ATTRIBUTION 7/3/2002 Table 1. Property Data for Materials In Disk Burst Tests Stainless 34 84 04 34.07 12936 0.432 162AI 0.27 Steel A-533B Low Alloy 74 96 0.17 74.15 112.32 0.157 139.41 0.12 Steel Cabon 39 64 0.31 39.03 33.34 0.270 10520 0.17 Steel Table 2. Comparison of Experimental to Predicted Failure Pressures In Ret III SS 304 A

15 Edge 12.3 Edge 1.22 B

6.3 Carter 4.8 Edge 1.42 C

7.7 Cater 7.4 Center 1.04 A5338 A

11 Edge 038 Edge 1.12 B

.3 Edge 42 Edge 1.28 C

6.7 Center 8.8 Ceroer

.n AS-C A

U.8 Edge a

Edge 1.23 B

3.75 Edge 3

Edge 1.25 C

4.94 Edge 7

DRAFT NOT OR ATTRIBUTION/

7/3/2002 Table Comparison of Experimental Burst Preinresto Three Predictions A30 Ege 323 Edge 1.2 398 Center 1.16 13.29 Edge 1313 B

63 Center 45 Edge 1.42 592 Center 1.35 612 Edge 109 C

7.7 Center 74 Center 1.04 649 Cetr 1.19 659 Center 117 A533B AX 11 Edge

9.

3.12 337 Center 0.9 3 26 Edge 090 B

5J usge 42 Edg 1.26 5.65 Center 0.94 5.24 Edge 1.01 C

67 Center 6S Center 0.99 619 Center 1.09 603 Edge Il

-XI!Z X

9.5 Ede a

Ed I.3 5.95 Center 1.10 9.05 Edge 1.05 B

3.75 Edge 3

Edge 1.25 4.01 Center 0.92 4.19 Edge 0.39 C

4.94 Edge 4.47 Caner 1.10 446 EdgsCeler 3.1 8

I Joelie btarefos - 0KNL Failure riternon.pdf Page 9I DRAFT NOT FOR ATTRIBUTION 7/3/2002 Table 4. Descriptive Statisticsfor the Ratio of Ecperinental Burst Pressum to Predicted Burst Pressures barn Si 9

9 Zo Mean 1.1902 1.0576 1.0549 1.0975 Standard Error 0.0484 0.0374 0.0331 0.0251 Median 1.2223 1.0953 1.0939 1.1057 Standard Deviation 0.1368 0.1123 0.0993 0.1281 Sample Variance 0.0187 0.0126 0.0099 0.0164 Xurtosis

-0.0506

-1.4799

-0.4349 0.2593 Skewness 0.0007

• 0.5892

-0.9683 0.1714 Range 0.4314 0.2979 0.2739 0.5277 Minim um 0.9853 0.8889 0.8943 0.8889 Maxim um 1.4167 1.1868 1.1682 1.4167 Confidence Level(95.0%/)

0.1144 0.0863 0.0764 0.0517 Table & Welbull Model Parameters and Median Rank Order Statisticsfor ABAQUS Predictions A533B A

0.89718 2

0.131 A533B B

1.0116 3

0.287 ABS-C A

1.0268 4

0.394 SS 304 B

1.09393 5

0.500 ABS-C C

1.10722 6

0.606 A533B C

1.11041 7

0.713 SS 304 A

1.12t76 S

0.819 SS 304 C

1.16S22 9

0.926

• .-4p-vnlue Locaiion g 04 0.2929 0.4236 Scale 0.232 Shape 2.352 Model Sample Mean 1.0535 1.0549 Variance 0.007 0.0099 Std. Dev.

0.0930 0.0993 Medi an 1.0464 1.0939 9

Joelle Starefos - ORNL Failure Criterion.gdf Paae1O DRAFT NOT FOR ATrRIBUTION 7/3/2002 Table 6. Welbull Model Parameters and Median Rank Order Statisticsfor Combined Predictions w~

1 1Hills T1heory A533B A

0.8889 0.U265 2

ABAQUS Soln.

ABS-C B

0.8943 0.0644 3

A3AQUS Soln.

A533B A

0.8972 0.1023 4

Hill's Theory ABS-C B

0.9180 0.1402 5

Hill's Theory A533B B

0.9382 0.1780 6

Ricarrdella(1972)

A533B C

0.9853 0.2159 7

ABAQUS Soln.

A533B B

1.0119 0.2538 8

Ricarrdella (1972)

SS304 C

1.0405 0.2917 9

ABAQUS Soln.

ABS-C A

1.0827 0.3295 10 Hill's Theory A533B C

1.029 0.3674 11 ABAQUS Soln.

SS 304 B

1.0939 0.4053 12 Hill's Theory ABS-C A

1.0953 0.4432 13 Hill'sTheory ABS-C C

1.1042 0.4811 14 ABAQUS Soln.

ABS-C C

1.1072 0.5189 15 ABAQUS Soln.

A533B C

1.1104 0.5568 16 Ricarrdella (1972)

A533B A

1.1224 0.5947 17 ABAQUS Soln.

SS 304 A

1.1288 0.6326 18 Hill's Theory SS 304 B

1.1479 0.6705 19 Hill's Theory SS 304 A

1.1560 0.7083 20 ABAQUS Soln.

SS 304 C

1.1682 0.7462 21 Hll's Theory SS 304 C

1.1868 0.7841 22 Ricarrdella (1972)

SS 304 A

1.2195 0.8220 23 Ricarrdella (1972)

ABS-C A

1.2250 0.8598 24 Ricarrdella (1972)

ABS-C B

1.2500 0.8977 25 Ricarrdlla (1972)

A533B B

1.2619 0.9356 26 Rlcarrdella (1972)

SS 304 B

1.4167 0.9735

= Experimental Burst Pressure/Predicted Burst Pressure Location 0.825 D i

r.

bOF Scale 0.308 Nornal 3.16240 0.07568 2

Shape 2.301 WeibUII 1.69430 0.42864 2

.69430 Model Sample Mean 1.0975 1.0975 Variance 0.0158 0.0164 Std. Dev.

0.1256 0.1281 Median 1.0876 1.1057 10

I Joelle Starefos - ORNL Failure Criterion.Ddf Pace 11I I

~~~~~~~~~~~

~

a DRAFT NOT FOR ATRIBUTION Table 7. Wastage-Arma-F ootprInt Geometry Data 7/3/20 02

~~

N w d p~~~~~~ c w

. s k 4~~~~~~~~

4~ ~ ~

t ~ ~ ~ 2 %

~ ~ ~ ~ Ap k ;~ z A gF T igEK-

__t8,.:Be~~i1 A&Fmd FpuiuL I

33 6

4122 4.1194 319 99933

-117.16 75.26 197.41

.0934. 4A753>

4.l4353. 0.004>

A4uruilFodpd j 0.5.

4006 31.73 36 0 4u5 129.02 13031.31.14.235 "9A0 243.71 4943. 4.4476>

4.4476, 0.943>

hr Dhdh O lahiha iFll Ca bi -wdiut. syas N z-a di dmp 4 Oh fl walk!

m il n.

mdt.

Th. s pl-dMb abs! s adisa qyl.Isa

• ab. ml phe with a Xi sgbw 5..

mbht s st nmwfi.rFsNds 3 ad 1.

'As Found" Footprlnt

/t Area -3536 Ins Perimeter - 30.36 In.

r, = r + a x;= -r, cos(Md Y, = r in(j 11

- I Joelle Starefcs - ORNL Failure Criterion.df Page 121 DRAFT NOT FOR ATRIBUTION 7/3/2002 Geometry A f UTSR 1 0.3 Geometry B

/

• O 1'Zig Geometry C 0.3M T

Us I -Xt Fig. 1. Geometric descriptions of three burst disk specinens used In 11 all dimenslonsare nche#.

Images on the right are Photoworks -rendered views of V.-symmetry solid models of the three specimens.

12

5 -

-I Joelle tarefos - ORNL Failure Criterion.ipdf Page 131

• I Joelle Staretos

- ORNL Failure Cntenon.Ddf Paae 133~~

DRAFT NOT FOR ATTRIBUTION 7/3/2002 aI Geometry A I

1.0 in.

I L

Geometry C S~~~~~~~~~~!

E-S 1.0 i.

I T

1.0 in.

IL II III t=0.125 in.

/

r = 0.375 in.

3in.

i I

5 in.

.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Fig. 2 Axisymmetrl c finite-element meshesusedin the analysesof disk burst testsreported In [11.

Quadratic 8-node axisyrnmetric (CAX OR) Iermentswlth reduced Integration were used In a nonlinear finite-straln faslc-plastic analysis of the three burst disk geometreswlth three materials.

13

oleSaeo LFiue Crt>,Cneion.df Paqe 41 I Joelle Starefos - ORNL Failure Criterion.pdf Page 141 DRAFT 140 120 0

100 0

E 80 CO i-60 40 20 NOT FOR ATTRIBUTION 7/3/20 02 0

0.1 0.2 0.3 0.4 0.5 True Straln (-)

06(11(2002.KI ptw Fig. 3. True trewvstrue strain curves of the three materials used In the disk burt testscompared to SS308 at 600 F. These curveswere developed using a power4aw straln-hardening model fitted to yield and ultimate strength/straln data for each materi l.

14

I I Joelle Starefos - ORNL Failure Criterion.Ddf Page 151 IJoelle Starefos - ORNL Failure Criterion.odf Paoe 151 DRAFT NOT FOR ATTRIRUTION 7/3/2002 Om.

II:

?"

Geometry A ABSC Predicted BP = 9.05 ksi Experimental BP = 9.8 ksl a

k.

t Out Goout A 0:

MokACU MAOSB3Uld 6.3.4 IW J. 11 tIWo, 3.1W, tblli lre zm1U2 Itr. atWI *2 Sla 11M -

r, ve: PcDa Ian kd n fee0 1 O.<

Ref. P. C. Riccardella, TEastDPlasffc Ana3ps of Consrined Disk Bus Tests,'

ASIMIE Paper No. 72-PVP-12, ASME Pirssure Wssels ad Poft Conference, New Orleans, L, Seplember 17-21,1972.

la)

(b)

Fig. 4. Effective plastic strain contours for the Geometry A ABS-C carbon steel) specimen at the point of numerical Instability. Highly localized plastic straining provides a precondition for plastic collapseat the edge of the specimen.

is

' Joelle Starefo - ORNL Failure riterlorimif Page 161 IJoelle Starefos - ORNL Failure Criterion.DdT Pacze 161 DRAFT NOT FOR ATTRIBUTION.

7/3/20 02 SS304 I

I I

(a)

I I

I (b)

I I

I (C)

Pfessure (ft) ov2eUMPtr.

Fig. 6. Comparison of experimental centerline vertical deflectionsat failure to FEM vertical deflection historlesat the center of the Geometry A and B specinuns for (a) SS 304, (b) A533-B, and (c) ABS-C materials, and 16

- WoelleStarefos-ORNL Failure Criterion.Ddf Pacie 171

..~el Strfs-ON alr neinofPa 7

DRAFT NOT FOR A RIBUTION 7/3/2002

. ABS-C Specimen Fa1lrMe SS304 Specimen Failure Geometry C 2

S

.1 S

V a

C is.

'I L.

1.5 I

0.5 A~~~~~~S.4..~~~~~~~.....

SS $ 4....F..

~~~~~'A 33B~~~~~...........

.,*j~~rw

-I~~~~~~~~~~........

al I..

OW-11V "',

I i__-

I n

I I

0 2

4 6

8 10 12 14 (d)

Pressure (ksl) 06/1212002.K4 ptw Fig. 6. {continued) (d) vertical deflection htstorlesat the center of Geometry C, all three materials.

17

0,,

- I -,.",

Joelle Starefos - ORNLFailureCriterion.pdf Page 181 I Joelle Starefos - ORNL Failure Criterlon.Ddt Pane 151 DRAFT 4

NOT FOR ATTRrBUTION 7/3/2002 a:,

ID C

Q a

20 3

2 I

n 0.6 0.8 1

1.2 1.4 Exp. Burst PressurelPredicted Burst Pressure, a 07101102.K1 ptw Fig. 6. Probability densitlesfor two continuousstatMical distributions fitted to the sample of 9 data points for a experimental burst pressurefFEM predicted burst presswe.

i2

-I Joelle Sarezfos -ORNL Failure Cterion.P~df Paae 19 1 I Joelle Starefos - ORNL Failure Criterion.odf Paoe 193 DRAFT NOT FOR ATRI3UTION 7/3/2002 3.5 w,

W,

Normal Distribution Mean

= 1.0975 StdDev=0.1281 2.5 -

\\.

/

5,

\\

mean = 1.098 co 2.5 -

F m

median = 1.088 C

a2 Weibull Distribution Locatqn=0.825 I\\

Scale

=0.308 0

1.-

Shape

= 2.302 0.5

/

/

,,,,~~~

, / **,a*

a I

Q%

6 0.8 1

12 1A Exp. Burst Pressure/Predicted Burst Pressure, at 07103/02.Kt ptw Fig. 7 Probability densitlesfor two continuous AsatisIcal distributions ftted to the combined sample of 26 data points for

-experlmental burst pressum I predlcted burst pressure.

19

,; fJoelleStarefos-ORNL Failure Criterion.pdlf Pag 201 IJoelle Starefos - ORNL Failure Cnterion.pdf Page 201 DRAFT NOT FOR ATTRIBUTION 7/3/2002 I

a3 0.8 L

0 go

.0 2

tL2 04 E=O02 a.

Order SWatd 95

• I P = i- 0.3 0.'

n+0.4 p

I I

I I

I 0.8 1

1.2 1.A Exp. Burst Pressure/Predicted Burst Pressure, a 07/01/02.K2 ptw Fig..Welb ull statIstlcalfallure model (in r-9) compared to a nonnal cumulative distribution function, median rank order statistic, and the 90% confidencelnterval on the order statlstic.ABAQUS FEM solutionswere usedto develop the models.N.B.: The order statistlcsand their 90% confidencelntervals are shown here for comparative purposesonly and were not used In the point-estimate procedures for the paramete is of either the Wel bull or Normal distributions.

20

I Joelle trefo-ORNL Failure Criterion.odf

_~~~~~~~~~~~~~Pg IJoelle Starefos - ORNL Failure Cnterlon.Ddf Paae 21 DRAFT NOT FOR ATTRIBUTION 7/3/2002 1_

0 Weibull Distribution

o.

0.8 Location=0.825 Scale

=0.308 Shape

=2.302 F

Ž0.6 2

Normal Distribution

/

10.

Mean

= 1.0975 0.4 StdDev=0.1281

/f.

E 0.2 Order0Stat tO

' 0o i,.

- 0.3 0.6 0.8 1

1.2 1.4 Exp. Burst Pressure/Predicted Burst Pressure, c 07/M2.K2 ptw Fig. 9. Welbull statlstlcalfilure model (n w 26) compared to a normal cumulative distribution function, medlan rnk order statistic, and the 90% confldencelnterval on the order statstic. Models developedwIth combined saipia N.B.: The order statisticsand their 90%

confidence Intervals are shown here for comparative purposesonly and were not used In the polnt4stImate procedures for the parameters of eIther the Wel bull or Normal distributions.

21

I Joelle Starefos - ORNL Failure CNrteon.odf Page 221 DRAFT (a)

NOT FOR ATRZSBUT!ON 7/3/2002 Submodel of Wastage Area 16,935 elements 52,887 nodes Nozzles 3, 11, 15, and 16 Base Material nflned dadding wun wastage area Ggh~hicknms pt VS20 strain gradients Fig. 10. Flniteelement global and submodelsof the Davis-Bessehead and wastage area. The displacemerts at the vertical side boundaries of the submodel are driven by the global model. Both models are exposedto the same Internal pressure loading.

22

-- 9 Joelle Starefos -ORNLFailureCniterionimpdf Paae 231 Iloelle Starefas

-QRNL Failure Cntenon.Ddf Pacie 231~~

DRAFT NOT FOR ATTRIBUTION 7/3/2002 I

I 80 9n 0

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I I

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Framatome a 8114.992 60f2 SS308 Curve

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0.15 0.2 06I1I12OO2.K1 ptw Fig. 11. Adjusted SS308 stressvsstrain curve usedin the bounding-casecalculations compared to curvesfrom a range of A8W heats.Straln hardening In the adjusted curve was reduced to lower-bound all of the data. The offsetyleld strength and strain at ultimate strength were retained from the unadjusted SS304 curve received from Fra matome.

23

I Joelle refos - ORNL Fallure Crfterion.pdf Pa-ie 241 DRAFT NOT FOR ATTMROSUTION 7/3/2002 Fig. 12. Geometry of udJusted wastagearea footprint Lower figure Isa Photoworks -rendered Image of the ubmodel with the adjusted as-found" footprint 24

Jl Strefs -ORNL Failure Criterion.bdf Pace 251 IS-.Ilel trf--ON aiueCieinnfPa 251 DRAFT NOT FOR ATTRIBUTION 7/3/2002 (a)

I.

j_

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Fig. 13 Effective plasticstraln histories at two high-straln locations in the wastagearea: (a) near the center and b) near Nozzle 3.

25

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- ORNL Failure Criterion.Ddf

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ge26'1 I ole*~eo RLFiueCtro~d ae2 DRAFT NOT FOR ATTRIBUTION 7/3/2002 Internal Pressure I Operating Pressure 2.5 3

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1.2 1.4 Exp. Burst PressurelPredicted Burst Pressure, a 07103102.K5 ptw Fig. 14. Application of the failure statistical criterion producesa cumulative probability of failure (based on a Weibull distribution) curve for the Bounding Case condition. Cumulative probability of failure as a function of normall zed Internal pressure.

26

I Joelle uc2tarefc - ORNL Failure critedon.pdf pg 271 I oler arfs-ONLFiueCrtro$dfPg 7

DRAFT NOT FOR ATTRIBUTION 7/3/2002 Intemal Pressure (ksi) 4.8 5.6 6.4 7.2 8

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1.2 1.A Exp. Burst PressurelPredicted Burst Pressure, 07103102.K4 ptw Fig. 15. Application of the failure statisticalcriterlon producesa cumulative probability of failure (based on a Welbull distribution) curve for the Bounding Case condition. Cumulative probability of failure as a function of Internal pressure.

27

Joelle Starefos - ORNL Failure Criterion. df Pae 28 DRAFT NOT FOR ATTRIBUTION 7/3/2002 References

1. P. C. Riccard ella, 'Elasto-Plastic Anialy sis of Constrained Disk Burst Tests," Paper No. 72-PVP-12, presented at the ASME Pressure Vessels and Piping Conference, Septem ber 17-21, 1972, New

Orleans, A.

2. R. Hill, A Theory of the Plastic Bulging of a Metal Diaphrag m by Lateral Pressure," Philos. Mag.

(Ser. 7 41, (1950) 1133.

3.

A. R. Ragab and S. E. Bayourn i, Engineering Solid Mechanics, Fundamentals and Applications, CRC Press LLC, Boca Raton, I, 1999.

4. W. E. Cooper, E R Kofteam p, and 0. A. Spiering, Experim ental Effort on Bursting of Constrained Disks as Related to the Effective Utilization of Yield Strength," Paper No. 71-PVP-49, ASME Pressure Vesselsandffpiig Conferenoe, May 1971.

S. S. A. Loehle i, Root Cause Analysis Report, Significant Degradation of Reactor Pressure Vessel Head, CR 2002-08 91, Dav is-Besse Power Station, April 15, 2002.

28

' I Joelle Starefos - Mime.822 ft

Starefos I

P I

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Date: Wed, 03 Jul 2002 14:53:45 -0400 From: "Paul T. Williams" <williamspt@om.gov>

Subject Failure Model for DB X-Sender ptw@ca03.cad.oml.gov To: mark Kirk <MTK@nrc.gov>

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Attached Is a summary with figures and tables of a letter report that I am still working on for the Davis-Besse failure criterion. I hope to have a draft of a more detailed report up to you by early next week.

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

Oak Ridge National Laboratory P.O. Box 2009,Bldg.9204-1,MS-8056,Rm.213A Oak Ridge, Tennessee 37831-8056 USA Intemetilliamsptcoml.gov FAX: (865) 574-0651 Phone:(865) 574-0649 http:/lvww.cped.oml.gov/bio/ptw.html

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