e-mail from hackett to db lltf, re: failure model for db. · the form of a numerical breakdown of...

Je Sta fos-Fwd: Failure ModelforDB Pa_

From: Edwin HackettTo: DB LLTFDate: 7/3/02 4:33PMSubject: Fwd: Failure Model for DB -

FYI - update on RES contractor efforts

I Joelle Stare=s - Fwd; Failure Model for PanPage---- � --- -- -

From: Mark Kirk CezTo: Steven Long , Date: 7/3/02 4:13PMSubject: 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 adraft).

The short summary of this report is as follows:

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

2. If instead we adopt a Normal cumulative probability function to represent the uncertainty associatedwith the failure criteria we arrive at a cumulative probability of failure of 8.4E-10 at the operating pressureof 2.165 ksi. At a slight overpressure (2.5 ksi) the probability of failure goes up by about an order ofmagnitude 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 1I 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 3:10PMSubject: Failure Model for DB

Mark:

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

Thanks

Paul

Paul T. Williams, Ph.D., P.E.Oak Ridge National LaboratoryP.O. Box 2009,Bldg.9204-1,MS-8056,Rm.213AOak Ridge, Tennessee 37831-8056 USAIntemetwilliamspteoml.govFAX: (865) 574-0651Phone:(865) 574-0649http:/hvww.cped.oml.gov/bio/ptw.html

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

Lileviui qtnr|a - n I .- JVz__V--r . CUUC ..c.ll rs--- X

Mora - -----ragei i

DRAFT NOT FR ATTRIBUTION 7/3/2002

ORNIUN RCILTR-

Contract Program orProject Title:

Subject of this Docu ment

Type of Docu ment:

Authors:

Date of Docu Mnt

Heay -Section Steel Technology (HSST) ProgramEngineering Technology Division

Statistical Failure Model for the Davis-B esse RPV Head

Letter Report

P. T. WilliamnsB. R. Bass

July 2002

Responsible NRC Individualand NRC Office or Division

M. T. KirkDivision of Engineering Technolog yOffice of Nuclear Regulatory Research

Prepared for theU. S. Nuclear Regulatory Commission

Washington, D.C. 20555-0001Under iteragency Areement DOE 186-NOI-9B

NRC CN NoY6533

OAK RIDE NATION AL LABOR ATORYOak Ridge, Tennessee 37S31-8056

managed and operated byUT-Battell e, LLC fr the

U. S. DEPAR TMENT OF ENERGYunder Contra ct No. DE-AC05-000R22 725

- - -.. - .. - - -

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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 2002Date Published -

Prepared for theUS. Nuclear Regul atory Comnmi ssion

Office of Nuclear Regulatory ResearchUnder Interagency Agrean ent DOE 1886-NO1I-9B

NRC JCN No. Y6533

OAK RIDE NATION AL LABOR ATORYOak Ridge, Tennessee 37831-4063

managed and operated byUT-Battell e, LLC for the

U. S. DEPAR TMENT OF ENERGYunder Contra ct No. DE-AC054000R22 725

2

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CAUTION

This document ha not be rn aven fial patent

docurn ent Isla be ven pubi reas a. It must behnae t oeT 3 0 _

MQ whthilo $ IQ the proper patent dtedmW el Information rev lws mm axnpl ted Mcord nce with the poides of Oak RidgeNational Laboratory and UT-Satteale tLC

This repot was prepared s n account of work sponsored by anagency of the Le d States gover nment. Neither the Unied Statesgovernment nor any agency there of, nor nyo thelir employees.makes any warranty, express or Implf ad, or assumes any legalflabily or responsibily, for he accsrac y, complete ness, orusefui ness of any hIfrrma on, appar atus, pro duct. or proces dbcos ad. or repress nts tat It use would not kfdnge privatelyowned ightb. Refere nce herein to ny spec We commercla I productprocess, or service by ade name, udemar K manamsctre r orother wise. does not necess arily constitute or inply Ks endorsement,reconme ndast on. or favorin g by the. Unite d States gover nment orany agency there. The views and ophions of aors expressedhere I do not necessar ly state or refect those of the Unite d Statesgovernment or any agency theref.

- I Joelle Starefoc - ORNL Failure Criterion.ocif PanpA I Jofl St ef- _QNL aiur Citrio.Df -;n4


Statistical Failure Model

for the Davis-BesseRPV Head

P. T. Williams and B. R. BassOak Ridge National Labor atory

P. O. Box 2009Oak 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

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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


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 02.165 S.43E-10 02.200 1.09E-09 02.225 1.30E-09 02.250 1.55E-09 02.275 I.86E-09 02.300 2.22E.09 a2.325 2.65E 09 02.350 3.15E-09 02.375 3.76E-09 02.400 4.47E-09 02.425 5.32E -09 02.450 6.32E-09 02.475 7.50E.09 02.500 8.89E-09 0

6

- joelle Wareos - UKNL -ailure Urnterlon.Ddt Pan 71* I


Table 1. Property Data for Materials In Disk Burst Tests

Stainless 34 84 04 34.07 12936 0.432 162AI 0.27

SteelA-533BLow 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 1.22B 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 1313B 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

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Table 4. Descriptive Statisticsfor the Ratio of Ecperinental Burst Pressumto Predicted Burst Pressures

barn Si 9 9 ZoMean 1.1902 1.0576 1.0549 1.0975Standard Error 0.0484 0.0374 0.0331 0.0251Median 1.2223 1.0953 1.0939 1.1057Standard Deviation 0.1368 0.1123 0.0993 0.1281Sample Variance 0.0187 0.0126 0.0099 0.0164Xurtosis -0.0506 -1.4799 -0.4349 0.2593Skewness 0.0007 *0.5892 -0.9683 0.1714Range 0.4314 0.2979 0.2739 0.5277Minim um 0.9853 0.8889 0.8943 0.8889Maxim um 1.4167 1.1868 1.1682 1.4167Confidence 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 0.131A533B B 1.0116 3 0.287ABS-C A 1.0268 4 0.394SS 304 B 1.09393 5 0.500ABS-C C 1.10722 6 0.606A533B C 1.11041 7 0.713SS 304 A 1.12t76 S 0.819SS 304 C 1.16S22 9 0.926

* .-4p-vnlue .:

Locaiion g 04 0.2929 0.4236Scale 0.232

Shape 2.352Model Sample

Mean 1.0535 1.0549Variance 0.007 0.0099

Std. Dev. 0.0930 0.0993Medi an 1.0464 1.0939

9

. Joelle Starefos - ORNL Failure Criterion.gdf Paae1O

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Table 6. Welbull Model Parameters and Median Rank Order Statisticsfor Combined Predictions

w~

1 1Hills T1heory A533B A 0.8889 0.U2652 ABAQUS Soln. ABS-C B 0.8943 0.06443 A3AQUS Soln. A533B A 0.8972 0.10234 Hill's Theory ABS-C B 0.9180 0.14025 Hill's Theory A533B B 0.9382 0.17806 Ricarrdella(1972) A533B C 0.9853 0.21597 ABAQUS Soln. A533B B 1.0119 0.25388 Ricarrdella (1972) SS304 C 1.0405 0.29179 ABAQUS Soln. ABS-C A 1.0827 0.3295

10 Hill's Theory A533B C 1.029 0.367411 ABAQUS Soln. SS 304 B 1.0939 0.405312 Hill's Theory ABS-C A 1.0953 0.443213 Hill'sTheory ABS-C C 1.1042 0.481114 ABAQUS Soln. ABS-C C 1.1072 0.518915 ABAQUS Soln. A533B C 1.1104 0.556816 Ricarrdella (1972) A533B A 1.1224 0.594717 ABAQUS Soln. SS 304 A 1.1288 0.632618 Hill's Theory SS 304 B 1.1479 0.670519 Hill's Theory SS 304 A 1.1560 0.7083

20 ABAQUS Soln. SS 304 C 1.1682 0.746221 Hll's Theory SS 304 C 1.1868 0.784122 Ricarrdella (1972) SS 304 A 1.2195 0.822023 Ricarrdella (1972) ABS-C A 1.2250 0.859824 Ricarrdella (1972) ABS-C B 1.2500 0.897725 Ricarrdlla (1972) A533B B 1.2619 0.935626 Rlcarrdella (1972) SS 304 B 1.4167 0.9735

= Experimental Burst Pressure/Predicted Burst Pressure

Location 0.825 D i r. ... : bOFScale 0.308 Nornal 3.16240 0.07568 2Shape 2.301 WeibUII 1.69430 0.42864 2

.. - .69430

Model SampleMean 1.0975 1.0975

Variance 0.0158 0.0164Std. Dev. 0.1256 0.1281

Median 1.0876 1.1057

10

I Joelle Starefos - ORNL Failure Criterion.Ddf Pace 11II - ~~~~~~~~~~~ ~ a

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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 dmp4

Oh fl walk! m il n. mdt.Th. s pl- dMb abs! s adisa qyl .Isa * ab. ml phewith a Xi sgbw 5.. mbht s st nmwfi .rFsNds 3 ad 1.

'As Found" Footprlnt /tArea -3536 Ins

Perimeter - 30.36 In.

r, = r + a

x;= -r, cos(MdY, = r in(j

11

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Geometry Af UTSR

1 0.3Geometry B

/ *O 1'Zig

Geometry C0.3M

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 thethree specimens.

12

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* I Joelle Staretos - ORNL Failure Cntenon.Ddf Paae 133~~~~~~~~~~~~~~~~~~~~~~~~~-


aI Geometry A

I1.0 in.

I

L Geometry CS~~~~~~~~~~! E-S

1.0 i.

IT1.0 in.

ILIIIII

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 anonlinear finite-straln faslc-plastic analysis of the three burst disk geometreswlth threematerials.

13

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140

120

0 100

0E 80

CO

i- 60

40

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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 testscomparedto SS308 at 600 F. These curveswere developed using a power4aw straln-hardening modelfitted to yield and ultimate strength/straln data for each materi l.

14

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Om. II: ?"

Geometry AABSC

Predicted BP = 9.05 ksiExperimental BP = 9.8 ksl

a k. t Out Goout A0: 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, NewOrleans, L, Seplember 17-21,1972.la)

(b)

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

is

' Joelle Starefo - ORNL Failure riterlorimif Page 161IJoelle Starefos - ORNL Failure Criterion.DdT Pacze 161

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SS304

II

I

(a)

III

(b)

III

(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-CSpecimen

Fa1lrMe

SS304Specimen

Failure Geometry C2

S.1S

Va

Cis.

'IL.

1.5

I

0.5

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

SS $ 4....F.. .. !...... .. .... .. ... .. . .. ... .. .. ... .. . .. . .. . .. .

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

. ,*j~~rw-I~~~~~~~~~~... ..... ..

... ... al -.........I.. .. ..

OW-11V "',

..... :.....

......

............

I..... i__-

.-. ; -----

...........

.....

In I I0 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

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I Joelle Starefos - ORNL Failure Criterlon.Ddt Pane 151

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a:,IDCQ

a

20

3

2

I

n 0.6 0.8 1 1.2 1.4

Exp. Burst PressurelPredicted Burst Pressure, a 07101102.K1 ptwFig. 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 1I Joelle Starefos - ORNL Failure Criterion.odf Paoe 193

DRAFT NOT FOR ATRI3UTION 7/3/2002

3.5 . . , , , . w , W ,

Normal DistributionMean = 1.0975StdDev=0.1281

2.5 - \. / 5, \ mean = 1.098co 2.5 - F m median = 1.088C

a2 Weibull DistributionLocatqn=0.825 I\

Scale =0.3080 1.- Shape = 2.302

0.5 / / .

:,,,,~~~ , / **,a* a '"*, IQ% 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 sampleof 26 data points for -experlmental burst pressum I predlcted burst pressure.

19

,; fJoelleStarefos-ORNL Failure Criterion.pdlf Pag 201IJoelle Starefos - ORNL Failure Cnterion.pdf Page 201


I

a3 0.8L

0

go

.02

tL2 04

E=O02a. Order SWatd95 %' *I P = i- 0.3

0.' . n+0.4p I . . . I . I I I

0.8 1 1.2 1.AExp. Burst Pressure/Predicted Burst Pressure, a 07/01/02.K2 ptw

Fig. .Welb ull statIstlcalfallure model (in r-9) compared to a nonnal cumulative distributionfunction, median rank order statistic, and the 90% confidencelnterval on the orderstatlstic.ABAQUS FEM solutionswere usedto develop the models.N.B.: The orderstatistlcsand their 90% confidencelntervals are shown here for comparative purposesonlyand were not used In the point-estimate procedures for the paramete is of either the Wel bullor Normal distributions.

20

I Joelle trefo- ORNL Failure Criterion.odf _~~~~~~~~~~~~~Pg -

IJoelle Starefos - ORNL Failure Cnterlon.Ddf Paae 21


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 .% Order0StattO ' 0o i,. - 0.3

0.6 0.8 1 1.2 1.4Exp. Burst Pressure/Predicted Burst Pressure, c 07/M2.K2 ptw

Fig. 9. Welbull statlstlcalfilure model (n w 26) compared to a normal cumulative distributionfunction, medlan rnk order statistic, and the 90% confldencelnterval on the orderstatstic. Models developedwIth combined saipia N.B.: The order statisticsand their 90%confidence Intervals are shown here for comparative purposesonly and were not used In thepolnt4stImate procedures for the parameters of eIther the Wel bull or Normal distributions.

21

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Submodel of Wastage Area

16,935 elements52,887 nodes

Nozzles 3, 11,15, and 16

Base Materialnflned dadding wun wastage area

Ggh~hicknms pt VS20strain gradients

Fig. 10. Flniteelement global and submodelsof the Davis-Bessehead and wastage area. Thedisplacemerts at the vertical side boundaries of the submodel are driven by the globalmodel. Both models are exposedto the same Internal pressure loading.

22

-- 9- Joelle Starefos -ORNLFailureCniterionimpdf Paae 231

Iloelle Starefas -QRNL Failure Cntenon.Ddf Pacie 231~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9


I I

80

9n0

U,CD 402

I I . . . I . . . . I. . .

Framatome a 8114.992 60f2 _. -SS308 Curve

" '4'~~~cra -69.65 ksi

~~ C,,a = 61.6i4 ksi

Adjusted SS30S Curvefor Bounding Calculation

08 cune C;L = 94-3 5 0l941

20 'At600 FE - 25,571 kslv - 0.295

-sSS 38- SS 308 adko~td. . - M10

- A8W*102. _,- A8W-103. -. - ASW-104* -- - AW-l105* -. - ASW-106

A8W data at 550 FI IIi.

0 0.05 0.1

True Strain f-)0.15 0.2

06I1I12OO2.K1 ptwFig. 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 tolower-bound all of the data. The offsetyleld strength and strain at ultimate strength wereretained 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 -renderedImage of the ubmodel with the adjusted as-found" footprint

24

- Jl Strefs - ORNL Failure Criterion.bdf Pace 251 IS- .Ilel trf--ON aiueCieinnfPa 251


(a)

I.

j_

lb)

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

25

- I Joelle �-�refo - ORNL Failure Criterion.Ddf -�Pa�ge26'1I ole*~eo RLFiueCtro~d ae2


Internal Pressure I Operating Pressure2.5 3 3.5 42 4.5

=0.

.0.

.4-

=0.

2

IL0

- Welbull Dlistrbution ... *......

-.Location =2.534 ..........Scale =0.94.....

8 Shape =2.302

Operain 2; 1 6 si urt = .65 ksia^Z *-*-*

Pressure ~~Pre ssue2 . . . L ~ | . 4 b. , , W e.l D .s.r.b.u. i o n

Normal ~~ ~cae =030 ..... _ ..... .... . ..... ..

t! . ..... .... ' ,~~.... ..... _

..Prssr .. . .esr .. .. . ........ L tio . 2j~~~~~~~~~~~~... .. = 2302_

*~~~~~~~J Shapeb-:-'nwv* --- s $wt-i t- -@t .S.

0.6 0.8 1 1.2 1.4Exp. 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. Cumulativeprobability of failure as a function of normall zed Internal pressure.

26

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


Intemal Pressure (ksi)4.8 5.6 6.4 7.2 84 8.8 9.6

tI ~-- _- -.... . .

IC

Is-

.0

to.02?a.

EV.

. . Weibull Dstribuon .

.. Location - 5486 . . . .. ....., Scale = 6.291 ..... ..

Shape = 2.302... ... ... ... .. , ~~~... ... . .....

_.'.j..,. ....;.t.. .|.,..t. ^-'vi-eet -'^wi!^¢.......... ..g......... ...IPredictedBurst .65 . . ....... ..... ......... .. .....

Pressure0.4 .

~~~~~. . . . . . . ,. . , . ., . . .. . . ~ . . . . . . . . . .. .... . . . . .

0.2 i-We.bul Dlst_.butionLocation 0.825.. ........ .. Scale 0.308

.urt=.5................ .. S. ......... .. .. hape 2302

0.6 0.8 1 1.2 1.AExp. 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. Cumulativeprobability of failure as a function of Internal pressure.

27

Joelle Starefos - ORNL Failure Criterion. df Pae 28


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, NewOrleans, 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, CRCPress LLC, Boca Raton, I, 1999.

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

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

28

' I Joelle Starefos - Mime.822ft�� Starefos - I P I

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Date: Wed, 03 Jul 2002 14:53:45 -0400From: "Paul T. Williams" <[email protected]>Subject Failure Model for DBX-Sender [email protected]: mark Kirk <[email protected]>Cc: [email protected], w1ilamspt~ornI.govMessage-id: <[email protected]>MIME-version: 1.0X-Mailer QUALCOMM Windows Eudora Version 5.1Content-type: multipart/mixed; boundary="===================204592859==-

-====================_204592859=-Content-Type: text/plain; charset="us-ascli"; forma lowed

Mark:

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

Thanks

Paul

Paul T. Williams, Ph.D., P.E.Oak Ridge National LaboratoryP.O. Box 2009,Bldg.9204-1,MS-8056,Rm.213AOak Ridge, Tennessee 37831-8056 USAIntemetilliamsptcoml.govFAX: (865) 574-0651Phone:(865) 574-0649http:/lvww.cped.oml.gov/bio/ptw.html

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e-mail from hackett to db lltf, re: failure model for db. · the form of a numerical breakdown of...

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