ML18038A735

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Final Rept, Elastic-Plastic Fracture Mechanics Assessment of Nine Mile Point Unit 1 Beltline Plates for Service Level C & D Loadings.
ML18038A735
Person / Time
Site: Nine Mile Point Constellation icon.png
Issue date: 02/22/1993
From:
NIAGARA MOHAWK POWER CORP.
To:
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ML17056C285 List:
References
MPM-USE-293216, NUDOCS 9303040167
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NMPCProject03-9425MPM-USE-293216 FINALREPORTentitledELASTIC-PLASTIC FRACTUREMECHANICS ASSESSMENT OFNINEMILEPOINTUNIT1BELTLINEPLATESFORSERVICELEVELCANDDLOADINGSMPMResearchdrConsuIting wi<~~~'//j~j~~Zp/>>

February22,19939303040ih7

'730226PDR.ADQCK.05000220 P'DR

3TableofContents1.0Introduction

~\~~~~~~2.0MaterialModel.3.0Transient Selection 3.1LevelCTransient Selection

....3.2LevelDTransient Selection

....3.3Screening Analysis3.3.1ModelDescription..........

3.3.2LevelCTransient Analysis3.3.3LevelDTransient Analysis3.3.4SummaryofCandidate Transients 7778899104.0FiniteElementAnalysis..........,.......

4.1ModelDescription

..4.2FiniteElementAnalysisResults4.3LimitingTransients

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

26262627'lastic-Plastic FractureMechanics Assessment

.....5.1ModelDescription....

5.1.1VesselGeometry............

5.1.2AppliedLoads5.1.3LimitsforSmallScaleYieldingAnalysis5.1.4FractureMechanics Model........

5.2Calculations forA302BMaterialModel......

5.2.1LevelCLoading......

5.2.2LevelDLoadingAnalysis,.........

5,2.3TensileInstability Analysis393939394040434343436.0SummaryandConclusions

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

t'.0References

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

5254Acknowledgement

.........

56A+0ppendtces

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

AppendixAAppendixB~~~~~~~~~~~~~~~~~~575883

1.0 Introduction

Nuclearreactorpressurevesselmaterials mustbetestedandevaluated toensurethattheyaresafeintermsofbothbrittleandductilefractureundernormaloperation andduringdesignbasistransients.

Withregardtoductilefractureprotection, AppendixGto10CFR50prescribes ascreening criterion of50ft-lbs.Ifanybeltlinematerials areexpectedtoexhibitCharpyUpperShelfEnergy(USE)(T-Lorientation) lev'elsbelow50ft-lbs,thenadditional analysesmustbeperformed toensurecontinued safeoperation.

TheDraftASMEAppendixX[ASME92]wasdeveloped toassistlicensees inperforming elastic-plastic fracturemechanics evaluations forbeltlinematerials withlowuppershelfenergies.

Thisreportdocuments application ofthedraftAppendixXcalculative procedures andcriteriatotwoNineMilePointUnit1(NMP-1)beltlineplatesforServiceLevelCandDloadings.

TheNMP-1beltlinematerials wereevaluated todetermine whetheranymaterials wouldexceedthe50ft-lbscreening criterion.

Theresultsoftheseevaluations aresummarized inReference

[MA93]andwerepresented intheresponsetoNRCGenericLetter92-01[MA92].Asaresultoftheseevaluations, NMPCconcluded thatanAppendixXanalysismustbeperformed forbeltlineplatesG-8-1and6-307-4.TheresultsoftheAppendixXanalysisforServiceLevelAandBloadingswerereportedinReference

[MA93].ThisreportpresentstheresultsoftheServiceLevelCandDloadinganalysis.

/

2.0MaterialModelTheNMP-1beltlineplateswerefabricated usingA302Bmodified(A302M)steel.Atpresent,sufficient J-Rdataarenotavailable toconstruct anA302Mmodel.Asdiscussed inReference

[MA93],theNMP-1platesarebestmodelledusinganA302BJ-Rmaterialmodel.TheA302Bmaterialmodelisfullydescribed inReference

[MA93].ForServiceLevelCloadings, theJ-RcurveinputsaretwosigmalowerboundcurveswhicharethesameasforServiceLevelsAandB.However,forServiceLevelDanalysis, Reference

[ASME92]allowstheuseofJ-Rcurveswhichareabestestimaterepresentation forthevesselmaterialbeinganalyzed.

Therefore, thebestestimate, ormean,J-Rcurves,asafunctionofUSElevel,weredetermined.

TheJ,cversusUSEmodelreportedinReference

[MA93]wasusedtocalculate themeanJ,cdatagiveninTable2-1.The6TJD-hadatareportedinReference

[HI89]wereusedtodetermine theJ-RcurvesattheUSElevelsshowninTable2-1.The6TJD-hadatawerereducedorincreased bythedifference betweenthe6TtestJ<<value(525in-lb/in')

andtheJ,cdatalistedinTable2-1.Theyieldstress,modulus,andPoissonratiousedintheanalysisareidentical totheReference

[MA93]data.

Table2-1MeanJ,cDataasaFunctionofUSELevelUSE-LBS10~J-LB79.220158.330237.540316.650395.860'0474.9554.18090100633.2712.4791.5

>p

3.0 Transient

Selection TheASMEdraftAppendixXdoesnotspecifyprocedures forcalculating LevelCandDserviceloadingssincethecombinations ofloadingsandmaterialproperties encountered inpracticearetoodiverse.Therefore, themostlimitingtransients forLevelsCandD,fromaductilefractureperspective, wereidentified asfollows:TheNMP-1andNMP-2plantdocumentation wascarefully examinedtoidentifypotential limitingtransients.

Ascreening calculation wasthenperformed toreducethespectrumoftransients toafewmostlikelycandidates.

Finiteelementcalculations wereperformed onthereducedsetoftransients todetermine themostlimitingLevelCtransient andthemostlimitingLevelDtransient andtheresultant loading.3.1.LevelCTransient Selection TheNMP-1andNMP-2updatedFSARsandthermalcyclediagramswerereviewedtodetermine aspectrumofcandidate LevelCtransients forfurtheranalysis.

Priortoperforming thescreening calculations, itwasnotclearwhethertherapidpressurelosstransients ortheslowdepressurization transients wouldprovidethelargestcombinedpressureand,thermal gradientloads.Therefore, thetransients showninFigure3-1werechosenforanalysissincetheyboundallLevelCtransients intermsofcooldownrate.Table3-1liststhetemperature/pressure variation atvarioustimesduringthetransient.

Theclassification oftheautomatic blowdowntransient andemergency cooldowntransient asLevel'Ceventsisconsistent withthedefinition oftheemergency condition transients.

,Figure3-1includestwoeventsdescribed intheUnit1updatedFSAR(References

[FSAR]and[CENC])andtheUnit2(References

[STRS]and[TCD])emergency condition automatic blowdown.

3.2LevelDTransient Selection AswiththeLevelCtransient selection, theLevelDtransients wereselectedaftercarefulexamination oftheNMP-1andNMP-2plantdocumentation.

Asetoftransients werechosenwhichboundallLevelDeventsintermsofcooldownrate.Plotsoftheselectedtransients areshowninFigures3-2through3-5(pressure/temperature profiledataarealsogiveninTables3-2and3-3.)TheNMP-2faultedcondition eventsarespecified basedontheReference

[NEDC]analysis.

Theeventsincludedforconsideration includethebreakspectrumfortherecirculation linebreaks,thesteamlinebreak,corespraylinebreak,andthefeedwater linebreak.

tp 3.3Screening Analysis3.3.1ModelDescription Thetransients described earlierwereanalyzedusingasimplelinearelasticfracturemechanics modeltodetermine thosetransients whichrequireadetailedfiniteelementanalysistodetermine thelimitingloads.Thetemperature difference acrossthevesselwallfortheLevelCtransients wascalculated usingtheTRUMP/MPM code[TRUMP].TheNMP-1vesselwasmodelledusingcylindrical coordinates, Thevesselis7.281in.thickwithaninnerradiusof106.5inches.The0.1563in.stainless steellinerwasmodelledashavingthephysicalproperties of316SS,andtherestofthevesselthickness wasmodelledasA302Bferriticsteel.Atotalof17radialnodes,eachofapproximately OA4in.thickness, wereusedtodiscretize thevesselthickness.

Anodeltemperature boundarycondition wasappliedattheIDsurfaceofthevessel.Thesurfacenodewasmodelledasbeinginthermalequilibrium withthedowncomer fluidtemperature.

Thisassumption leadstoconservative throughwallgradientestimates, particularly fortheLevelDtransients duringwhichphasechangeoccurs.Therefore, theinitialtemperature ofallvesselnodesweresetto500'F.Oncethetemperature difference acrossthewallwascalculated, therelativecontribution ofthepressureloadingandthethermalloadingwasapproximated usingthelinearelasticfracturemechanics modelgiveninAppendixGtotheASMEcode.Itshouldbeemphasized thattheseequations arebasedonlinearelasticfracturemechanics principles andarestrictlyapplicable forthermalrampsofupto100'F/hr.

Nevertheless, forscreening

purposes, theseequations areadequateforassessing therelativecontributions ofthepressureandthermalloadstothetotalcracktipstressintensity forthevariousLevelCandDevents.AppendixGusesthefollowing equations tocalculate thestressintensities:

IK=K~+K~where,K~=Ma=membranestressintensity factor(ksiVin)K~=MTbT=stressintensity factorduetothermalgradient(ksi0in)M=ASMEmembranefactor(0in)MT=ASMEthermalfactor(ksi0in/'F) lpe

!bT=temperature difference acrossvesselwall('F)o=stress(ksi)(A~+B~)(B~-A2)(3-2)A=vesselinnerradius(in.)B=vesselouterradius(in.)P=internalpressure(psig)SincetheAppendixXflawgrowthcriterion ismoresevereatdeepcrackdepthsunderLevelCandDeventloads,thescreening calculations wereperformed assumingaone-quarter thickness flaw.Thisflawexceedsthedeepestpostulated flawanalyzedundertheLevelCandDanalysis.

3.3.2LevelCTransient AnalysisTheblowdowntransients areterminated whenthepressurereaches35psigtoaccountforthecontainment pressurelevelatthattimeinthetransient.

IntheTRUMP/MPM calculations, thesetransients wereextendedtolongertimes,conservatively assuminga300'F/hrcooldowntoa212'FvesselIDtemperature.

ThethermalgradientandpressuredatafortheLevelCtransients aresummarized inTable3-4.BasedonthedatainTable3-4,the250'F/7.5 min.BlowdownandtheThermalTransient Blowdownarelimitingintermsofductilefracture.

Therefore, detailedfiniteelementcalculations wereperformed forbothofthesetransients todetermine themostlimitingvesselwallstressdistribution.

3.39LevelDTransient AnalysisSincetheLevelDtransient depressurization occursoverarelatively shorttimeperiod,andithasbeenassumedthatthedowncomer fluidtemperature equalsthewallsurfacetemperature forthepurposeofperforming ascreening

analysis, itwasnotnecessary toperformathermaltransient heattransferanalysisfortheLevelDtransients.

BasedontheLevelCanalysisresults,thevesselwallbTisapproximately equalto528'Fminusthecurrentdowncomer fluidtemperature fortheinitialfiveminutesofthetransient.

Therefore, thecracktipstressintensities canbecalculated directly.

Itshouldberecognized thattheseassumptions areincreasingly over-conservative aftertheinitialfiveminutesofthetransient.

Theresultsofthestressintensity factorcalculations fortheServiceLevelD

10transients areshowninTables3-5and3-6.Basedonthesecalculations, theSteamLineBreakTransient, NMP-2Recirculation LineBreakTransient, andtheNMP-1Recirculation LineBreakTransient wereanalyzedinfurtherdetailusingthefiniteelementmethod.Theothertransients yieldlowerpeakstressintensities.

Inaddition, thestressintensity factorestimates fortheothertransients areveryconservative sinceasignificant portionofthetransient isspentinasteamforcedconvection and/orsubcooled freeconvection heattransferregime.3.3.4SummaryofCandidate Transients Asimplified modelwasdeveloped todetermine thelimitingServiceLevelCandDtransients.

Perfectheattransferbetweenthedowncomer fluidandthevesselwallsurfacewasassumedtoprovideconservative estimates ofthethroughwallthermalgradient.

Aquarterthickness flawwasassumedandtheASMEAppendixGlinearelasticmodelwasusedtoestimatethecracktipstressintensities.

Basedonthesimplified modelforscreening calculations, themostlimitingtransients, fromaductilefractureperspective, aresummarized inTables3-7and3-8.

/<x Table3-1LevelCTransient Temperature/Pressure Variation asaFunctionofTimeMeasuredFromtheInitiation oftheEventEmergency Condition LevelCTransients Unit1DesignBasisUnit2DesignBasis250'F/7.5 minThermalTransient BlowdownBlowdownUnit1Emergency Cooldown300'F/brUnit1SB-LOCAADSBlowdown((Ioo(IOlOoOOI(

SIoooooo(SS(SP((Ioo(IOONOOO(

SIooooIo(SS(S((lIII~(oIkIIloo(

SIooooI~(pS(o)(IIop(SJ((Ioo(oIooOoI(SIooooI@SoSlA)JOS50JOSSJJdoJOSS$1$3.337$10$$6478730$08196zoog0121342203444307.711033$87JJog587318301917.$48pro206229$4010333025$0281$0$02816020228*NominalSubcooling 100%PowerRatedFeedwater Temperature 0

12Table3-2LevelDSteamLineBreakTemperature/Pressure Variation asaFunctionofTimeMeasuredFromtheInitiation oftheEventSteamLineBreakTime(sec)Reference (1)Pressure(PSIA)TempOFTime(sec)OysterCreekAnalysisReference (2)Pressure(PSIA)TempoF0204060801001201401601803001045660310200130906040312515528*497420381347320.2922672522402120703004501050120035552350'12281Reference 1-NMP1SAFER/CORECOOL/GESTR-LOCA AnalysisNEDC-31456P, 1987,NMP1,FigureA017Reference 2-OysterCreekReportGENE-523-70-0692 August'92"OysterCreekVesselFractureMechanics Analysis" foruppershelfenergyrequirement.

Figure5-6Page5-13*NominalSubcooling 100%PowerRatedFeedwater Temperature

+c~p0 13Table3-3LevelDRecirculation LineBreakSpectrumTemperature/Pressure Variation asaFunctionofTimeMeasuredFromInitiation oftheEventRecirculation LineBreakSpectrumDBA40%DBA.05ft~Tiae(eee)PrrnPS(ATrap(shTiae(eeelPrnrI'SIATeap(rhTlae(eeetPrrssPS(ATear(ehTlae(eee)PrrsrPSIAleap(ehTiae(eeeiPrrnPS!ATeaprehIINIr(srr)PrrrsI'SIATeap10450104S0104$0104$0IO4$1045lo760S12ddo52120920$3$50$39960S40240S32'20417660491$0dooSld100SldIdod60S212doSld3080312404304526001$0520411790$1113040402615026040490400Ido2do4113004do463$60419$02022d601503$d100320423200Sdl34044040044$IS2127032d1301103008031241132042390602931$0120341400402614102203902103ds320IS2122001103004026180312Iodo40261 tc4/

Table3-4StressIntensity FactorEstimates forServiceLevelCTransients'50'F/7.5 Min.BlowdownThermalTransient BlowdownEmergency Cooldown300'F/hr.

Time(Min.)PhTK~Krr1030574018KPhT5810309140K~K2968PhTK~1030104043500101193251500137194362103015404510203040506050014619461812067653324417733245177651691557216916278169167781691684955515753595359103020401030304010303940541482132981131761077881203351301514001215.2534384144464952363840414244'nits-P=psig;AT=maxtempdiff.('F);K,=membrane stressintensity (ksidin);K~thermal stressintensity (ksidin);K=totalstressintensity (ksidin)'eakwallthermalgradient tC 15Table3-5AStress.Intensity FactorEstimates forServiceLevelDTransients'lnle (Sec.)PhTSteamLineBreakFeedwaterLineBreakCoreSprayLineBreakPhTKPRecirc.LineBreakNMP-2Recirc.LineBreakDBAPATRecirc.LineBrcak4¹DBAKP6T10615SlIO352$$I$52143QSSl$157433103335115117135$70$375115Ill754545N10SN071NIa715S3'nits-P=psig;hT=maxtempdiff.('F);KtM=membrane stressintensity (ksidin);Kn--thermalstressintensity (ksidin);K=totalstressintensity (ksidin)

+c~f 16Table3-5BStressIntensity FactorEstimates forServiceLevelDTransients'rme (Sec.)SteamLineBreakPdTFeedwater LineBreakKPCoreSprayLineBreakRecirc.LineBreakNMP-2PdTKPRecirc.LineBreakDBAPRecirc.LineBreak40%DBAdT270~I7152l2lSr501527SIl0210<<7120551247<<75<<7511557SIl<<lt<<tt217SI5<<7l<<tt<<tt'nits-P=psig;AT=maxtempdiff.(F);Km=membrane stressintensity (ksidin);Kn--thermalstressintensity (ksidin);K=totalstressintensity (ksidin)

J

'17.Table3-6AStressIntensity FactorEstimates forServiceLevelDTransients'lmc sec.1015Recirc.LineBreak1ft'~KRecirc.LineBreak0.5ft'ecirc.

LineBreak0.1ft'MK~Recirc.LineBreak0.05ftPhTKM3035237507851030333885113770585754213369038530512013015514014583105160152641123345505678510303394512364150105187596350557191837'nits-P=psig;AT=maxtempdiff.('F);K~=membrane stressintensity (ksidin);Krr=thermal stressintensity (ksidin);K=totalstressintensity (ksidin)

18Table3-6BStressIntensity FactorEstimates forServiceLevelDTransients'llllC sec.160175Recirc.LineBreak1ft'ecirc.

LineBreak0.5ft'~K~KPRecirc.LineBreak0.1ft'ecirc.

LineBreak0.05ft'TKlMK~K180280552252717326518511714710374784546537753330333378510.303333202611828365216368714656518387152028634440470<316026182833852051111513883543505138583152641<316<99<9930510512334563019514384553951934616593010801420mts-<3160=pstg;=maxtemp1.;,=mern ranestresstntenstty stm;K~thermal stressintensity (ksidin);K=totalstressintensity (ksidin)65<216325<2161<3160<68<82<83<99<99 It 019Table3-7LevelCTransients forFiniteElementAnalysisNMP-1DesignBasis250'F/7.5 Min,Blowdown'MP-2 DesignBasisThermalTransient Blowdown~

Time(Min.)7.520.7Pressure(psig)10305001817233Temp.528470380318278212HeatTransferCoefficient h=BTU/(hr ft'F)10,00010,00010,00010,00010,000500Time(Min.)3.31015202538.8Pressure(psig)1030169106724735Temp.P)528375342318295281212HeatTransferCoefficient h=BTU/IhrfPF)10,00010,00010,00010,00010,00010,000500'MP-1UpdatedFSAR~Reference

[STRS]

ecIt Table3-8LevelDTransients forFiniteElementAnalysis20SteamLineBreak'ecirculation LineBreak'NMP-2Recirculation LineBreak'NMP-1DBATime(Sec.)pressureTemp(psig)('F)HeatTransferCoefficient h=BTU/(hr ftF)Time(Sec.)Pressure(psig)Temp.('F)HeatTransferCoefficient h=BTU/(hr ftF)Time(Sec.)Pressure(psig)Temp('F)HeatTransferCoefficient h=BTU/(hr ftF)20401030295528497-42010,00010,00010,0001520,1030352352828126469,1881641641015103047452851246410,00010,000164608018538111534710,00010,0006010023182642561641642030285417312164164100120140160180300380400754525161032029226725224021221221210,00010,00010,00010,00010,00010,00016450020030013003.523522221216416450040508025267228212164164500Reference

[NEDC]References

[NMP2TC],

[STRS],and[NMP1DP]

Emergency Condition LevelCTransients 600528'F500400--300--~~281'F@35slg200100-0-Data

References:

%300'F/hrEmergency

+Unit2DesignBasisCooldownUnit1FSARThermalTransient Blowdownfrom762E673~'250'F/7.5'min

'.'vent23NMP2.Vessel.

'ooldownUnit1FSARStressAnalysis(SixERV'sopen)STRS16.010-5039A

-Reliefvalvesresetat50psia(35psig),cooldownassumedat300'F/hrto0psig-..".0510IS202530354045505560Time(minutes)

Unit1DesignBasis%Unit2DesignBasisAUnitIEmerCool~Nom.ADSBD3ERVsopenFigure3-1LevelCTransients AnalyzedtoDetermine theMostLimitingTransient forNMP-1

+ct SteamBreak22600500TAFU-Uncover380secTAFR-RecoverQ400sec-OysterCreekGENE-523-70-0692 Steamllne Breakprofile400300TAFUTAFRIIII281'F+35psfg200212'FQ0psig100DATAREFERENCE AssumeboilingHTC=NEOC4N56P, tg87,NMPt(0000gTUthl.ft).oF

.Safei/CoreooofLGESTR-LOCA

....until.TAFR

analysis, FigureA-17Subcooled BoilingHTCthereafter fromECCSflowHTC=500BTR/hr-ft2-'F 050100150200250300350400450500550600"NominalSubcooling 100%powerratedfeedwater temperature Figure3-2LevelDSteamLineBreakTransient PressureProfile ect Feedvater Linereak23600528'F500400300TAFUTAFRTAFU-Uncover145secTAFR-RecoverI265sec281'FQ85psig200100DATA

REFERENCE:

NEDC-31446P 1987,'NMP1Safer/Corecool/

GESTR-LOCA.

Fig.A-19AssumeBoilingHTC10,000BTU/hr-ft2-'F untilTAFRSubcooled HTCthereafter...

fromECCSflowHTC=500-BTU/hr-ft2-'F 050100150200250300350400450500550600650700Time(sec)Pressure(I'SIR)1,04510960751002008007204001408050300400500Saturaled Temp('F)W528~528"518506444353312281*NominalSubcooling 100%powerratedfeedwater temperature Figure3-3LevelDFeedwater LineBreakTransient PressureProfile C

CoreSprayLineBreak'4600528'Fi500TAFU-UncoverQ245secTAFR-Recover320sec400300IIITAFUTAR281'FO35psig200100DATA

REFERENCE:

NEDC-31446P, 1987,"NMP1Safer/Corecool/G ESTR-LOCA FigureA-16-AssumeBoltingHTC10,000---BTU/hr-ft2-'F untilTAFRSubcooled HTCthereafter fromECCSflowHTC=500BTU/hr-ft2-'F00100200300400500600700800Time(sec)Pressure(I'SIA1,04514580017573040040022050013063050*Saturated Temp('F)W528~518507444390347281'ominalSubcoollng 100%powerratedfeedwater temperature Figure3-4LevelDCoreSprayLineBreakPressureProfile JcC Recirculation LineBreakSpectrum25528F600-$00-IAfV4IItIIAfV~---..300.F/hr--AKISASIICKS.

llAAIIHtOIHHWIVClltlb4lv Isa>>45OCSllif4, I&Sf'NVAISAfe4co4ecoovoes'lll.locA'5e IIVvff.fffeff5.l4fvoevoooNIIIOIAIAI CICloA40028toF@35psig+IAf4IIAfll+IAfllIprAIR.I.II200100-Reference 2In'a'llcases,levelisatTAFpriortocompletedepressurization.

Downcomer Levelisassumedtofollowcorelevel.Therefore,

.assurpe.saturated steam.conditions.

in,cfowncomqr.during,...

depressurization untilTAFisrecoverbyECCS.Thenassumefreeconvection tosubcooled ECCS.0100200300400$006007008009001,0001,100Time(Seconds)

~DBA+40%DBAIFt2+.$Ft2Hj.lFl2+.0$Ft2Figure3-5LevelDRecirculation LineBreakSpectrumPressureProfile Jf4 FiniteElementAnalysis26Thecandidate transients listedinTables3-7and3-8wereanalyzedusingthefiniteelementmethodtodetermine themostsevereLevelCandLevelDloadings.

TheWELD3finiteelementcodepackageIWELD3]wasusedtoperformthecalculations.

4.1ModelDescription TheWELD3modelassumesaxisymmetric behavior.

Asinglecolumnofelementswasused,thusmakingthesolutionessentially onedimensional (i.e.,temperatures andstressesonlydependontheradialpositionwithinthevesselwall).ThefiniteelementgridisshowninFigure4-1.Elements1and2represent thecladding.

Thecladdinginnersurfaceradiusis106.344inches,thebasemetaVclad interface isat106.5inches,andthevesselouterradiusis113.781inches.Theaxialdimension ofthemodelis0.15inches.Forthermalmodeling, theoutervesselsurfacewastreatedasperfectly insulated.

Theinnersurfacehasaprescribed heattransfercoefficient andfluidtemperature (bothfunctions oftime).Allheatflowisradial.Temperature dependent properties wereusedinthethermalanalysis.

Themechanical modelisconstrained to'aveauniformaxialstrainsothatplanesectionsremainplane.Theaverageaxialstressandtheinternalpressureareinputtothemodelbasedonthepressuretransient input.Thermaltransients areinputviaelementtemperatures.

Temperature dependent properties arealsousedforthestresscalculations.

TheWELD3calculations assumedlinearelasticbehaviorforboththecladdingandbasemetalsoastobeconsistent withtheuseofthesmallscaleyieldingassumption (linearelasticfracturemechanics withplasticzonecorrections) inthesubsequent fracturemechanics analyses.

4.2FiniteElementAnalysisResultsTwoLevelCcasesandthreeLevelDcaseswereanalyzed.

Thetransient thermalandpressureboundaryconditions aredescribed inTables3-7and3-8.Althoughthepressureandthermalloadingscouldbeanalyzedseparately duetotheuseoflinearelasticity, itwasjudgedmoreexpedient tocombinetheloadings.

Thecladdinghasadifferent coefficient ofthermalexpansion thanthebasemetal.Thisimpactedtheanalysisinseveralways..First,therewillbesomeresidualstressevenwhenthevesselisatauniformtemperature.

Assumingthatthevesselis100%stressfreeatthestressrelieftemperature of1150'F,theoriginalcoolingto528'Finducedtensileresidualstressesinthecladdingthuscontributing tocracktipstressintensity factors.Thisuniformcoolingwasmodeledinaseparateanalysistodetermine thelevelofinitialresidualstress.Thedifference inthermalexpansion behavioralsoresultsindiscontinuous WC 27axialandhoopstressesacrossthematerialinterface.

Sincethefracturemechanics evaluation involvesfittingthestresseswithacubicpolynomial, thisdiscontinuous behaviorimpactsthequalityofthepolynomial fits.Therefore, asdescribed inSection5.0,thefracturemechanics modelwasconfigured tominimizethesensitivity oftheanalysistotheeffectsofstressfielddiscontinuities attheinterface.

Figure4-2showstheaxialandhoopresidualstressesthatexistduetouniformcoolingfromastressfreecondition at1150'Fto528'F.Thisresidualstresswasnotincludedinthest:ssdistribution plotsforthevariousLevelCandLevelDtransients thatfollow.Thisapproachwasadoptedaspartoftheapproachtomoreaccurately handlethediscontinuous stressfield.Thefinalstressdistributions doincludethedifferential expansion coefficient effectsduetocoolingfrom528'Fduringthetransient.

Themethodforincluding theresidualstressloadinthefracturemechanics analysisisdescribed inSection5.0.TheWELP3stressoutputforeachanalysiswasscannedforthetimeofthemostseverestressesinducedbythecombinedtransient thermalandpressureloading.Sincecrackdepthsofnolargerthanoneinchareofinterest[ASME92],

thetimeatwhichthestresseswouldbemostsevereforaoneinchdeepcrackwasidentified.

Thiswasdonewithoutactuallycalculating stressintensity factorsforeachtransient stressdistribution andwaspossibleonlybecausethestressesovertheinnerinchofthewalltendedtopeakataboutthesamepointintime.Figures4-3through4-10containplotsofthetransient temperatures andstresses.

Thetimesofthemostdamagingstressesforcrackdepthsofaboutaninchareplottedwithasolidline.Temperatures andstressesatothertimesareplottedusingbrokenlines.Itcanbeseenfromtheseplotsthatfordeepercracks,thecriticaltimewouldtendtobelaterinthetransient.

Forveryshallowcracks,slightlylargerstressintensity factorsmayoccuratearliertimesthanfortheidentified times.Table4-1summarizes theresultsoftheWELD3analyses.

4.3,LimitingTransients Thehoopandaxialstressbehaviors areverysimilarandtendtoexperience theirpeakvaluesataboutthesametime.Themagnitudes ofthehoopstressestendtobelargerthantheaxialstresses.

Withoutinputting thesestressesintoafracturemechanics analysisitisnotpossibletodetermine whichstresscomponent islimiting.

Asdiscussed furtherinSection5.0,theaxiallyorientedflaw(hoopstressloading)isthelimitingcase.OfthetwoLevelCcasesconsidered; the"NMP-1DesignBasis250'F/7.5 min.Blowdown" resultedinthelargerstresses.

OfthethreeLevelDcases,the"SteamLineBreak"resultedinthelargeststresses.

AsshowninFigures4-3through4-5,thetimedependence oftheheattransfercoefficient playsanimportant roleindefiningthelimitingLevelDtransient.

Inparticular, althoughtheSteamLineBreakisnotthemostrapiddepressurization transient, itislimitingsincetheheattransferismoreefficient overthefirst300secondsoftheevent.

rc 28Table4-1SummofPeakCladdinandPeakBaseMetalStressesattheIndicated TimesstressunitsareksiCaseresidualC1D1D2D3CriticalTimeNA9.15min6.65min240sec500sec320sec~Hoo20.660.642.678.447.765.5CladAxial20.050.234.865.939.554.6~Hoo-0.740.529.652.331.743.9BaseAxial-1.329.821.539.423.232.7C1:NMP-1DesignBasis250'F/7.5 min,BlowdownC2:NMP-2DesignBasisThermalTransient BlowdownD1:SteamlineBreakD2:Recirculation LineBreakNMP-2D3:Recirculation LineBreakNMP-1DBA ec

'912345678913141516171819202122 23242526272829303132333435363738Figure4-1OneDimensional FiniteElementMeshforNMP-1PressureVesselAnalysis er 2220HC20.6ksi)A(20.0ksi)30181614A:AxialStressH:HoopStress12(o802356.Distancefrominnersurface(in)Figure4-2ResidualStressat528'FDuetoCladdingDifferential Expansion

316DD1$t1.65min.2$t=3.3min.9$t=6.65min.500400I-300r//4//c'//g6/J'1$t=2min.2$t~4min.3$t=6min.4$t=7.5min.5$t=9.15min.6$t14.1min.5008I4000I8oEI-300t~15min.6$t20min.2<(/3r/~s(y6e7Hr~r~84$t=10min./5$7$t~20.7min.'\S$t=25min.t=98.8min.20D0l2345678Distancefrominnersurface(in)LevelCI250F/7.5-min.'lowdown 2000l2345678Distancefrominnersurface(in)LevelC:NMP-2BlowdownFigure4-3PressureVesselThermalGradients forLevelCTransients pc

'26005004003003st18Dsec.7stSDDsec.1(/2/'//y6t'1st6Dsec.I/yw2st120sec./III//IIy4st240sec.II/ISst30Dsec./I/r/6st400sec.540520,500480460440420a4003803603403206st20Dsec.II34/g//S/////I///7Y/II//~8II/~g~I//y1st~1Ssec.II/2st~20sec.I/3st40sec.I/I4st60sec./Sst1DDsec.//7st30Dsec.I8stSDDsec./gst700sec.2000l2345678Distancefrominnersurface(in)LevelDsSteamLineBreok3000l2345678Distancefrominnersurfoca(in)LevelDsRecirculation LineBreokFigure4-4PressureVesselThermalGradients forLevelDTransients c

60033500~.4000LaE3003ctBDsec.4ct140sec.G:t320sec.Bst5GDsec.gstGBDsec.1~~rr/r5//1st15sec.//r'/.2t30sec./////I///i(/p///7st440sec.2000l2345678DistancefrominnersUrface(in)LevelDsRecirculation LineBreakNHP-lDBAFigure4-5PressureVesselThermalGradients forLevelDTransients

347060504pg30o20alp00D-10-20L+2:3rt4:t5:t6rt7:t02min.4min.6min.7.5min.9.15min.14.1min.ZO.7min.23605040ro3p20100-100:t-01rt2min.2:t~4min.3rt~6min.4rt7.5min.5rt~9.15min.6:t14.1mfn.7r't20.7mfn.01--~23-300123456-78Distancefrominnersurface(in)LovelC:250F/7.5min.Blowdown2D012345678Distancefrominnersurface(in)LevelC:250F/?.5min.BlowdownFigure4-6AxialandCircumferential StressDistributions forLevelC250'F/7.5 Min.Blowdown

"354030Dst0t1.65min.2st=3.3min.3st6.65min.4st=1Dmin.5st-"15min.6st~2Dmin.4030Dst-01stI.65min.2st~9.9min.9st=6.65min.4st=10min.5st=15min.20vl10007st8s=25min."98.8min.20106st=20min.7st~25min.8st=98.8min.-103020012345678Distancefrominnersvrface(in)LevelCsNMP-2Blowdown10012345678Distancefrominnersvrface(in)LevelCsNMP-2BlowdownFigure4-7AxialandCircumferential StressDistributions forLevelCNMP-2Blowdown

BD70605040e3020ao10OLtD1st=60sec.2:t=1ZDsec.3:t1BOsec.4:t240sec.5:t=3DOsec.6:t400sec.7:t-500sec.70605040e3020ox10D:t=O1~t60sec.2~t120sec.9:t1BOsec.4st240sec.5st3DDsec.6:t400sec.7st500sec.-10-2023w----5-1030012345678Distancefrom.innersurface(in)LevelD:SteamLineBreak20012345678Distancefrominnersurface(in)LevelD:SteamLineBreakFigure4-8AxialandCircumferential StressDistributions forLevelDSteamLineBreak

/>>

7060504030u)2010QotaDi:ti5sec.2:tZDsec.9:t4Dsec.4st6Dsec.5:t-i00sec.6st200sec.7st~300sec.B:t5DOsec.gst700sec.70605040e30200x10il0:t-0isti5sec.2:t2Dsec.9:t40sec.60sec.5:ti00sec.6:t2DOsec.7:t=900sec.B:t5DOsec.gct700sec.-105--67-10-20012345678Distoncafrominnersurface(in)LevelD:Recirculation LineBreah20012345678Distancefrominnersurface(in)LevelD~Recirculation LineBreakFigure4-9AxialandCircumferential StressDistributions forLevelDRecirculation LineBreakforNMP-2

"38706050403020o10000-10-2030Ost0lst15sec.Zst9st30sec.~80sec.4stGs7:8:t9s140200320440560-680sec.sec.sec.sec.sec>>sec.94.-56~=z.e.a0123456786040w308820U)10-1020Ost01:t15sec.2:t90sec.9:t80sec.4:t140sec.Sst200sec.6:t920sec.7st440sec.8st560sec.9:t680sec.9456z<<=7.8,9012345678Distancefrominnersurface(in)LevelDcRecirculotion LineBreakNHP-1DBADistancefrominnersurfoce(in)LevelD~Recirculation LineBreakNHP-1DBhFigure4-10AxialandCircumferential StressDistributions forLevelDRecirculation LineBreakforNMP-1DBA gC 39~~~5.0Elastic-Plastic FractureMechanics Assessment ThelimitingLevelCandDtransient loadswereappliedtoafracturemechanics modeloftheNMP-1pressurevesselinaccordance withtheguidanceprovidedinReferences

[ASME92]and[WGFE92].

TheUSEŽ(3.0)codepackage[USE93]wasusedtoperformthecalculations.

AcopyofthedraftAppendixX[ASME92]isprovidedinAppendixAandtheASMEWorkingGrouponFlawEvaluation draftstressintensity calculation procedure

[WGFE92]isgiveninAppendixB.5.1ModelDescription 5.1.1VesselGeometryTheA302Bmaterialmodelusedintheanalysiswasdescribed inSection2.0.Inadditiontothematerialmodel,USEŽ(3.0)requiresthefollowing parameters:

VesselWallThickness VesselInnerRadiusVesselCladThickness CrackDepth/Length Ratio5.12AppliedLoads7.281in.(UFSARTableV-1)106.344in.(UFSARTableV-1)0.15625in.0.166667Theresultsofthefiniteelementcalculations todetermine thelimitingLevelCandDtransients andloadingsaredescribed inSection4.0.Asaresultofthesecalculations, thelimitingLevelCtransient isthe"NMP-1DesignBasis250'F/7.5 min.Blowdown",

andthelimitingLevelDtransient isthe"SteamLineBreak".Thelimitingstressdistribution wasdetermined byexamining theradialstressprofilesatvarioustimesinthetransient.

Asmentioned inSection4.0,usingstressdistribution dataatatimewhenthestressesaremostsevereforaone-inchcrackmaybeslightlynon-conservative whenshortercracksareconsidered.

Thissmallnon-conservatism wasciicumvented byusinganupperboundenvelopeoftheactualstressdistributions.

Thelimitingstressdistributions werefittoacubicpolynomial usingtheguidancegivenin[WGFE92].

Inordertoprovidegoodfitstothedata,thebasemetalstresseswereextrapolated totheIDsurface.Theremaining discontinuous component ofthecladstressesaretreatedusingalineloadformulation asdescribed inSection5.1.4.Theequivalent cladlineloadsaregiveninTable5-1.Thepressureactingalongthecracksurfacewasconservatively includedinthecladlineload.Thefittothebasemetalstressdistribution isshowninFigures5-1 gC'1 40through5-4.Table5-2summarizes thestressdistribution coefficients foruseintheAppendixXanalysis.

TheR-squared valueforallofthefitsisveryclosetounitywhichindicates accuraterepresentation ofthedata.5.19LimitsforSmallScaleYieldingAnalysisa=:a+-(-)1K2eP6mayawhere,a,=effective crack'size(in.)a=physicalcrackdepth(in.)K=linearelasticstressintensity (ksi4in)a~=yieldstress(ksi).AsstatedinReference

[ASME92],

whentheconditions fallinthecategoryofelasticfracturemechanics withsmall-scale

yielding, theJ-integral maybecalculated usingcrack-tip stressintensity formulaewithplastic-zone correction.

Inordertoestimatethelimitsofvalidityofthesmall-scale yieldingassumption, anaxiallycrackedcylindrical vesselwitharadiustothickness ratioof10,awallthickness t=10inandacrackdepthtothickness ratioa/t&.25,wasloadedbyinternalpressureandtheresulting stressintensities werecalculated, Theeffective crackdepthswerecalculated using:TwoRamberg-Osgood stress-strain modelswereanalyzed:

onewithn=8.4andalpha=2,6; thesecondwithri=5.3andalpha=7.2.

Thehighern-valuecaseismorerepresentative oftheNMP-1plates.Theelasticcalculations approximated pressurestressesbyalineardistribution thatmatchedtheexactthickwalledcylindersolutionattheinnerandoutersurfaces.

Theplasticsolutionwas'calculated usingtheexactinternalpressureinducedstresses.

Theresultsaresummarized inFigure5-5.Thedifference insolutions forsmallloadsisduetotheuseofdifferent elasticsolutionFfactorsinthetwomodels.Basedonthisanalysis, itisconcluded thatthesmall-scale yieldingformulation isvalidforstressintensity levelsupto100ksi4in(J-335in-lbfin)foranaxialcrackinacylinderwithanaspectratioof10.Sincethecalculated stressintensities forNMP-1arewellbelow100ksi4in.,thesmallscaleyieldinganalysisisappropriate fortheNMP-1vesselanalysis.

5.1.4FractureMechanics ModelTheReference PVGFE92]methodforcalculating stressintensities forsurfaceflawswasused.Acopyoftheprocedure proposedbytheASMEWorkingGrouponFlawEvaluation isgiveninAppendixB.Theprocedure requiresaccurately fittingthestressdistribution usingthefollowing polynomial fit:

>r 41a=A,+A,X'+APE+A,X'here, (5-1)A,=regression constants X=distancethroughthewallThepostulated flawisasemi-elliptical surfacecrackwithasurfacelengthwhichissixtimesthedepth.Thestressintensity forthecontinuous component ofthestresseswascalculated fromthefollowing expression:

Kz=[AG+A~G~a+A~G~a+A3G3a']~ira7g(5-2)where,a=crackdepthA,=coefficients fromEq.3-1whichrepresent thestressdistribution overthecrack(0(X(a)G,=influence coefficients asafunctionofflawaspectratioandcrackpenetration (Appendix B)Q=flawshapeparameter Q=1+4.593(a/1)'qy1=flawsurfacelengthq=plasticzonecorrection factorq=0.212(AJa,)',=materialyieldstressSincetheslopeofthestressdistribution attheclad-base metalinterface changesabruptly, thebasemetalstressdistribution wasextrapolated totheIDsurfacetoprovideanaccurateflitoverthepostulated flawdepths.TheReference

[TA73]linearelasticformulation wasusedtocalculate thediscontinuous component ofthestressfieldscontribution tothecracktipstressintensity using:

/p 42Kres~2PP~mawhere,'~52(1-c/a)4~35-5.28c/a(1-a/b)(1-a/b)1303(c/a)i.s~+('+0.83-1.76c/a)

(1-(1-c/a) a/b)(1-(c/a)')"P=equivalent lineloada=flawdepthb=wallthickness c=loadapplication positionasmeasuredfromtheIDsurfaceEquation5-3providesconservative estimates ofthediscontinuous stresscomponent contribution ofthetotalstressintensity sincetheformulation isforaninfinitecracklength,SinceEq,(3-3)isalinearelasticequation, thesmallscaleyieldingcorrection wasapplied:where,a=physicalcrackdeptha,=effective crackdepthInordertosimplifythecomputeralgorithm andtoensureconservative results,thesmallscaleyieldingcorrection wasappliedtoboththecladdingandbasemetalstressintensity factors.Thisapproachyieldsveryconservative resultssincetheflawshapeparameter inequation5-2includesaplasticzonecorrection factor.Thetotalstressintensity factorwasobtainedbysuperposition:

KcoHTLNPN/s

+KDLscoNTLNUoUs ZZ rc 43Inaccordance withReference

[ASME92],

aspectrumofinitialflaws,upto1/10ofthebasemetalwallthickness, wereassumed.Thesmallestflawassumedwas0.05in.,andthepostulated flawswereincreased insizebyincrements of0.05in.,uptoamaximumflawdepthof0.75in.5.2Calculations forA302BMaterialModelThepointwise inputmodelwasusedfortheA302Bmaterialmodelcalculations.

Usingthismodel,theJ-Rcurveisassumedflataftertheinitial0.1in.ofcrackextension.

TheG-8-1platewasanalyzedusingtheA302Bmaterial.

modelsinceitisthelimitingplatefromaductilefractureperspective (Reference

[MA93]).5.2.1LevelCLoadingTheresultsofthecalculations fortheLevelCloadinghaveshownthatthelimitingflaworientation istheaxialflaw.Forinitialbasemetalflawdepthsofupto1/10ofthevesselwallthickness, theASMEAppendixXcriteriaaresatisfied atUSElevelsaslowas10ft-lbs.Inallcases,thelargestapplied-J valuesfortheflawgrowthof0.1in.criterion areobtainedatthedeepestinitialpostulated flawdepth.TheresultsfortheLevelCanalysisaresummarized inTable5-3fortheaxialflaw.5.22LevelDLoadingAnalysisTheresultsofthecalculations fortheLevelDloadingalsoshowthatthelimitingflaworientation istheaxialflaw.Forinitialbasemetalflawdepthsofupto1/10ofthevesselwallthickness, theASMEAppendixXcriteriaaresatisfied atUSE'levelsaslowas20ft-lbs.TheresultsfortheLevelDanalysisaresummarized inTable5-4fortheaxialflaw.5.2.3TensileInstability AnalysisBasedontheanalysisperformed, thedeepestflawduringthemostsevereLevelCorDtransient islessthan1.2inches.Conservatively assumingtheflawextendscompletely aroundthecircumference, andusingthefiniteelementstressprofiles, theremaining ligamentwillexperience stresseswellbelowtheyieldstrengthandistherefore safeintermsoftensileinstability.

Table5-1NMP-1CladStressesCaseHoop-Level CAxial-Level CHoop-Level DAxial-Level DExtrapolated SurfaceStress(ksi)45.20735.26458.69045.476CladStressMinusExtrapolated SurfaceStress(ksi)16.55716.79019.88621.377ResidualStress(ksi)20.620.020.620.0CladTotalStress(ksi)37.15736.79040.48641.377CrackSurfacePressure(ksi)1.051.051.051.05CladEquivalent LineStress(kp/in)6.8566.7987.3767.515Table5-2BaseMetalStressDistribution Coefficients LevelC--HoopLevelC-AxialLevelD-HoopLevelD-AxialAo45.16535.29458.79145.651A,-22.335-25.420-33.934-33.6362.5719.9417.96712.136A,0.228-2.183-1.052-2.263 pCr"cC

'able5-3Comparison ofAppliedLoadswithASMECriteriaforLevelCLoadingConditions andanAxialFlawOrientation'5 ha&.lCriterion FlawStabiliCriterion USELevel102030405060708090100AppliedJ~in-1bin'83,183183183183183183183183183MaterialJ~in-1bini199230261292323353384438517AppliedT<0.5<0.5<0.5<0.5MaterialT2.63.77.313.218.3CriteriaSatisfied yesyesyesyesyesyes,J,cJ<<yes,J,<J<<yes,J<Jicyes,J,<J,cyes,J,<J,c'esultsshownareforthemostlimitinginitialflawoverthespectrumofflawsanalyzed

'able5-4Comparison ofAppliedLoadswithASMECriteriaforLevelDLoadingConditions andanAxialFlawOrientation

'6USELevel10~AIiedTJapeJMAxMaterialTFlawStabilitCriterion CriteriaSatisfied no20<0.811.0yes30<0.818.3yes405060708090100yes,J,~<Juncyes,J~<Jicyes'app~rc yes'app~tc yes,Jo~<JrcyesJ<Jrcyes,J,<Jrc'esultsshownareforthemostlimitinginitialflawoverthespectrumofflawsanalyzed.

,~

47HOOPSTRESSDISTRIBUTION FORLEVELCTRANSIENT 10080co60COU)LU40CO200.00.61.01.5CRACKLENGTH(In.)2.0Figure5-1PeakCircumferential BaseMetalStressDistribution forNMP-1DesignBasis250'F/7.5 Min.BlowdownTransient

48AXIALSTRESSDISTRIBUTION FORLEVELCTRANSIENT 1008060'COCOUJ40CO2000.00.5CRACKLENGTH(In.)2.0Figure5-2PeakAxialBaseMetalStressDistribution forNMP-1DesignBasis250'F/7.5 Min.BlowdownTransient

49HOOPSTRESSDISTRIBUTION FORLEVELDTRANSIENT 1008060402000.00.5<3RACKLENGTH(In.)2.0Figure5-3PeakCircumferential BaseMetalStressDistribution forSteamLineBreakTransient gC 50O'XIALSTRESSDISTRIBUTIONFORLEVELDTRANIENT1008060CO03LLI40K2000.00.51.01.52.0CRACKLEN9TH(ln.)Figure5-4PeakAxialBaseMetalStressDistribution forSteamLineBreakTransient In SmallScaleYieldLimitsStudyAxiallyCrackedCylinder{R/t=10)4.53.53.~2.520.5000.51.6-22.5Pressure(ksi)3.5~J(BSY/ae)

~Jep(n=5.3)

~Jep(n=8.4)

Figure5-5Comparison BetweenSmallScaleYieldingSolution(J(SSY/ae))

andtheElastic-Plastic Solutions withHardening Exponents of5.3(Jep(n=5.3))

and8.4(Jep(n=8.4))

/'

6.0 SummaryandConclusions

52Theresultsoftheelastic-plastic fracturemechanics assessment areshowninTable6-1.Asdiscussed inReference tMA93],theA302Bmaterialmodelbestrepresents theNMP-1beltlineplates.TheA302Bmaterialmodel,appliedtothecaseofanaxialflaworientation, yieldsthemostconservative results.Basedonthecalculations reportedinReference PvIA93]andherein,ithasbeenconcluded thattheNMP-1plateG-8-1islimitingfromaductilefractureperspective, andtheUSEmustbemaintained above23ft-lbs.BasedonthedatareportedinReference

[MA93],noneoftheNMP-1beltlineplatesareexpectedtofallbelowthe23ft-lblevel.AlthoughtheAppendixXcriteriaaresatisfied atorabovethe23ft-lblevel,itisnotclearthattheplantshouldbeoperatedatthisductility level.Itisanticipated thatfuturefederally fundedresearchandsubsequent regulations willaddressthisissue.

fi~

53Table6-1MinimumUpperShelfEnergyLevelforNMP-1PlatesBasedontheASMEDraftAppendixXEvaluation CriteriaforServiceLevelsA,B,CandDMinimumUSE(Ft-Lbs)PlateASMEServiceLevelA&BMaterialModelFlawGrowthof0.1in.Criterion Ji(Jo.iFlawStability Criterion G-8-1A&BA302B1323G-307-4A&BA302B1323G-8-1G-8-1DA302BA302B101020

7.0 References

54[ASME92]ASMEDraftCodeCaseN-XXX,"Assessment ofReactorVesselswithLowUpperShelfCharpyEnergyLevels",Revision11;May27,1992.[CENC][FSAR]Unit1Analytical ReportforNiagaraMohawkReactorVessel,ReportNo.CENC1142,ACCNo.002301187, AppendixBThermalAnalysis.

UpdatedFSARVolumeIV,SectionI,PageI-11.[HI89],'iser,A.L.,Terrell,J.B.,"SizeEffectsonJ-RCurvesforA302BPlate",NUREG/CR-5265, January,1989.[MA92][MA93][NEDC]Manahan,M.P.,Soong,Y.,"Response toNRCGeneralLetter92-01forNineMilePointUnit1",NMPCProject03-9425,June12,1992.Manahan,M.P.,FinalReporttoNRC,"Elastic-Plastic FractureMechanics Assessment ofNineMilePointUnit1BeltlinePlatesforServiceLevelAandBLoadings",

February19,1993.NEDC-31446P, NMP-1SAFER/CORECOOL/GESTR-LOCA LossofCoolantAccidentAnalysis.

[NMP1DP]NMP-1DrywellPressureCalculation, SO-TORUS-M009, GENE-770-91-34.

[NMP2TC]NMP-2,762E673,ReactorVesselThermalCycles.[STRS]SectionE9,Emergency'&

FaultedAnalysisofRecirculation OutletNozzle251"BWRVessel.STRS16.010-5039A, pageE11,12.Unit2StressAnalysis.

[TA73]Tada,H.,Paris,P.C.,Irwin,G.R.,"TheStressAnalysisofCracksHandbook",

DelResearchCorp.,1973.[TCD]Unit2ReactorVesselThermalCyclesDiagram762E673.[TRUMP)Manahan,M.P.,'TRUMP/MPM:

ThermalTransient HeatTransferAnalysisCode,Version1.0,September, 1989.[USE93][WELD3]USEŽ(3.0)Code PackageforElastic-Plastic FractureMechanics Assessment ofNuclearReactorPressureVessels,MPMResearch&Consulting, 1993."WELD3ComputerCodeVerification",

MPMResearch&Consulting, Calculation No.MPM-NMPC-99205, Rev.0,January21,1993.-

~<

55[WGFE92]ASMEWorkingGrouponFlawEvaluation, ProposedChangestoArticleA-3000entitled, "MethodforK,Determination",

August,1992.

56Acknowledgement Dr.RandallB.Stonesifer ofComputational Mechanics, Inc.performed allofthefiniteelementanalysesandprovidedmanyvaluablesuggestions related-tothefracturemechanics model.

57Appendices

58AppendixA'SMEDraftAppendixX"Assessment ofReactorVesselswithLowUpperShelfCharpyEnergyLevels" (i

DRAFTCODECASEN-XXXASSESSMENT OFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSMay27,1992REVISZON11REVISIONREVISION)REVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONDRAFTHISTORY0123456.788-MARKEDCOPY910llAUGUST25g1987JANUARY19,1988APRIL19,1988AUGUST30,1988NOVEMBER30,1988FEBRUARY27,1989JANUARY5i1990APRIL12,1990JANUARY10,1991APRIL15,1991JANUARY17,1992APRIL171992CURRENT gC(-

ASSESSMENT OFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSTABLEOFCONTENTSCASEN-XXXASSESSMENT OFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSAPPENDIXAASSESSMENT OFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELS A-1000INTRODUCTION A-1100A-1200A-1300ScopeProcedure OverviewGeneralNomenclature A-2000ACCEPTANCE CRITERIAA-3000ANALYSISA-3100A-3200A-3300A-3400A-3500ScopeAppliedJ-Integral Selection oftheJ-Integral Resistance CurveFlawStability Evaluation ApproachforLevelAandBServiceLoadingsA-4000rEVALUATION PROCEDURES FORLEVELAANDBSERVICELOADINGSA-4100A-4200A-4210A-4220A-4300A-4310ScopeEvaluation Procedure fortheAppliedJ-Integral Calculation oftheAppliedJ-Integral Evaluation UsingCriterion forFlawGrowthof0.1in.Evaluation Procedures forFlawStability J-RCurve-CrackDrivingForceDiagramProcedure rl A-4320A-4321A-4322A-4322.1A-4322.2A-4323A-4330A-4331A-4332A-4333FailureAssessment DiagramProcedure FailureAssessment

'DiagramCurveFailureAssessment, PointCoordinates AxialFlawsCircumferentialFlawsEvaluation UsingCriterion forFlawStability J-Integral/Tearing ModulusProcedure J-Integral atFlawInstability InternalPressureatFlawInstability Evaluation UsingCriterion forFlawStability A-5000LEVELCANDDSERVICELOADINGS

/i CaseN-XXXAssessment ofReactorVesselsNithLowUpperShelfCharpyEnergyLevelsSectionXI,Division1Inquiry:SectionXI,Division1,XWB-3730, requiresthatduringreactoroperation, loadandtemperature conditions shallbemaintained to'provideprotection againstfailureduetothepresenceofpostulated flawsintheferriticportionsofthereactorcoolantpressureboundary.

UnderSectionXI,Division1,whatprocedure maybeusedtoevaluateareactorvesselwithalowupper,shelfCharpy.impact energylevelasdefinedinASTME185-82to.demonstrate integrity forcontinued serviceatuppershelfconditions?

Rep2y:Itistheopinion.'f theCommittee thatareactorvesselwithalowuppershelfCharpyimpactenergylevelmaybeevaluated todemonstrate integrity forcontinued serviceforupper.shelfconditions inaccordance withthefollowing.

1.0 EVALUAT1ON

PROCEDURES ANDACCEPTANCE CRITERIASectionXI,Division1,AppendixG,"Fracture Toughness CriteriaforProtection AgainstFailure",

providesanalytical procedures basedontheprinciples oflinear-elastic fracturemechanics thatmaybeusedtodefineloadandtemperature conditions toprovideprotection againstnonductile failureduetothepresenceofpostulated flawsintheferriticportionsofthereactorcoolantpressureboundary.

TopreventductilefailureofareactorvesselwithalowuppershelfCharpyimpactenergylevelthevesselshallbeevaluated usingtheprinciples

'ofelastic-plastic fracturemechanics.

Flawsshallbepostulated inthereactorvesselat,locations ofpredicted lowuppershelfCharpyimpa'ctenergyandtheappliedZ-integral fortheseflawsshallbecalculated andcomparedwith'heJ-integral fractureresistance ofthematerialtodetermine acceptability.

Factorsofsafetyonappliedloadforlimitedductileflawgrowth,andonflawstability duetoductiletearing,shallbesatisfied.

Allspecified design'transients forthereactorvesselshallbeconsidered.

Evaluation procedures andacceptance criteriabasedontheprinciples

.ofelastic-plastic fracturemechanics aregiveninAppendixAofthisCodeCase.Theevaluation shallbetheresponsibility oftheOwnerandshallbesubjecttoreviewbytheregulatory andenforcement authorities

-havingjurisdiction attheplantsite.

I APPENDIXATOCODECASEN-XXXASSESSMENT OFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSARTICLEA-1000INTRODUCTION A-1100SCOPEThisAppendixprovidesacceptance criteriaandevaluation procedures fordetermining theacceptability foroperation ofareactorvesselwhenthevesselmetaltemperature isintheuppershelfrange.Themethodology isbasedontheprinciples ofelastic-plastic fracturemechanics.

Flawsarepostulated inthereactorvesselatlocations ofpredicted lowuppershelfCharpyimpactenergyandtheappliedJ-integral fortheseflawsiscalculated andcomparedwithth'eJ-integral fractureresistance ofthematerialtodetermine acceptability.

Allspecified designtransients forthereactorvesselshallbeconsidered.

A-1200PROCEDURE OVERVIEWThefollowing isasummaryoftheanalytical procedure whichmaybeused.(a)Postulate flawsinthereactorvesselaccording tothecriteriainA-2000.(b)Determine theloadingconditions atthelocationofthepostulated flawsforLevelA,B,CandDServiceloadings.

(c)Obtainthematerialproperties, including Z,a~,andtheJ-integralresistance curve(J-Rcurve),atthelocations ofthepostulated flaws.Requirements fordetermining theJ-RcurvearegiveninA-3300'd)Evaluatethepostulated flawsaccording totheacceptance criteriain'A-2000.Requirements forevaluating theappliedJ-integralaregiveninA-3200,andfordetermining flawstability inA-3400'hreepermissible evaluation approaches aredescribed in~~A-3500.Detailedcalculation procedures forLevelAandBServiceloadingsaregiveninA-4000.A-1

A-1300GENERALNOMENCLATURE flawdepthwhichincludesductileflawgrowtheffective flawdepthwhichincludesductileflawgrowthandaplastic-zone correction (in.)(in.)BeBoeffective flawdepthatflawinstability, whichincludesductileflawgrowthanda-plastic-zone

.correction postulated initialflawdepthamountofductileflawgrowth(in.)(in.)(in.)dB'mountofductileflawgrowth,atflawinstability (in.)E'oung'smodulusE/(2-VR)CCR=materialconstants usedtodescribethepower-law fittotheJ-integral resistance curveforthematerial,.

ZR=C,(dB)'CR)=cooldownrate(F/hour)(ksi)(ksi)FzrF~rF~geometryfactorsusedtocalculate thestressintensity factor(dimensionless)

FarFurFggeometryfactorsusedtocalculate thestressintensity factoratflawinstability IJ-integral'ue totheappliedloads(dirtensionless

)(in.-lb/in.')

+RJ-integral fractureresistance forthematerial(in.-,1b/in.~)

A-2

J-integral fractureresistance forthematerialataductileflawgrowthof0.10in.(in.-lb/in.~)

JzKzappliedJ-integral ataflawdepthofa,+0.10in.J-integral atflawinstability modeIstressintensity factorC(in.-lb/in.')

(in.-lb/in.~)

(ksiv'in.)KzpmodeI'stressintensity factorduetointernalpressure, calculated withnoplastic-zone correction (ksiv'in.)KzpKzpca1cu1atedwithap1astic-zone correction (ksiV'in.)KzpKzpatflaw-instability, calculated withaplastic-zone correcti'on (ksiV'in.)KzeKzmodeIstressintensity factorduetoaradialthermalgradientthroughthevesselwall,calculated withnoplastic-zone correction Kcalculated withaplastic-zone correction (ksiV'in.)'I(ksiMin.)KzeKatflawinstability, calculated withaplastic-zone correction ordinateofthefailureassessment diagramcurve(ksiMin.)(dizransionless) ratioofthestressintensity factortothefracturetoughness forthematerialinternalpressure(dixransionless)

(ksi)accumulation pressureasdefinedintheplant-specific Overpressure Protection Report,butnotexceeding l.ltimesthedesignpressure(ksi)A-3

PsPPoRqpressureusedtocalculate theappliedJ-integral/tearing moduluslineinternalpressureat'lawinstability reference limit-load internalpressureinnerradiusofthevessel'bscissa ofthefailureassessment diagramcurve(ksi)(ksi)(ksi)(in.)(LQmnsionless

)ratioofinternalpressuretoreference limit-.loadinternalpressure(SF)=safetyfactorvesselwallthickness (dhransionless)

(dhransionless

)(in.)tearingmodulusduetotheappliedloadstearingmodulusresistance forthematerial(diz~nsionless)

(dUransionless) parameter usedtorelatetheappliedJ-integral totheappliedtearingmodulus(dimensionless)

Poisson's ratioreference flowstress,specified as85ksi(dirmnsionless)

(ksi)yieldstrengthforthematerial(ksi)

ARTICLEA-2000ACCEPTANCE CRITERIATheadequacyoftheuppershelftoughness ofthereactorvesselshallbedetermined byanalysis.

Thereactorvesselis.acceptable forcontinued servicewhenthecriteriaofParagraphs (a),(b),and(c)aresatisfied.

(a)LevelAandBServiceLoadingsWhenevaluating theadequacyoftheuppershelftoughness fortheweldmaterialforLevelAandBServiceloadings, postulate an.interior semi-elliptical surfaceflawwithadepthone-quarter ofthewallthickness andalengthsixtimesthedepth,withtheflaw'.smajoraxisorientedalongtheweldofconcernandtheflawplaneorientedintheradialdirection.

Whenevaluating.

theadequacyoftheuppershelftoughness forthebasematerial, postulate bothinterioraxialandcircumferential flawswithdepthsone-quarter ofthewallthickness andlengthssixtimesthedepthandusethetoughness properties forthecorresponding orientation.

Smallerflawsizesmaybeusedon-anindividual casebasiswhenjustified.

Twocriteriashallbesatisfied:

(i)TheappliedJ-integral evaluated atapressurewhichis1.15timestheaccumulation pressureasdefinedintheplant-specificOverpressure Protection Report,withafactorofsafetyof1.0onthermalloadingfortheplantspecified heatupandcooldownconditions, shallbeshowntobelessthantheJ-integral characteristic ofthematerialresistance toductiletearingataflawgrowthof0.10in.(2)Theflawshallbeshowntobestable,withthepossibility ofductileflawgrowth,atapressurewhichis1.25timestheaccumulation pres'sure definedinSubparagraph (1),withafactorofsafetyof1.0onthermalloadingfortheplantspecified heatupandcooldownconditions.

TheJ-integral resistance versuscrackgrowthcurveshallbeaconservative representation forthevesselmaterialunderevaluation.

A-5

~/(

(b)LevelCServiceLoadingsWhene:aluatintheadegquacyoftheuppershelftoughness fortheweldmaterialforLevelCServiceloadings, postulate interiorsemi-elliptical surfaceflawswithdepthsupto1/10ofthebasemetalwallthickness, plusthecladdingthickness, withtotaldepthsnottoexceed1.0in.,andasurfacelengthsixtimesthedepth,withtheflaw'smajoraxisorientedalongtheweldofconcernandtheflawplaneorientedintheradialdirection.

Whenevaluating theadequacyoftheuppershelftoughness forthebasematerial, postulate bothinterioraxialandcircumferential flaws,andusethetoughness properties forthecorresponding orientation.

Flawsofvariousdepths,ranginguptothemaximumpostulated depth,shallbeanalyzedtodetermine themostlimitingflawdepth.Smallermaximumflawsizesmaybeusedonanindividual casebasiswhenjustified.

Twocriteriashallbesatisfied:

(1)TheappliedJ-integral shallbeshowntobelessthantheJ-integralcharacteristic ofthematerialresistance toductiletearingataflawgrowthof0.10in.,usingafactorofsafetyof1.0onloading.,

(2)Theflawsshallbeshowntobestable,withthepossibility ofductileflawgrowth,usingafactorofsafetyof1.0onloading.TheJ-integral'esistance versuscrackgrowthcurveshallbeaconservative representation forthevesselmaterialunderevaluation.

(c)LevelDServiceLoadingsWhenevaluating theadequacyoftheu'ppershelftoughness forLevelDServiceloadings, post'ulate flawsasspecified forLevelCServiceloadings'inParagiaph b),andusethetoughness properties forthecorresponding orientation.

Flawsofvariousdepths,ranginguptothemaximumpostulated depth,shallbeanalyzedtodetermine themostlimitingflawdepth.Smallermaximumflawsizesmaybeusedonanindividual casebasiswhenjustified.

Theflawsshallbeshowntobestable,withthepossibility ofductileflaw"'rowth,usingafactorofsafetyof1.0onloading.TheJ-integral resistance versuscrackgrowthcurveshallbeabestestimaterepresentation forthevesselmaterialunderevaluation.

Thestableflawdepth.shallnotexceed75%ofthevesselwall~~~~~~~~thickness, andtheremaining ligamentshallbesafefromtensileinstability.

A-6

ARTICLEA-3000\ANALYSISA-3100SCOPEThisArticlecontainsageneraldescription ofprocedures whichshallbeusedtoevaluatetheappliedfracturemechanics parameters, aswellasrequirements forselecting theJ-Rcurveforthematerial.

References aremadetoacceptable approaches toapplythecriteria.

A-3200APPLIEDJ-INTEGRAL Thecalculation oftheJ-integral duetotheappliedloads.shallaccountforthefullelastic.-plastic behaviorofthestress-straincurveforthematerial.

Whentheconditions fallintothecategoryofelasticfracturemechanics withsmall-scale

yielding, theJ-integral mayalternately becalculated

.byusingcrack-tip stressintensity factorformulaewithaplastic-zone correction.

Themethodofcalculation shallbevalidated anddocumented.

A-3300SELECTION OFTHEJ-INTEGRAL RESISTANCE CURVEWhenevaluating thevesselforLevelA,BandCServiceloadings, theJ-integral

'resistance versuscrackgrowthcurve(J-Rcurve)shallbeaconservative representation ofthetoughness ofthecontrolling beltlinematerialatuppershelftemperatures intheoperating range.Whenevaluating thevesselforLevelDServiceloadings, theJ-Rcurveshallbeabestestimate.representation ofthetoughness ofthecontrolling beltlinematerialatuppershelftemperatures intheoperating range.Oneofthefollowing optioris:

shallbeusedtodetermine theJ-Rcurve.(a)AJ-Rcurvegenerated fortheactualmaterialunderconsideration byfollowing acceptedtestprocedures maybeused.TheJ-Rcurveshallbebasedonthe'roper combination ofcrackorientation, temperature andfluencelevel.'he crackgrowthshallincludeductiletearingwithnooccurrence ofcleavage.

A-7 S'

AJ-Rcurvegenerated fromaJ-integral databaseobtainedfromthesameclass.ofmaterialunderconsideration withthesameorientation usingappropriate correlations fortheeffectsoftemperature, chemicalcomposition andfluencelevelmayheused.Thecrackgrowthshallincludeductiletearingwithnooccurrence ofcleavage.

(c)Whentheapproaches of(a)or(b)arenotpossible, indirectmethodsofestimating theJ-Rcurvemaybeusedprovidedthesemethodsarejustified forthematerialunderconsideration.

A-3400FLAWSTABILITY Theequilibrium equationforstableflawgrowthisJ=JwhereJistheJ-integral dueto-theappliedloadsforthepostulated flawinthe'vessel, andJistheJ-integral resistance toductiletearingforthematerial.

Theinequality forflawstability duetoductiletearingisQJdLTgaadawhereBJ/Baisthepartialderivative oftheappliedJ-integral withrespecttotheflawdepthawithloadheldconstant, anddJ/daistheslopeoftheJ-Rcurve.'nderacondition ofincreasing load,stableflawgrowthwillcontinueaslongasBJ/BaremainslessthandJ/da.A-3500EVALUATION APPROACHFORLEVELAANDBSERVICELOADINGSTheprocedure giveninA-4200shallbeusedtoevaluatetheappliedJ-integral

-foraspecified amountofductileflawgrowth.Therearethreeapproaches thatareequallyacceptable forapplyingtheflawstability acceptance criteriaaccording tothegoverning flawstability rulesinA-3400.ThefirstisaJ-Rcurvecrackdrivingforcediagramapproach.

Inthisapproachflawstability isevaluated byadirectapplication oftheflawstability rulesgiveninA-3400.Guidelines forusingthis~~~approacharegiveninA-4310.Thesecondisafailureassessment diagramapproach.

Aprocedure basedonthisapproachfortheA-8 tI~

postulated initialone-quarter wallthickness flawisgiveninA-4320.ThethirdisaJ-integral/tearing modulusapproach.

Aprocedure basedonthisapproachforthepostulated initialone-quarterwallthickness flawisgiveninA-4330.ARTICLEA-4000EVALUATION PROCEDURES FORLEVELAANDBSERVICELOADINGSA-4100SCOPEThisArticlecontainscalculation procedures tobeusedto.satisfytheacceptance criteriainA-2000forLevelAandBServiceloadings.

Aprocedure tobeusedtosatisfytheJ-integral criterion foraspecified amountofflawgrowthof0.10in.isgiveninA-4200.Procedures tosatisfy-theflawstability criterion aregiveninA-4300.Theseprocedures includetheax'ialandcircumferential flaworientations.

A-4200EVALUATION PROCEDURE FORTHEAPPLIEDJ-INTEGRAL A-4210CALCULATION OFTHEAPPLIEDJ-INTEGRAL Thecalculation of.the"appliedJ-integral consistsoftwosteps:Step1istocalculate theeffective flawdepthwhichincludesaplastic-zone correction; and-Step2istocalculate theJ-integral forsmall-scale yieldingbasedonthiseffective flawdepth.~Ste1For.anaxialflawwithadeptha,calculate thestressintensity factorduetointernalpressurewithasafetyfactor(SF)onpressurebyusingR>>=(SF)p(I+(R,/t)J(na)',F~=0.982+1.006(a/t)~

ThisequationtheeffectofforR>>isvalidfor0.20sa/ts0'0,andincludespressureactingontheflawfaces.A-9

~~~Foracircumferential flawwithadeptha,calculate thestressintensity factorduetointernalpressurewithasafetyfactor(SF)onpressureby'usingKzp=(SF)p(1+(RE/(2t))J(za).FzF,=0.885+0.233(a/t)

+0.345(a/t)3 (2)ThisequationforK>>isvalidfor0.20sa/ts0.50,andincludestheeffectofpressureactingontheflawfaces.Foranaxialorcircumferential flawwithadeptha,calculate thestressintensity factorduetoradialthermalgradients byusingKE0=((CR)/I000)tF3F,=.0.584+2;647(a/t)

-6.294(a/t)'

2.990(a/t)3 (3)ThisequationforKz,isvalidfor0.20ca/t~0.50,and0c(CR)~100F/hour.Calculate theeffective flawdepthforsmall-scale

yielding, abyusinga,=a+(I/(6'))((Kzp

+KE0)/<yJ~Ste2Foranaxialflaw,calculate-thestressintensity factorduetointernalpressureforsmall-scale

yielding, Kzp,bysubstituting a,inplaceofainequation(1),including theequationforF,.Foracircumferential flaw,calculate Kzpysubstituting a,inplaceofainequation(2),including theequationforF,.Foranaxialorcircumferential.

flaw,calculate thestressintensity factorduetora'dialthermalgradients forsmall-scale

yielding, Kzbysubstituting ainplaceofainequation(3),including theequationforF3.Equations (1),(2)and(3)arevalidfor0.20ca,/tc0.50.TheJ-integral duetotheappliedloadsforsmall-scale yieldingisgivenbyZ=1000(Kzp+K'/E'

A-4220EVALUATIONgUSING CRITERION FORFLANGRONTHOF0.1ZNCalculate theJ-integral duetotheapple.edloads,Jbyfollowing A-4210.Useaflawdepthaequalto0.25t+0.10in.;apressurepequaltotheaccumulation pressureforLevelAandBServiceloadings,'

andasafetyfactor(SF)onpressureequalto1;Z5.Theacceptance.

criterion forLevelAandBServiceloadingsbasedonaductileflawgrowthof'.10in.inA-2000(a)(1')

issatisfied whenthefollowing inequality issatisfied.

Js~Jo.iwhereJ,=theappliedJ-integral fora=safetyfactoronpressureof1.15,andasafetyfactorof1.0onthermalloading,J,,=theJ-integral resistance ataductileflawgrowthof0.10in.A-4300EVALUATION PROCEDURES FORFLANSTABILITY A-4310J-RCURVE-CRACKDRIVINGFORCEDIAGRAMPROCEDURE

~~Znthxsprocedure flawstabzlzty xsevaluated byadirectapplication oftheflawstability rulesgiveninA-3400.TheappliedJ-integral iscalculated foraseriesofflawdepthscorresponding toincreasing amountsofductileflawgrowth.TheappliedJ-integral forLevelAandBServiceloadingsshallbecalculated byusingtheprocedures giveninA-4210.Theapplieppressurepissetequaltotheaccumulation pressureforLevelAandBServiceloadings, p;andthesafetyfactor(SF)onpressureisequalto1.25.TheappliedJ-integral is.plottedagainstcrackdepthonthecrackdrivingforcediagramtoproducetheappliedJ-integralcurve,asillustrated inFigureA-4310-1.

TheJ-Rcurveisalsoplottedonthecrackdrivingforcediagram,andintersects thehorizontal axisattheinitialflawdepth,a,.Flawstability atagivenappliedloadisdemonstrated whentheslopeoftheappliedJ-integral curveislessthantheslopeoftheJ-RcurveatthepointontheJ-Rcurvewherethetwocurvesintersect.

Jr MaterialJREvaluation Point'ppliedJapFIGUREA-4310-1COMPARISON OFTHESLOPESOFTHEAPPLIEDJ-INTEGRAL CURVEANDTHEJ-RCURVE~

I~

A-4320FAILUREASSESSMENT DIAGRAMPROCEDURE Thisprocedure isrestricted toapostulated initialflawdepthequaltoone-quarter ofthewallthickness.

A-4321FAZLUREASSESSMENT DIAGRAMCURVEThesamefailureassessment diagramcurveshallbeusedforaxialandcircumferential flaws,andisgivenin.FigureA-4320-1.

Thecoordinates (SR,)ofthefailureassessment diagramcurvearegiveninTableA-4320-1.

Thiscurveisbasedonmaterialproperties whicharecharacteristic ofreactorpressurevesselsteels.A-4322FAILUREASSESSMENT POINTCOORDINATES Theflawdepthafor,aductileflawgrowthofh,aisgivenbya-=0250+ha~~Thefailureassessment pointcoordinates (S',K')foraductileflawgrowthofhashallbecalculated byusingthefollowing expressions:

KzR~(I000/(EJ))Vwherethestressintensity factorshallbecalculated usingtheflaw.depthawithouttheplastic-zone correction, andisgivenbyK~=Kzp+R~,ands:=(sz)p/p.where(SZ)istherequiredsafetyfactoronpressure.

Theprocedure forcalculating Kz~Kzandp,foraxialflawsisgiveninA-4322.1, andfor.circumferential flawsinA-4322.2.

A-13

-0 A-4322.1AxialFlawsThestressintensity factorduetointernalpressureforaxialflawswithasafetyfactor(SZ)onpressureisgivenbyequation(1').Thestressintensity factordue,toradialthermalgradients isgivenbyequation(3)~Thereference limit-load pressureisgivenbyH(2/~3}o[Q.905-Q.379(h,a/t)I[0.379+(R~/t)+0.379(ha/t}1Formaterials withayieldstrengthogreaterthan85ksi,setaequalto85ksiinthisequation.

Thisequationforp,isvalidfor0sza/ts0.10.A-4322.2Circumferential Flaws()thermalgradients is>givenbyequation(3).Thereference limit-load pressureisgivenbyCThestressintensity factorduetointernalpressureforcircumferential flawswithasafetyfactor(SF)onpressureisgivenbyequation2.Thestressintensitfactorduetoradialpo[1-0.91(0.25+(Aa/t})~(t!R~)l[1+(R/(2t)Formaterials withayieldstrengthozgreaterthan85ksi,setoyequalto85ksiinthisequation. Thisequationforpisvalidfor0sza/'ts0.25.A-4323EVALUATION USINGCRITERION FORFLAN'TABILITY Assessment pointsshallbecalculated foreachloadingcondition according toA-4322,andplottedonFigureA-4320-1asfollows.Plotaseriesofassessment pointsforvariousamountsofductileflawgrowthbauptothevaliditylimitoftheJ-Rcurve.Useapressurepequaltotheaccumulation pressureforLevel.AandBServiceloadings, pandasafetyfactor(SF)onpressureequalto1.25.Whenoneormoreassessment pointslieinsidethefailureassessment curve,theacceptance criterion basedonflawstability. inA-2000(a)(2) issatisfied. /r TABLEA-4320-1COORDINATES OFTHEFAILUREASSESSMENT DIAGRAMCURVEOPFIGUREA-4320-10.0000.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.8500.9000.9501.0001.0501.1001.150'.K1.0001F0000.9990.998'.996 0.9930.9900.9870.9810.9730.9600.9390.9080.8640.8070.7370.6600.5810.5050'350.3740.3210.2760.238A-15 Js 1.21.0,0.80.6K,0.40.20.00.00.20.40.60.81.01.2S,1.4FIGUREA-4320-1FAILUREASSESSMENT DIAGRAMFORTHEONE-QUARTER MALLTHICKNESS FLANA-16 J A-4330J-ZNTEGRAL/TEARZNG MODULUSPROCEDURE Thisprocedure isrestricted toapostulated initialflawdepthequaltoone-quarter ofthewall.thickness. A-4331J-ZNTEGRAL ATFLANZNSTABZLZTY 1Referring toFigureA-4330-1, theonsetof.flawinstability isthepointofintersection oftheappliedandmaterialcurvesplottedonagraphoftheJ-integral versustearingmodulus(JversusT).Theexpression fortheappliedJ/TcurveisgivenbyJ=(1000VtOi/Z)T(4)(5)whereoiisareference flowstresswhichissetto85ksiinequation(4).Foraxialflawsp=0.235(l+(0.083x10')(CR)t'/((SF)p,)J wherep,isthepressureunderevaluation. Equation(5)isvalidfor6sts12in.,2.25s((SF)p,)s5.00ksi,and0s(CR)100F/hour.Forcircumferential flaws~~~~~V=0.21(1+(0.257x10)(CR)t/((SF)p,) J(6)Equation(6)isvalidfor6sts12in.,2.25s((SF)p,)s9.00ksi,and0s(CR)s100F/hour.Equations (4),(5)and(6)arebasedonmaterialproperties whicharecharacteristic ofreactorpressurevesselsteels.Thetearingmodulusforthematerialisdetermined bydifferentiation oftheJ-Rcurvewithrespecttoflawdeptha.(Z/(1000Qi))dJ/da(7)The-samevaluesforZandoishallbeusedinequations (4)and(7).TheJ-integral versustearingmodulusJ~/T~curveforthematerialisgivenbyplottingJagainstT~foraseriesofincrements inductileflawgrowth.Eachcoordinate forJRisevaluated atthesameamountofductileflawgrowthasthecoordinate forT~. / ~~~~~~~~The'value oftheJ-integral attheonsetofflawinstability, J',corresponds totheintersection oftheappliedJ/Tcurvegiven:byequation(4)withthematerialJ~/T~curve,asillustrated inFigureA-4330-1. hTheJ-integral attheonsetofflawinstability maybedetermined analytically whenapower-law curvefittotheJ-RcurveoftheformJ-Ci(ha)+isavailable. TheJ-integral attheonsetofflawinstability, J,inthiscaseisgivenbyA-4332ZNTERNALPRESSUREATFLANZNSTABZLZTY ~~~~~~~~~~~Thecalculation oftheinternalpressureattheonsetofflawinstability isbasedonthevalueoftheJ-integral at.theonsetofflawinstability, J.Theductileflawgrowthattheonset.offlawinstability, ha,istakenfromtheJ-Rcurve.Theeffective flawdepthattheonsetofflawinstability includestheductileflawgrowthb.a',andisgivenbya=0.25t+ha+(1/(6n))fZ'8'/(1000 o~'))Thestressintensity factorduetoradialthermalgradients attheonsetofflawinstability, Ziforaxial:orcircumferential flawsisgivenby.."Zzi=((CR)/1000) t~'~Z'~=0.584+2.647(a,'/t) -6.294(a,'/t)~ +2.990(a,'/t)~ Thisequationfor'Ri,isvalidfor0.20~a,/t~0.50,'nd0s(CR)s100'F/hour. Thestressintensity factorforsmall-scale yieldingduetointernalpressureattheonsetofflawinstability, Eppesisgivenby ,0 ForagivenvalueofK,'~,theinternalpressureattheonsetofflawinstability foraxialflawsisgivenbyp=Ksp/((1+(R,/t))(za)o.sF,']F~.=0.982+,,2.006(a,/t)~ andforcircumferential flawsbyp=Ki/((1+(Ri/(2t))) (za,)'~JF'0.885+0.233(a,/t) +0.345(a,/t) Theseequations forparevalidfor0.20sa,/ts0.50,andincludetheeffectofpressureactingontheflawfaces.A-4333EVALUATION USINGCRITERION FORFLANSTABILITY Calculate thevalueoftheJ-integral attheonsetofflawinstability, J',byfollowing A-4331usingapressurep,inequations (5)and(6)equaltotheaccumulation pressureforLevelAandBServiceloadings, pandasafetyfactor(SF)onpressureequalto1.25.Calculate theinternalpressureattheonsetofflawinstability, p,byfollowing A-4332.Theacceptance criterion basedonflawstability inA-2000(a)(2) issatisfied whenthefollowing inequality issatisfied. p>I25p,ARTICLEA-5000LEVELCANDDSERVICELOADINGSThepossiblecombinations ofloadingsandmaterialproperties whichmaybeencountered duringLevelCandDServiceloadingsaretoodiversetoallowtheapplication ofpre-specified procedures anditisrecommended thateachsituation beevaluated onanindividual casebasis.A-19 0 Instability .Material JRvsTRJtcAppliedJvsTFIGUREA-4330-1ILLUSTRATION OPTHEJ-INTEGRAL/TEARING MODULUSPROCEDURE A-20 A 83AppendixBASMEWorkingGrouponFlawEvaluation DraftModification toArticleA-3000

ART<.CI,E A.-3OoONETHODFOREsDETERMINATION pg~WCVriHABC&A-3100SCOPEThisAtticleprovidesamethodforcalculating stressintensity factorKrfromthemembraneandbendingstressesdetermined fromstressanalysis. A-3100SCOPEThiaAructeprovideramethodforcalculating atrcaaintcnrity factorK<fromthereprerenrartve arreraerattheflawlocationdetermined fromarrearanalysis. Moreaophirticatcd techniques maybeusedlndetermining I4pmvldcdthemethodsaedaeatyaeaaredocumented. fA-3MOSTRE55ESThestressesattheflawlocationshouldberesolvedintomembraneandbendingstresseswithrespecttothewallthickness. Residualstressesandappliedstressesfromallformsofloading.including pressurestresses, thermalstresses. discontinuity stresses. andcladdinginducedstresses. shouldbeconsidered. lnthecaseofanonlinear stressdistribution throughthewall,theac-tualstressdistribution shouldbeconservatively ap-proximated usingthelinearigation technique illustrated inFig.A-3200-1. Thelinearized stressdistribution shouldthenbecharicterized bythemembranestresscrandthcbendingstressera,asshowninFig.A-3200-1~h-3200STQBSES(a)Forthecaroofasubsurface fiaw,thatromcaattheflawlocationshallberesolvedintomembraneandbendingatrcrrcawithrespecttothewallthlcknecr. Rertduatstrcascaandappliedarrccacafromallfonnaofloadmg,including pressurearreaaeeandchddag.inducedatrearor, abaQbeoonrutcred. Fornonlinear strcaavarianres throughthewall,theactualarreaadistributio canbeconaervanvely approximated bythelinearization techruque illuarrared inFig.h-3200-1(b). Thebncariaed atrea'edtrrributton ahoutdrbcnbecharacterised bythemembraneatrcaae'ndthebeudurgarreeagaarhowninFig.A-3200.1(b). (b)Forthecareofasurfaceflaw,rhearrerrcaattheflawlocationshallbereprerrntrd byapolynornlat fitgivenbythefoUowiagrelationship: o-A,~A,x~A,xa-A,x'wherexisthedirraucethroughthowallandAA,.AandA,areconstants. Thederermiua6on ofcodflcteors Aothrough+rhallprovideaconservative reprrccntation ofatrearoverrhecrackone0cx4aforauvat~ofcrackdcpthacoveredbytheanalysis. StresreafromaourceaiMocr&dlnA-3200(a) ahallbecoasidcrcd. lnthecasewhraanonlinear arrcaadlarrlbutiou ladlfflcutt tofitbeEq.1,thcactualdlrrribunon canbecoeacrvarlvely appro6rnared by0>>hncarizatlon rcchntquo Ulurrrared tnFigureA-3200t(a)fottowteg thediacuaaion giventnh-3200(a) foraubcuzface flawa.

A-3300STRESSINTENSITY EQUATION(a)Stressintensity factorsfortheAawmodelshouldbecalculated fromthemembraneandbendingstressesattheflawlocationusingthefollowing equation: K/~eNYrr~alQ+ tr>M>Va'Valg (I)wherecr,tre~membraneandbendingstresses. psi.inac-cordance'withA-3200aminorhaifdiamcter, in.,ofembeddedflaw:flawdepthforsurfaceflawQmflawshapeparameter asdetermined fmmFig.A-3300-lusing(tr+rr,)/a,andtheRawgeometryM=correction factorformembranestress(sceFig.A-3300-2forsubsurface flaws;Fig.A-3300-3forsurfaceflaws)~'emcorrcction factorforbendingstress(seeFig.A-3300-4forsubsurface laws:Fig.A-D~~~~~~~3300-5forsurfaceflaws)%herevariations inK/amundthcperiphery ofoccur.thcmaximumvalueistobeused.(c)TheuseofEq.(1)isonlyatecomn>>ndation fordetermination ofA'/.Moresophisticated techniques maybcused,providedthemethodsandanalysesaredoc-urnented. Inmanycasesinvolving complexgeometries andsttessdistributions, themethodsoutlinedabovemaybeinadequate. h-3300SIILESSINTENSITY FACTOREQUATIONS Theflawshallbetepteseated byanelGpsethatcbcumacdbaa thedetectedflawasiilutttated inFig.A33001.Thestressiattosity iactotsfortheflawmodelshallbodetencined ftomthestressesandflawgeometryasdesctibed iah-3310forsubsurface flawsaadlnh-3320forsutfacoflaws.h-3310Subsuttace FlawEquations atoMm+obMbjf~0/0(2)where,0>>IJgA-3200(a) aMFig.A3200-2M,Pig.h-3200.3QMembraneandbeadingstressesiaaccordance withMinorhalMmnetes Conection factorformembranesttessglvcatinConection factorforbeadingstressgivtstinFlawsbapopataateter asgivenbyEq.3Theflawshapepanttnctct Qiscalculated firomthefollowing equatioa: Q1-4.598(a/>)Ž-q(a)Stressattensity factorsforsubsurface flawshallbecalculated fromthoas:mbrane andbeadingsuessesatthefLawlocationbythefollowing cquatioa: whetea/ristheflawaspectratio0sa/rs'8,aadq,istheptasticsouecottectioa factorequalto0.212I(o+eJ/o)'.(b)Whetevariatioas iaK,aroundthepcriphetv oftbeflavvoccur.themaximumvalueistobeusediathedelcnniaatioa oftbectiticatflawluuamctcra a,and+.(c)TheusoofEq.2isonlyatecomaamdatioa foedetenainatioa ofKvIasomecasesiavolviag comptcageometries andsttessdistribution. themethodoutlinedabovemayaotbeadequate. I A.3320Sur&ceFlawEquations (a)Stressintensity factorsforstrrfsceflawsshouldbecalculated fromthecubicpolyaoaual stressrelationbythefollowieg equstlorv(4)KQOo'At3tarAtotat AsOsaj~xCrackdepthA,AAs,A,~Coefficieats fromEq.1that~utsrtsrts thestressdistribution overthecrack(0s.x5a)OorOoGteOrQwithq,defiaedasFreesurfacecorrection factorsfortbegivenstressvariation providediaTablesA-33201andA.3320.2asafunctionotflawaspeNratioa/f,crackeaetration s/t,aadcracktippositiott (PTLaadF72)Flawshapepsrstaetcr ssgivenbyEg.30.212[A,/trP(b)~theLineIraaenmethodlsusedtoconvertthoactualstressfieMintotraadtr,stressesasillustrated iaHg.A-3200-1(a), thenEq.2shallbeUsedtocalculate )(twiththofollowing equations forM,MsrdQ:MMiGo2(a/t)GrQ~Sq.3whereq,isdefinedas0.212((re+ ~/o'e)%huevariation iaKrsratheperipherofthefLawoccur,thetrLaxitaum valueistobeusediathedetertainatlon ofa,aadtt(d)TheusooftheabovemethodsIsonlyarecotrutMadatlcsr fordetermination ofQ.lnsomecasesiavolviag complygeotnesries andstressduuribunons. themethodsoutlinedabovemayncebeadequate.

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GFUNCTIONRESULTSFORA/L=O.11.4CfKKTlPPT1aShiratori, oRaju-Newman +Extropofated PointG2.0.4G3Q.QO.QS.10.>0~0.4un0,7OZQSu)CrackOeptha/t ~eJ .GFUNCTIONRESULTSFORA/L=0.12.0CRACKTlPPT20Shiratori oRaju-Neo<man +Extrapolated PointgU)Ž0.60.4G20.00.10.203OA0.50.60.70309IQCrackDeptha/t 0 GFUNCTiONRESULTSFORA/L=D.2CRACK-TlP PT3Shiratori 0Raju-Newman' Extrapolated PointQHlCDOg0.40.2.0OoO.~0.20,304Oa0.S07Oa09]aCrackDeptha/t

0FUNCTII3N RfSULTSFORA/L=022.0CRACKTlPPT20Shiratori oRoju-Newman eExtrapolated Point0.4G4.0,00.102030.40.50.607B095CrackOaptha/t f GFUNCTIONRESULTSFORA/L=0.3'2.01,61.41+21.0-0.8CRACKTIPPT1oShirotori oRaju-Newman +Extrapotated Point000,60.20.00.102030.4.0.50.60,7030.91.0CrackDeptha/t

GFUNCTIONRESULTSFORA/L=D32,0CRACKTIPPT2c3Shiratori 0Raju-Newman +Extrapofated Point0.2G]0.00,00.10203040.50.6070,809$0CrackDeptha/t 0 GFUNCTIQNRESULTSFQRA/L=D.52.01,8IICRACKTIPPT50Shiratori oRoju-Newman +Extrapoloted PointU1.00,40,20,0oaO.~OaO,Za.4O,S0.60.70309ICrackDeptha/t

2.01.8GFUNCTIONRESULTSFORA/L=O.5CfIACKTePt20Shirotori 0Raju-Headman +Extrapolated PointGO.=1ll0.602.00.00.102030.40.5(M0.7(M095CrackDeptha/t

GFUNCTIONRESULTSFORAjL=D.D4.0CRACKTlPPT1xTgdg3.91.00.0000.$02030.40.50.6070809UlCrxkDeptha/t 8%0}}

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