ML18038A735

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
Issue date:	02/22/1993
From:	NIAGARA MOHAWK POWER CORP.
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ML17056C285	List: ML17056C284 ML18038A735
References
MPM-USE-293216, NUDOCS 9303040167
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NMPCProject03-9425MPM-USE-293216FINALREPORTentitledELASTIC-PLASTICFRACTUREMECHANICSASSESSMENTOFNINEMILEPOINTUNIT1BELTLINEPLATESFORSERVICELEVELCANDDLOADINGSMPMResearchdrConsuItingwi<~~~'//j~j~~Zp/>>February22,19939303040ih7'730226PDR.ADQCK.05000220P'DR

3TableofContents1.0Introduction~\~~~~~~2.0MaterialModel.3.0TransientSelection3.1LevelCTransientSelection....3.2LevelDTransientSelection....3.3ScreeningAnalysis3.3.1ModelDescription..........3.3.2LevelCTransientAnalysis3.3.3LevelDTransientAnalysis3.3.4SummaryofCandidateTransients7778899104.0FiniteElementAnalysis..........,.......4.1ModelDescription..4.2FiniteElementAnalysisResults4.3LimitingTransients............26262627'lastic-PlasticFractureMechanicsAssessment.....5.1ModelDescription....5.1.1VesselGeometry............5.1.2AppliedLoads5.1.3LimitsforSmallScaleYieldingAnalysis5.1.4FractureMechanicsModel........5.2CalculationsforA302BMaterialModel......5.2.1LevelCLoading......5.2.2LevelDLoadingAnalysis,.........5,2.3TensileInstabilityAnalysis393939394040434343436.0SummaryandConclusions...................t'.0References...................5254Acknowledgement.........56A+0ppendtces...................AppendixAAppendixB~~~~~~~~~~~~~~~~~~575883

1.0IntroductionNuclearreactorpressurevesselmaterialsmustbetestedandevaluatedtoensurethattheyaresafeintermsofbothbrittleandductilefractureundernormaloperationandduringdesignbasistransients.Withregardtoductilefractureprotection,AppendixGto10CFR50prescribesascreeningcriterionof50ft-lbs.IfanybeltlinematerialsareexpectedtoexhibitCharpyUpperShelfEnergy(USE)(T-Lorientation)lev'elsbelow50ft-lbs,thenadditionalanalysesmustbeperformedtoensurecontinuedsafeoperation.TheDraftASMEAppendixX[ASME92]wasdevelopedtoassistlicenseesinperformingelastic-plasticfracturemechanicsevaluationsforbeltlinematerialswithlowuppershelfenergies.ThisreportdocumentsapplicationofthedraftAppendixXcalculativeproceduresandcriteriatotwoNineMilePointUnit1(NMP-1)beltlineplatesforServiceLevelCandDloadings.TheNMP-1beltlinematerialswereevaluatedtodeterminewhetheranymaterialswouldexceedthe50ft-lbscreeningcriterion.TheresultsoftheseevaluationsaresummarizedinReference[MA93]andwerepresentedintheresponsetoNRCGenericLetter92-01[MA92].Asaresultoftheseevaluations,NMPCconcludedthatanAppendixXanalysismustbeperformedforbeltlineplatesG-8-1and6-307-4.TheresultsoftheAppendixXanalysisforServiceLevelAandBloadingswerereportedinReference[MA93].ThisreportpresentstheresultsoftheServiceLevelCandDloadinganalysis.

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2.0MaterialModelTheNMP-1beltlineplateswerefabricatedusingA302Bmodified(A302M)steel.Atpresent,sufficientJ-RdataarenotavailabletoconstructanA302Mmodel.AsdiscussedinReference[MA93],theNMP-1platesarebestmodelledusinganA302BJ-Rmaterialmodel.TheA302BmaterialmodelisfullydescribedinReference[MA93].ForServiceLevelCloadings,theJ-RcurveinputsaretwosigmalowerboundcurveswhicharethesameasforServiceLevelsAandB.However,forServiceLevelDanalysis,Reference[ASME92]allowstheuseofJ-Rcurveswhichareabestestimaterepresentationforthevesselmaterialbeinganalyzed.Therefore,thebestestimate,ormean,J-Rcurves,asafunctionofUSElevel,weredetermined.TheJ,cversusUSEmodelreportedinReference[MA93]wasusedtocalculatethemeanJ,cdatagiveninTable2-1.The6TJD-hadatareportedinReference[HI89]wereusedtodeterminetheJ-RcurvesattheUSElevelsshowninTable2-1.The6TJD-hadatawerereducedorincreasedbythedifferencebetweenthe6TtestJ<<value(525in-lb/in')andtheJ,cdatalistedinTable2-1.Theyieldstress,modulus,andPoissonratiousedintheanalysisareidenticaltotheReference[MA93]data.

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

>p 3.0TransientSelectionTheASMEdraftAppendixXdoesnotspecifyproceduresforcalculatingLevelCandDserviceloadingssincethecombinationsofloadingsandmaterialpropertiesencounteredinpracticearetoodiverse.Therefore,themostlimitingtransientsforLevelsCandD,fromaductilefractureperspective,wereidentifiedasfollows:TheNMP-1andNMP-2plantdocumentationwascarefullyexaminedtoidentifypotentiallimitingtransients.Ascreeningcalculationwasthenperformedtoreducethespectrumoftransientstoafewmostlikelycandidates.FiniteelementcalculationswereperformedonthereducedsetoftransientstodeterminethemostlimitingLevelCtransientandthemostlimitingLevelDtransientandtheresultantloading.3.1.LevelCTransientSelectionTheNMP-1andNMP-2updatedFSARsandthermalcyclediagramswerereviewedtodetermineaspectrumofcandidateLevelCtransientsforfurtheranalysis.Priortoperformingthescreeningcalculations,itwasnotclearwhethertherapidpressurelosstransientsortheslowdepressurizationtransientswouldprovidethelargestcombinedpressureand,thermalgradientloads.Therefore,thetransientsshowninFigure3-1werechosenforanalysissincetheyboundallLevelCtransientsintermsofcooldownrate.Table3-1liststhetemperature/pressurevariationatvarioustimesduringthetransient.TheclassificationoftheautomaticblowdowntransientandemergencycooldowntransientasLevel'Ceventsisconsistentwiththedefinitionoftheemergencyconditiontransients.,Figure3-1includestwoeventsdescribedintheUnit1updatedFSAR(References[FSAR]and[CENC])andtheUnit2(References[STRS]and[TCD])emergencyconditionautomaticblowdown.3.2LevelDTransientSelectionAswiththeLevelCtransientselection,theLevelDtransientswereselectedaftercarefulexaminationoftheNMP-1andNMP-2plantdocumentation.AsetoftransientswerechosenwhichboundallLevelDeventsintermsofcooldownrate.PlotsoftheselectedtransientsareshowninFigures3-2through3-5(pressure/temperatureprofiledataarealsogiveninTables3-2and3-3.)TheNMP-2faultedconditioneventsarespecifiedbasedontheReference[NEDC]analysis.Theeventsincludedforconsiderationincludethebreakspectrumfortherecirculationlinebreaks,thesteamlinebreak,corespraylinebreak,andthefeedwaterlinebreak.

tp 3.3ScreeningAnalysis3.3.1ModelDescriptionThetransientsdescribedearlierwereanalyzedusingasimplelinearelasticfracturemechanicsmodeltodeterminethosetransientswhichrequireadetailedfiniteelementanalysistodeterminethelimitingloads.ThetemperaturedifferenceacrossthevesselwallfortheLevelCtransientswascalculatedusingtheTRUMP/MPMcode[TRUMP].TheNMP-1vesselwasmodelledusingcylindricalcoordinates,Thevesselis7.281in.thickwithaninnerradiusof106.5inches.The0.1563in.stainlesssteellinerwasmodelledashavingthephysicalpropertiesof316SS,andtherestofthevesselthicknesswasmodelledasA302Bferriticsteel.Atotalof17radialnodes,eachofapproximatelyOA4in.thickness,wereusedtodiscretizethevesselthickness.AnodeltemperatureboundaryconditionwasappliedattheIDsurfaceofthevessel.Thesurfacenodewasmodelledasbeinginthermalequilibriumwiththedowncomerfluidtemperature.Thisassumptionleadstoconservativethroughwallgradientestimates,particularlyfortheLevelDtransientsduringwhichphasechangeoccurs.Therefore,theinitialtemperatureofallvesselnodesweresetto500'F.Oncethetemperaturedifferenceacrossthewallwascalculated,therelativecontributionofthepressureloadingandthethermalloadingwasapproximatedusingthelinearelasticfracturemechanicsmodelgiveninAppendixGtotheASMEcode.Itshouldbeemphasizedthattheseequationsarebasedonlinearelasticfracturemechanicsprinciplesandarestrictlyapplicableforthermalrampsofupto100'F/hr.Nevertheless,forscreeningpurposes,theseequationsareadequateforassessingtherelativecontributionsofthepressureandthermalloadstothetotalcracktipstressintensityforthevariousLevelCandDevents.AppendixGusesthefollowingequationstocalculatethestressintensities:IK=K~+K~where,K~=Ma=membranestressintensityfactor(ksiVin)K~=MTbT=stressintensityfactorduetothermalgradient(ksi0in)M=ASMEmembranefactor(0in)MT=ASMEthermalfactor(ksi0in/'F) lpe

!bT=temperaturedifferenceacrossvesselwall('F)o=stress(ksi)(A~+B~)(B~-A2)(3-2)A=vesselinnerradius(in.)B=vesselouterradius(in.)P=internalpressure(psig)SincetheAppendixXflawgrowthcriterionismoresevereatdeepcrackdepthsunderLevelCandDeventloads,thescreeningcalculationswereperformedassumingaone-quarterthicknessflaw.ThisflawexceedsthedeepestpostulatedflawanalyzedundertheLevelCandDanalysis.3.3.2LevelCTransientAnalysisTheblowdowntransientsareterminatedwhenthepressurereaches35psigtoaccountforthecontainmentpressurelevelatthattimeinthetransient.IntheTRUMP/MPMcalculations,thesetransientswereextendedtolongertimes,conservativelyassuminga300'F/hrcooldowntoa212'FvesselIDtemperature.ThethermalgradientandpressuredatafortheLevelCtransientsaresummarizedinTable3-4.BasedonthedatainTable3-4,the250'F/7.5min.BlowdownandtheThermalTransientBlowdownarelimitingintermsofductilefracture.Therefore,detailedfiniteelementcalculationswereperformedforbothofthesetransientstodeterminethemostlimitingvesselwallstressdistribution.3.39LevelDTransientAnalysisSincetheLevelDtransientdepressurizationoccursoverarelativelyshorttimeperiod,andithasbeenassumedthatthedowncomerfluidtemperatureequalsthewallsurfacetemperatureforthepurposeofperformingascreeninganalysis,itwasnotnecessarytoperformathermaltransientheattransferanalysisfortheLevelDtransients.BasedontheLevelCanalysisresults,thevesselwallbTisapproximatelyequalto528'Fminusthecurrentdowncomerfluidtemperaturefortheinitialfiveminutesofthetransient.Therefore,thecracktipstressintensitiescanbecalculateddirectly.Itshouldberecognizedthattheseassumptionsareincreasinglyover-conservativeaftertheinitialfiveminutesofthetransient.TheresultsofthestressintensityfactorcalculationsfortheServiceLevelD

10transientsareshowninTables3-5and3-6.Basedonthesecalculations,theSteamLineBreakTransient,NMP-2RecirculationLineBreakTransient,andtheNMP-1RecirculationLineBreakTransientwereanalyzedinfurtherdetailusingthefiniteelementmethod.Theothertransientsyieldlowerpeakstressintensities.Inaddition,thestressintensityfactorestimatesfortheothertransientsareveryconservativesinceasignificantportionofthetransientisspentinasteamforcedconvectionand/orsubcooledfreeconvectionheattransferregime.3.3.4SummaryofCandidateTransientsAsimplifiedmodelwasdevelopedtodeterminethelimitingServiceLevelCandDtransients.Perfectheattransferbetweenthedowncomerfluidandthevesselwallsurfacewasassumedtoprovideconservativeestimatesofthethroughwallthermalgradient.AquarterthicknessflawwasassumedandtheASMEAppendixGlinearelasticmodelwasusedtoestimatethecracktipstressintensities.Basedonthesimplifiedmodelforscreeningcalculations,themostlimitingtransients,fromaductilefractureperspective,aresummarizedinTables3-7and3-8.

/<x Table3-1LevelCTransientTemperature/PressureVariationasaFunctionofTimeMeasuredFromtheInitiationoftheEventEmergencyConditionLevelCTransientsUnit1DesignBasisUnit2DesignBasis250'F/7.5minThermalTransientBlowdownBlowdownUnit1EmergencyCooldown300'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*NominalSubcooling100%PowerRatedFeedwaterTemperature 0

12Table3-2LevelDSteamLineBreakTemperature/PressureVariationasaFunctionofTimeMeasuredFromtheInitiationoftheEventSteamLineBreakTime(sec)Reference(1)Pressure(PSIA)TempOFTime(sec)OysterCreekAnalysisReference(2)Pressure(PSIA)TempoF0204060801001201401601803001045660310200130906040312515528*497420381347320.2922672522402120703004501050120035552350'12281Reference1-NMP1SAFER/CORECOOL/GESTR-LOCAAnalysisNEDC-31456P,1987,NMP1,FigureA017Reference2-OysterCreekReportGENE-523-70-0692August'92"OysterCreekVesselFractureMechanicsAnalysis"foruppershelfenergyrequirement.Figure5-6Page5-13*NominalSubcooling100%PowerRatedFeedwaterTemperature

+c~p0 13Table3-3LevelDRecirculationLineBreakSpectrumTemperature/PressureVariationasaFunctionofTimeMeasuredFromInitiationoftheEventRecirculationLineBreakSpectrumDBA40%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/

Table3-4StressIntensityFactorEstimatesforServiceLevelCTransients'50'F/7.5Min.BlowdownThermalTransientBlowdownEmergencyCooldown300'F/hr.Time(Min.)PhTK~Krr1030574018KPhT5810309140K~K2968PhTK~1030104043500101193251500137194362103015404510203040506050014619461812067653324417733245177651691557216916278169167781691684955515753595359103020401030304010303940541482132981131761077881203351301514001215.2534384144464952363840414244'nits-P=psig;AT=maxtempdiff.('F);K,=membranestressintensity(ksidin);K~thermalstressintensity(ksidin);K=totalstressintensity(ksidin)'eakwallthermalgradient tC 15Table3-5AStress.IntensityFactorEstimatesforServiceLevelDTransients'lnle(Sec.)PhTSteamLineBreakFeedwaterLineBreakCoreSprayLineBreakPhTKPRecirc.LineBreakNMP-2Recirc.LineBreakDBAPATRecirc.LineBrcak4¹DBAKP6T10615SlIO352$$I$52143QSSl$157433103335115117135$70$375115Ill754545N10SN071NIa715S3'nits-P=psig;hT=maxtempdiff.('F);KtM=membranestressintensity(ksidin);Kn--thermalstressintensity(ksidin);K=totalstressintensity(ksidin)

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

J

'17.Table3-6AStressIntensityFactorEstimatesforServiceLevelDTransients'lmcsec.1015Recirc.LineBreak1ft'~KRecirc.LineBreak0.5ft'ecirc.LineBreak0.1ft'MK~Recirc.LineBreak0.05ftPhTKM3035237507851030333885113770585754213369038530512013015514014583105160152641123345505678510303394512364150105187596350557191837'nits-P=psig;AT=maxtempdiff.('F);K~=membranestressintensity(ksidin);Krr=thermalstressintensity(ksidin);K=totalstressintensity(ksidin)

18Table3-6BStressIntensityFactorEstimatesforServiceLevelDTransients'llllCsec.160175Recirc.LineBreak1ft'ecirc.LineBreak0.5ft'~K~KPRecirc.LineBreak0.1ft'ecirc.LineBreak0.05ft'TKlMK~K180280552252717326518511714710374784546537753330333378510.303333202611828365216368714656518387152028634440470<316026182833852051111513883543505138583152641<316<99<9930510512334563019514384553951934616593010801420mts-<3160=pstg;=maxtemp1.;,=mernranestresstntensttystm;K~thermalstressintensity(ksidin);K=totalstressintensity(ksidin)65<216325<2161<3160<68<82<83<99<99 It 019Table3-7LevelCTransientsforFiniteElementAnalysisNMP-1DesignBasis250'F/7.5Min,Blowdown'MP-2DesignBasisThermalTransientBlowdown~Time(Min.)7.520.7Pressure(psig)10305001817233Temp.528470380318278212HeatTransferCoefficienth=BTU/(hrft'F)10,00010,00010,00010,00010,000500Time(Min.)3.31015202538.8Pressure(psig)1030169106724735Temp.P)528375342318295281212HeatTransferCoefficienth=BTU/IhrfPF)10,00010,00010,00010,00010,00010,000500'MP-1UpdatedFSAR~Reference[STRS]

ecIt Table3-8LevelDTransientsforFiniteElementAnalysis20SteamLineBreak'ecirculationLineBreak'NMP-2RecirculationLineBreak'NMP-1DBATime(Sec.)pressureTemp(psig)('F)HeatTransferCoefficienth=BTU/(hrftF)Time(Sec.)Pressure(psig)Temp.('F)HeatTransferCoefficienth=BTU/(hrftF)Time(Sec.)Pressure(psig)Temp('F)HeatTransferCoefficienth=BTU/(hrftF)20401030295528497-42010,00010,00010,0001520,1030352352828126469,1881641641015103047452851246410,00010,000164608018538111534710,00010,0006010023182642561641642030285417312164164100120140160180300380400754525161032029226725224021221221210,00010,00010,00010,00010,00010,00016450020030013003.523522221216416450040508025267228212164164500Reference[NEDC]References[NMP2TC],[STRS],and[NMP1DP]

EmergencyConditionLevelCTransients600528'F500400--300--~~281'F@35slg200100-0-Data

References:

%300'F/hrEmergency+Unit2DesignBasisCooldownUnit1FSARThermalTransientBlowdownfrom762E673~'250'F/7.5'min'.'vent23NMP2.Vessel.'ooldownUnit1FSARStressAnalysis(SixERV'sopen)STRS16.010-5039A-Reliefvalvesresetat50psia(35psig),cooldownassumedat300'F/hrto0psig-..".0510IS202530354045505560Time(minutes)Unit1DesignBasis%Unit2DesignBasisAUnitIEmerCool~Nom.ADSBD3ERVsopenFigure3-1LevelCTransientsAnalyzedtoDeterminetheMostLimitingTransientforNMP-1

+ct SteamBreak22600500TAFU-Uncover380secTAFR-RecoverQ400sec-OysterCreekGENE-523-70-0692SteamllneBreakprofile400300TAFUTAFRIIII281'F+35psfg200212'FQ0psig100DATAREFERENCEAssumeboilingHTC=NEOC4N56P,tg87,NMPt(0000gTUthl.ft).oF.Safei/CoreooofLGESTR-LOCA....until.TAFRanalysis,FigureA-17SubcooledBoilingHTCthereafterfromECCSflowHTC=500BTR/hr-ft2-'F050100150200250300350400450500550600"NominalSubcooling100%powerratedfeedwatertemperatureFigure3-2LevelDSteamLineBreakTransientPressureProfile ect FeedvaterLinereak23600528'F500400300TAFUTAFRTAFU-Uncover145secTAFR-RecoverI265sec281'FQ85psig200100DATA

REFERENCE:

NEDC-31446P1987,'NMP1Safer/Corecool/GESTR-LOCA.Fig.A-19AssumeBoilingHTC10,000BTU/hr-ft2-'FuntilTAFRSubcooledHTCthereafter...fromECCSflowHTC=500-BTU/hr-ft2-'F050100150200250300350400450500550600650700Time(sec)Pressure(I'SIR)1,04510960751002008007204001408050300400500SaturaledTemp('F)W528~528"518506444353312281*NominalSubcooling100%powerratedfeedwatertemperatureFigure3-3LevelDFeedwaterLineBreakTransientPressureProfile C

CoreSprayLineBreak'4600528'Fi500TAFU-UncoverQ245secTAFR-Recover320sec400300IIITAFUTAR281'FO35psig200100DATA

REFERENCE:

NEDC-31446P,1987,"NMP1Safer/Corecool/GESTR-LOCAFigureA-16-AssumeBoltingHTC10,000---BTU/hr-ft2-'FuntilTAFRSubcooledHTCthereafterfromECCSflowHTC=500BTU/hr-ft2-'F00100200300400500600700800Time(sec)Pressure(I'SIA1,04514580017573040040022050013063050*SaturatedTemp('F)W528~518507444390347281'ominalSubcoollng100%powerratedfeedwatertemperatureFigure3-4LevelDCoreSprayLineBreakPressureProfile JcC RecirculationLineBreakSpectrum25528F600-$00-IAfV4IItIIAfV~---..300.F/hr--AKISASIICKS.llAAIIHtOIHHWIVClltlb4lvIsa>>45OCSllif4,I&Sf'NVAISAfe4co4ecoovoes'lll.locA'5eIIVvff.fffeff5.l4fvoevoooNIIIOIAIAICICloA40028toF@35psig+IAf4IIAfll+IAfllIprAIR.I.II200100-Reference2In'a'llcases,levelisatTAFpriortocompletedepressurization.DowncomerLevelisassumedtofollowcorelevel.Therefore,.assurpe.saturatedsteam.conditions.in,cfowncomqr.during,...depressurizationuntilTAFisrecoverbyECCS.ThenassumefreeconvectiontosubcooledECCS.0100200300400$006007008009001,0001,100Time(Seconds)~DBA+40%DBAIFt2+.$Ft2Hj.lFl2+.0$Ft2Figure3-5LevelDRecirculationLineBreakSpectrumPressureProfile Jf4 FiniteElementAnalysis26ThecandidatetransientslistedinTables3-7and3-8wereanalyzedusingthefiniteelementmethodtodeterminethemostsevereLevelCandLevelDloadings.TheWELD3finiteelementcodepackageIWELD3]wasusedtoperformthecalculations.4.1ModelDescriptionTheWELD3modelassumesaxisymmetricbehavior.Asinglecolumnofelementswasused,thusmakingthesolutionessentiallyonedimensional(i.e.,temperaturesandstressesonlydependontheradialpositionwithinthevesselwall).ThefiniteelementgridisshowninFigure4-1.Elements1and2representthecladding.Thecladdinginnersurfaceradiusis106.344inches,thebasemetaVcladinterfaceisat106.5inches,andthevesselouterradiusis113.781inches.Theaxialdimensionofthemodelis0.15inches.Forthermalmodeling,theoutervesselsurfacewastreatedasperfectlyinsulated.Theinnersurfacehasaprescribedheattransfercoefficientandfluidtemperature(bothfunctionsoftime).Allheatflowisradial.Temperaturedependentpropertieswereusedinthethermalanalysis.Themechanicalmodelisconstrainedto'aveauniformaxialstrainsothatplanesectionsremainplane.Theaverageaxialstressandtheinternalpressureareinputtothemodelbasedonthepressuretransientinput.Thermaltransientsareinputviaelementtemperatures.Temperaturedependentpropertiesarealsousedforthestresscalculations.TheWELD3calculationsassumedlinearelasticbehaviorforboththecladdingandbasemetalsoastobeconsistentwiththeuseofthesmallscaleyieldingassumption(linearelasticfracturemechanicswithplasticzonecorrections)inthesubsequentfracturemechanicsanalyses.4.2FiniteElementAnalysisResultsTwoLevelCcasesandthreeLevelDcaseswereanalyzed.ThetransientthermalandpressureboundaryconditionsaredescribedinTables3-7and3-8.Althoughthepressureandthermalloadingscouldbeanalyzedseparatelyduetotheuseoflinearelasticity,itwasjudgedmoreexpedienttocombinetheloadings.Thecladdinghasadifferentcoefficientofthermalexpansionthanthebasemetal.Thisimpactedtheanalysisinseveralways..First,therewillbesomeresidualstressevenwhenthevesselisatauniformtemperature.Assumingthatthevesselis100%stressfreeatthestressrelieftemperatureof1150'F,theoriginalcoolingto528'Finducedtensileresidualstressesinthecladdingthuscontributingtocracktipstressintensityfactors.Thisuniformcoolingwasmodeledinaseparateanalysistodeterminethelevelofinitialresidualstress.Thedifferenceinthermalexpansionbehavioralsoresultsindiscontinuous WC 27axialandhoopstressesacrossthematerialinterface.Sincethefracturemechanicsevaluationinvolvesfittingthestresseswithacubicpolynomial,thisdiscontinuousbehaviorimpactsthequalityofthepolynomialfits.Therefore,asdescribedinSection5.0,thefracturemechanicsmodelwasconfiguredtominimizethesensitivityoftheanalysistotheeffectsofstressfielddiscontinuitiesattheinterface.Figure4-2showstheaxialandhoopresidualstressesthatexistduetouniformcoolingfromastressfreeconditionat1150'Fto528'F.Thisresidualstresswasnotincludedinthest:ssdistributionplotsforthevariousLevelCandLevelDtransientsthatfollow.Thisapproachwasadoptedaspartoftheapproachtomoreaccuratelyhandlethediscontinuousstressfield.Thefinalstressdistributionsdoincludethedifferentialexpansioncoefficienteffectsduetocoolingfrom528'Fduringthetransient.ThemethodforincludingtheresidualstressloadinthefracturemechanicsanalysisisdescribedinSection5.0.TheWELP3stressoutputforeachanalysiswasscannedforthetimeofthemostseverestressesinducedbythecombinedtransientthermalandpressureloading.Sincecrackdepthsofnolargerthanoneinchareofinterest[ASME92],thetimeatwhichthestresseswouldbemostsevereforaoneinchdeepcrackwasidentified.Thiswasdonewithoutactuallycalculatingstressintensityfactorsforeachtransientstressdistributionandwaspossibleonlybecausethestressesovertheinnerinchofthewalltendedtopeakataboutthesamepointintime.Figures4-3through4-10containplotsofthetransienttemperaturesandstresses.Thetimesofthemostdamagingstressesforcrackdepthsofaboutaninchareplottedwithasolidline.Temperaturesandstressesatothertimesareplottedusingbrokenlines.Itcanbeseenfromtheseplotsthatfordeepercracks,thecriticaltimewouldtendtobelaterinthetransient.Forveryshallowcracks,slightlylargerstressintensityfactorsmayoccuratearliertimesthanfortheidentifiedtimes.Table4-1summarizestheresultsoftheWELD3analyses.4.3,LimitingTransientsThehoopandaxialstressbehaviorsareverysimilarandtendtoexperiencetheirpeakvaluesataboutthesametime.Themagnitudesofthehoopstressestendtobelargerthantheaxialstresses.Withoutinputtingthesestressesintoafracturemechanicsanalysisitisnotpossibletodeterminewhichstresscomponentislimiting.AsdiscussedfurtherinSection5.0,theaxiallyorientedflaw(hoopstressloading)isthelimitingcase.OfthetwoLevelCcasesconsidered;the"NMP-1DesignBasis250'F/7.5min.Blowdown"resultedinthelargerstresses.OfthethreeLevelDcases,the"SteamLineBreak"resultedinthelargeststresses.AsshowninFigures4-3through4-5,thetimedependenceoftheheattransfercoefficientplaysanimportantroleindefiningthelimitingLevelDtransient.Inparticular,althoughtheSteamLineBreakisnotthemostrapiddepressurizationtransient,itislimitingsincetheheattransferismoreefficientoverthefirst300secondsoftheevent.

rc 28Table4-1SummofPeakCladdinandPeakBaseMetalStressesattheIndicatedTimesstressunitsareksiCaseresidualC1D1D2D3CriticalTimeNA9.15min6.65min240sec500sec320sec~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/7.5min,BlowdownC2:NMP-2DesignBasisThermalTransientBlowdownD1:SteamlineBreakD2:RecirculationLineBreakNMP-2D3:RecirculationLineBreakNMP-1DBA ec

'91234567891314151617181920212223242526272829303132333435363738Figure4-1OneDimensionalFiniteElementMeshforNMP-1PressureVesselAnalysis er 2220HC20.6ksi)A(20.0ksi)30181614A:AxialStressH:HoopStress12(o802356.Distancefrominnersurface(in)Figure4-2ResidualStressat528'FDuetoCladdingDifferentialExpansion

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.'lowdown2000l2345678Distancefrominnersurface(in)LevelC:NMP-2BlowdownFigure4-3PressureVesselThermalGradientsforLevelCTransients 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)LevelDsRecirculationLineBreokFigure4-4PressureVesselThermalGradientsforLevelDTransients c

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

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.BlowdownFigure4-6AxialandCircumferentialStressDistributionsforLevelC250'F/7.5Min.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-2BlowdownFigure4-7AxialandCircumferentialStressDistributionsforLevelCNMP-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:SteamLineBreakFigure4-8AxialandCircumferentialStressDistributionsforLevelDSteamLineBreak

/>>

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:RecirculationLineBreah20012345678Distancefrominnersurface(in)LevelD~RecirculationLineBreakFigure4-9AxialandCircumferentialStressDistributionsforLevelDRecirculationLineBreakforNMP-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)LevelDcRecirculotionLineBreakNHP-1DBADistancefrominnersurfoce(in)LevelD~RecirculationLineBreakNHP-1DBhFigure4-10AxialandCircumferentialStressDistributionsforLevelDRecirculationLineBreakforNMP-1DBA gC 39~~~5.0Elastic-PlasticFractureMechanicsAssessmentThelimitingLevelCandDtransientloadswereappliedtoafracturemechanicsmodeloftheNMP-1pressurevesselinaccordancewiththeguidanceprovidedinReferences[ASME92]and[WGFE92].TheUSEŽ(3.0)codepackage[USE93]wasusedtoperformthecalculations.AcopyofthedraftAppendixX[ASME92]isprovidedinAppendixAandtheASMEWorkingGrouponFlawEvaluationdraftstressintensitycalculationprocedure[WGFE92]isgiveninAppendixB.5.1ModelDescription5.1.1VesselGeometryTheA302BmaterialmodelusedintheanalysiswasdescribedinSection2.0.Inadditiontothematerialmodel,USEŽ(3.0)requiresthefollowingparameters:VesselWallThicknessVesselInnerRadiusVesselCladThicknessCrackDepth/LengthRatio5.12AppliedLoads7.281in.(UFSARTableV-1)106.344in.(UFSARTableV-1)0.15625in.0.166667TheresultsofthefiniteelementcalculationstodeterminethelimitingLevelCandDtransientsandloadingsaredescribedinSection4.0.Asaresultofthesecalculations,thelimitingLevelCtransientisthe"NMP-1DesignBasis250'F/7.5min.Blowdown",andthelimitingLevelDtransientisthe"SteamLineBreak".Thelimitingstressdistributionwasdeterminedbyexaminingtheradialstressprofilesatvarioustimesinthetransient.AsmentionedinSection4.0,usingstressdistributiondataatatimewhenthestressesaremostsevereforaone-inchcrackmaybeslightlynon-conservativewhenshortercracksareconsidered.Thissmallnon-conservatismwasciicumventedbyusinganupperboundenvelopeoftheactualstressdistributions.Thelimitingstressdistributionswerefittoacubicpolynomialusingtheguidancegivenin[WGFE92].Inordertoprovidegoodfitstothedata,thebasemetalstresseswereextrapolatedtotheIDsurface.TheremainingdiscontinuouscomponentofthecladstressesaretreatedusingalineloadformulationasdescribedinSection5.1.4.TheequivalentcladlineloadsaregiveninTable5-1.Thepressureactingalongthecracksurfacewasconservativelyincludedinthecladlineload.ThefittothebasemetalstressdistributionisshowninFigures5-1 gC'1 40through5-4.Table5-2summarizesthestressdistributioncoefficientsforuseintheAppendixXanalysis.TheR-squaredvalueforallofthefitsisveryclosetounitywhichindicatesaccuraterepresentationofthedata.5.19LimitsforSmallScaleYieldingAnalysisa=:a+-(-)1K2eP6mayawhere,a,=effectivecrack'size(in.)a=physicalcrackdepth(in.)K=linearelasticstressintensity(ksi4in)a~=yieldstress(ksi).AsstatedinReference[ASME92],whentheconditionsfallinthecategoryofelasticfracturemechanicswithsmall-scaleyielding,theJ-integralmaybecalculatedusingcrack-tipstressintensityformulaewithplastic-zonecorrection.Inordertoestimatethelimitsofvalidityofthesmall-scaleyieldingassumption,anaxiallycrackedcylindricalvesselwitharadiustothicknessratioof10,awallthicknesst=10inandacrackdepthtothicknessratioa/t&.25,wasloadedbyinternalpressureandtheresultingstressintensitieswerecalculated,Theeffectivecrackdepthswerecalculatedusing:TwoRamberg-Osgoodstress-strainmodelswereanalyzed:onewithn=8.4andalpha=2,6;thesecondwithri=5.3andalpha=7.2.Thehighern-valuecaseismorerepresentativeoftheNMP-1plates.Theelasticcalculationsapproximatedpressurestressesbyalineardistributionthatmatchedtheexactthickwalledcylindersolutionattheinnerandoutersurfaces.Theplasticsolutionwas'calculatedusingtheexactinternalpressureinducedstresses.TheresultsaresummarizedinFigure5-5.ThedifferenceinsolutionsforsmallloadsisduetotheuseofdifferentelasticsolutionFfactorsinthetwomodels.Basedonthisanalysis,itisconcludedthatthesmall-scaleyieldingformulationisvalidforstressintensitylevelsupto100ksi4in(J-335in-lbfin)foranaxialcrackinacylinderwithanaspectratioof10.SincethecalculatedstressintensitiesforNMP-1arewellbelow100ksi4in.,thesmallscaleyieldinganalysisisappropriatefortheNMP-1vesselanalysis.5.1.4FractureMechanicsModelTheReferencePVGFE92]methodforcalculatingstressintensitiesforsurfaceflawswasused.AcopyoftheprocedureproposedbytheASMEWorkingGrouponFlawEvaluationisgiveninAppendixB.Theprocedurerequiresaccuratelyfittingthestressdistributionusingthefollowingpolynomialfit:

>r 41a=A,+A,X'+APE+A,X'here,(5-1)A,=regressionconstantsX=distancethroughthewallThepostulatedflawisasemi-ellipticalsurfacecrackwithasurfacelengthwhichissixtimesthedepth.Thestressintensityforthecontinuouscomponentofthestresseswascalculatedfromthefollowingexpression:Kz=[AG+A~G~a+A~G~a+A3G3a']~ira7g(5-2)where,a=crackdepthA,=coefficientsfromEq.3-1whichrepresentthestressdistributionoverthecrack(0(X(a)G,=influencecoefficientsasafunctionofflawaspectratioandcrackpenetration(AppendixB)Q=flawshapeparameterQ=1+4.593(a/1)'qy1=flawsurfacelengthq=plasticzonecorrectionfactorq=0.212(AJa,)',=materialyieldstressSincetheslopeofthestressdistributionattheclad-basemetalinterfacechangesabruptly,thebasemetalstressdistributionwasextrapolatedtotheIDsurfacetoprovideanaccurateflitoverthepostulatedflawdepths.TheReference[TA73]linearelasticformulationwasusedtocalculatethediscontinuouscomponentofthestressfieldscontributiontothecracktipstressintensityusing:

/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=equivalentlineloada=flawdepthb=wallthicknessc=loadapplicationpositionasmeasuredfromtheIDsurfaceEquation5-3providesconservativeestimatesofthediscontinuousstresscomponentcontributionofthetotalstressintensitysincetheformulationisforaninfinitecracklength,SinceEq,(3-3)isalinearelasticequation,thesmallscaleyieldingcorrectionwasapplied:where,a=physicalcrackdeptha,=effectivecrackdepthInordertosimplifythecomputeralgorithmandtoensureconservativeresults,thesmallscaleyieldingcorrectionwasappliedtoboththecladdingandbasemetalstressintensityfactors.Thisapproachyieldsveryconservativeresultssincetheflawshapeparameterinequation5-2includesaplasticzonecorrectionfactor.Thetotalstressintensityfactorwasobtainedbysuperposition:KcoHTLNPN/s+KDLscoNTLNUoUsZZ rc 43InaccordancewithReference[ASME92],aspectrumofinitialflaws,upto1/10ofthebasemetalwallthickness,wereassumed.Thesmallestflawassumedwas0.05in.,andthepostulatedflawswereincreasedinsizebyincrementsof0.05in.,uptoamaximumflawdepthof0.75in.5.2CalculationsforA302BMaterialModelThepointwiseinputmodelwasusedfortheA302Bmaterialmodelcalculations.Usingthismodel,theJ-Rcurveisassumedflataftertheinitial0.1in.ofcrackextension.TheG-8-1platewasanalyzedusingtheA302Bmaterial.modelsinceitisthelimitingplatefromaductilefractureperspective(Reference[MA93]).5.2.1LevelCLoadingTheresultsofthecalculationsfortheLevelCloadinghaveshownthatthelimitingflaworientationistheaxialflaw.Forinitialbasemetalflawdepthsofupto1/10ofthevesselwallthickness,theASMEAppendixXcriteriaaresatisfiedatUSElevelsaslowas10ft-lbs.Inallcases,thelargestapplied-Jvaluesfortheflawgrowthof0.1in.criterionareobtainedatthedeepestinitialpostulatedflawdepth.TheresultsfortheLevelCanalysisaresummarizedinTable5-3fortheaxialflaw.5.22LevelDLoadingAnalysisTheresultsofthecalculationsfortheLevelDloadingalsoshowthatthelimitingflaworientationistheaxialflaw.Forinitialbasemetalflawdepthsofupto1/10ofthevesselwallthickness,theASMEAppendixXcriteriaaresatisfiedatUSE'levelsaslowas20ft-lbs.TheresultsfortheLevelDanalysisaresummarizedinTable5-4fortheaxialflaw.5.2.3TensileInstabilityAnalysisBasedontheanalysisperformed,thedeepestflawduringthemostsevereLevelCorDtransientislessthan1.2inches.Conservativelyassumingtheflawextendscompletelyaroundthecircumference,andusingthefiniteelementstressprofiles,theremainingligamentwillexperiencestresseswellbelowtheyieldstrengthandisthereforesafeintermsoftensileinstability.

Table5-1NMP-1CladStressesCaseHoop-LevelCAxial-LevelCHoop-LevelDAxial-LevelDExtrapolatedSurfaceStress(ksi)45.20735.26458.69045.476CladStressMinusExtrapolatedSurfaceStress(ksi)16.55716.79019.88621.377ResidualStress(ksi)20.620.020.620.0CladTotalStress(ksi)37.15736.79040.48641.377CrackSurfacePressure(ksi)1.051.051.051.05CladEquivalentLineStress(kp/in)6.8566.7987.3767.515Table5-2BaseMetalStressDistributionCoefficientsLevelC--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

'able5-3ComparisonofAppliedLoadswithASMECriteriaforLevelCLoadingConditionsandanAxialFlawOrientation'5ha&.lCriterionFlawStabiliCriterionUSELevel102030405060708090100AppliedJ~in-1bin'83,183183183183183183183183183MaterialJ~in-1bini199230261292323353384438517AppliedT<0.5<0.5<0.5<0.5MaterialT2.63.77.313.218.3CriteriaSatisfiedyesyesyesyesyesyes,J,cJ<<yes,J,<J<<yes,J<Jicyes,J,<J,cyes,J,<J,c'esultsshownareforthemostlimitinginitialflawoverthespectrumofflawsanalyzed

'able5-4ComparisonofAppliedLoadswithASMECriteriaforLevelDLoadingConditionsandanAxialFlawOrientation'6USELevel10~AIiedTJapeJMAxMaterialTFlawStabilitCriterionCriteriaSatisfiedno20<0.811.0yes30<0.818.3yes405060708090100yes,J,~<Juncyes,J~<Jicyes'app~rcyes'app~tcyes,Jo~<JrcyesJ<Jrcyes,J,<Jrc'esultsshownareforthemostlimitinginitialflawoverthespectrumofflawsanalyzed.

,~

47HOOPSTRESSDISTRIBUTIONFORLEVELCTRANSIENT10080co60COU)LU40CO200.00.61.01.5CRACKLENGTH(In.)2.0Figure5-1PeakCircumferentialBaseMetalStressDistributionforNMP-1DesignBasis250'F/7.5Min.BlowdownTransient

48AXIALSTRESSDISTRIBUTIONFORLEVELCTRANSIENT1008060'COCOUJ40CO2000.00.5CRACKLENGTH(In.)2.0Figure5-2PeakAxialBaseMetalStressDistributionforNMP-1DesignBasis250'F/7.5Min.BlowdownTransient

49HOOPSTRESSDISTRIBUTIONFORLEVELDTRANSIENT1008060402000.00.5<3RACKLENGTH(In.)2.0Figure5-3PeakCircumferentialBaseMetalStressDistributionforSteamLineBreakTransient gC 50O'XIALSTRESSDISTRIBUTIONFORLEVELDTRANIENT1008060CO03LLI40K2000.00.51.01.52.0CRACKLEN9TH(ln.)Figure5-4PeakAxialBaseMetalStressDistributionforSteamLineBreakTransient 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)Figure5-5ComparisonBetweenSmallScaleYieldingSolution(J(SSY/ae))andtheElastic-PlasticSolutionswithHardeningExponentsof5.3(Jep(n=5.3))and8.4(Jep(n=8.4))

/'

6.0SummaryandConclusions52Theresultsoftheelastic-plasticfracturemechanicsassessmentareshowninTable6-1.AsdiscussedinReferencetMA93],theA302BmaterialmodelbestrepresentstheNMP-1beltlineplates.TheA302Bmaterialmodel,appliedtothecaseofanaxialflaworientation,yieldsthemostconservativeresults.BasedonthecalculationsreportedinReferencePvIA93]andherein,ithasbeenconcludedthattheNMP-1plateG-8-1islimitingfromaductilefractureperspective,andtheUSEmustbemaintainedabove23ft-lbs.BasedonthedatareportedinReference[MA93],noneoftheNMP-1beltlineplatesareexpectedtofallbelowthe23ft-lblevel.AlthoughtheAppendixXcriteriaaresatisfiedatorabovethe23ft-lblevel,itisnotclearthattheplantshouldbeoperatedatthisductilitylevel.Itisanticipatedthatfuturefederallyfundedresearchandsubsequentregulationswilladdressthisissue.

fi~

53Table6-1MinimumUpperShelfEnergyLevelforNMP-1PlatesBasedontheASMEDraftAppendixXEvaluationCriteriaforServiceLevelsA,B,CandDMinimumUSE(Ft-Lbs)PlateASMEServiceLevelA&BMaterialModelFlawGrowthof0.1in.CriterionJi(Jo.iFlawStabilityCriterionG-8-1A&BA302B1323G-307-4A&BA302B1323G-8-1G-8-1DA302BA302B101020

7.0References54[ASME92]ASMEDraftCodeCaseN-XXX,"AssessmentofReactorVesselswithLowUpperShelfCharpyEnergyLevels",Revision11;May27,1992.[CENC][FSAR]Unit1AnalyticalReportforNiagaraMohawkReactorVessel,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.,"ResponsetoNRCGeneralLetter92-01forNineMilePointUnit1",NMPCProject03-9425,June12,1992.Manahan,M.P.,FinalReporttoNRC,"Elastic-PlasticFractureMechanicsAssessmentofNineMilePointUnit1BeltlinePlatesforServiceLevelAandBLoadings",February19,1993.NEDC-31446P,NMP-1SAFER/CORECOOL/GESTR-LOCALossofCoolantAccidentAnalysis.[NMP1DP]NMP-1DrywellPressureCalculation,SO-TORUS-M009,GENE-770-91-34.[NMP2TC]NMP-2,762E673,ReactorVesselThermalCycles.[STRS]SectionE9,Emergency'&FaultedAnalysisofRecirculationOutletNozzle251"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:ThermalTransientHeatTransferAnalysisCode,Version1.0,September,1989.[USE93][WELD3]USEŽ(3.0)CodePackageforElastic-PlasticFractureMechanicsAssessmentofNuclearReactorPressureVessels,MPMResearch&Consulting,1993."WELD3ComputerCodeVerification",MPMResearch&Consulting,CalculationNo.MPM-NMPC-99205,Rev.0,January21,1993.-

~<

55[WGFE92]ASMEWorkingGrouponFlawEvaluation,ProposedChangestoArticleA-3000entitled,"MethodforK,Determination",August,1992.

56AcknowledgementDr.RandallB.StonesiferofComputationalMechanics,Inc.performedallofthefiniteelementanalysesandprovidedmanyvaluablesuggestionsrelated-tothefracturemechanicsmodel.

57Appendices

58AppendixA'SMEDraftAppendixX"AssessmentofReactorVesselswithLowUpperShelfCharpyEnergyLevels" (i

DRAFTCODECASEN-XXXASSESSMENTOFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSMay27,1992REVISZON11REVISIONREVISION)REVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONREVISIONDRAFTHISTORY0123456.788-MARKEDCOPY910llAUGUST25g1987JANUARY19,1988APRIL19,1988AUGUST30,1988NOVEMBER30,1988FEBRUARY27,1989JANUARY5i1990APRIL12,1990JANUARY10,1991APRIL15,1991JANUARY17,1992APRIL171992CURRENT gC(-

ASSESSMENTOFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSTABLEOFCONTENTSCASEN-XXXASSESSMENTOFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSAPPENDIXAASSESSMENTOFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSA-1000INTRODUCTIONA-1100A-1200A-1300ScopeProcedureOverviewGeneralNomenclatureA-2000ACCEPTANCECRITERIAA-3000ANALYSISA-3100A-3200A-3300A-3400A-3500ScopeAppliedJ-IntegralSelectionoftheJ-IntegralResistanceCurveFlawStabilityEvaluationApproachforLevelAandBServiceLoadingsA-4000rEVALUATIONPROCEDURESFORLEVELAANDBSERVICELOADINGSA-4100A-4200A-4210A-4220A-4300A-4310ScopeEvaluationProcedurefortheAppliedJ-IntegralCalculationoftheAppliedJ-IntegralEvaluationUsingCriterionforFlawGrowthof0.1in.EvaluationProceduresforFlawStabilityJ-RCurve-CrackDrivingForceDiagramProcedure rl A-4320A-4321A-4322A-4322.1A-4322.2A-4323A-4330A-4331A-4332A-4333FailureAssessmentDiagramProcedureFailureAssessment'DiagramCurveFailureAssessment,PointCoordinatesAxialFlawsCircumferentialFlawsEvaluationUsingCriterionforFlawStabilityJ-Integral/TearingModulusProcedureJ-IntegralatFlawInstabilityInternalPressureatFlawInstabilityEvaluationUsingCriterionforFlawStabilityA-5000LEVELCANDDSERVICELOADINGS

/i CaseN-XXXAssessmentofReactorVesselsNithLowUpperShelfCharpyEnergyLevelsSectionXI,Division1Inquiry:SectionXI,Division1,XWB-3730,requiresthatduringreactoroperation,loadandtemperatureconditionsshallbemaintainedto'provideprotectionagainstfailureduetothepresenceofpostulatedflawsintheferriticportionsofthereactorcoolantpressureboundary.UnderSectionXI,Division1,whatproceduremaybeusedtoevaluateareactorvesselwithalowupper,shelfCharpy.impactenergylevelasdefinedinASTME185-82to.demonstrateintegrityforcontinuedserviceatuppershelfconditions?Rep2y:Itistheopinion.'ftheCommitteethatareactorvesselwithalowuppershelfCharpyimpactenergylevelmaybeevaluatedtodemonstrateintegrityforcontinuedserviceforupper.shelfconditionsinaccordancewiththefollowing.1.0EVALUAT1ONPROCEDURESANDACCEPTANCECRITERIASectionXI,Division1,AppendixG,"FractureToughnessCriteriaforProtectionAgainstFailure",providesanalyticalproceduresbasedontheprinciplesoflinear-elasticfracturemechanicsthatmaybeusedtodefineloadandtemperatureconditionstoprovideprotectionagainstnonductilefailureduetothepresenceofpostulatedflawsintheferriticportionsofthereactorcoolantpressureboundary.TopreventductilefailureofareactorvesselwithalowuppershelfCharpyimpactenergylevelthevesselshallbeevaluatedusingtheprinciples'ofelastic-plasticfracturemechanics.Flawsshallbepostulatedinthereactorvesselat,locationsofpredictedlowuppershelfCharpyimpa'ctenergyandtheappliedZ-integralfortheseflawsshallbecalculatedandcomparedwith'heJ-integralfractureresistanceofthematerialtodetermineacceptability.Factorsofsafetyonappliedloadforlimitedductileflawgrowth,andonflawstabilityduetoductiletearing,shallbesatisfied.Allspecifieddesign'transientsforthereactorvesselshallbeconsidered.Evaluationproceduresandacceptancecriteriabasedontheprinciples.ofelastic-plasticfracturemechanicsaregiveninAppendixAofthisCodeCase.TheevaluationshallbetheresponsibilityoftheOwnerandshallbesubjecttoreviewbytheregulatoryandenforcementauthorities-havingjurisdictionattheplantsite.

I APPENDIXATOCODECASEN-XXXASSESSMENTOFREACTORVESSELSWITHLOWUPPERSHELFCHARPYENERGYLEVELSARTICLEA-1000INTRODUCTIONA-1100SCOPEThisAppendixprovidesacceptancecriteriaandevaluationproceduresfordeterminingtheacceptabilityforoperationofareactorvesselwhenthevesselmetaltemperatureisintheuppershelfrange.Themethodologyisbasedontheprinciplesofelastic-plasticfracturemechanics.FlawsarepostulatedinthereactorvesselatlocationsofpredictedlowuppershelfCharpyimpactenergyandtheappliedJ-integralfortheseflawsiscalculatedandcomparedwithth'eJ-integralfractureresistanceofthematerialtodetermineacceptability.Allspecifieddesigntransientsforthereactorvesselshallbeconsidered.A-1200PROCEDUREOVERVIEWThefollowingisasummaryoftheanalyticalprocedurewhichmaybeused.(a)PostulateflawsinthereactorvesselaccordingtothecriteriainA-2000.(b)DeterminetheloadingconditionsatthelocationofthepostulatedflawsforLevelA,B,CandDServiceloadings.(c)Obtainthematerialproperties,includingZ,a~,andtheJ-integralresistancecurve(J-Rcurve),atthelocationsofthepostulatedflaws.RequirementsfordeterminingtheJ-RcurvearegiveninA-3300'd)Evaluatethepostulatedflawsaccordingtotheacceptancecriteriain'A-2000.RequirementsforevaluatingtheappliedJ-integralaregiveninA-3200,andfordeterminingflawstabilityinA-3400'hreepermissibleevaluationapproachesaredescribedin~~A-3500.DetailedcalculationproceduresforLevelAandBServiceloadingsaregiveninA-4000.A-1

A-1300GENERALNOMENCLATUREflawdepthwhichincludesductileflawgrowtheffectiveflawdepthwhichincludesductileflawgrowthandaplastic-zonecorrection(in.)(in.)BeBoeffectiveflawdepthatflawinstability,whichincludesductileflawgrowthanda-plastic-zone.correctionpostulatedinitialflawdepthamountofductileflawgrowth(in.)(in.)(in.)dB'mountofductileflawgrowth,atflawinstability(in.)E'oung'smodulusE/(2-VR)CCR=materialconstantsusedtodescribethepower-lawfittotheJ-integralresistancecurveforthematerial,.ZR=C,(dB)'CR)=cooldownrate(F/hour)(ksi)(ksi)FzrF~rF~geometryfactorsusedtocalculatethestressintensityfactor(dimensionless)FarFurFggeometryfactorsusedtocalculatethestressintensityfactoratflawinstabilityIJ-integral'uetotheappliedloads(dirtensionless)(in.-lb/in.')+RJ-integralfractureresistanceforthematerial(in.-,1b/in.~)A-2

J-integralfractureresistanceforthematerialataductileflawgrowthof0.10in.(in.-lb/in.~)JzKzappliedJ-integralataflawdepthofa,+0.10in.J-integralatflawinstabilitymodeIstressintensityfactorC(in.-lb/in.')(in.-lb/in.~)(ksiv'in.)KzpmodeI'stressintensityfactorduetointernalpressure,calculatedwithnoplastic-zonecorrection(ksiv'in.)KzpKzpca1cu1atedwithap1astic-zonecorrection(ksiV'in.)KzpKzpatflaw-instability,calculatedwithaplastic-zonecorrecti'on(ksiV'in.)KzeKzmodeIstressintensityfactorduetoaradialthermalgradientthroughthevesselwall,calculatedwithnoplastic-zonecorrectionKcalculatedwithaplastic-zonecorrection(ksiV'in.)'I(ksiMin.)KzeKatflawinstability,calculatedwithaplastic-zonecorrectionordinateofthefailureassessmentdiagramcurve(ksiMin.)(dizransionless)ratioofthestressintensityfactortothefracturetoughnessforthematerialinternalpressure(dixransionless)(ksi)accumulationpressureasdefinedintheplant-specificOverpressureProtectionReport,butnotexceedingl.ltimesthedesignpressure(ksi)A-3

PsPPoRqpressureusedtocalculatetheappliedJ-integral/tearingmoduluslineinternalpressureat'lawinstabilityreferencelimit-loadinternalpressureinnerradiusofthevessel'bscissaofthefailureassessmentdiagramcurve(ksi)(ksi)(ksi)(in.)(LQmnsionless)ratioofinternalpressuretoreferencelimit-.loadinternalpressure(SF)=safetyfactorvesselwallthickness(dhransionless)(dhransionless)(in.)tearingmodulusduetotheappliedloadstearingmodulusresistanceforthematerial(diz~nsionless)(dUransionless)parameterusedtorelatetheappliedJ-integraltotheappliedtearingmodulus(dimensionless)Poisson'sratioreferenceflowstress,specifiedas85ksi(dirmnsionless)(ksi)yieldstrengthforthematerial(ksi)

ARTICLEA-2000ACCEPTANCECRITERIATheadequacyoftheuppershelftoughnessofthereactorvesselshallbedeterminedbyanalysis.Thereactorvesselis.acceptableforcontinuedservicewhenthecriteriaofParagraphs(a),(b),and(c)aresatisfied.(a)LevelAandBServiceLoadingsWhenevaluatingtheadequacyoftheuppershelftoughnessfortheweldmaterialforLevelAandBServiceloadings,postulatean.interiorsemi-ellipticalsurfaceflawwithadepthone-quarterofthewallthicknessandalengthsixtimesthedepth,withtheflaw'.smajoraxisorientedalongtheweldofconcernandtheflawplaneorientedintheradialdirection.Whenevaluating.theadequacyoftheuppershelftoughnessforthebasematerial,postulatebothinterioraxialandcircumferentialflawswithdepthsone-quarterofthewallthicknessandlengthssixtimesthedepthandusethetoughnesspropertiesforthecorrespondingorientation.Smallerflawsizesmaybeusedon-anindividualcasebasiswhenjustified.Twocriteriashallbesatisfied:(i)TheappliedJ-integralevaluatedatapressurewhichis1.15timestheaccumulationpressureasdefinedintheplant-specificOverpressureProtectionReport,withafactorofsafetyof1.0onthermalloadingfortheplantspecifiedheatupandcooldownconditions,shallbeshowntobelessthantheJ-integralcharacteristicofthematerialresistancetoductiletearingataflawgrowthof0.10in.(2)Theflawshallbeshowntobestable,withthepossibilityofductileflawgrowth,atapressurewhichis1.25timestheaccumulationpres'suredefinedinSubparagraph(1),withafactorofsafetyof1.0onthermalloadingfortheplantspecifiedheatupandcooldownconditions.TheJ-integralresistanceversuscrackgrowthcurveshallbeaconservativerepresentationforthevesselmaterialunderevaluation.A-5

~/(

(b)LevelCServiceLoadingsWhene:aluatintheadegquacyoftheuppershelftoughnessfortheweldmaterialforLevelCServiceloadings,postulateinteriorsemi-ellipticalsurfaceflawswithdepthsupto1/10ofthebasemetalwallthickness,plusthecladdingthickness,withtotaldepthsnottoexceed1.0in.,andasurfacelengthsixtimesthedepth,withtheflaw'smajoraxisorientedalongtheweldofconcernandtheflawplaneorientedintheradialdirection.Whenevaluatingtheadequacyoftheuppershelftoughnessforthebasematerial,postulatebothinterioraxialandcircumferentialflaws,andusethetoughnesspropertiesforthecorrespondingorientation.Flawsofvariousdepths,ranginguptothemaximumpostulateddepth,shallbeanalyzedtodeterminethemostlimitingflawdepth.Smallermaximumflawsizesmaybeusedonanindividualcasebasiswhenjustified.Twocriteriashallbesatisfied:(1)TheappliedJ-integralshallbeshowntobelessthantheJ-integralcharacteristicofthematerialresistancetoductiletearingataflawgrowthof0.10in.,usingafactorofsafetyof1.0onloading.,(2)Theflawsshallbeshowntobestable,withthepossibilityofductileflawgrowth,usingafactorofsafetyof1.0onloading.TheJ-integral'esistanceversuscrackgrowthcurveshallbeaconservativerepresentationforthevesselmaterialunderevaluation.(c)LevelDServiceLoadingsWhenevaluatingtheadequacyoftheu'ppershelftoughnessforLevelDServiceloadings,post'ulateflawsasspecifiedforLevelCServiceloadings'inParagiaphb),andusethetoughnesspropertiesforthecorrespondingorientation.Flawsofvariousdepths,ranginguptothemaximumpostulateddepth,shallbeanalyzedtodeterminethemostlimitingflawdepth.Smallermaximumflawsizesmaybeusedonanindividualcasebasiswhenjustified.Theflawsshallbeshowntobestable,withthepossibilityofductileflaw"'rowth,usingafactorofsafetyof1.0onloading.TheJ-integralresistanceversuscrackgrowthcurveshallbeabestestimaterepresentationforthevesselmaterialunderevaluation.Thestableflawdepth.shallnotexceed75%ofthevesselwall~~~~~~~~thickness,andtheremainingligamentshallbesafefromtensileinstability.A-6

ARTICLEA-3000\ANALYSISA-3100SCOPEThisArticlecontainsageneraldescriptionofprocedureswhichshallbeusedtoevaluatetheappliedfracturemechanicsparameters,aswellasrequirementsforselectingtheJ-Rcurveforthematerial.Referencesaremadetoacceptableapproachestoapplythecriteria.A-3200APPLIEDJ-INTEGRALThecalculationoftheJ-integralduetotheappliedloads.shallaccountforthefullelastic.-plasticbehaviorofthestress-straincurveforthematerial.Whentheconditionsfallintothecategoryofelasticfracturemechanicswithsmall-scaleyielding,theJ-integralmayalternatelybecalculated.byusingcrack-tipstressintensityfactorformulaewithaplastic-zonecorrection.Themethodofcalculationshallbevalidatedanddocumented.A-3300SELECTIONOFTHEJ-INTEGRALRESISTANCECURVEWhenevaluatingthevesselforLevelA,BandCServiceloadings,theJ-integral'resistanceversuscrackgrowthcurve(J-Rcurve)shallbeaconservativerepresentationofthetoughnessofthecontrollingbeltlinematerialatuppershelftemperaturesintheoperatingrange.WhenevaluatingthevesselforLevelDServiceloadings,theJ-Rcurveshallbeabestestimate.representationofthetoughnessofthecontrollingbeltlinematerialatuppershelftemperaturesintheoperatingrange.Oneofthefollowingoptioris:shallbeusedtodeterminetheJ-Rcurve.(a)AJ-Rcurvegeneratedfortheactualmaterialunderconsiderationbyfollowingacceptedtestproceduresmaybeused.TheJ-Rcurveshallbebasedonthe'ropercombinationofcrackorientation,temperatureandfluencelevel.'hecrackgrowthshallincludeductiletearingwithnooccurrenceofcleavage.A-7 S'

AJ-RcurvegeneratedfromaJ-integraldatabaseobtainedfromthesameclass.ofmaterialunderconsiderationwiththesameorientationusingappropriatecorrelationsfortheeffectsoftemperature,chemicalcompositionandfluencelevelmayheused.Thecrackgrowthshallincludeductiletearingwithnooccurrenceofcleavage.(c)Whentheapproachesof(a)or(b)arenotpossible,indirectmethodsofestimatingtheJ-Rcurvemaybeusedprovidedthesemethodsarejustifiedforthematerialunderconsideration.A-3400FLAWSTABILITYTheequilibriumequationforstableflawgrowthisJ=JwhereJistheJ-integraldueto-theappliedloadsforthepostulatedflawinthe'vessel,andJistheJ-integralresistancetoductiletearingforthematerial.TheinequalityforflawstabilityduetoductiletearingisQJdLTgaadawhereBJ/BaisthepartialderivativeoftheappliedJ-integralwithrespecttotheflawdepthawithloadheldconstant,anddJ/daistheslopeoftheJ-Rcurve.'nderaconditionofincreasingload,stableflawgrowthwillcontinueaslongasBJ/BaremainslessthandJ/da.A-3500EVALUATIONAPPROACHFORLEVELAANDBSERVICELOADINGSTheproceduregiveninA-4200shallbeusedtoevaluatetheappliedJ-integral-foraspecifiedamountofductileflawgrowth.TherearethreeapproachesthatareequallyacceptableforapplyingtheflawstabilityacceptancecriteriaaccordingtothegoverningflawstabilityrulesinA-3400.ThefirstisaJ-Rcurvecrackdrivingforcediagramapproach.InthisapproachflawstabilityisevaluatedbyadirectapplicationoftheflawstabilityrulesgiveninA-3400.Guidelinesforusingthis~~~approacharegiveninA-4310.Thesecondisafailureassessmentdiagramapproach.AprocedurebasedonthisapproachfortheA-8 tI~

postulatedinitialone-quarterwallthicknessflawisgiveninA-4320.ThethirdisaJ-integral/tearingmodulusapproach.Aprocedurebasedonthisapproachforthepostulatedinitialone-quarterwallthicknessflawisgiveninA-4330.ARTICLEA-4000EVALUATIONPROCEDURESFORLEVELAANDBSERVICELOADINGSA-4100SCOPEThisArticlecontainscalculationprocedurestobeusedto.satisfytheacceptancecriteriainA-2000forLevelAandBServiceloadings.AproceduretobeusedtosatisfytheJ-integralcriterionforaspecifiedamountofflawgrowthof0.10in.isgiveninA-4200.Procedurestosatisfy-theflawstabilitycriterionaregiveninA-4300.Theseproceduresincludetheax'ialandcircumferentialflaworientations.A-4200EVALUATIONPROCEDUREFORTHEAPPLIEDJ-INTEGRALA-4210CALCULATIONOFTHEAPPLIEDJ-INTEGRALThecalculationof.the"appliedJ-integralconsistsoftwosteps:Step1istocalculatetheeffectiveflawdepthwhichincludesaplastic-zonecorrection;and-Step2istocalculatetheJ-integralforsmall-scaleyieldingbasedonthiseffectiveflawdepth.~Ste1For.anaxialflawwithadeptha,calculatethestressintensityfactorduetointernalpressurewithasafetyfactor(SF)onpressurebyusingR>>=(SF)p(I+(R,/t)J(na)',F~=0.982+1.006(a/t)~ThisequationtheeffectofforR>>isvalidfor0.20sa/ts0'0,andincludespressureactingontheflawfaces.A-9

~~~Foracircumferentialflawwithadeptha,calculatethestressintensityfactorduetointernalpressurewithasafetyfactor(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.Foranaxialorcircumferentialflawwithadeptha,calculatethestressintensityfactorduetoradialthermalgradientsbyusingKE0=((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.Calculatetheeffectiveflawdepthforsmall-scaleyielding,abyusinga,=a+(I/(6'))((Kzp+KE0)/<yJ~Ste2Foranaxialflaw,calculate-thestressintensityfactorduetointernalpressureforsmall-scaleyielding,Kzp,bysubstitutinga,inplaceofainequation(1),includingtheequationforF,.Foracircumferentialflaw,calculateKzpysubstitutinga,inplaceofainequation(2),includingtheequationforF,.Foranaxialorcircumferential.flaw,calculatethestressintensityfactorduetora'dialthermalgradientsforsmall-scaleyielding,Kzbysubstitutingainplaceofainequation(3),includingtheequationforF3.Equations(1),(2)and(3)arevalidfor0.20ca,/tc0.50.TheJ-integralduetotheappliedloadsforsmall-scaleyieldingisgivenbyZ=1000(Kzp+K'/E'

A-4220EVALUATIONgUSINGCRITERIONFORFLANGRONTHOF0.1ZNCalculatetheJ-integralduetotheapple.edloads,JbyfollowingA-4210.Useaflawdepthaequalto0.25t+0.10in.;apressurepequaltotheaccumulationpressureforLevelAandBServiceloadings,'andasafetyfactor(SF)onpressureequalto1;Z5.Theacceptance.criterionforLevelAandBServiceloadingsbasedonaductileflawgrowthof'.10in.inA-2000(a)(1')issatisfiedwhenthefollowinginequalityissatisfied.Js~Jo.iwhereJ,=theappliedJ-integralfora=safetyfactoronpressureof1.15,andasafetyfactorof1.0onthermalloading,J,,=theJ-integralresistanceataductileflawgrowthof0.10in.A-4300EVALUATIONPROCEDURESFORFLANSTABILITYA-4310J-RCURVE-CRACKDRIVINGFORCEDIAGRAMPROCEDURE~~ZnthxsprocedureflawstabzlztyxsevaluatedbyadirectapplicationoftheflawstabilityrulesgiveninA-3400.TheappliedJ-integraliscalculatedforaseriesofflawdepthscorrespondingtoincreasingamountsofductileflawgrowth.TheappliedJ-integralforLevelAandBServiceloadingsshallbecalculatedbyusingtheproceduresgiveninA-4210.TheapplieppressurepissetequaltotheaccumulationpressureforLevelAandBServiceloadings,p;andthesafetyfactor(SF)onpressureisequalto1.25.TheappliedJ-integralis.plottedagainstcrackdepthonthecrackdrivingforcediagramtoproducetheappliedJ-integralcurve,asillustratedinFigureA-4310-1.TheJ-Rcurveisalsoplottedonthecrackdrivingforcediagram,andintersectsthehorizontalaxisattheinitialflawdepth,a,.FlawstabilityatagivenappliedloadisdemonstratedwhentheslopeoftheappliedJ-integralcurveislessthantheslopeoftheJ-RcurveatthepointontheJ-Rcurvewherethetwocurvesintersect.

Jr MaterialJREvaluationPoint'ppliedJapFIGUREA-4310-1COMPARISONOFTHESLOPESOFTHEAPPLIEDJ-INTEGRALCURVEANDTHEJ-RCURVE~

I~

A-4320FAILUREASSESSMENTDIAGRAMPROCEDUREThisprocedureisrestrictedtoapostulatedinitialflawdepthequaltoone-quarterofthewallthickness.A-4321FAZLUREASSESSMENTDIAGRAMCURVEThesamefailureassessmentdiagramcurveshallbeusedforaxialandcircumferentialflaws,andisgivenin.FigureA-4320-1.Thecoordinates(SR,)ofthefailureassessmentdiagramcurvearegiveninTableA-4320-1.Thiscurveisbasedonmaterialpropertieswhicharecharacteristicofreactorpressurevesselsteels.A-4322FAILUREASSESSMENTPOINTCOORDINATESTheflawdepthafor,aductileflawgrowthofh,aisgivenbya-=0250+ha~~Thefailureassessmentpointcoordinates(S',K')foraductileflawgrowthofhashallbecalculatedbyusingthefollowingexpressions:KzR~(I000/(EJ))Vwherethestressintensityfactorshallbecalculatedusingtheflaw.depthawithouttheplastic-zonecorrection,andisgivenbyK~=Kzp+R~,ands:=(sz)p/p.where(SZ)istherequiredsafetyfactoronpressure.TheprocedureforcalculatingKz~Kzandp,foraxialflawsisgiveninA-4322.1,andfor.circumferentialflawsinA-4322.2.A-13

-0 A-4322.1AxialFlawsThestressintensityfactorduetointernalpressureforaxialflawswithasafetyfactor(SZ)onpressureisgivenbyequation(1').Thestressintensityfactordue,toradialthermalgradientsisgivenbyequation(3)~Thereferencelimit-loadpressureisgivenbyH(2/~3}o[Q.905-Q.379(h,a/t)I[0.379+(R~/t)+0.379(ha/t}1Formaterialswithayieldstrengthogreaterthan85ksi,setaequalto85ksiinthisequation.Thisequationforp,isvalidfor0sza/ts0.10.A-4322.2CircumferentialFlaws()thermalgradientsis>givenbyequation(3).Thereferencelimit-loadpressureisgivenbyCThestressintensityfactorduetointernalpressureforcircumferentialflawswithasafetyfactor(SF)onpressureisgivenbyequation2.Thestressintensitfactorduetoradialpo[1-0.91(0.25+(Aa/t})~(t!R~)l[1+(R/(2t)Formaterialswithayieldstrengthozgreaterthan85ksi,setoyequalto85ksiinthisequation.Thisequationforpisvalidfor0sza/'ts0.25.A-4323EVALUATIONUSINGCRITERIONFORFLAN'TABILITYAssessmentpointsshallbecalculatedforeachloadingconditionaccordingtoA-4322,andplottedonFigureA-4320-1asfollows.PlotaseriesofassessmentpointsforvariousamountsofductileflawgrowthbauptothevaliditylimitoftheJ-Rcurve.UseapressurepequaltotheaccumulationpressureforLevel.AandBServiceloadings,pandasafetyfactor(SF)onpressureequalto1.25.Whenoneormoreassessmentpointslieinsidethefailureassessmentcurve,theacceptancecriterionbasedonflawstability.inA-2000(a)(2)issatisfied. /r TABLEA-4320-1COORDINATESOFTHEFAILUREASSESSMENTDIAGRAMCURVEOPFIGUREA-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'.9960.9930.9900.9870.9810.9730.9600.9390.9080.8640.8070.7370.6600.5810.5050'350.3740.3210.2760.238A-15 Js 1.21.0,0.80.6K,0.40.20.00.00.20.40.60.81.01.2S,1.4FIGUREA-4320-1FAILUREASSESSMENTDIAGRAMFORTHEONE-QUARTERMALLTHICKNESSFLANA-16 J A-4330J-ZNTEGRAL/TEARZNGMODULUSPROCEDUREThisprocedureisrestrictedtoapostulatedinitialflawdepthequaltoone-quarterofthewall.thickness.A-4331J-ZNTEGRALATFLANZNSTABZLZTY1ReferringtoFigureA-4330-1,theonsetof.flawinstabilityisthepointofintersectionoftheappliedandmaterialcurvesplottedonagraphoftheJ-integralversustearingmodulus(JversusT).TheexpressionfortheappliedJ/TcurveisgivenbyJ=(1000VtOi/Z)T(4)(5)whereoiisareferenceflowstresswhichissetto85ksiinequation(4).Foraxialflawsp=0.235(l+(0.083x10')(CR)t'/((SF)p,)Jwherep,isthepressureunderevaluation.Equation(5)isvalidfor6sts12in.,2.25s((SF)p,)s5.00ksi,and0s(CR)100F/hour.Forcircumferentialflaws~~~~~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)arebasedonmaterialpropertieswhicharecharacteristicofreactorpressurevesselsteels.ThetearingmodulusforthematerialisdeterminedbydifferentiationoftheJ-Rcurvewithrespecttoflawdeptha.(Z/(1000Qi))dJ/da(7)The-samevaluesforZandoishallbeusedinequations(4)and(7).TheJ-integralversustearingmodulusJ~/T~curveforthematerialisgivenbyplottingJagainstT~foraseriesofincrementsinductileflawgrowth.EachcoordinateforJRisevaluatedatthesameamountofductileflawgrowthasthecoordinateforT~. / ~~~~~~~~The'valueoftheJ-integralattheonsetofflawinstability,J',correspondstotheintersectionoftheappliedJ/Tcurvegiven:byequation(4)withthematerialJ~/T~curve,asillustratedinFigureA-4330-1.hTheJ-integralattheonsetofflawinstabilitymaybedeterminedanalyticallywhenapower-lawcurvefittotheJ-RcurveoftheformJ-Ci(ha)+isavailable.TheJ-integralattheonsetofflawinstability,J,inthiscaseisgivenbyA-4332ZNTERNALPRESSUREATFLANZNSTABZLZTY~~~~~~~~~~~ThecalculationoftheinternalpressureattheonsetofflawinstabilityisbasedonthevalueoftheJ-integralat.theonsetofflawinstability,J.Theductileflawgrowthattheonset.offlawinstability,ha,istakenfromtheJ-Rcurve.Theeffectiveflawdepthattheonsetofflawinstabilityincludestheductileflawgrowthb.a',andisgivenbya=0.25t+ha+(1/(6n))fZ'8'/(1000o~'))Thestressintensityfactorduetoradialthermalgradientsattheonsetofflawinstability,Ziforaxial:orcircumferentialflawsisgivenby.."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.Thestressintensityfactorforsmall-scaleyieldingduetointernalpressureattheonsetofflawinstability,Eppesisgivenby ,0 ForagivenvalueofK,'~,theinternalpressureattheonsetofflawinstabilityforaxialflawsisgivenbyp=Ksp/((1+(R,/t))(za)o.sF,']F~.=0.982+,,2.006(a,/t)~andforcircumferentialflawsbyp=Ki/((1+(Ri/(2t)))(za,)'~JF'0.885+0.233(a,/t)+0.345(a,/t)Theseequationsforparevalidfor0.20sa,/ts0.50,andincludetheeffectofpressureactingontheflawfaces.A-4333EVALUATIONUSINGCRITERIONFORFLANSTABILITYCalculatethevalueoftheJ-integralattheonsetofflawinstability,J',byfollowingA-4331usingapressurep,inequations(5)and(6)equaltotheaccumulationpressureforLevelAandBServiceloadings,pandasafetyfactor(SF)onpressureequalto1.25.Calculatetheinternalpressureattheonsetofflawinstability,p,byfollowingA-4332.TheacceptancecriterionbasedonflawstabilityinA-2000(a)(2)issatisfiedwhenthefollowinginequalityissatisfied.p>I25p,ARTICLEA-5000LEVELCANDDSERVICELOADINGSThepossiblecombinationsofloadingsandmaterialpropertieswhichmaybeencounteredduringLevelCandDServiceloadingsaretoodiversetoallowtheapplicationofpre-specifiedproceduresanditisrecommendedthateachsituationbeevaluatedonanindividualcasebasis.A-19 0 Instability.MaterialJRvsTRJtcAppliedJvsTFIGUREA-4330-1ILLUSTRATIONOPTHEJ-INTEGRAL/TEARINGMODULUSPROCEDUREA-20 A 83AppendixBASMEWorkingGrouponFlawEvaluationDraftModificationtoArticleA-3000

ART<.CI,EA.-3OoONETHODFOREsDETERMINATIONpg~WCVriHABC&A-3100SCOPEThisAtticleprovidesamethodforcalculatingstressintensityfactorKrfromthemembraneandbendingstressesdeterminedfromstressanalysis.A-3100SCOPEThiaAructeprovideramethodforcalculatingatrcaaintcnrityfactorK<fromthereprerenrartvearreraerattheflawlocationdeterminedfromarrearanalysis.MoreaophirticatcdtechniquesmaybeusedlndeterminingI4pmvldcdthemethodsaedaeatyaeaaredocumented.fA-3MOSTRE55ESThestressesattheflawlocationshouldberesolvedintomembraneandbendingstresseswithrespecttothewallthickness.Residualstressesandappliedstressesfromallformsofloading.includingpressurestresses,thermalstresses.discontinuitystresses.andcladdinginducedstresses.shouldbeconsidered.lnthecaseofanonlinearstressdistributionthroughthewall,theac-tualstressdistributionshouldbeconservativelyap-proximatedusingthelinearigationtechniqueillustratedinFig.A-3200-1.Thelinearizedstressdistributionshouldthenbecharicterizedbythemembranestresscrandthcbendingstressera,asshowninFig.A-3200-1~h-3200STQBSES(a)Forthecaroofasubsurfacefiaw,thatromcaattheflawlocationshallberesolvedintomembraneandbendingatrcrrcawithrespecttothewallthlcknecr.Rertduatstrcascaandappliedarrccacafromallfonnaofloadmg,includingpressurearreaaeeandchddag.inducedatrearor,abaQbeoonrutcred.Fornonlinearstrcaavarianresthroughthewall,theactualarreaadistributiocanbeconaervanvelyapproximatedbythelinearizationtechruqueilluarraredinFig.h-3200-1(b).Thebncariaedatrea'edtrrributtonahoutdrbcnbecharacterisedbythemembraneatrcaae'ndthebeudurgarreeagaarhowninFig.A-3200.1(b).(b)Forthecareofasurfaceflaw,rhearrerrcaattheflawlocationshallbereprerrntrdbyapolynornlatfitgivenbythefoUowiagrelationship:o-A,~A,x~A,xa-A,x'wherexisthedirraucethroughthowallandAA,.AandA,areconstants.Thederermiua6onofcodflcteorsAothrough+rhallprovideaconservativereprrccntationofatrearoverrhecrackone0cx4aforauvat~ofcrackdcpthacoveredbytheanalysis.StresreafromaourceaiMocr&dlnA-3200(a)ahallbecoasidcrcd.lnthecasewhraanonlineararrcaadlarrlbutiouladlfflcutttofitbeEq.1,thcactualdlrrribunoncanbecoeacrvarlvelyappro6rnaredby0>>hncarizatlonrcchntquoUlurrraredtnFigureA-3200t(a)fottowtegthediacuaaiongiventnh-3200(a)foraubcuzfaceflawa.

A-3300STRESSINTENSITYEQUATION(a)StressintensityfactorsfortheAawmodelshouldbecalculatedfromthemembraneandbendingstressesattheflawlocationusingthefollowingequation:K/~eNYrr~alQ+tr>M>Va'Valg(I)wherecr,tre~membraneandbendingstresses.psi.inac-cordance'withA-3200aminorhaifdiamcter,in.,ofembeddedflaw:flawdepthforsurfaceflawQmflawshapeparameterasdeterminedfmmFig.A-3300-lusing(tr+rr,)/a,andtheRawgeometryM=correctionfactorformembranestress(sceFig.A-3300-2forsubsurfaceflaws;Fig.A-3300-3forsurfaceflaws)~'emcorrcctionfactorforbendingstress(seeFig.A-3300-4forsubsurfacelaws:Fig.A-D~~~~~~~3300-5forsurfaceflaws)%herevariationsinK/amundthcperipheryofoccur.thcmaximumvalueistobeused.(c)TheuseofEq.(1)isonlyatecomn>>ndationfordeterminationofA'/.Moresophisticatedtechniquesmaybcused,providedthemethodsandanalysesaredoc-urnented.Inmanycasesinvolvingcomplexgeometriesandsttessdistributions,themethodsoutlinedabovemaybeinadequate.h-3300SIILESSINTENSITYFACTOREQUATIONSTheflawshallbetepteseatedbyanelGpsethatcbcumacdbaathedetectedflawasiilutttatedinFig.A33001.Thestressiattosityiactotsfortheflawmodelshallbodetencinedftomthestressesandflawgeometryasdesctibediah-3310forsubsurfaceflawsaadlnh-3320forsutfacoflaws.h-3310SubsuttaceFlawEquationsatoMm+obMbjf~0/0(2)where,0>>IJgA-3200(a)aMFig.A3200-2M,Pig.h-3200.3QMembraneandbeadingstressesiaaccordancewithMinorhalMmnetesConectionfactorformembranesttessglvcatinConectionfactorforbeadingstressgivtstinFlawsbapopataateterasgivenbyEq.3TheflawshapepanttnctctQiscalculatedfiromthefollowingequatioa:Q1-4.598(a/>)Ž-q(a)Stressattensityfactorsforsubsurfaceflawshallbecalculatedfromthoas:mbraneandbeadingsuessesatthefLawlocationbythefollowingcquatioa:whetea/ristheflawaspectratio0sa/rs'8,aadq,istheptasticsouecottectioafactorequalto0.212I(o+eJ/o)'.(b)WhetevariatioasiaK,aroundthepcriphetvoftbeflavvoccur.themaximumvalueistobeusediathedelcnniaatioaoftbectiticatflawluuamctcraa,and+.(c)TheusoofEq.2isonlyatecomaamdatioafoedetenainatioaofKvIasomecasesiavolviagcomptcageometriesandsttessdistribution.themethodoutlinedabovemayaotbeadequate. I A.3320Sur&ceFlawEquations(a)Stressintensityfactorsforstrrfsceflawsshouldbecalculatedfromthecubicpolyaoaualstressrelationbythefollowiegequstlorv(4)KQOo'At3tarAtotatAsOsaj~xCrackdepthA,AAs,A,~CoefficieatsfromEq.1that~utsrtsrtsthestressdistributionoverthecrack(0s.x5a)OorOoGteOrQwithq,defiaedasFreesurfacecorrectionfactorsfortbegivenstressvariationprovidediaTablesA-33201andA.3320.2asafunctionotflawaspeNratioa/f,crackeaetrations/t,aadcracktippositiott(PTLaadF72)FlawshapepsrstaetcrssgivenbyEg.30.212[A,/trP(b)~theLineIraaenmethodlsusedtoconvertthoactualstressfieMintotraadtr,stressesasillustratediaHg.A-3200-1(a),thenEq.2shallbeUsedtocalculate)(twiththofollowingequationsforM,MsrdQ:MMiGo2(a/t)GrQ~Sq.3whereq,isdefinedas0.212((re+~/o'e)%huevariationiaKrsratheperipherofthefLawoccur,thetrLaxitaumvalueistobeusediathedetertainatlonofa,aadtt(d)TheusooftheabovemethodsIsonlyarecotrutMadatlcsrfordeterminationofQ.lnsomecasesiavolviagcomplygeotnesriesandstressduuribunons.themethodsoutlinedabovemayncebeadequate.

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