Yaghi - Abaqus Thermal Analysis of the Fusion Welding of a P92

18 Pages·2011·1.21 MB·English

Abaqus Thermal Analysis of the Fusion Welding of
a P92 Steel Pipe
A.H.Yaghi,D.W.J.Tanner,T.H.Hyde,A.A.Becker, W. Sun
Materials,MechanicsandStructuresResearchDivision,FacultyofEngineering
UniversityofNottingham,NottinghamNG72RD,UK
Fusionweldingiscommoninsteelpipelineconstructioninfossil-fuelpowergenerationplants.
Steelpipesinservicecarrysteamathightemperatureandpressure,undergoingcreepduring
yearsofservice;theirintegrityiscriticalforthesafeoperationofaplant. Thehigh-grade
martensiticP92steelissuitableforplantpipesforitsenhancedcreepstrength. P92steelpipes
areusuallyjoinedtogetherwithasimilarweldmetal. Martensiticpipesaresometimesjoinedto
austeniticsteelpipesusingnickelbasedweldconsumables. Weldinginvolvesseverethermal
cycles,inducingresidualstressesintheweldedstructure,which,withoutpostweldheattreatment
(PWHT),canbedetrimentaltotheintegrityofthepipes. Weldingresidualstressescanbe
numericallysimulatedbyapplyingthefiniteelement(FE)methodinAbaqus. Thesimulation
consistsofathermalanalysis,determiningthetemperaturehistoryoftheFEmodel,followedbya
sequentially-coupledstructuralanalysis,predictingresidualstressesfromthetemperaturehistory.
Inthispaper,theFEthermalanalysisofthearcweldingofatypicalP92pipeispresented. The
twopartsoftheP92steelpipearejoinedtogetherusingadissimilarmaterial,madeofInconel
weldconsumables,producingamulti-passbuttweldfrom36circumferentialweldbeads.
FollowingthegenerationoftheFEmodel,theFEmeshiscontrolledusingModelChangein
Abaqustoactivatetheweldelementsforeachbeadatatimecorrespondingtowelddeposition.
Thethermalanalysisissimulatedbyapplyingadistributedheatfluxtothemodel,theaccuracyof
whichisjudgedbyconsideringthefusionzonesinboththeparentpipeaswellasthedeposited
weldmetal. Forrealisticfusionzones,theheatfluxmustbeprescribedinthedepositedweldpass
andalsotheadjacentpipeelements. TheFEthermalresultsarevalidatedbycomparing
experimentaltemperaturesmeasuredbyfivethermocouplesonthepipeoutsidesurfacewiththe
FEtemperaturehistoryatcorrespondingnodalpoints.
Keywords:FiniteElement(FE),ThermalAnalysis,FusionWelding,P92SteelPipe,Inconel625.
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1. Introduction
Thenumericalsimulationoftheprocessoffusionweldingofsteelpipesinpowergeneration
plantshasbeenthesubjectofresearchandpublicationforafewdecades. Steelpipesarean
essentialcomponentinfossil-fuelandotherpowerplants,deliveringsteamathightemperature
andpressure. Theconstructionofthepipesrequiresjoiningthembyapplyingfusionwelding,
involvingintensethermalcycles,causingrapidheatingandcoolingoftheweldedmetal. This
inducesresidualstressesintheweldmaterialandtheheataffectedzone(HAZ)ofthepipes,which
usuallyexceedthematerialyieldstressatcertainlocations. Thelargemagnitudeofthewelding-
inducedresidualstressescanbedetrimentaltothemechanicalperformanceofthewelded
componentsduringservice. Thisproblemisusuallyovercomebythepost-weldheattreatment
(PWHT)oftheweldedpipes,whichiscostlyandcanbetechnicallychallenging;PWHT
significantlyreducesthemagnitudeofresidualstressesbutitcannoteliminatethem. Therefore,
thedeterminationofresidualstressesthroughouttheweldedpipescanbevaluablefordeciding
howtoapplyPWHTorindeedhowtomodifyweldingprocedurestomitigatetheill-effectsof
residualstresses.
Thedeterminationofresidualstressesinweldedpipescanbeachievedbyexperimental
procedures,suchastechniquesbasedoncentre-holedrilling,deep-holedrilling,X-raydiffraction
andneutrondiffraction,whicharecostlyanddifficultattimes,andcaninvolvedestructiveor
semi-destructiveprocedures,otherwisetherevealedstressfieldislimitedtothesurfaceornearthe
surface(Yaghi,2010). Theexperimentally-determinedresidualstressfieldismeasuredatspecific
locationsonlyandtheexperimentalmethodsinvolveaveragingoveranarea,possiblymissingout
onsharpchangesintheresidualstressfieldwhicharetypicalofwhatisinducedbytheprocessof
welding. Thefiniteelement(FE)numericalmethod,however,canprovideresidualstress
predictionsthroughouttheweldedcomponent,capturingthesharppeaksofthestressfield,
dependingontherefinementofthegeneratedFEmesh. Thechallengingpartofproviding
accuratenumericalresultsliesinacquiringasetofmaterialpropertieswhichtrulyreflectthe
behaviourofthemodelledmaterial. Iftherequiredsetofmaterialpropertiesforthenumerical
simulationisavailableandthegeneratedFEmeshhassufficientrefinement,theresidualstress
fieldduetoweldingcanbeaccuratelyobtainedthroughouttheFEmodel,makingtheFEmethod
highlyeffectiveatpredictingweldingresidualstresses.
TheFEmethodcomprisestwoparts:athermalanalysis,simulatingtheweldingthermalcycles
anddeliveringatemperaturehistorythroughouttheweldingprocess,andasequentially-coupled
structuralanalysis,processingthetemperaturehistoryasinputdataanddeterminingthe
developingthermalstressesandtheresidualstressfieldinducedbythethermalcycles. Evidently,
theaccuracyofresidualstressesisdependentontheaccuracyofthetemperaturehistory
determinedbythethermalanalysis. Inthispaper,thethermalanalysisofanarcweldedsteelpipe,
typicallyfoundinpowergenerationplants,ispresented. ThepipeismadeofP92steelandis
dissimilarinthesensethattheweldmetalisdifferentfromthetwoP92partsbeingjoined
together. P92steelpipesareusuallyjoinedtogetherwithasimilarweldmetal. Martensiticpipes
aresometimesjoinedtoausteniticsteelpipesusingnickelbasedweldconsumables. Inthisstudy,
theP92steelpipehasbeenweldedwithadissimilarweldmetalforresearchpurposes. Theweld
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isacircumferentialbutt-weldconsistingof36beads. Thefirstbeadorweldpassismadeof
Inconel82(IN82)andtheremaining35beadsorweldpassesaremadeofInconel625(IN625).
P92,alsoknownasNF616inJapan,isarelativelynewly-developed9-12%Crferriticsteelthat
canbeusedinhightemperatureapplications,suchasinfossil-fuelandnuclearpowerstationsas
wellaschemicalplants. P92isamodifiedformofitspredecessorP91. Molybdenum,Mo,inP91
(9Cr1Mo)hasbeenpartiallyreplacedbyTungsten,W,forP92(9Cr2W). P92hascreepstrength
approximately30%higherthanthecurrentlywidelyusedsteelP91(Brózda,2005),andithas
provedsuitableforpipingandheadersattemperaturesuptoaround625°C(Richardot,2000).
Hence,inmodernsuper-criticalsteampowerplants,P92allowshigheroperatingparametersand
thereforehigherefficiencies.
Ingeneral,anFEsimulationofaweldedpipecanbethree-dimensional(3D)or,whenappropriate,
canbetwo-dimensional(2D)axisymmetric(Deng,2006). A3Dsimulationisdesirablewhen
effectsthatcannotbeotherwisemodelledarerevealed,suchasstressesatweldingstartingand
stoppinglocations. A2Daxisymmetricsimulation,however,canbemoresuitable,whensuch
effectsaretobeignored,andwhenthemoreuniformresidualstressfieldisofinterest. Thisis
becausea2DaxisymmetricsimulationcanhaveamuchfinerFEmeshforthesamecomputational
processingtimeincomparisonwitha3Dsimulationofthesamemodel,whichcanleadto
significantlymoreaccurateresultsforlargemodelswithnumerousweldpasses. 3Dmodelsof
weldswithmanypassescanovercomethenecessityofrunningprohibitivelylargeanalysesby
employingtechniquessuchaslumpingoftheweldpassestogetherandkeepingtheFEmesh
relativelycoarse,whichwouldreducetheaccuracyoftheresults.
Figure1. P92pipebeforewelding.
Thereportedthermalanalysisisbasedona2Daxisymmetricmodeloftheweldedpipewiththe
FEmeshcontrolledusingthefacilitynamedModelChangeinAbaqus(ABAQUSUserManual,
2009). ModelChangeallowstheweldmaterialforeachweldpasstobecomeactiveduringthe
numericalsimulationatthetimecorrespondingtothedepositionofthepass. Theheatdelivered
bytheweldingarchasbeenmodelledbyprescribingauniformlydistributedheatflux,whichisa
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triangularfunctionagainsttime,correspondingtotheapproachingandthendepartingweldingarc.
Thedistributedheatfluxhasbeenappliedtoeachweldpasswhenitisdepositedandalsotothe
surroundingpipe(parent)materialinordertoobtainthedesiredthermalcontoursintheFEmodel.
IntheFEthermalstudy,considerationhasbeengiventofusionzonesintheweldandparent
material,peaktemperaturecontoursthroughouttheHAZandthetemperaturehistoryatlocations
correspondingtoasetofattachedthermocouples. Theactualweldedpipehadfivethermocouples
attachedatdifferentlocations,makingitpossibletovalidatethetemperaturehistorydetermined
bythereportedFEthermalanalysis.
2. Dissimilar Welded Pipe
TheFEthermalanalysishasbeenconductedtomodelthethermalbehaviourofaweldedsteel
pipe. Priortowelding,theP92pipewascutintotwohalvesandtheendspreparedforjoining,a
photographofwhichisshowninFigure1. Thetwohaveswereaxisymmetricallyalignedandheld
inlargemetalvicesandthenweldedtogetherusing36weldbeads(orpasses)ofdissimilarweld
materials. Theright-handsidewasreleasedafterthethirdweldpasshadbeencompleted,andthe
left-handsideremainedfixedthroughouttheprocessofwelding,ascanbeseeninFigure2.
Figure2. P92pipeduringwelding.
2.1 PipeGeometry,WeldDetailsandMaterialSpecifications
ThegeometryanddimensionsoftheweldedP92pipe,aswellastheweldingsequence,areshown
inFigure3. Theweldedpipehasanoutsidediameterof355mmandatotallengthof700mm.
Thefirstweldpasswasdepositedbytungsteninertgas(TIG)weldingusingthenickelbasedweld
materialInconel82(IN82),havingthemanufacturer’sbrandnameUTPA068HH,witharod
diameterof2.4mm,duringwhichargongaswasusedtoshieldtheweldfromatmosphericgases.
Weldpasses2to36weredepositedbymanualmetalarc(MMA)weldingusingthenickelbased
weldmaterialInconel625(IN625),havingthemanufacturer’sbrandnameNIMROD625KS,
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withthefillerrodforweldpasses2and3havingadiameterof3.2mmandtheremainingpasses
havingadiameterof4.0mm. Thechemicalcompositionsfortheparentandweldmaterialsare
showninTable1. Thematerialpropertiesarediscussedinsection3.2.
32mm
28mm
32 34 35 36 33 2.0-2.5mm
28 30 31 29
24 26 27 25
20 22 23 21
19
17 18
30mm 14 16 15
13 15°
11 12
10
8 9
6 7
4 5
4.35mm 2 3 1mm 30°
1
1.5mm
3mm
Figure3. Sketchofweldbeadsequenceshowingoverallwelddimensions.
Table1. Chemicalcompositionofthepipeandweldmaterials.
Fe C Mn P S Si Cr W Mo V Nb N B Al Ni
P92 Bal 0.10 0.45 0.015 0.002 0.45 8.62 1.86 0.33 0.21 0.076 0.047 0.003 0.019 0.27
IN625 1.48 0.03 0.76 0.005 0.005 0.33 21.9 - 8.67 - 3.340 - - - Bal
IN82 0.80 0.01 3.00 - - 0.10 20.0 - - - 2.700 - - - Bal
2.2 ThermocouplesandWeldProcedure
Thetemperatureofthepipewasmonitoredduringweldingbyattachingfivethermocouplestothe
surfaceofthepipeandrecordingthetemperatureswithachartplotterthroughoutthewelding
process. Thethermocouplesmeasuredthesurfacetemperatureatfivedifferentlocationswith
varyingdistancefromtheweldcentreline(WCL)andalsoatdifferentangularpositionsaround
thepipecircumference. SincetheFEanalysisisaxisymmetric,theangularpositionofthe
thermocouplesaroundthecircumferenceisirrelevanttothereportedstudy. Thefactthatthe
angularpositionvariesforthethermocouples,however,isrelevantinexplainingsomeofthe
scatternoticedinthetemperatureresultsaswellassomeofthediscrepanciesobservedbetween
theexperimentallymeasuredandtheFEdeterminedtemperatures,aswillbediscussedlaterinthe
paper. Thermocouples1and2(TC1andTC2)areclosesttotheweldandarelocatedontheleft-
handpipesection,bothatanaxialdistanceof32.4mmfromtheWCL. Theotherthermocouples,
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TC3,TC4andTC5,arelocatedontheright-handpipesectionataxialdistancesof35.0mm,
40.5mmand70.3mmfromtheWCLrespectively. Allthedistancesweremeasuredafter
depositingthethirdweldpassandbeforetherestofthepassesweredeposited,i.e.beforeany
significantdeformationtookplace. Itisworthnotingthatthedistancesrelatingtothe
thermocouplesareaccuratetowithin±0.5mm;theyare,however,quotedheretothestated
precisiontocorrespondtothematchingnodalpositionsintheFEmesh,wheretemperature
comparisonsaremade.
Thethermocoupleswereusedtomonitorthetemperatureofthepipetomaintaintherequired
preheatandinterpasstemperature,necessaryinthecaseofP92steelforaweldingprocedure
whichwouldlikelybefreefromtheriskofmicroormacro-crackingduringweldingorjustafter,
asthepipecooledtoroomtemperature. Thetemperaturehistoryobtainedfromthethermocouples
hasalsobeenusedtovalidatethethermalbehaviourdeterminedbytheFEsimulation. Thepipe
washeatedbyanelectricblanketonbothsidesascanbeseeninFigure2. Althoughtheblanket
wouldgoonandoffandwouldreachrelativelyhightemperatureswhenswitchedon,the
temperaturesattheweldregionandtheHAZwererelativelysteady,andthereforetheFE
modellingoftheblanketeffectwasachievedbyprescribingasinktemperatureatthesurface
wheretheblanketwasincontactwiththepipe. Thesinktemperaturewasvariedfromoneweld
passtotheother,duringtheFEsimulation,toemulatetheexperimentallymeasuredtemperatures
duringtheinterpassperiods. Duringtheactualweldingofthepipe,asrecommendedbyliterature,
itwasaimedtokeepthepreheatandinterpasstemperaturesfortheTIGweldingofthefirstpass
between100°Cand150°C(Holloway,2008)andfortheMMAweldingofalltheotherpasses
between200°Cand250°C(Richardot,2000).
3. FE Thermal Analysis
TheFEthermalanalysisreportedinthispaperispartofamorecompleteFEsimulationintended
bytheauthorstodetermineweldingresidualstressesforthedissimilarweldedP92pipe. TheFE
thermalanalysis,whichformsthefirstpartofthesimulation,isreportedhere,whereasthe
sequentiallycoupledstructuralanalysis,whichformsthesecondpartofthesimulation,istobe
reportedinafuturepublication. Thetypeofsimulationadoptedbytheauthorsisdescribedas
solid-mechanical,modellingtheheatfluxdeliveredtothepipebytheheatsourceandallowingfor
thethermo-physicalbehaviour,suchasconductivity,andthentranslatingthethermaleffectsinto
structuralmechanicaleffects,suchasvolumeexpansionsandplasticity,withoutallowingforany
fluideffectsofthemoltenregions. Thesolidmechanicsapproachisjustifiedinignoringthefluid
effects,sincestressesbecomesignificantonlywhenthematerialhassolidifiedandisrelatively
cool. Whenthematerialismoltenorclosetobeingmolten,itissoftenoughnottosustainany
significantstresses. Aslongasthemechanicalpropertiesusedinthesimulationrepresentthe
actualbehaviourofthematerial,fluideffectsdonothavetobetakenintoconsideration.
3.1 FEModeloftheWeldedPipe
TheFEsimulationofthefusionweldingofthedissimilarweldedP92pipestartswithgenerating
anFEmodelbyfirstlycreatinganFEmesh. Thecommercialpackageusedforthispurposeand
indeedforperformingthecompleteFEthermalanalysis,reportedinthispaper,isAbaqus
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(ABAQUSUserManual,2009). AcompleteFEmeshhasbeengeneratedfromthestart,which
includesthepipeandtheweldregion.
TheweldpasssequenceintheFEmodelisidenticaltothatintheactualweld,asshowninFigure
4. TheshapeoftheweldpassesintheFEmodeldoesnothavetoaccuratelymatchtheactual
shapeoftheweldbeadstoproducerepresentativeandrealisticthermalcontours(Yaghi,2010).
AlthoughtheshapesoftheFEpassesarerathersquarecomparedtotheactualweld,theresulting
thermalcontoursemergeroundedandrealistic.Nonetheless,itisbelievedthatthefinallayerof
weldpasseshasthemostsignificanteffectonresidualstresses,andthereforeanattempthasbeen
madetomakethefinallayercloserinshapetotheactualweldbeads. Theshapeofthefinallayer
ofbeadscaneasilybeadjustedwithoutundulycomplicatingtheFEmodel,whichisnotthecase
fortheotherbeads. TheactualFEmeshwhichhasbeengeneratedforthemodelisshownin
Figures5and6. ItcanbeseeninFigure5thatthemeshisrefinedintheweldregionandHAZ
andthatitbecomesgraduallycoarserasitmovesawayfromtheweld,asshowninFigure6. The
complete2DaxisymmetricFEmeshcomprises9022nodesand2919elements. Theelementtype
usedthroughouttheFEmodelisaneight-nodecontinuumsolidquadraticaxisymmetricdiffusive
heattransferquadrilateral,giventhenameDCAX8inAbaqus.
Figure4. WeldpasssequenceintheFEmodel.
TheelementsintheFEmeshformingeachweldpassareassignedagroupnamesothateachpass
canbedepositedindependentlyduringthesimulation. Attheinceptionofthesimulation,the
elementsofalltheweldpassesaremadetobecomeinactive,renderingthemthermallydormant,
whilestillkeepingalltheelementsofthemeshattachedtogether. ThisisachievedinAbaqusby
usingthecommand“ModelChange,Type=Element,Remove”atthebeginningofthefirststepin
theinputfileofthethermalanalysis. Eachweldpassisdepositedinthecorrespondingstepinthe
thermalanalysisbyusingthecommand“ModelChange,Type=Element,Add”,whichreactivates
thecorrespondingelementsintheFEmesh.
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Figure5. FEmeshshowingtheweld,HAZandpartofthepipe.
TherequirementoftheFEmodeltoexchangeheat,atitssurface,withthesurrounding
environmentisfacilitatedusingtheoption“sfilm”intheinputfile. Asurfacefilmor“sfilm”is
generatedbyselectingtheoutsidesurfaceofrelevantelementswhichareexpectedtoexchange
heatwiththesurroundingsbyconvectionandradiationorduetodirectcontactwithasolid
materialasinthecaseoftheelectricblanket. Thesurfacefilmisspecifiedandthefilmproperties
areassignedvaluestoallowappropriateamountofheattobeexchangedatthesurface. The
temperatureoftheenvironmentsurroundingthemodelisspecifiedbyprescribingasink
temperatureattherelevantsurfaces. Therefore,byspecifyingsetsofsurfacefilmsandfilm
properties,theFEmodelcanexchangeheatwiththesurroundings,simulatingtheheatflow
betweenthesurfaceofthemodelandtheenvironment,whetherthesurfacebelongstotheweldor
pipe,andalsobetweenthepipeandtheelectricblanket. Thesurfacefilmismadetofollowthe
evolutionoftheoutsidesurfaceasthedepositionofeachweldpassissimulated.
Figure6. Complete2DaxisymmetricFEmesh.
3.2 MaterialProperties
ThematerialpropertydatarequiredfortheFEthermalanalysishavebeenobtainedforthree
differentmaterials,namely,P92steel,Inconel82(IN82)andInconel625(IN625). Someofthe
dataareavailableinliterature,butsomehavebeenderivedeitherbyextrapolationtohigher
temperaturesorbyreferringtoothersimilarmaterialswithknownmaterialpropertydata. This
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approachhasbeenadopted,sinceparametricanalysesbytheauthorsofweldingresidualstresses
fordifferentmaterialshaveindicatedthatweldingresidualstressesingeneralaremostlysensitive
tothevalueofyieldstressaswellasthatofthecoefficientoflinearthermalexpansion(whichare
partoftheFEstructuralanalysis);theyaresignificantlylesssensitivetochangesinthermal
properties;moreover,heatfluxeswouldhavetobeadjustedtoobtainrealisticmoltenzones,which
wouldinturncompensateforinaccuraciesinthethermalproperties. Ithasalsobeenpossibleto
calculatemeltingtemperaturesfromthermodynamicsoftwarepackages. Thematerialproperties
thatneedtobespecifiedinthethermalanalysisarethethermalconductivity,density,specificheat
capacity,latentheatcapacity,solidusandliquidustemperaturesandheattransfercoefficients.
Figure7. ThermalconductivityandspecificheatcapacityintheFEmodel.
ThethermalconductivityofP92steelhasbeenassumedtobethesameasthatforP91steel,which
isavailableinliterature(Yaghi,2010). ThespecificheatcapacityofP92steelhasbeenobtained
fromliterature(Richardot,2000)fromroomtemperatureupto650°C,abovewhichithasbeen
assumedtoremainunchanged. BothmaterialpropertiesareshowninFigure7. Thesolidusand
liquidustemperaturesforP92steelhavebeencalculatedas1420°Cand1500°Cbyusing
MTDATAsoftwaredevelopedattheNationalPhysicalLaboratory(NPL)intheUKandtheyhave
beencorroboratedbythesamevaluespublishedforP91steel(Yaghi,2010). ThedensityforP92
steelisspecifiedinliterature(Richardot,2000)as7850kg/m3. ThelatentheatcapacityforP92
steelhasbeenassumedtobethesameasthatforP91steel,specifiedas260kJ/kg(Yaghi,2010).
ThethermalconductivityandspecificheatcapacityofIN625areprovidedinliterature(Special
Metals,2006)fortemperaturesupto982°Cand1093°Crespectively. Thesamevalueshavebeen
assumedfortheweldmaterialNIMROD625KSforthegiventemperaturerange,abovewhichthe
twothermalpropertiesareassumedtoremainconstantuptothemeltingpoint. Asthematerial
goesfromthesolidustotheliquidustemperature,thethermalconductivityisdoubledin
magnitudetocompensateforthestirringeffectsinthemoltenstate(Brickstad,1998). Thesame
thermalconductivityandspecificheatcapacityhavebeenassumedfortheweldmaterialUTP
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A068HHusedforthefirstpassduetothelackofdataforIN82. Itisworthnotingthattheeffect
ofthefirstweldpassonresidualstressesneartheoutsidesurfaceofthepipe,wheremostinterest
liesforsuchwallthickness,isexpectedtobenegligible. Thethermalconductivityandspecific
heatcapacityfortheweldmaterialsareshowninFigure7. ThedensityforIN625isgivenas
8440kg/m3(SpecialMetals,2006). Thisvaluehasbeenassumedforbothweldmaterials. The
latentheatcapacityforpurenickelislistedas297kJ/kg(TheEngineeringToolBox,cited2011).
Therefore,anapproximateandintermediatevaluebetweenthoseofP92steelandpurenickelof
280kJ/kghasbeenassumedfortheweldmaterials. Thesolidusandliquidustemperaturesfor
UTPA068HHhavebeencalculatedtobe1301°Cand1368°CandforNIMROD625KStobe
1250°Cand1345°Crespectively,usingthesoftwareThermoCalcClassicVersionS(TCC),
developedbytheFoundationofComputationalThermodynamicsinStockholmofSweden,and
utilisingThermotechNickelsDatabaseVersion7(TTNi7)(Saunders,1996).
Heatlossesatthesurfaceofthepipehavebeenmodelledbyprescribingappropriatevaluesforthe
coefficientofheattransferundertheAbaquscommandFilmProperty. Heatlosscoefficientsfor
P92steelandalsotheInconelweldmaterialhavebeenassumedtobethesameasthoseforP91
steel,giveninliterature(Yaghi,2005)tobe0.0668T(W/m2K)whenthetemperatureTisbelow
500°Cand0.231T–82.1(W/m2K)whenTisabove500°C. Asimilarapproachhasbeenadopted
tomodeltheeffectoftheelectricblanketonthepipe. Recognisingthattheblanketwould
fluctuateintemperaturesubstantiallyandwouldbeswitchingonandofftocontroltheinterpass
temperatureduringwelding,themodellinghasbeensimplifiedtohavingtheblanketataconstant
temperatureduringthedepositionofanyoneweldpass,prescribingaveryhighvaluetothe
coefficientofheattransferatthesurfacewithwhichtheblankethascontact,andcontrollingthe
sinktemperatureatthatsurfacetoobtainthedesiredtemperaturehistoryatthefive
thermocouples. Thevalueprescribedforthecoefficientofheattransferforthispurposeis200T
(W/m2K),whereTisthetemperatureofthepipe.
3.3 HeatFluxesandFusionZonesintheFEModel
Themainpartofthethermalanalysisistomodeltheeffectoftheheatsourceonthepipeduring
fusionwelding,i.e.theheatdeliveredbytheweldingarcintotheweldandsurroundingmaterial.
Thishasbeencoveredindetailforsimilarweldedpipesinapreviouspublication(Yaghi,2005).
Themodellingmethod,however,needstobemodifiedforthethermalanalysisofadissimilar
weldedpipe,asisthecasehere.
Ingeneral,theheateffectoftheweldingarconapipecanbemodelledbyprescribingauniformly
distributedheatflux(DfluxinAbaqus)foreachoftheweldpassesastheyaredeposited. Inthe
reportedwork,thefluxisassumedtofollowatriangularfunction(Yaghi,2005),whichstartsfrom
zeroandriseslinearlytoreachapeakathalftime,tosignifytheapproachoftheweldarc,and
thenitdecreaseslinearlybacktozeroatfulltime,tosignifythedepartureofthearc. Thewelding
speedwasdeterminedtobearound50mm/minforthefirstpassandrangedbetween152and
207mm/minfortheremainingpasses. Theweldingcurrentrangedbetween90and130A,andthe
DCvoltagerangedbetween9and10forthefirstpassandbetween24.3and26.5Vforpasses2to
36. TheheatfluxintheFEmodellastedfor10.7sforthefirstpass,5.9sforeachofthesecond
andthirdpasses,andbetween6.6sand7.6sforeachoftheremainingpasses. Themethodof
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