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Journal of Materials Science & Technology
jo u r n a l h o m e p a g e :w w w . j m s t . o r g
Research Article
Numerical investigation of a novel pattern for reducing residual stress in metal additive manufacturing
Li Sun
a, Xiaobo Ren
b, Jianying He
a, Zhiliang Zhang
a,∗aDepartmentofStructuralEngineering,NorwegianUniversityofScienceandTechnology(NTNU),Trondheim7491,Norway
bSINTEFIndustry,Trondheim7456,Norway
a rt i c l e i nf o
Articlehistory:
Received29March2020
Receivedinrevisedform19May2020 Accepted25May2020
Availableonline7August2020
Keywords:
Additivemanufacturing(AM) Depositionpattern Temperaturedistribution Residualstress Warpage
a b s t ra c t
Depositionpatternscansignificantlyaffectresidualstressdistributioninadditivemanufacturingpro- cesses.Inthispaper,anovelpattern,theS-pattern,isproposedforthemetaladditivemanufacturing process.Thefiniteelementmethodisusedtostudythetemperaturefieldandthestressfieldofacuboid structureundertheS-patternandfiveotherrepresentativepatterns:zig-zag,raster,alternate-line,in-out spiral,andout-inspiral.TheresultsshowthattheS-patternachievesthelowestvaluesofbothequivalent residualstressandmaximumprincipalresidualstress,andthewarpageoftheS-patternisclosetothat ofcounterparts.Byanalyzingthetemperatureandstressfieldsunderallpatterns,itisfoundthatthe residualstressdistributionisdeterminedbytheuniformityoftemperaturedistributionwhichiscorre- latedwiththepeaktemperaturesofcorners.Theequivalentresidualstressandthemaximumprincipal residualstressareinverselycorrelatedwiththeaveragepeaktemperatureandtheminimumpeaktem- peratureofcorners,respectively.Thesecorrelationsbetweentemperatureandresidualstressprovidean effectiveapproachtoevaluatetheresidualstressofdifferentpatternsandguidethedepositionprocess inpractice.
©2020PublishedbyElsevierLtdonbehalfofTheeditorialofficeofJournalofMaterialsScience&
Technology.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/
licenses/by/4.0/).
1. Introduction
Additivemanufacturing(AM)canbeusedtoprintaproductby successivelyaddingthemateriallayerbylayerguidedbyathree- dimensionaldigitalmodel[1,2].Accordingtothefeedstockdelivery system,AMcanbedividedintotwocategories:directedenergy depositionandpowderbedfusion[3].Forbothprocesses,thepow- derorwireismeltedbyafocusedenergysourceandconsolidated rapidly[4].Residualstressandresidualdeformationwillinevitably beinducedbytemperaturegradient,whichwillworsenfatigueand fractureresistance,andevenleadtothefailureofcomponents[5].
AsoneofthekeychallengesinAM,residualstressissignificantly influencedbytheprintingprocess[6].Hence,theoptimizationof theprintingprocessesforreducingresidualstressanddeformation isacriticalissue.
Scanningordepositionpatternhasaremarkableeffectonresid- ualstresssinceitinfluencesthetransienttemperaturedistribution intheprintingprocessgreatly[7].Itisanessentialandcomplex issueforAMbecauseitaffectsmanyotheraspects,suchasdefor-
∗Correspondingauthor.
E-mailaddress:[email protected](Z.Zhang).
mation,partstrength,fabricationquality,anddepositionefficiency.
Inthepresentstudy,sixrepresentativebasicpatternsareusedfor AM,raster,zig-zag,alternate-line,in-outspiral,out-inspiral[8], andfractal,asshowninFig.1.Theraster,zig-zagandalternate- linearedirection-parallelpatterns,whileout-inspiralandin-out spiralarethecontour-parallelpatterns.Thedirection-parallelpat- ternsaremostcommonlyusedduetogoodproductquality,simple planningalgorithmsandwideapplicabilityforvariousstructures.
Amongthem,therasteristhemostpopularpatternforthedirected energydepositionprocess.The alternatelinepattern is derived fromtherasterpattern,inwhichthepassesarealternateandthe accumulationofheatcanbedepressed,sothatthetemperaturegra- dientandtheresidualstressarereduced.However,itisinsufficient duetotheneedoftheintervalsbetweendepositionpasses.The zig-zagpatternismoreefficientthantherasterpatternbecauseof fewerstartsandstopsoftheenergysource,whichisthemostcom- monapproachincommercialAMsystems[9].Duetotheexcessive accumulationattheturningpointsofthepatterns,precisecon- trolofprocessparametersisrequiredforthezig-zagpattern[7].
Incontrast,thecontour-parallelpatternsarecontinuousbutthey arenotsuitableforfillingpatterns.Theyarenotallowedtogener- ateweavepatternswhichishelpfultoreducedefectsandimprove thestrength.Inordertoobtainbothgoodgeometricaccuracyand https://doi.org/10.1016/j.jmst.2020.05.080
1005-0302/©2020PublishedbyElsevierLtdonbehalfofTheeditorialofficeofJournalofMaterialsScience&Technology.ThisisanopenaccessarticleundertheCCBY license(http://creativecommons.org/licenses/by/4.0/).
L.Sunetal. JournalofMaterialsScience&Technology67(2021)11–22
Fig.1.Representativedepositionpatterns:(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;(f)Hilbert.
highconstructionefficiency,thecombinationofcontour-parallel patternsandzig-zagpatternisdeveloped,andthecontourandzig- zagpatternsareappliedtofilltheinternalareaandtheboundary areaofthepart,respectively[10,11].Thefractalpatternisstillat theprimarystageoftheapplicationasitisonlyusedinthelaser processduetomanycorners[7].
Manyresearchershavestudiedresidualstressesandwarpage underdifferentpatterns[7,[12–18,20],[12–18,20][49]].Thecuboid structures with rectangular or square section, thin-walled, enclosed, and cross structures were investigated, and the fac- tors affecting residualstressand warpage wereanalyzed. Most studies focusedonthewidth-wisezig-zag,length-wise zig-zag, out-inspiral,andin-outspiralpatterns.Amongdirection-parallel patterns,thewidth-wisezig-zagpattern showedthemaximum residualstressanddistortion,whilethelength-wisezig-zagpattern resultedinlowerdistortionduetomorehomogeneoustempera- turedistribution.Forcontour-parallelpatterns,theout-inspiral resultedinhigherresidualstressesbecausetheheatwasaccumu- latedinwardandconcentratedinthecenterpartasthedeposition process, while the heat dissipated outward and thus the tem- peraturedistributionwasmorehomogeneousunderin-outspiral pattern[21].Manystudieshaveinvestigatedtheeffectofpattern elementlengthontheresidualstressandconcludedthatashorter elementcouldlowertheresidualstressandtheislandscanning couldreducetheresidualstressandpartdeformation[16,22–25].
Schröfferetal.[26]proposedtheislandplanningstrategywhich achievedmorehomogeneoustemperatureandstressdistributions.
Zaehetal.[27]comparedtheresidualstressunderisland,unidi- rectional,andalternatingscanningstrategiesandconcludedthat chequerboardproducedlowestresidualstress.Luetal.[28]stud- iedtheislandsizeeffectonresidualstressinselectivelasermelting andfoundthatislandwithadimensionof5mm×5mmexhibited lowerresidualstressthantheislandswithadimensionof7mm×7 mmor3mm×3mm.Basedontheislandpattern,Ramosetal.[29]
proposedtheintermittentstrategytocontrolthescanningorder for theselectivelasermeltingprocess,whichcouldreduceheat accumulationbyavoidingtheflowingislandadjacenttothetwo previousislands.Parryetal.numerallystudiedtheeffectofdepo- sitionpartgeometryontheresidualstressdistributioninselective lasermelting.Theresultsshowedthatwhenthescanningvector
lengthwaslessthan3mm,thelaserscanningstrategyplayedan importantroleintheresidualstress,whilewhenthescanningvec- torlengthwasmorethan3mm,thelaserscanningstrategyhad nosignificanteffectontheresidualstress.Parryetal.alsocon- cludedalternatescanvectordirections producedlowerresidual stress,whichwasveryusefulforscanningstrategydesign[30,31].
Somestudieshavecomparedtheresidualstressesofdirection- parallel,contour-parallel,andfractalpatterns.Somashekara’s[32]
workshowedthattherasterpatternachievedthelowerresidual stressesthanthespiralpatterns,owingtothesmallerthermalmis- matchbetweenthedepositionmaterialandthesubstrateaswellas thelowersecant-mismatchtemperaturerateatthetopandbottom surfaceofthesubstrate.Maetal.[33]numerallystudiedthemax- imumdeformationunderzig-zagandfractalscanningpatternsin theselectivelasermeltingprocess,andfoundthefractalscanning patternexhibitedsmallerdistortion.Yuetal.[34]experimentally studiedthepartdistortionofraster,fractal,out-inspiral,andin-out spiralpatternsinlasersolidforming.Theresultssuggestedthatthe Hibertpatternpossessedthelowestdistortionfollowedbythein- outspiralpattern.Yan[7]comparedthesixrepresentativepatterns andconcludedthatthealternate-linepatternexhibitedthemini- mumresidualstressandwarpagewhich wasmainlydependent onthetransienttemperaturegradients.Chengetal.[21]evaluated theresidualstressanddeformationoftheisland,spiral,andzig-zag patternswithdifferentanglesofrotationinselectivelasermelting.
Theirfindingsshowedthattheout-inscanningpatternproduced themaximumresidualstress.Comparedtootheranglesofrotation inzig-zagpatterns,the45◦inclinedlinezig-zagpatternattainedthe lowestresidualstressesanddeformation.Despitethoseresearches ontheoptimalpatternforreducingresidualstress,mostofthem focusonthesixtypicalpatternsandtheresidualstressisstilla challengeforAM.Noneoftheexistingpatternscanperformwellin allaspects:partstrength,printingefficiency,applicability,surface accuracy,andreducingresidualstress.Moreover,therelationships betweentransienttemperatureandresidualstressareonlyquali- tativelydiscussedtoexplainhowthepatternsaffectresidualstress [7,14,17].Renetal.appliedtwocriteriatoevaluatethelocalized andoverallheataccumulationandproposedawaytofindtheopti- malscanningpatternwithminimumdistortion[19].However,the residualstresswasnotconsideredinthiswork.Hencenewpattern
Fig.2. Finiteelementmodel.
possessingmultipleadvantages,especiallyminimizingtheresidual stress,isrequired.Simplebutquantitativecorrelationsbetween temperature and residualstress arehighly desiredfor compar- ingresidualstressesunderdifferentpatternsandoptimizingAM patternforindustrycontext.
Inthispaper,anovelS-patternisproposedforreducingresid- ualstressinmetalAMbasedonfiniteelement(FE)analyses.The temperature,residualstress,andresidualwarpageunderthenew patternarestudiedandcomparedwiththeresultsoffivetypical patterns.Thecorrelationsbetweenthetransienttemperatureand resultedresidualstressareestablishedforscreeningthepatterns.
Insection2,a3Dthermal-mechanicalmodelisconstructedtostudy thethermalfieldandresidualstressdistribution.Therequirements ofapatternplanningstrategyforAMandtheadvantagesanddis- advantages ofsixtypicalpatternsareanalyzed.Accordingly,the S-patternisproposedinsection3.Detailedresultsabouttheeffect ofpatternsonthetransienttemperaturefield,residualstress,and warpagearepresentedinsection4.Thecorrelationbetweentem- perature andresidualstressis discussedinsection5.The main conclusionsandfutureworkaresummarizedinsection6.
2. Numericalmethodology
Numericalmodelingisagoodwaytostudythecomplexthermo- mechanical performance with relations to process [35]. In this work,theFEmethodwasusedtoscrutinizetheeffectofdeposi- tionpatternsonthetransienttemperaturefield,residualstress, andwarpage.
Themodelwasonesquaredepositionlayerwiththedimen- sions of120mm×120mm×2.23mmandasquare substrate withthedimensionsof200mm×200mm×20mm,asshown inFig.2.Thedepositionlayerwasdividedinto36×36×2ele- mentsandtheaveragemeshsizewas3.3mm×3.3mm×1.1175 mm.Relativelycoarsemeshwasassignedintheremainingpart.
Aluminumalloy2319wasselectedinthisstudy.Themeltingrange was543−643◦C,andthemassdensitywasassumedtobe2823 kg/m3andtemperatureindependent.Thetemperature-dependent materialpropertiesofAA2319,suchasthethermalconductivity coefficient,thermalexpansioncoefficient,temperature-dependent yieldstress,areobtainedfromRef.[36,37]andpresentedinFig.3.
Thewirearcadditivemanufacturingprocesswassimulatedin ABAQUS2018andthepathsoftheaddingmaterialandheatinput weredefinedbyadditivemanufacturingplugin[39].Theelements areactivatedbytheefficientmethod ¨progressiveelementactiva- tion ¨and theprocessiscontrolledbytheprogrammedtime[39].
Theuncoupledthermal-mechanicalanalysisincludedtwostages:
thethermalanalysisandmechanicalanalysis.Theproceduretypes wereheattransfer(transient)andstaticgeneral,respectively.There
Table1
Parametersofthedouble-ellipsoidheatsource.
af(mm) ar(mm) b(mm) c(mm) Q(w) ff fr
4 6 5 5 5000 0.6 1.4
weremanyfactorsaffectingthemignitudeofresidualstress,such asheatsource,weldingspeed,pre-heattemperature[6].Tomake theresidualstressresultsunderdifferentpatternscomparable,all thesimulationswereperformedunderthesameparametersand theonlyvariablewasthedepositionpattern.
Forthethermalanalysis,theelementtypewaseight-nodelinear brick(DC3D8).Theconductionlossofthebottomsurfaceismod- eledbyanequivalentconvectioncoefficient(123W/m2k)[40–42].
Whiletheothersurfacesofthemodelweresubjectedtoradiation andconvectionheatloss(radiationcoefficientof0.8andconvective coefficientof8.5W/(m2K)[41,42]).Asufficientlylongwaitingtime (5000s)wasusedinthecoolingstagetoguaranteethemodelto becooleddowntoroomtemperaturenaturally.Themovingheat sourcewasa double-ellipsoidheatsource[43],whereaf andar werethelengthofthefrontandtherearellipsoidoftheheatsource.
bwasthehalfwidthandcwasthedepthoftheheatsource.Qwas thepowerinput.Thefractionfactorsoftheheatfluxinthefront andrearpartswererepresentedbyffandfr,respectively,andthey heldtherelationthatff+fr=2.Theparametervaluesareshown inTable1.
Afterthethermalanalysis,thetransienttemperaturefieldout- putwasimportedintothemechanicalanalysis.ThesameFEmesh wasusedwhiletheelementtypechangedtoC3D8R.Thebottom ofthesubstrateismechanicallyfixedduringthedepositionpro- cessandthenreleasedafterthemodelhasbeencooleddownto roomtemperaturetoobtaintheresidualstressanddeformationof thepart.Thephasetransformationandthesofteningeffectofthe materialarenotconsideredinthismodel.
3. Depositionpatternsinadditivemanufacturing
Themost representative patterns used in AM areshown in Fig.1(a–e).Anidealpatternshouldperformwellinmanyaspects.
Therequirementsofapatternaresummarizedasfollows[9].
1Fewerpatternpasses:thenumberofpatternpassesdependson thenumberof startsand stopsof energy source.More starts andstopswillintroducelargercumulativedeviationsandlower depositionefficiency.Therefore,toimprovethesurfaceaccuracy anddepositionefficiency,thenumberofpatternpassesshould beminimizedwithineachlayertoreducethenumberofstarts andstops.Withthisregardacontinuouspatternispreferable[9].
2Fewerpatternelements:patternelementsareasequenceofline segmentsconnectingtoformthepattern,dependingonthenum- berofturns.Thefeedstockandheatinputareeasilyexcessiveat thestartandendpositionsofpatternelements.Excessiveenergy inputwillleadtovoids[44].Hence,thenumberofpatternele- mentsshouldbeminimizedtoimprovethesurfaceaccuracyand finalpartquality.
3Allowancetogenerateaweavepattern:theweavepatterncan begeneratedbythecrosspassesamonglayers,whichisbenefi- cialforthecomponentstrength.Thedirectional-parallelpatterns allowgeneratingweavepatternsbychangingthedepositionori- entationamongdifferentlayers.Thecontour-parallelpatterns are rarely used as fill patterns becauseeach path is directly aboveeachotheroneach layer.Thatcanseverelydeteriorate thestrengthoftheparts[7].
4Minimumresidualstressandwarpage:thepatternshaveagreat impactonresidualstressandwarpagewhicharethekeychal- lengesin termsofstructuralintegrity andthefinal qualityof
L.Sunetal. JournalofMaterialsScience&Technology67(2021)11–22
Fig.3.PhysicalpropertiesofAA2319:(a)thermalconductivityandspecificheat,(b)coefficientofthermalexpansion,(c)Young’smodulusandyieldstrength,and(d) strain-hardening[36,38].
Fig.4. Theproposeddepositionpattern:Spattern(a)Onelayer;(b)Multi-layer.
printedcomponentsinAM.Thepatternswhichcanachievemin- imumresidualstressesandwarpagearefavorable.
5 Adjustable passlength: themaximum residual stress can be reducedbyshorteningthelengthoftheconstituentpassesofthe pattern.Hence,adjustablepasslengthhelpstoreduceresidual stressandwarpage.Besides,adjustablepasslengthallowsthe patterntobeappliedindifferentstructures.
Table2summarizestheadvantagesanddisadvantagesofeach pattern.Asisshown,noneoftheexistingpatternscanpossessall theadvantageslistedabove.In thiswork,a newpattern,which combinesmultipleadvantagesofotherexistingpatterns,isdevel- oped. Since the pattern is similartothe letter “S”,it is named S-pattern,asshowninFig.4(a).
InFig.4(a),thestartandendpositionofSpatternaremarked ingreenandpurplepoints.Thenumbersshowthesegmentorder.
ItisobviousthattheS-patterniscontinuousandhas13lineele- mentsduetotheturns,whilethelineelementsnumbersofthesix typicalpatternsinFig.1(a)-(f)are8,8,8,16,16,51,respectively.
Hence,thelineelementnumberofS-patternissmallerthanother contour-parallelpatterns,whichwillleadtolessdepositionerror.
Fig.5.Spatternintheshapemadeupofsquaresandrectangles.
TheS-patternallowsgeneratingaweavepatternamongdifferent layers,asshowninFig.4(b).Forshapesmakingupofsquaresand rectangles,thematchingSpatterncanbegeneratedbyadjusting thelengthofpassesandthenumberofturns,asshowninFig.5.
Besides,itshouldbenotedthatthelengthofthehorizontalpasses,
Fig.6. Thetransienttemperaturedistributionsofallpatternsattheendofdepositionprocess(unit:◦C,thecolorscaleofallsubfiguresisfrom20◦Cto643◦C(liquidus temperature)),(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;(f)S.
likesegments2,4,6,shouldbeconsistentsincethenumbersofthe verticalpassesaroundthehorizontalpassesarethesame.However, theSpatternisunsuitableforround,irregular,orothercomplex shapes.Forlargesizesorcomplexstructures,itisrecommended todivideintosmallsquaresorrectangles,thenapplytheSpattern toeachsub-dividedregion.Inthiswork,theeffectofdifferentpat- ternsontheresidualstressandwarpagewillbeinvestigated.Since fractalpatternsarepresentlyusedonlyinselectivelasersintering [7],itisnotconsidered.
4. Results
4.1. Transienttemperaturefield
Tostudythetemperaturedistributionhistoryunderdifferent patterns,thetransienttemperaturedistributionsofallpatternsat theendofthedepositionprocessareshowninFig.6.Thegreycolor showsthemeltingzone.Itisobservedthatthetemperaturegradi- entsarerelativelyhighnearthemeltingpoolsandthedeposition patternshavelittleeffectonthemeltingpoolsize.
However, the deposition pattern remarkably influences the temperature distribution. For zig-zag, raster, and alternate-line deposition patterns (Fig. 6(a–c)), the temperature distribution characteristicsaresimilarsinceallofthesepatternsaredirection- parallelpatterns.Allofthemaresymmetricallydistributedalong the x-direction,and thehigh-temperatureregions are nearthe bottom.Thecorrespondingtemperaturesforrasterandzig-zagpat- ternsareveryclose,whilethetemperaturesunderalternate-line patterns are relatively high. Hence the alternate-line deposi- tion pattern yields more uniformtemperature distributionand lowertemperaturegradient.Similartoalternate-linepattern,the S-pattern(Fig.6(f))alsoachievesmoreuniformtemperaturedis- tribution than others. It is because both alternate-line pattern and S-pattern havegood heat transferperformance. Theout-in spiraldepositionpattern(Fig.6(d))produces acircular symme-
trytemperaturedistributionandconcentratesahigh-temperature area(over400◦C)aroundthemeltingpool.Comparedwithother depositionpatterns,ithasamoreconcentratedheatdistribution.
Theapproximatediagonalsymmetrytemperaturedistributionis shownunderthein-outspiraldepositionpattern(Fig.6(e)),which caneffectivelyreducethesubstratedistortion.
4.2. Residualstresses
Inthiswork,theequivalentandmaximumprincipalresidual stress(eand1)arestudied,sinceeisrelevanttoplasticyielding andthe1canbeconsideredasaprimeindicatoroffatigueand fractureperformance[45].Figs.7and8showthetopvieweand 1 distributionofthesixdepositionpatternsafterremovingthe constrainsfromthesubstratebase.
Itisobservedthat,forallthepatterns,themaximum1(1,max) isattheedgeofthesquaredepositionarea.Thisisbecausethat thecoolingrateattheedgeofthesquaredepositionareaishigher than the interior and the temperature difference between the depositionareais larger. 1 is usuallydependentonthelongi- tudinalstress(paralleltothescanvector),whichincreaseswith scanvector lengthduetothepresence ofthethermal gradient paralleltothescanvector.Hence,1,maxisatthesquaredeposi- tionareainsteadofthesubstrate.However,stressconcentration happensaroundthefourcornersofthesquare depositionarea, whichiscausedbythesuddenchangeinthegeometryofthemode.
Hence,themaximume(e,max)occursnearthefourcornersofthe squaredepositionareaatthesubstrate.Thestressdistributionsof zig-zag(Fig.7and8(a))andraster(Fig.7and8(b))depositionpat- ternsareprettysimilar.Bothofthemhavehigherresidualstress atthe top.The out-inspiral(Fig.7 and 8(d)) and in-outspiral (Fig.7and8(e))patternproducecircularsymmetrystressdistri- butions,andtheresidualstress oftheout-inspiral isrelatively higher.Thealternate-linepattern(Fig.7and8(c))andS-pattern (Fig.7and8(f))showlowerandmorehomogeneousresidualstress
L.Sunetal. JournalofMaterialsScience&Technology67(2021)11–22
Fig.7. Equivalentresidualstressdistributionofdifferentdepositionpatterns,(topview,unit:Pa),(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;
(f)S.
Table2
SummaryofAMdepositionpatterns.
Zig-zag Raster Alternate-line In-outspiral Out-inspiral Hilbert S
Continuous √ × × √ √ √ √
Lesspatternelements √ √ ×
weavepattern √ √ √
× × √ √
Adjustablepasslength × × × × × √ √
Lowerresidualstress × × √ √
× √ √
Lowerwarpage × × √
Note:√
-Positive;×-Negative;-Medium(betweentheworstandbest).
distributionsthanotherpatterns,inconsistentwithtemperature distribution.
Thenormalizede and1 alongthediagonalofthetopsur- face of the deposition layerare plotted in Fig. 9. Asindicated, for all patterns, the maximum magnitudesof residual stresses occur at both ends of the curves. For most of nodes, the S- pattern achieves thelowestnormalized residualstresses, while theout-inspiralpatterninducesthehighestnormalizedresidual stresses.
Inordertocomparethemaximumresidualstress,thee,max
and1,maxfromlargesttosmallestaresummarizedinFig.10.For botheand1,theS-patternhastheminimumvalues.Indetail, thee,maxand1,maxofS-patternare10.8%–36.9%and9.5%–32.7
%lowerthanthoseoftheotherfivepatterns,respectively.
4.3. Warpage
WarpageisanothermajorchallengeintheAMprocess,which cancausepartdistortion,lossofgeometrictolerances,andcracks [46,47].Moreover,residualstressandwarpageoftenoccursimulta- neouslybecausetheyinteractwitheachother.Hence,inthiswork, thewarpagesunderdifferentpatternsarealsostudied.
Fig.11 shows thewarpage inZ-directionunder thesixpat- terns. For all patterns, the warpage at the starting deposition positionislargerduetothehighertemperaturegradientbetween
thedepositionmaterialandthesubstrateattheinitialposition.
Thewarpage distributionofthezig-zag patternand rasterpat- tern are similar and almost symmetric in theY-direction. The warpagedistributionoftheout-inspiralandin-outspiralpattern areapproximativelysymmetricalongthediagonallineofthesub- strate.Fortheout-inspiralpattern,thedisplacementofthecenter partisnegativewhilethein-outspiralpatternleadstoopposite results. Smallerwarpage canbe foundunderthe alternate-line pattern,andpositiveandnegativedisplacementarealternatecor- respondingtothepattern inthedepositionarea.For Spattern, thewarpage offourcornersandthefirstScontourisrelatively high.Amongallpatterns,thein-outspiralpatterncanachievethe mosthomogeneouswarpage,sincetheheatisaccumulatedout- ward.
InordertocomparethedeformationofthesubstrateinFig.11, theUzalongthediagonaldirectionisnormalizedbythethicknessof thesubstrate(d)andthenormalizedwarpageUz/dissummarized inFig.12.Forthecenterpart,allthecurvescollapse.Attheedge, itisobservedthatthein-outspiralpatternachievestheminimum normalizedwarpage.
Thenormalized warpages at both ends are added toobtain themaximumnormalizedwarpageUz,max/dofdifferentpatterns, whichareplottedinFig.13.Thein-outspiralpatterncanachieve thelowestwarpage,whiletherasterpatternproducesthehighest.
Thereisnomajordifferencebetweenotherpatterns.
Fig.8. Maximumprincipalresidualstressdistributionofdifferentdepositionpatterns,(topview,unit:Pa),(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e) In-outspiral;(f)S.
Fig.9. Normalizedresidualstressalongthediagonaldirectionofdifferentpatterns,(a)equivalentresidualstress;(b)maximumprincipalresidualstress.
Fig.10.Normalizedmaximumresidualstressalongthediagonaldirectionofdifferentpatterns,(a)equivalentresidualstress(b)maximumprincipalresidualstress.
L.Sunetal. JournalofMaterialsScience&Technology67(2021)11–22
Fig.11. Deformationdistributionofdifferentdepositionpatterns(unit:mm),(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;(f)S.
Fig.12.Normalizedwarpageofdifferentdepositionpatterns.
Fig.13.Normalizedmaximumwarpageamongdifferentdepositionpatterns.
5. Discussion
5.1. Residualstressforvariouspatterns
Asabovementioned,thedepositionpatternsshowasignificant influenceonresidualstress.Toexploretheoriginoftheresidual stressdifferencesin thesixpatterns,thetemperatureand final residualstressdistributionresultsareanalyzedfromtheperspec- tiveofdepositionvectorsequence,lengthanddirections.
ForSpattern,thepriordepositionvectors(1,2,3,4,5)inFig.4 aremoredispersedinthedepositionareacomparedwithotherpat- terns,whichhelpstoimprovetheefficiencyofheatdiffusiondueto agreatersurfaceareaforheatdissipation.Hencethetemperature distributionismoreuniforminsteadofheatbeingconcentrated inthedepositionarea.Thepriordepositionvectors(1,2,3,4,5)can alsohelptoquicklypreheatthewholesubstrateandreducethe magnitudeof thetemperature gradientfor thenextdeposition vector.Furthermore,theSpatternis acontinuouscontourpat- tern,andthesubsequentdepositionvectors(6,7,8,9...)arealong thepreviousvectors. Thiswill alsopreventthe heatfrom get- tingconcentratedin thewholedepositionprocess.In thesame manner,thealternate-linepatterncanachievemorehomogeneous temperaturedistributionand lowerresidualstressesthanother typicalpatterns.Fortheraster, zig-zagand out-inpatterns,the subsequentdepositionvectorsareadjacenttothepriordeposi- tionvectors. Dependingonthedepositionvector sequence,the heataccumulatedat oneside or thecenterpartof thedeposi- tionareaover time, asshown in Fig. 6(a),(b) and (d).For the in-outpattern, theheat willaccumulate around theedges due totheoutwarddepositionvectors.However,thehighheatdissi- pationefficiencyattheedgewillreduceheataccumulation.The temperaturedistributionunderthein-outpatternbecomesmore uniformandthustheresultantresidualstressislowerthanthat oftheraster,zig-zag,andout-inpatterns.Inconclusion,themain reasonthattheSpatterncanobtainthelowerresidualstressis thatthedepositionvectorsaremoreuniformlydistributed over time.
Parryetal.foundthatanincreasingmeanscanvectorlength couldraisetheoverallmagnitudeofresidualstresses.Thisisdueto
Fig.14.edistributionofthesubstratebeforeremovingtheconstraint(bottomview,unit:Pa),(a)Zig-zag;(b)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;
(f)S.
Table3
Meanandvarianceofdepositionvectorlengthsfordifferentpatterns.
Patterns Raster Zig-zag Alternate-line Out-inspiral In-outspiral S
Mean(mm) 12 12 12 6.545 6.545 7.15
Variance 0 0 0 9.840 9.840 7.028
theriseofthelongitudinalstresswithscanvectorlength,whichis themaincontributiontostressbecauseofitslargethermalgradi- entparalleltothescanvector[30,31].However,shortscanvector lengthmightcauseaheataccumulationwhichmayleadtohigh residual stress locally. Hence,lower fluctuations of scan vector lengthcouldreducetheriskofhigherresidualstress.Themean andvarianceofdepositionvectorlengthsfordifferentpatternsin thisworkaresummarizedinTable3.Themeandepositionvector lengthoftheSpatternismuchshorterthanthatofraster,zig-zag andalternate-linepatterns,whichisoneofthereasonswhythe residualstressoftheSpatternissmaller.Forout-inandin-outpat- terns,themeandepositionvectorlengthsareslightlysmallerthan thatofSpatterns.However,duetotheveryshortdepositionvec- torsinthecenter,theirvariancesarelargerthanthatofSpattern.
Thispartlyexplainswhytheout-inandin-outpatternsshowhigher residualstressthanSpattern.
Accordingtotheabovediscussion,boththemeanandvariance ofdepositionvectorlengthsareimportantforresidualstress.In Parry’swork,itisrecommendedthattoavoidtheshortadjacent depositionvectors(<2.5mm)andlongdepositionvectors(>5mm) inselectivelasermelting.Itisthusrecommendedtodividethelarge structuresintosmallislands.ThiscanbeachievedbytheSpat- tern,inwhichthedepositionvectorlengthisadjustable.Theexact valueofthecriticaldepositionvectorlengthremainstobestudied forwirearcadditivemanufacturing.However,itshouldbenoted thatdifferentresidualstressdistributionmaystilloccur,likeout-in spiral,in-outspiralorraster,alternate-linepatterns,eventhough theypossessthesamemeanorvarianceofthedepositionvectors lengths.Thismaystemfromthefactthattheresidualstressesare alsodependentontheotherfactors.
Moreover, the alternate directions of scan vectors can also reducetheresidualstressandproduceamoreanisotropicstress fieldin thecomponent[31]. Comparedtootherpatterns,theS patternhasamoreuniformdistributionofthedepositionvector directions,andmostoftheadjacentvectorsareindifferentdirec- tions,asshowninFig.5.Hence,itcanbeexpectedthatthealternate directionsofscanvectorshelpSpatterntoachievemoreanisotropic stressfieldandlowerresidualstress.
Insummary,uniformlydistributeddepositionvectorsequence, lower mean and variance of the deposition vector length, and alternatedepositionvectordirectionsfavorreducedresidualstress withinamesoscaleregion.
5.2. Correlationsbetweenthetemperatureandresidualstresses Asmentionedbefore,theresultedresidualstressandwarpage aredependentonthe temperaturefield. For mechanical analy- sis,therearetwostages:beforeremovingtheconstraintandafter removingtheconstraint.Toanalyzetherelationshipbetweenthese two stages, the equivalent stress distributions of the substrate undersixpatternsbeforeandafterremovingtheconstraintare showninFigs.14and15.Itcanbefoundthatthecorresponding stressfieldsbeforeandafterremovingtheconstraintarecorre- lated.ThemoreuniformthestressdistributionisinFig.14,the lowertheresidualstressisinFig.15.Forexample,thesubstrate residualstressdistributionoftheS-patternisrelativelyhomoge- neous,whileaheterogeneousdistributionisobservedintheout-in spiralpatternforming,seeFig.14(d)and(f).Afterremovingthe constraint,theS-patternshowsthemosthomogeneousdistribu- tionofresidualstress,whiletheout-inspiralpatternshowsthe
L.Sunetal. JournalofMaterialsScience&Technology67(2021)11–22
Fig.15.edistributionofthesubstrateafterremovingtheconstraints(bottomview,unit:Pa),(a)Zig-zag;(s)Raster;(c)Alternate-line;(d)Out-inspiral;(e)In-outspiral;
(f)S.
Fig.16. Peaktemperaturesofthecornersofdifferentdepositionpatterns.
mostnon-uniformdistributionofresidualstress,seeFig.15(d)and (f).
Theaboveanalysissuggeststhatthefinalresidualstressisdeter- minedbytheuniformityofthestressdistributionbeforeremoving theconstraintwhichdependsonthemagnitudeoftheedgestress sincetheresidualstressesinthecenterportionarealmostequalto theyieldstress.Furthermore,thetemperaturedistributiondeter- minestheuniformityofthestressdistributionbeforeremovingthe constraintandtheedgestressdistributionisrelatedtothepeak temperaturesofedgenodes.Hence,thepeaktemperaturesofthe fourcorners,whichrepresenttheuniformityofthetemperature distribution,canbeusedtoanalyzetheresidualstressdistribution.
Fig.16summarizesthepeaktemperaturesofthefourcorners underthesixdifferentdepositionpatterns.Thepeaktemperatures oftherasterisveryclosetothatofthezig-zag,andsameapplies totheout-inandin-outspiral,owingtothesimilardepositionpat- terns.Forraster,zig-zagandalternate-linepatterns,theTp1andTp2 aresmallerthanTp3andTp4,whileallofthefourpeaktemperatures arecloseforout-inspiralandin-outspiralpatterns.Itisbecause
thecontour-parallelpatterns(in-outspiral,out-inspiral)canpro- ducerelativelyuniformtemperaturedistributioninalldirections whilethedirection-parallelpatterns(raster,zig-zag,andalternate- line)generateconcentratedhightemperatureatoneend.Sinceheat accumulationinthedepositionareaisdepressed,thepeaktemper- aturesunderalternate-linepatternandS-patternarehigherthan thoseofotherpatterns.
Todeveloptherelationshipsbetweentheresidualstressandthe peaktemperaturesofthecorners,theaveragepeaktemperatures andminimumpeaktemperaturesunderthedifferentdeposition patternsareplottedinFig.17(aandb).Itcanbeseenthattheorder ofTp,aveandTp,minareoppositetothatofe,maxand1,max(Fig.10).
Hencee,maxand1,maxareinverselycorrelatedwiththeaverage peaktemperatureandtheminimumpeaktemperatureofcorners, respectively.Inotherwords,ifthepatternproduceshigherpeak temperatureattheedgepart,itwillachievelowerresidualstress.
Thecorrelationsprovideasimpleyeteffectiveapproachtocom- paretheresidualstressunderdifferentpatternsandguidancefor optimizingpatterntoreduceresidualstress,whichcanbeeasily usedinpractice.
Basedonthesimulatedthermalfield,Renetal.proposedan evaluationmethodtodeterminetheoptimalscanningpatternwith minimaldistortion [49]. In this method,twocriteria werepro- posed: (1) theaverageand maximum temperatureswithinthe movingmelt-poolregionateveryunitsimulationstep;(2)tem- peraturedistributionvarianceofthewholepart[49].Theywere usedtoevaluatetheextentoflocalizedandoverallheataccumula- tion.Inourwork,themaximumtemperaturesofthefourcorners ofthesubstrateduringtheentiredepositionprocesswereusedto evaluatetheextentofoverallheataccumulation.Thatistosay, theuniformityoftemperaturedistributionofcuboidstructurewas representedbythepeaktemperaturesofthefourcorners.Thecor- relationsbetweenthepeaktemperatureandtheresidualstress weredeveloped.Thelocalizedheataccumulationwasnotconsid- eredinthisworkduetoitsdependenceontheoveralltemperature distributionuniformity.ItwasalsodemonstratedinRen’sworkthat thelargestvalueoftemperaturedistributionvarianceofthewhole
Fig.17.(a)Averageand(b)minimumpeaktemperaturesofdifferentdepositionpatterns.
partwaspositivelycorrelatedwiththelargestnormalizedmelt- poolregionmeantemperature[49].ComparedwithRen’smethod, theevaluationmethodinourworkismorestraightforwardand themaximumtemperaturescanbeeasilyobtainedinexperiments, withoutsimulations.
Since the heat transfer process and deposition process of directed energy deposition are similar to those of the powder bed additive manufacturingprocess, theS-pattern and correla- tionsbetweenthepeaktemperatureandtheresidualstresscan alsobeappliedinthepowderbedadditivemanufacturingprocess.
However,thecorrelationsarelimitedtothecuboidstructure.For othergeometries,althoughtheresidualstressdistributionisalso relatedtotheuniformityoftemperaturedistribution,theunifor- mityoftemperaturedistributionshouldbere-evaluated,especially forcomplexstructures.Itshouldbenotedthatthisworkisathe- oretical study,and potentialcollaborationsontheexperimental studyarealwayswelcome.
6. Conclusion
Inthiswork,aso-calledS-patternwasproposed.Theresidual stressandwarpageoftheS-patternandtheotherfivetypicalpat- ternswerestudiedbytheFEmethod.Theresultsshowedthatthe S-patternachievedtheminimumresidualstressincludingequiv- alentresidualstressandmaximumprincipalresidualstressdue tomoreuniformlydistributeddepositionvectorsequence,lower meanandvarianceofthedepositionvectorlength,andalternate depositionvectordirections,whilethewarpageofS-patternwas veryclosetothelevelofotherpatterns.Inaddition,therequire- ments ofa pattern planningstrategyfor AMweresummarized andtheS-patterncouldcombinethevariousadvantagesofexist- ingmethods,suchascontinuous,fewersegments,adjustablepass length,andallowinggeneratingaweavepatternamongdifferent layers.TheS-patterncouldbeusednotonlyinthedirectedenergy depositionbutalsointhepowderbedfusionadditivemanufactur- ingprocess.Hence,theS-patterncanbeconsideredastheoptimum oneamongthesixdepositionpatternsandispromisingforAM.
Theresidualstressdistributionwasdeterminedbytheunifor- mity oftemperature field, which wascorrelated withthepeak temperaturesof corners.Theequivalentresidualstressand the maximumprincipalresidualstresswereinverselycorrelatedwith theaverageandtheminimumpeaktemperatureofcorners,respec- tively.Thecorrelationsprovidedasimpleyeteffectiveapproachfor evaluatingdepositionpatterns.Hence,theresidualstressofdiffer- entpatternscouldbecomparedbyanalyzingthepeaktemperature ofthecorners.
Sofar,onlynumericalstudieswereperformedandconclusions weremadebasedonthefiniteelementanalyses.Inthenearfuture, theexperimentalstudyoftheS-patternwillbeplanned,andthe effectofpasslengthofS-patternontheresidualstressshouldbe consideredtofurtheroptimizethepattern.Theresidualstressand warpageofthemulti-layermodelandcuboidstructureswithrect- angularsectionsundertheS-patternwillbestudied.
Acknowledgments
ThisresearchisfundedbytheChineseScholarshipCounciland theResearchCouncilofNorwaythroughthePetromaks2program (ProjectNo.281927)andtheBIAProgram(ProjectNo.269558)).
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