Numerical investigation of a novel pattern for reducing residual stress in additive manufacturing

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ContentslistsavailableatScienceDirect

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.

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

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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

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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 änd 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],wherea_f anda_r werethelengthofthefrontandtherearellipsoidoftheheatsource.

bwasthehalfwidthandcwasthedepthoftheheatsource.Qwas thepowerinput.Thefractionfactorsoftheheatﬂuxinthefront andrearpartswererepresentedbyf_fandfr,respectively,andthey heldtherelationthatf_f+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

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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,

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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 deposition 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

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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

and_1,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 thesixpatterns. 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.

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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.

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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

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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

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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,theT^p₁andT^p₂ aresmallerthanT^p₃andT^p₄,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,aveandT_p,minareoppositetothatofe,maxand_1,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

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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,therequirements 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,respectively.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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