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Numerical modelling and parametric study of grain morphology and resultant mechanical properties from selective laser melting process of Ti6Al4V

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In this paper, a transient 3-dimensional thermal model for the selective laser melting process, based on the finite volume method, has been developed, which takes into account the phase change and powder to bulk material transition. A parametric study has been performed for the temperature field as well as the melt pool dimensions, and the results show the impact on melt pool size. Also, in this paper, a straightforward metallurgical model has been coupled to a thermal model, which uses the temperature gradient and the cooling rate on the melt pool borders at the onset of solidification to determine whether the grains have columnar or equiaxed morphology. Furthermore, the effect of process parameters on the size of grains and subsequently the yield stress has been studied via empirical equations. The results show that lower values of speed along with higher values of laser power (higher laser energy density) will cause lower cooling rates that prompt the formation of bigger grain. This would consequently give rise to lower tensile strength, as compared to lower laser energy density where smaller grains are formed due to higher cooling rates. SLM-Thermal model-Finite volume method-grain morphlogy-parametric study
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euspen’s18thInternationalConference&
Exhibition,Venice,IT,June2018
www.euspen.eu
Numericalmodellingandparametricstudyofgrainmorphologyandresultant
mechanicalpropertiesfromselectivelasermeltingprocessofTi6Al4V  
MohamadBayat1,*,SankhyaMohanty1,JesperH.Hattel1

1DepartmentofMechanicalEngineering,DTU,Lyngby, Denmark    
*mbayat@mek.dtu.dk  

Abstract
Inthispaper,atransient3‐dimensionalthermalmodelfortheselectivelaser meltingprocess,basedonthefinitevolumemethod,
hasbeendeveloped,whichtakesintoaccountthephasechangeandpowdertobulkmaterialtransition.Aparametricstudyhasbeen
performedforthetemperaturefieldaswellasthemeltpooldimensions,andtheresultsshowtheimpactonmeltpoolsize.Also,in
thispaper,astraightforwardmetallurgicalmodelhasbeencoupledtoathermalmodel,whichusesthetemperaturegradientand
thecoolingrateonthemeltpoolbordersattheonsetofsolidificationtodeterminewhetherthegrainshavecolumnarorequiaxed
morphology.Furthermore,theeffectofprocessparametersonthesizeofgrainsandsubsequentlytheyieldstresshasbeenstudied
viaempirical equations. Theresultsshowthat lower valuesofspeedalongwith higher valuesoflaserpower(higher laser energy
density)willcauselowercoolingratesthatprompttheformationofbiggergrain.Thiswouldconsequentlygiverisetolowertensile
strength,ascomparedtolowerlaserenergydensitywheresmallergrainsareformedduetohighercoolingrates. 

SLM–Thermalmodel–Finitevolumemethod–grainmorphlogy–parametricstudy 
1.Introduction
Additivemanufacturingiscurrentlyfindingnew andgrowing
applications in many industries such as aerospace, medical,
automobile,etc.Inselectivelasermelting(SLM),whichisatype
of powder bed fusion additive manufacturing technique, the
processbeginswhenalayeroffinemetallicpowder(withsizes
around20to 50micrometers)isevenlydistributedoverasolid
substrate.Afterthefirstlayerhasbeenaccreted,thelaserscans
thepredefinedlocationsandbyselectivelymeltingthepowder,
thefirstsolid layer is fabricated. After thefirstlayerhas been
cooleddown,thesameprocessisrepeatedforsubsequent
layersuntilthewholemetalpartisproduced.
SLM has many advantages over conventional production
methods(e.g.castingandforging),suchaslowermaterialwaste
andfasterproductionspeed.However,tocompetewithexisting
conventionalprocesses,thequalityofitsfinalproductsneedto
bemorepredictable.Astraightforwardwaytopredicttheeffect
ofprocess parameters on theparts’ quality would bethrough
productionoflargenumberofsamples.Themoreelegentway,
however, would be via proper numerical modelling that takes
intoaccountproperphysicsandisabletoreplicateexperimental
observations.
LiteratureisabundantinthermalmodellingofSLMprocess.
More recently, Li and Gu developed a finite element thermal
modelfor SLMofcommerciallypuretitanium powder[1]. They
investigated the effect of laser power input and the scanning
speedontheshapeandsizeofthemeltpool,aswellasits
impact on the maximum temperatures formed during the
process. Huang et al, studied the effect of SLM process
parameterson boththetemperaturefield and morphologyof
theparts [2],whileconsideringmaterialshrinkage duringSLM,
andwereabletoshowthatignoringthiseventwouldresultin
lowertemperaturepredictions.
Similair works for heat conduction modellingof SLM canbe
foundinliteraturefordifferenttypesofpowders,e.g.AISI316L
[3,4], Nitinol [5], W‐Ni‐Fe [6], Aluminum [7], Inconel 718 [ 8],
Inconel625[9].Anumber ofresearchershave alsoconsidered
the fluid dynamics in thermal models and suggested that
neglectingthisphenomenoncanresultinoverestimationofthe
temperaturefield[10,11].
Apar tfr omthe therma lfi el dan dit sef fectsonr esi dua lstre sses
andpartdimensional accuracy,themicrostructuremorphology
andthecrystallographictexturealsohasahighlevelofinterest,
especiallyforindustrieswheretargetedmaterialpropertiesare
required.RaghavanetalstudiedtheimpactoftheEBMprocess
parameters on the grain morphology of the samples [12].
BonthaetalalsostudiedtheeffectofEBMscanningspeedand
input power on the grain morphology of Ti6Al4V, where they
assumedapointheatsourcefortheirsimulation[13].
In this paper, the effects of the process parameters on the
thermalfieldandmeltpooldimensionhasbeenstudiedindetail
usinga3Dthermalmodel.Also,ametallurgicalmodelhasbeen
developed to predict the grain morphology (equiaxed ot
columnar)oftheSLMparts,andthesubsequenteffectonthe
yieldstressandaveragegrainsizesareanalysed.
2.Numericalmodel
The 3D thermal model is based on the conventional heat
conductionequationwithNewtoniancoolingandsurface
radiation similar to that described in Mohanty et al[14] . The
modelleddomainof2mmby2mmby1mmisdiscretizedinto
50000elements.AGaussianheatfluxhasbeenimposedonthe
topsurfacetoresembletheactuallaser‐powderinteraction.The
effective value for powder material properties are also
considerede.g.thepowderspecificheatheatcapacity(basedon
asoliddensityofandporosityof)iscalculatedas[7]:
1
 

1
 

(1)
3.Resultsanddiscussions
 
Figure1.(a)Longitudinaltemperatureprofile.Meltpooldimensionsfor
differentvaluesof(b)laserpowersand(c)scanspeeds
Longitudinaltemperatureprofilesforscanspeedof400mm/s
and three different values of laser input power have been
plottedinFigure1a,andshow thatanincreaseinlaserpower
can elevate the temperature to a large extent and produce
longermeltpools.Length,widthanddepthofthemeltpoolfor
twoadditionalsetsoflaserpowerandscanspeedhasbeen
plottedinFigure1bandcrespectively.Itcanbeobservedthat
decreasingthe scan speed and increasingthelaser power will
expandthesizeofthemeltpoolinanon‐isotropicmanner.
a)
Figure2:Grainmorphologymapsfordifferenta)speedsandb)powers
Solidification data, including temperature gradients, cooling
ratesandgrowthvelocities,weredeterminedonthebordersof
themeltpool at the start of solidification fordifferent setsof
laser powers and scan speeds (plotted in Figure 2a and b
respectively).InFigure2a,eachcolorstandsforacertainvalue
of laser power. Increase in laser power reduces the average
coolingrate,leadingtocoarsergrainsizesascanbeobservedin
Figure2a.Decreaseinthelaserscanspeedhasasimilarimpact
onthecoolingrateandthusthegrainsizes.Thediscontinuous
linesin Figure2aandbcorrespondto the curvesofconstant
coolingrates,andthusbasedonthefigure,lowercoolingrates
arepredictedforhigherlaserpowersandlowerscanspeeds.
Figure2.Effectof(a)laserpowerand(b)scanspeed,onyieldstress
andaveragegrainsizes
Figure3furthervalidatesthehypothesisthatincreasedlevel
oflaserpowerandlowerlaservelocitiesresultinbiggergrain
sizes.Toevaluatetheaveragesizeofgrains,anempirical
equationforrapidsolidification(highcoolingrates)ofTi6Al4Vis
implementedthatrelatescoolingratetoβgrainsizes[15]:
3.1

..
(2)
where d is the grains size and Cr is the cooling rate.
Additionally,to study the effect of grainsizes(d) on the yield
strength(Y),a Hall‐PetchlikeempiricalequationforTi6Al4V is
used[15]:
  802.66  1236.5/

(3)
Figure3aandb,suggeststhatlowerlaserpoweralongwith
higherlaserspeedendsinfinergrainswhichconsequentlygive
risetohigherlevelsoftensilestrength.
4.Conclusion
Inthisworkatransient3‐DthermalmodelforSLMprocessfor
Ti6Al4V has been developed, which uses temperature‐
dependant themal properties and takes phase transitions into
account. Subsequently, based on the results of the thermal
model, and for different values of laser power and scanning
speed,grain morphology maps weredrawn.Thesemaps show
thathighervaluesofinputpowerandlowervaluesofscanspeed
result in lower cooling rates. A ccording to rapid solidification
models,suchlowercoolingratescausetheformationofcoarser
grains,givingrisetolowervaluesofyieldstressinthematerial.
Future works will attempt at directly modelling the
microstructure evolution, and then compare the results with 
correspondingexperiments,tocorroboratethefindings.
Acknowledgement
This work has been funded by the EU Horizon2020 Marie
Skłodowska‐CurieITNprojecttitledPAM^2‐ PrecisionAdditive
MetalManufacturing(GrantAgreementNo721383).
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0
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The fabrication of 3-D parts from CAD models by additive manufacturing (AM) is a disruptive technology that is transforming the metal manufacturing industry. The correlation between solidification microstructure and mechanical properties has been well understood in the casting and welding processes over the years. This paper focuses on extending these principles to additive manufacturing to understand the transient phenomena of repeated melting and solidification during electron beam powder melting process to achieve site-specific microstructure control within a fabricated component. In this paper, we have developed a novel melt scan strategy for electron beam melting of nickel-base superalloy (Inconel 718) and also analyzed 3-D heat transfer conditions using a parallel numerical solidification code (Truchas) developed at Los Alamos National Laboratory. The spatial and temporal variations of temperature gradient (G) and growth velocity (R) at the liquid-solid interface of the melt pool were calculated as a function of electron beam parameters. By manipulating the relative number of voxels that lie in the columnar or equiaxed region, the crystallographic texture of the components can be controlled to an extent. The analysis of the parameters provided optimum processing conditions that will result in columnar to equiaxed transition (CET) during the solidification. The results from the numerical simulations were validated by experimental processing and characterization thereby proving the potential of additive manufacturing process to achieve site-specific crystallographic texture control within a fabricated component.
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Additive Manufacturing, 1
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Li, Y. and Gu, D., 2014. Additive Manufacturing, 1, pp.99-109.
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