International Journal of Machine Tools & Manufacture 88 (2015) 95–107

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International Journal of Machine Tools & Manufacture

http://d0890-69

n CorrUniversPR Chin

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journal homepage: www.elsevier.com/locate/ijmactool

Tailoring surface quality through mass and momentum transfermodeling using a volume of fluid method in selective laser melting ofTiC/AlSi10Mg powder

Donghua Dai a,b, Dongdong Gu a,b,n

a College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, PR Chinab Institute of Additive Manufacturing (3D Printing), Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, PR China

a r t i c l e i n f o

Article history:Received 18 July 2014Received in revised form20 September 2014Accepted 25 September 2014Available online 2 October 2014

Keywords:Selective laser meltingAdditive manufacturingSurface tensionSurface morphology

x.doi.org/10.1016/j.ijmachtools.2014.09.01055/& Elsevier Ltd. All rights reserved.

esponding author at: College of Materials Scieity of Aeronautics and Astronautics, Yudaoa. Fax: þ86 25 52112626.ail address: dongdonggu@nuaa.edu.cn (D. Gu)

a b s t r a c t

A selective laser melting (SLM) physical model of coupled radiation transfer and thermal diffusion isproposed, which provides a local temperature field. A strong difference in thermal conductivity betweenthe powder bed and dense material is taken into account. Both thermo-capillary force and recoil pressureinduced by the material evaporation, which are the major driving forces for the melt flow, areincorporated in the formulation. The effect of the laser energy input per unit length (LEPUL) on thetemperature distribution, melt pool dynamics, surface tension and resultant surface morphology hasbeen investigated. It shows that the surface tension plays a crucial role in the formation of the terminallysolidified surface morphology of the SLM-processed part. The higher surface tension of the lowertemperature metal near the edge of the melt pool and the thermal-capillary force induced by the surfacetemperature gradient tend to pull the molten metal away from the center of the melt pool. For arelatively high LEPUL of 750 J/m, the molten material in the center of the melt pool has a tendency toflow towards the rear part, resulting in the stack of molten material and the attendant formation of apoor surface quality. For an optimized processing condition, LEPUL¼500 J/m, a complete spreading of themolten material driven by the surface tension is obtained, leading to the formation of a fine and flat meltpool surface. The surface quality and morphology are experimentally acquired, which are in a goodagreement with the results predicted by simulation.

& Elsevier Ltd. All rights reserved.

1. Introduction

Laser-based additive manufacturing (LAM) techniques gener-ally have the capacity to provide an almost unlimited flexibility ofgeometry and complexity, offering special opportunities in variousindustries including aerospace, automotive, electronic, chemicaland biomedical, and as well as other high tech areas [1,2].Compared to other LAM technologies, selective laser melting(SLM) allows the fabrication of three-dimensional (3D) and fully-dense physical models, parts and tools directly from computer-aided design (CAD) data using various metal powders, includingmetals, alloys and metal matrix composites (MMCs) [3,4].Although the SLM process provides many advantages comparedto the conventional processes, the low surface quality is one of themajor drawbacks in the SLM-processed parts [5]. On the otherhand, despite the fact that the process is capable of making almost

nce and Technology, NanjingStreet 29, Nanjing 210016,

.

fully dense parts, the residual porosity may be still present in thesolidified SLM-processed parts and even problematic for someapplications where high strength is necessary [6,7]. The surfaceroughness of a part is significantly critical in many applications,requiring a fine surface to avoid premature failure from surfaceinitiated cracking. Therefore, the SLM-processed parts generallyrequire post-processing operations such as surface machining,polishing and shot peening to attain an excellent part surfacefinish [8,9]. However, it seems that the mentioned post processingoperations simply relate to the laser enhancement of surface orsub-surface properties of parts produced by SLM [10]. Generally,these mentioned post processing operations do not aim theenhancement of core material properties, nor surface enhance-ment of (rough) surfaces produced in a powder metallurgical (PM)way by SLM. Meanwhile, these post processing operations even-tually incur further time and delay part completion.

The top surface behavior of a melt pool can be significantlyinfluenced by a rippling effect because of a shear force exerting onthe liquid surface caused by the surface tension [11]. This phe-nomenon primarily results from the surface temperature differ-ence between the laser beam and the solidifying zone due to the

Nomenclature

B view factorCp specific heat at constant pressure, J/(kg K)Dp average diameter of the powder particles, mE energy, JF body force, e.g. gravity and buoyancy forces, Ng gravity, m/s2

h species enthalpyhc convective heat-transfer coefficient, W/(m2 K)href reference enthalpyH enthalpy of the materialΔH latent heat of the phase changeΔHLV latent heat of vaporizationI turbulent intensityMs mass source, kg

ξζ•

M , ζξ•

M mass transfer from phase ξ (ζ) to phase ζ (ξ)N normal componentp,p0 pressure, N/m2

P laser power, Wqv heat losses due to vaporization, JR gas constant

′R radius of the surface curvatureSH source item of the energy conservation

αξS mass source for each phaset time, sT ,TLV temperature, K

∞T ambient temperature, KTp temperature of the powder particles, K→V ,V velocity vector, m/su v w, , velocity magnitude, m/sx y z, , coordinates, mα,αi,αξ volume fractionαp fraction of particlesβ Drag coefficientγ surface tension, kg/mε radiation emissivityκ thermal conductivity of the powder bed, W/(m K)κeff effective thermal conductivity of liquid-solid-gas mul-

ti-phases, W/(m K)κ f thermal conductivity of the fluid, W/(m K)κr thermal conductivity due to the radiation among

particles, W/(m K)κs thermal conductivity of the solid, W/(m K)μ dynamic viscosity, Pa sρ,ρi,ρξ coupled density, kg/m3

σe Stefan–Boltzmann constantω radius of the Gaussian laser beam, m

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–10796

motion of the laser beam. The effect of the laser process para-meters on the formation of part surface roughness for multi-layerparts were studied through experiments by Mumtaz [12]. It wasconfirmed that processing parameters (e.g. laser power, scanspeed, etc.) had a specific influence on the top surface and sideroughness. The study of the laser re-melting using a continuouswave laser during SLM production of 316L stainless steel andTi6Al4V parts to overcome insufficient surface quality of producedparts was conducted by Kruth [6]. It is concluded that laser re-melting is a promising method to enhance the density and surfacequality of SLM parts at a cost of longer production time. However,SLM is a considerably complicated process, accompanying with theheat conduction, melting, boiling, evaporation, and even the phaseexplosion [13,14]. Therefore, experiments alone are far insufficientfrom revealing the mechanisms of the interaction between thelaser beam and materials, thermal behavior and eventually thevariation of the surface quality. With the development of thecomputer technology, numerical simulation has become a power-ful tool to help researchers discern the mechanisms behind thephenomena of the SLM process. A modified level-set method wasdeveloped by Shen in order to trace the liquid-gas interface as wellas consider mass loss during boiling and evaporation, takingaccount of the gravity, recoil pressure of the metallic vapor, surfacetension, and Marangoni effect [15]. Compared with some corre-sponding experiment results, the validity of the established modelwas verified and the mechanisms of phenomena during laserprocessing were analyzed. The influence of the laser scan speedand the laser intensity parameter on the melt pool size during theheating of titanium and steel surfaces by a moving CO2 laser beamwas analytically modeled and examined by Yilbas [16]. It wasfound that the influence of laser scan speed on the temperaturefield, cooling rate, surface tension and resultant melt pool size wasconsiderable. Nevertheless, the SLM process is still poorly under-stood, making further investigations indispensable to allow aprediction of the part's surface quality. To date, few existingmodels have fully solved the thermal behavior and the flow fieldstogether with the evaporation process and the transient evolutionof the surface activity during the SLM process. It is important to

understand the specific contributions of various processing para-meters to a surface finish of the SLM-processed part, consideringsimultaneously the variation of melt pool characteristics, with theterminal objective of reaching optimum surface finishes free of anypost-machining steps.

In this paper, the numerical simulation regarding the influenceof the laser energy input per unit length (LEPUL, Laser power, P/Scan speed, V) on the melt pool dynamics and resultant variationof the top surface finish during SLM of TiC/AlSi10Mg compositematerials was presented, using a Fluent 6.3.26 commercial finitevolume method (FVM) software. The TiC/AlSi10Mg compositematerials, due to the combined excellent physical and mechanicalproperties, have been attracted a lot of focuses and are reasonablyused in this paper [17,18]. The fluid flow driven by surface tensiongradient and recoil pressure is considered in the physical modeland the temperature distribution, melt pool dynamics and theresultant top surface morphology were simulated. Furthermore,the top surface morphologies of the SLM-processed parts obtainedby numerical simulation were compared with those acquired viaexperiments, in order to testify the accuracy of the developedsimulation model and obtain the reasonable SLM processingconditions to produce parts with a fine surface finish.

2. Model descriptions

Fluent 6.3.26 software, which enables the simulation of pro-cesses with molten metal flow and behavior of the metal vapor-ization, is introduced to simulate SLM process. To simplify theproblem, the following assumptions are made in this study:(1) The melt in the molten pool is assumed to be laminar andincompressible homogeneous Newtonian fluid. (2) Except thermalconductivity, surface tension, viscosity and specific heat, someother thermal physical constants are considered to be temperatureindependent.

Fig. 1. Schematic of the SLM physical model (a), the initial stage of the established mathematical model (b), the SLM processing procedure (c) and the microstructure of theball milled composite powder used for SLM (d).

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 97

2.1. Physical model

The schematic of SLM physical model is depicted in Fig. 1a.Laser beam is generally treated by a surface heat flux boundarycondition in analysis and it is defined as a Gaussian function whichis related to the TEM00 mode in laser activity. The TiC/AlSi10Mgphase defined in the present mathematical model cannot have afull accordance with the spherical shape of the powder particleused in the SLM process. Therefore, in order to significantlyminimize the calculation error, the volume of the mesh definedin the present model is close to that of the TiC/AlSi10Mg compo-site material, with the three dimensions of 30�30�30 μm3. Thefree surface fluctuation of the melt pool is accordingly influencedby the rippling effect caused by the surface tension forces, playinga crucial role in affecting the solidified surface quality of the SLM-processed part. Therefore, an interface between the argon protect-ing atmosphere and the melt pool free surface is reasonablyestablished in the physical model, taking into account the mass,heat and momentum transfer in the interface as being irradiatedby the laser beam. The initial stage of the established mathema-tical model is depicted in Fig. 1b. The three-dimensions of thenumerical model are 6�3�1 mm3. The argon atmosphere isinitiated in the Z-axis direction ranging from 0.6 to 1 mm andthus the other region is the metal powder material consisting ofthe AlSi10Mg and TiC with the volume ratio of 9:1. The

considerations about the definition of the Argon atmosphere,ranging from 0.6 to 1 mm in the Z-direction are as follows:

(1)

SLM is a net-shaping fabrication process, combined with theapplication of a refined radius of the laser beam (35 μm) and athin powder layer thickness (50 μm). Generally, the averagetop surface roughness obtained in the SLM-processed parts isless than 20 μm [6]. Therefore, there is enough space for thefree surface of the molten pool driven by the surface tension tobe freely deformed.

(2)

Due to the limitation of the CPU computation and processingcapacity, the realistic processing conditions in the SLM experi-ment are not completely fulfilled in the numerical simulation.However, in order to obtain a compromise of computationtime and accuracy, the protection atmosphere region in themathematical model is defined in a reasonable range of 0.6 to1 mm in the Z-direction in the numerical simulation work.

The heat losses from the six surfaces of the model are assumedto result from the natural convection and radiation. The initialtemperature of the powder layer, Ti, is treated as the roomtemperature. In order to investigate the influence of the surfacetension of the molten pool on the resultant surface quality, thetemperature distribution and surface tension magnitude arequantitatively extracted at the region of X¼0.0024 m and iterationtime of 0.006 s (V¼400 mm/s), 0.008 s (V¼300 mm/s), 0.012 s

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–10798

(V¼200 mm/s) and 0.024 s (V¼100 mm/s), respectively. As thelaser beam interacts with the powder, a melt pool is subsequentlyformed and the melt infiltrates into the powder layer driven by thecapillary forces and gravitational forces. The real-time SLM processis shown in Fig. 1c.

2.2. Governing equations

Based on the mass, momentum and energy equation, thegoverning equations in the Cartesian coordinate system aresummarized as follows [19,20]:

2.2.1. Mass conservation equation

ρ ρ∂∂

+ ∇→

=( )tV M (1)s

2.2.2. Momentum conservation equation

⎛⎝⎜⎜

⎞⎠⎟⎟ρ μ∂

→

∂+

→⋅∇

→= ∇

→− ∇ + ⋅

→+V

tV V V p M V F

(2)s

2

2.2.3. Energy conservation equation

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

ρ ρ ρ ρ

κ κ κ

∂∂

+∂

∂+

∂∂

+∂

∂

= ∂∂

∂∂

+ ∂∂

∂∂

+ ∂∂

∂∂

+

Tt

uTx

vTy

wTz

xTx y

Ty z

Tz

S

( ) ( ) ( ) ( )

(3)H

where ρ, κ, m and p are the density, thermal conductivity,viscosity and pressure, respectively. Ms is a mass source, including

the particle mass.→V is the molten metal velocity. SH is the source

item of the energy conservation equation in the X, Y and Zdirections and can be defined by

⎜ ⎟⎛⎝⎜

⎛⎝

⎞⎠

⎞⎠⎟ρ ρ= − ∂

∂Δ + ∇⋅ Δ

→S

tH V H( )

(4)H

where ΔH is the latent heat of phase change. The enthalpy of thematerial is computed as the sum of the sensible enthalpy, h, andthe latent heat, ΔH . The enthalpy of the material, H , can be definedby

= + ΔH h H (5)

where ∫= +h h C dTref T

Tp

ref.

The turbulent intensity is defined as:

=Δ + Δ + Δ

+ +I

u v w

u v w

(1/3)( )

(6)

2 2 2

2 2 2

where Δu, Δv, Δw are the velocity fluctuations in the X, Y and Z-axes direction, respectively.

2.3. Equations of volume of fluid (VOF) model

The volume fraction equation for the i phase is [21]

αα

ρ∂∂

+→

⋅∇ =α

tV

S

(7)i

ii

i

where α∑ == 1in

i1 , n represents the phase number.

A single momentum equation is solved throughout the domain,and the resulting velocity field is shared among the phases [21]

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥ρ ρ μ ρ∂

∂→

+ ∇→

= − ∇ + ∇ ∇→

+ ∇→

+ +→( ) ( )t

V V p V V g F(8)

T

The density ρ and dynamic viscosity μ in the Eq. (8) dependsstrongly on the volume fraction of all phases:

∑ρ α ρ= (9)i i

∑μ α μ= (10)i i

The energy equation is also shared among the phases [21]:

⎡⎣⎢

⎤⎦⎥ρ ρ ρ κ∂

∂+ ∇ + = ∇ ∇ +

→

( )t

E V E T S( ) ( )(11)eff H

The VOF model treats energy, E, and temperature, T, as mass-averaged variables:

α ρα ρ

=∑∑

=

=

EE

(12)in

i i i

in

i i

1

1

where Ei for each phase is based on the specific heat of that phaseand the shared temperature. The effective thermal conductivity, κeff, is also shared by the phases. The source term, SH, containscontributions from radiation as well as any other volumetric heatsources.

The tracking of the interface(s) between the phases is accom-plished by the solution of a continuity equation for the volumefraction of one (or more) of the phases. For the ξ phase, thisequation has the following form [22]:

⎜ ⎟⎡⎣⎢

⎤⎦⎥

⎛⎝

⎞⎠∑

ρα ρ α ρ∂

∂+ ∇

→= + −

ξξ ξ ξ ξ ξ α

ζξζ ζξ

=

• •

ξ( )tV S M M

1( )

(13)

n

1

where ξζ•

M is the mass transfer from phase ξ to phase ζ and ζξ•

M isthe mass transfer from phase ζ to phase ξ. αξS is the user-definedmass source for each phase.

2.4. Boundary conditions

The boundary condition at the interface (Z¼0.0006 m) is givenby [23]

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟κ

πω ω

σ ε

− ∂∂

= − + − −

− − −

= =

∞

∞( )

Tt

P x yh T T

T T q

3exp 3 ( )

(14)

z z

c

e v

0.00062

2 2

20.0006

4 4

ω = + −r a z z (15)0 0

where ω is the radius of the Gaussian laser beam and thecoefficient 3 means that 95% of the total power irradiates in thearea of effective radius ω. The absorption coefficient is dependenton the angle of incidence and thus it is given by the Fresnelequations [24]. The attenuation of the energy of the laser beam inthe metal follows the Beer–Lambert law [24]. T1 is the ambienttemperature, hc is the heat transfer coefficient of natural thermalconvection, se is the Stefan–Boltzmann constant and ε is theemissivity. qv denotes the heat losses because of the vaporization.

Calculated surface heat flux in Eq. (14) quickly melts andevaporates the material surface. Then the vaporization acts as arepulsive force on the molten pool surface referred to as a recoil

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 99

pressure [23]:

⎛⎝⎜

⎞⎠⎟μ γ− +

∂= − Δ

−+

‵p

VN

p HT TRTT R

2 0.54 exp(16)

NLV

LV

LV0

Eq. (16) means the pressure boundary condition for the inter-face including the surface tension in flow. N denotes the normalcomponent and, γ and ′R indicate the surface tension coefficientand radius of the surface curvature, respectively. p0 denotes theargon protecting atmosphere and ΔHLV is the latent heat ofvaporization. T, TLV and R indicate the surface temperature,liquid–vapor equilibrium temperature and universal gas constant,respectively.

To simulate the Marangoni flow caused by the temperaturegradient at the free surface of the melt pool, the surface tension isgiven by [19]

μ γ− ∂∂

= ∂∂

∂∂

uz T

Tx (17)

μ γ− ∂∂

= ∂∂

∂∂

vz T

Ty (18)

The temperature on the lateral surfaces is defined as theambient temperature and the mechanism of the heat loss isassumed to be the radiation transfer. The bottom of the powder

Fig. 2. Thermal physical properties of as-used material: (a) thermal conductivity and (b)and specific heat at constant pressure of TiC, respectively.

layer is connected to the metal substrate with larger heat con-ductivity in comparison with the protection atmosphere. As aresult, the heat loss through interface between powder layer andsubstrate is faster.

2.5. Physical properties

The particles are assumed to be spheres and no flattening ofcontact surfaces is present. Therefore, the effective thermal con-ductivity of the powder bed, κ, is estimated [25]

⎛⎝⎜⎜

⎞⎠⎟⎟

⎡⎣⎢⎢

⎛⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟

⎞⎠⎟⎟

⎤⎦⎥⎥

κκ

αακκ

ακ κ κ κ

κκ

κκ

= − − +

+ −− −

− +

( )1 1 1

12

1 /1

1 /ln 1

(19)

f

r

f

f s f s

s

f

r

f

where α indicates the fractional porosity of the powder bed, κf andκs are the thermal conductivity of the melt surrounding thepowder particles and the thermal conductivity of the solid,respectively. κr is the thermal conductivity of the powder bedbecause of the radiation among particles, which is further defined

specific heat at constant pressure of AlSi10Mg; (c) and (d) are thermal conductivity

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107100

by

κ σ= B T D4 (20)r e p p3

where se is the Stefan–Boltzmann constant, Dp is the averagediameter of the powder particles, Tp is the temperature of thepowder particles, and B is a view factor which is approximatelytaken as 1/3.

2.6. Numerical simulation

The simulation is carried out using the FLUENT commercialfinite volume method package (version 6.3.26) to simulate thethermal behavior, velocity field, melt pool vaporization behaviorand the resultant top surface quality. The thermal physical proper-ties of AlSi10Mg and TiC components are depicted in Fig. 2 [26,27].The SLM processing parameters depending on our previousresearch are chosen and shown in Table 1. In order to have anaccurate definition of the interaction of the laser power and scanspeed, the laser power (P) was preset at 150 W and the scan speed(V) was periodically set at 400 mm/s, 300 mm/s, 200 mm/s and100 mm/s. Four different “laser energy input per unit length”(LEPUL) of 375, 500, 750, and 1500 J/m, which was defined by

= PV

LEPUL (21)

was used to investigate the effect of SLM processing parameters onthe layer-by-layer fabrication process, the thermal behavior of themolten pool and the response of the surface quality of the SLM-processed parts. The behavior of the top surface in the SLM-processed parts is the metallurgical activity under the condition ofthe existence of the molten pool. As a result, the surface quality ofthe SLM-processed part does not show any change after solidifica-tion with the movement of the laser beam.

3. Experimental procedures

3.1. Powder materials

The 99.0% purity TiC nanopowder with a near spherical shapeand a mean particle size of 50 nm and the 99.7% purity AlSi10Mgpowder with a spherical shape and an average particle diameter of30 μmwere used. Using the ball milling process, the TiC/AlSi10Mgcomposite powder system with a near spherical shape and ahomogeneous particle size distribution is experimentally obtained,leading to the isotropous physical properties (Fig. 1d). It is obviousthat the nanoscaled TiC particles are homogeneously distributedaround the AlSi10Mg particle surface, leading to a good flowabilityand a homogeneous physical property.

Table 1As-used material properties and SLM processing conditions.

Parameter Value

Ambient temperature, T1 300 KConvective heat-transfer coefficient, hc 80 W/(m2 K)The Stefan–Boltzmann constant, s 5.67�10�8 W/( m2 K4)Radiation emissivity, ε 0.36Powder layer thickness, lp 50 μmLaser power, P 150 WScan speed, V 100–400 mm/sRadius of laser beam, ω 35 μmMelting and evaporation point of TiC 3430 K, 5090 KMelting and evaporation point of AlSi10Mg 893 K, 2743 K

3.2. Processing and characterization

The SLM system consisted mainly of a YLR-200-SM ytterbiumfiber laser with a power of �200 W and a spot size of 70 μm (IPGLaser GmbH, Germany), an automatic powder spreading device, aninert argon gas protection system, and a computer system forprocess control. Details of the SLM process have been thoroughlysummarized in the previous research paper [2,14]. The processingconditions investigated are the same as the data in the numericalsimulation. Specimens for metallographic examinations were pre-pared according to the standard procedures, and then etched witha solution composing HF (2 ml), HCl (3 ml), HNO3 (5 ml) anddistilled water (190 ml) for 10 s. A PMG3 optical microscope (OM)(Olympus Corporation, Japan) was used to observe the low-magnification inter-layer microstructures of the SLM-processedspecimens. The typical top surface morphology study of the SLM-processed parts was performed using a S-4800 field emission SEM(FE-SEM) (Hitachi, Japan) at 5 kV.

4. Results and discussion

4.1. Temperature distribution

Fig. 4 shows the temperature distribution on the XY plane atZ¼0.0006 m using various LEPULs during the laser irradiation. Itshows that the typical contours of the temperature distributionare strictly symmetrical in the laser beam scan direction (X-axisdirection) and abide by the Gaussian function in the shapes of aseries of ellipses. The center of the melt pool does not locate at thecenter of the laser beam (X¼0.0024 m; Y¼0), but slightly shiftstowards the side of the decreasing X-axis (Fig. 4). Moreover, theprofiles of the temperature distribution depict that there is amonotonous enhancement in temperature with an increase in theapplied LEPUL. For a relatively low LEPUL of 375 J/m, the max-imum operating temperature is merely 900 K (close to the melting

Fig. 3. Flow chart of the calculation procedure. Superscripts pre express the valueof the previous time increment.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 101

point of AlSi10Mg, 893 K), caused by the inadequate energyprovided by the laser beam (Fig. 4a). As the applied LEPUL furtherincreases to 750 J/m, the maximum temperature in the melt poolis as high as 1600 K (Fig. 4c), indicating a complete melting of thematrix metal and the attendant long lifetime of the melt pool.Whereas a considerably elevated LEPUL of 1500 J/m is applied, it isinteresting to find that the maximum temperature obtained in themelt pool decreases to 1300 K. This may be primarily due to thehigh peak laser energy input and resultant material vaporization,resulting in the occurrence of the severe mass and heat losses.Under the combined effect of the spatter generation and thematerial vaporization, it seems that no efficient metallurgicalbonding is obtained between the neighboring tracks, since thelimited amount of liquid prevents the sufficient melt spreading.Moreover, with the material vaporization, the energy obtained bythe melt pool decreases, resulting in a decrease in the workingtemperature and accordingly the diameter of cylindrical moltentrack. The melt instability, consequently, increases significantly.Therefore, a number of small-sized liquid droplets tend to splash

Fig. 4. Temperature distribution contours using different laser energy input per unit lengt(b) P¼150W, v¼300 mm/s, LEPUL¼500 J/m, t¼0.008 s; (c) P¼150W, v¼200 mm/s, LEPU

from the surface of the molten track, promoting the formation ofthe micrometer-scaled spheres around the processed surface.

4.2. Dimensional analysis of the melt pool

In order to investigate the influence of the applied LEPUL onthe melt pool physical phenomena, the detail information aboutthe melt pool is depicted in Fig. 5. It shows that the metal meltsand the recoil pressure leads to a deformation of the free surface ofthe melt pool (Fig. 5a). During the continuous laser deep penetra-tion melting, a keyhole is generated and maintains the balancebetween the surface tension and the recoil pressure boundarycondition.

On the other hand, the laser penetration depth is larger thanthe powder layer thickness (50 μm), in order to ensure that theneighboring layers are well bonded. As shown in Fig. 4, the lengthand width of the melt pool change with the increase of the appliedLEPUL. According to Gusarov's research, the surface tension has atendency to transform this molten metal to a shape similar to a

h (LEPUL) on the scan path: (a) P¼150W, v¼400mm/s, LEPUL¼375 J/m, t¼0.006 s;L¼750 J/m, t¼0.012 s; and (d) P¼150W, v¼100mm/s, LEPUL¼1500 J/m, t¼0.024 s.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107102

circular cylinder with the same length of the melt pool under thevolume conservation [28] (Fig. 5b). As the applied LEPUL are below500 J/m, it is evident that the circumference of the circularcylinder (e.g. 1050 μm for LEPUL of 500 J/m) is generally higherthan the length of the melt pool (e.g. 800 μm for LEPUL of 500 J/m). While the opposite trends are analytically observed as theapplied LEPUL surpass 750 J/m (Fig. 5c). The circumference of thiscylinder is about its length, which is the limit of the Plateau–Rayleigh capillary instability of a liquid cylinder. Namely, thecylinder tends to break into droplets if the length exceeds thecircumference and thus the Plateau–Rayleigh instability can ex-plain the melt pool capillary instability effect. The influence of theapplied LEPUL on the conductive heat transfer is estimated by thePeclet number with thermal diffusivity, χ. The thermal diffusivityof the dense solid phase and the powder are respectively esti-mated as 6 mm2/s and 0.08 mm2/s from the parameters fromSection 2. As shown in Fig. 5d, it is clear that there is a significantdifference in Peclet number in dense phase and powder materialwith the value of �5 and �340. At the edge of the melt pool andespecially near the powder phase, the Peclet number is large and,

Fig. 5. Cross-section of the melt pool caused by the recoil pressure due to the vaporizatioof the melt pool various laser input energy (c) and Peclet number of the dense and pow

thus the melt pool is highly stretched along the scan direction(Fig. 3). The sharp edge in the temperature distribution of Fig. 5a atthe powder–liquid boundary (front boundary of the melt pool)appears due to a high difference in thermal conductivity. Thesimilar edge at the rear boundary of the melt pool is caused by theliberation of the latent heat at solidification.

4.3. Surface tension

Surface tensions obtained along the laser scan direction on thefree surface using various LEPULs are depicted in Fig. 6. It is worthnoting that the higher surface tensions are generally located nearthe edge of the melt pool rather than in the center. The surfacetension of the Al-alloy melt, significantly depending on theoperating temperature, is experimentally studied and measuredby researcher Dou et al. [29]. It can be concluded that the higherthe operating temperature of the irradiation region, the responseof the lower surface tension of Al-alloy melt is realized. Accordingto Zhang's research, under the combined effect of the highersurface tension near the edge of the melt pool and the thermal-

n phenomenon (a), schematic of the molten pool transformation (b), characteristicsder phase (d).

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 103

capillary force induced by the surface temperature gradient, themolten metal tends to flow away from the center of the liquidpool, where the surface tension is lower caused by the higheroperating temperature [30]. For a relatively low LEPUL of 375 J/m,the surface tension along the scan direction exhibits a relativelysteady-state behavior with the average value of 0.855 N/m. AsLEPUL increases to 500 J/m, a significant variation of the surfacetension in the melt pool is obviously observed, with the maximumand minimum value of 0.88 and 0.83 N/m near the center andedge part of the melt pool respectively. However, for a relativelyhigh LEPUL of 750 J/m, there is a severe difference in the surfacetension with the highest value of 0.88 N/m in the rear scan part ofthe melt pool, while the lowest surface tension, s¼0.755 N/m, isstill appeared near the center of the melt pool. It seems that the

Fig. 6. Surface tension obtained along the laser scan direction (X-axis direction)using various laser energy input at the iteration time of 0.006 s (LEPUL¼375 J/m),0.008 s (LEPUL¼500 J/m), 0.012 s (LEPUL¼750 J/m) and 0.024 s (LEPUL¼1500 J/m).

Pores

1500µm

1500µm

a

c

Fig. 7. Typical morphologies of the solidified top surface predicted by the simulation mLEPUL¼500 J/m; (c) P¼150 W, v¼200 mm/s, LEPUL¼750 J/m; and (d) P¼150 W, v¼10

melt in the center of the melt pool has a tendency to flow towardsthe rear part caused by the serious surface tension difference withthe value of 0.125 N/m. As LEPUL further increases to 1500 J/m, thevariation trend of the surface tension is apparently similar to thatobtained in the LEPUL of 500 J/m with the maximum and mini-mum surface tension of 0.875 and 0.82 N/m, respectively.

4.4. Morphologies of the top surface

Typical morphologies of the top surface predicted by thesimulation using various LEPULs are depicted in Fig. 7. It is appa-rent that the surface quality of the SLM-processed part is sig-nificantly sensitive to the applied LEPUL. For a relatively low LEPULof 375 J/m, the obtained surface roughness of the solidified part isobviously greater than the set layer thickness caused by theappearance of the serious surface curvatures and residual pores(Fig. 7a). As LEPUL increases to 500 J/m, it is interesting to find thatthe top surface is completely dense, showing no apparent pores orserious curvatures (Fig. 7b). For a relatively high LEPUL of 750 J/m,the surface combined with a serious fluctuation and the materialstacking is produced, eventually resulting in a poor surface quality(Fig. 7c). As LEPUL further increases to 1500 J/m, although thesurface is relatively flat, the generated layer thickness aftersolidification is obviously less than the starting powder depositionthickness, implying a serious occurrence of the material vaporiza-tion (Fig. 7d). Meanwhile, a poor interlayer bonding ability, causedby the shrinkage phenomenon and the attendant interlayer pores,is generally produced, contributing to the formation of the poorsurface quality.

In order to investigate the influence of the applied LEPUL onthe top surface of the melt pool, the volume fraction contours andthe velocity field of the longitudinal sections under various LEPULare depicted in Fig. 8. It is noted that the input LEPUL has asignificant effect on the top surface of the melt pool. For arelatively low LEPUL of 375 J/m, the obtained top surface fluctuatesin the vicinity of line Z¼0.0006 m and, the maximum andminimum height of the melt pool respectively reaches

Pores

1500µm

1500µm

b

d

ethod: (a) P¼150 W, v¼400 mm/s, LEPUL¼375 J/m; (b) P¼150 W, v¼300 mm/s0 mm/s, LEPUL¼1500 J/m.

Materials stacking Splash

Fig. 8. Volume fraction contours of the cross-sections along the laser scan direction under various LEPULs: (a) P¼150 W, v¼400 mm/s, LEPUL¼375 J/m; (b) P¼150 W,v¼300 mm/s, LEPUL¼500 J/m; (c) P¼150 W, v¼200 mm/s, LEPUL¼750 J/m; and (d) P¼150 W, v¼100 mm/s, LEPUL¼1500 J/m.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107104

Z¼0.0008 m and Z¼0.0005 m, implying a considerably seriousdisturbance in the melt pool (Fig. 8a). The vector of the velocityfield in the vicinity of the free surface is obviously downward andpoints to the bottom of the melt pool, enhancing the energytransfer rate from the free surface to the bottom of the melt pool(Fig. 8a). As LEPUL increases to 500 J/m, the top surface along thescan direction exhibits a relatively steady-state behavior with fewlocal fluctuations just around line Z¼0.00055 m (Fig. 8b). Itindicates that under this processing condition the fluctuation ofthe melt pool is considerably slight. Meanwhile, it is clear that thevector of the velocity field in the free surface is absolutely upward,implying the occurrence of the material vaporization (Fig. 8b). Fora relatively high LEPUL of 750 J/m, it is observed that materialstacking is apparently located in the rear part of the laser beam-powder interaction region with the maximum height lineZ¼0.001 m, while the minimum height of the free surface ismerely Z¼0.0004 m (Fig. 8c). The vector of the velocity field,deriving from the bottom part and the free surface of the meltpool, tends to encounter in the rear region of the melt pool,resulting in the stack of molten material. Therefore, it is reasonableto conclude that a poor surface quality of the solidified part will beobtained. As LEPUL further increases to 1500 J/m, it is worthnoting that the average free surface of the melt pool is as low as0.0004 m, implying a severe material vaporization being resul-tantly produced due to the over-heating in the local region under

the effect of the excessive laser energy input (Fig. 8d). Meanwhile,it is interesting to find that material splash phenomenon isattendant generated, which is detrimental to the surface qualityof the solidified part caused by the typical metallurgy defect,balling phenomenon. It is analytically confirmed by the vector ofthe velocity field in Fig. 8d.

The influence of the fluid flow on the top surface of the meltpool is depicted in Fig. 9. For a relatively low LEPUL of 375 J/m, alower operating temperature (Fig. 4a) and attendant higher meltviscosity are obtained in the melt pool. As a result, a limitedsurface tension difference acting on a liquid surface cannot providesufficient driving forces against viscous drags to promote theefficient spreading of the molten material. Therefore, a pro-nounced difference in radius of curvature of the local liquidsurface is eventually produced (Fig. 9a), resulting in the formationof a poor surface finish (Figs.7a and 8a). As the applied LEPULincreases to 500 J/m, the significantly decreased viscosity contri-butes to the formation of lower viscous drags, leading to anelevated spreading ability of the molten material driven by thesurface tension (Fig. 9b). Thereafter, a flat melt pool surface isattendant formed, thus achieving the appearance of a reducedsurface roughness (Figs. 7b and 8b). However, for a relatively highLEPUL of 750 J/m, in the combination of the sharply reduced meltviscosity and the formation of a high surface tension in the rearpart of the melt pool, the molten material in the center of the melt

Fig. 9. Schematics of the change in cross-sections along the laser scan direction of the melt pool during SLM process on increasing LEPULs: (a) P¼150 W, v¼400 mm/s,LEPUL¼375 J/m; (b) P¼150 W, v¼300 mm/s, LEPUL¼500 J/m; (c) P¼150 W, v¼200 mm/s, LEPUL¼750 J/m; and (d) P¼150 W, v¼100 mm/s, LEPUL¼1500 J/m.

Pores filled with

un-molten powder

Flat surface with a

sound density

Materials stacking

Balls

Discontinuous scan

tracks

Fig. 10. SEM images showing typical surface morphologies of SLM-processed TiC/AlSi10Mg parts with different LEPULs: (a) P¼150 W, v¼400 mm, LEPUL¼375 J/m; (b)P¼150 W, v¼300 mm, LEPUL¼500 J/m; (c) P¼150 W, v¼200 mm, LEPUL¼750 J/m; and (d) P¼150 W, v¼100 mm, LEPUL¼1500 J/m.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 105

pool has a tendency to flow towards the rear part (Fig. 9c) and,thus a stack of the material is subsequently generated in the rearpart (Figs. 7c and 8c). As LEPUL further increases to 1500 J/m, asevere material vaporization is subsequently produced owing tothe over-heating of local region, limiting the complete spreading of

the molten material (Fig. 9d). Consequently, the non-continuousvectors and the drops formation are produced caused by theincomplete spreading of the melt pool and the vaporization ofmolten material (Figs. 7d and 8d). Therefore, it can be reasonablyconcluded that as the volume of the melt pool is insufficient, the

200µm 200µm

200µm 200µm

Fig. 11. Optical microscopy images showing interlayer microstructures on cross-sections along the laser scan direction of SLM-processed TiC/AlSi10Mg parts with differentLEPULs: (a) P¼150 W, v¼400 mm, LEPUL¼375 J/m; (b) P¼150 W, v¼300 mm, LEPUL¼500 J/m; (c) P¼150 W, v¼200 mm, LEPUL¼750 J/m; and (d) P¼150 W, v¼100 mm,LEPUL¼1500 J/m.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107106

surface tension has a tendency to break the melting vector into aseries of individual droplets.

4.5. Experiment verification

The typical surface morphologies of SLM-processed TiC/Al-Si10Mg parts at a relatively low magnification are depicted inFig. 10. At a relatively low LEPUL of 375 J/m, a large amount ofelongated pores, containing some residual un-molten powderparticles, were present on the surface of the SLM-processed partdue to the insufficient laser energy input (Fig. 10a), resulting in aconsiderably low relative density. As the applied LEPUL increasesto 500 J/m, continuous scan tracks with sound inter-track bondingwere generally formed and thus a pretty dense surface of SLM-processed AlSi10Mg part was successfully obtained, showing noapparent pores or cracks (Fig. 10b). However, for a relatively highLEPUL of 750 J/m, a serious of material stacking were considerablyproduced on the surface of the SLM-processed part caused by theencounter of the molten material driven by the surface tension(Figs. 10c and 9c). Under this processing condition, a poor surfacequality with a high roughness was obtained, which needed thepost processing and limited the industrial application. As LEPULfurther increased to 1500 J/m, a rough surface consisting ofdiscontinuous scan tracks was produced, owing to the occurrenceof material vaporization and subsequently the formation of alimited volume of the melt pool (Figs.10d and 9d).

Fig. 11 shows the interlayer microstructures on cross-sectionsof SLM-processed TiC/AlSi10Mg parts with different LEPULs. Uponetching, the layerwise microstructure features became visible, dueto the additive manufacturing nature of SLM. The contour linescorrespond to the regions of scan tracks in the individual layersand reasonably indicate the influence of the applied LEPUL on theobtained SLM-processed part surface. At a relatively low LEPUL of375 J/m, the cross-section of the SLM-processed parts showed arelatively heterogeneous layerwise microstructure with the for-mation of the irregular shaped interlayer pores on a scale of

�100 μm (Fig. 11a). The interlayer pores were generally found tobe appeared in the layer-peak encounter region.

As the applied LEPUL increased to 500 J/m, the cross-sectionshowed a homogeneous microstructure with the evenly distrib-uted layers, showing the coherent interlayer bonding ability free ofany residual pores (Fig. 11b). However, for a relatively high LEPULof 750 J/m, a layerwise microstructure of the violently undulatecharacteristic in the adjacent layers was produced, resulting in theformation of the interlayer pores aggregated in the layer-peakencounter region (Fig. 11c). As LEPUL further increased to 1500 J/m, although a slightly heterogeneous layerwise microstructurewas obtained, a significantly poor interlayer bonding ability wasapparently produced due to the appearance of the residual poreson a scale of 200 μm (Fig. 11d). This is reasonably caused by thecombined effect of the material vaporization and the layer-peakencounter phenomenon (Fig. 9d). Therefore, a close look at theexperiment and simulation results reveals that the formation anddevelopment behaviors of surface quality are in a good agreementwith the simulation results.

5. Conclusions

The simulation of the melt pool dynamics and the top surfacequality of selective laser melting (SLM) TiC/AlSi10Mg compositepowder system has been performed, using a finite volume method(FVM), and the following conclusions can be drawn.

(1)

The temperature increases with the applied LEPUL and, thesharp edge in the temperature distribution at the powder-liquid boundary (front boundary of the melt pool) appears dueto a high difference in thermal conductivity. While the similaredge at the rear boundary of the melt pool is due to liberationof the latent heat at solidification.

(2)

There is a significant difference in Peclet number in densephase and powder material with the value of �5 and �340.

D. Dai, D. Gu / International Journal of Machine Tools & Manufacture 88 (2015) 95–107 107

Consequently, at the edge of the melt pool and especially nearthe powder phase, the Peclet number is large and, thus themelt pool is highly stretched along the scan direction.

(3)

During the SLM process, the higher surface tension of thelower temperature metal near the edge of the melt pool andthe thermal-capillary force induced by the surface tempera-ture gradient tend to pull the molten metal away from thecenter of the melt pool. For a relatively high LEPUL of 750 J/m,the molten material in the center of the melt pool has atendency to flow towards the rear part, resulting in the stackof molten material and attendant a poor surface quality.

(4)

The applied LEPUL plays a crucial role in determining thesurface quality of SLM-processed parts. It can be reasonablyconcluded that as the volume of the melt pool is insufficient,surface tension has tendency to break the melting vector into aseries of individual droplets. For an optimized LEPUL of 500 J/m, an elevated spreading of the molten material driven by thesurface tension is obtained, leading to the formation of a flatmelt pool surface.

(5)

The surface quality and morphology are experimentally ac-quired, which are in a good agreement with the resultspredicted by simulation. These physical phenomena consid-ered in the physical model are a general issue during theinteraction of the laser beam and powder material. Therefore,the SLM physical model established in this paper is suitable forother material system.

Acknowledgements

We gratefully appreciate the financial support from the Na-tional Natural Science Foundation of China (No. 51322509), theOutstanding Youth Foundation of Jiangsu Province of China (No.BK20130035), the Program for New Century Excellent Talents inUniversity (No. NCET-13-0854), the Program for DistinguishedTalents of Six Domains in Jiangsu Province of China (No. 2013-XCL-028), the Science and Technology Support Program (TheIndustrial Part), Jiangsu Provincial Department of Science andTechnology of China (No. BE2014009-2), and the FundamentalResearch Funds for the Central Universities (No. NE2013103).

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