Balling Phenomenon in Metallic Laser Based 3D Printing Process

International Journal of Thermal Sciences 167 (2021) 107011 Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts Balling phenomenon in metallic laser based 3D printing process M’hamed Boutaous a, Xin Liu a, Dennis A. Siginer b, *, Shihe Xin a a b Université de Lyon, CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621, Villeurbanne, France Centro de Investigación en Creatividad y Educación Superior & Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago, Chile A R T I C L E I N F O A B S T R A C T Keywords: Additive manufacturing Selective laser melting 3D discrete element method Balling phenomenon A comprehensive model is developed coupling major physical phenomena inherent to the Selective Laser Melting process together with a 3D numerical model based on the discrete element method to study the effect of the process parameters on the generation of balling droplets in the laser melting process. Effects of several process parameters as well as material properties on the balling phenomenon are investigated. Simulation results compare well to the experimental findings in the literature. 1. Introduction Selective laser melting (SLM) is the most innovative and promising non-contact additive manufacturing process developed and in wide spread use today with many applications and advantages easy control and flexibility among them, Loh et al. [1], Hu et al. [2], Ho et al. [3] and Schwab et al. [4]. Several components of the physical phenomenon underlying the SLM process are still not well understood including the balling phenomenon an extremely undesirable occurrence in the manufacturing process. Particles in the metallic powder bed in the SLM may either not be sintering at all or may be coalescing into rather large droplets triggering the balling phenomenon if the process and laser parameters are not correctly chosen resulting in a powder bed which is neither sintered at all or completely melted resulting ultimately into particles joined into rather large drops, Bourel et al. [5], Tolochko et al. [6] and Li et al. [7]. Usually the drops quickly spread out and their sizes may exceed the diameter of the laser spot, which triggers instability and distortion of the molten track, Fig. 1. As the physics underlying the SLM is not well understood the process cannot be thoroughly modeled. Thus, it is not possible at this time to devise accurate numerical tools useful in improving the quality of the parts made through the SLM. Increasing applications of the laser melting/sintering technologies over the years brought the balling phenomenon more in focus and studies were undertaken to clarify the underlying physics. To our knowledge the balling phenomenon has only been studied experimentally. Niu and Chang [8,9] are among the pioneers to study the balling phenomenon in the laser melting process. They investigated laser sintering of steel powders by scanning a single track on the powder bed at various laser powers and scanning speeds to establish an understanding of the underlying principles of the laser sintering of these powders and to determine a window of optimum processing conditions to avoid the balling phenomenon. Tolochko et al. [10,11] investigated the occurrence of the balling phenomenon under different processing conditions, especially analyzing the relationship between laser parameters and formation of “melted cakes”. Das [12] identified some of the important physical mechanisms in the direct SLM process of metals and provided an insight into the phenomena observed during the direct SLM of a variety of metallic materials. In his work, he concluded that balling occurs when the laser melted powder layer does not wet the underlying substrate. Two kinds of balling phenomena during direct SLM of 316L stainless steel powders were investigated by Gu and Shen [13] and Gu [14]. They found that using a low laser power gives rise to the first kind of balling characterized by highly coarsened balls possessing an interrupted dendritic structure in the surface layer. On the other hand, a high scan speed caused the second kind of balling featured by a large amount of micrometer-scale (10μm) balls on the laser sintered surface. Recently, Zhou et al. [15] studied the balling phenomenon in the SLM of pure tungsten powder bed. The surface morphology of the SLM manufactured part was investigated by SEM images. They concluded that the dominant solidification yields balling of large melt droplets causing surface roughness and instability due to the high surface tension and viscosity of tungsten. Few works focused on the numerical simulation of the balling phenomenon compared to experimental studies. This is because the SLM is a very complex process coupling many physical phenomena, which is hard to be modeled numerically, Yadroitsev et al. [16]. However, a numerical model of the SLM is desired and necessary for industrial manufacturers to optimize the process, reduce the cost and increase the product quality. This is the original motivation of this work. The aim of this work is to develop an accurate model to simulate the * Corresponding author. E-mail address: dennis.siginer@usach.cl (D.A. Siginer). https://doi.org/10.1016/j.ijthermalsci.2021.107011 Received 21 August 2016; Received in revised form 28 March 2021; Accepted 8 April 2021 1290-0729/© 2021 Elsevier Masson SAS. All rights reserved. M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Nomenclature I(s) Iλ0 Re P RL x, y z w Qc;i,j Qe;i,j Qi,j Hc kc ki Ac a d Ri r0 He H′e Cp Csp,i Clp,i Hp,i T Tm Ta Hm h ke Pl Ps ΔPp Radiation energy intensity Initial radiation energy intensity Reflective coefficient on the surface Power of the laser beam Radius of the laser beam Coordinates of the center of the laser beam Depth Correction coefficient in the Beer-Lambert law Conduction through the contact area between two particles i and j Conduction through air between two particles i and j Total heat flow between two particles i and j Heat transfer coefficient Harmonic mean of the conductivity of the particles i and j Conductivity of the ith particle Contact area between particles / radius of the contact area between two particles i and j/ radius of the grains Thickness of the contact region between two particles i and j Radius of the ith particle Initial radius of the sphere Thermal conductance for two particles in contact Heat flow from particle i to particle j when particle i is in contact with N particles Specific heat [J/(kg⋅K)] a(ΔPp ) ȧ Specific heat of the solid phase Specific heat of the liquid phase Volumetric enthalpy Temperature Melting temperature Ambient temperature Latent heat of melting Convective heat transfer coefficient [w/m2K] Effective thermal conductivity Liquid pressure Sintering atmospheric pressure Difference in gas pressure between the pore and the atmosphere Critical grain size under ΔPp ∕ =0 Rate of change of the grain radius in time Greek Symbols λ Wave length α Extinction coefficient Particle density [kg.m−3 ] ρp σ Stefan-Boltzmann constant εR Surface emissivity of the material Γ​ Surface tension η Dynamic viscosity θ Coalescence angle Radius of the liquid meniscus at the pore ρs Radius of the liquid meniscus at the compact surface ρp Strack [17], to study the effect of the process and material parameters on the generation of balling droplets in the laser melting process. The heat source with Gauss distribution is assumed to be volumetric and attenuates following the Beer-Lambert law. A heat transfer sub-model capable of describing thermal conduction in a discrete system is developed. The model makes it possible to estimate the effect of air between grains on the laser melting process. The effect of scanning speed on the generation of balling droplets is studied at a constant input heat flux. To highlight the importance of introducing the discrete model to describe the thermal behavior of granular materials and to validate our model, simulation results are compared with experimental works of other researchers taken from the literature. Finally, the effect of several laser parameters on the balling phenomenon is also analyzed. 2. Theoretical model of the SLM Physical phenomena that occur during the SLM process are multiple and complex. They can be divided into three groups: radiation transfer, heat conduction and melting behavior, Dong et al. [18], Defauchy [19], Jodhpur [20] and Peyré et al. [21]. Fig. 2 shows the operational process of the integrated model: the radiation transfer sub-model uses laser beam parameters, such as the laser power, scanning speed and radius of the laser beam. It also makes use of the optical properties of the material and the geometry of the grains to calculate the energy absorbed by the powder bed. The heat flux from radiation transfer sub-model is regarded as the heat source in the heat conduction sub-model. The temperature field of the powder bed is calculated by the discrete heat conduction sub-model. The model has the capability of describing the thermal history of each grain in the powder bed. Sintering sub-model uses temperature data and calculates values of the rheological properties corresponding to the temperature, and then estimates the change in the geometry of the powder bed caused by the coalescence and densification. The single layer simulation consists of these three sub-models as described and shown in Fig. 2. Fig. 1. Instability of the laser sintered tracks of 316L powder on steel substrate [12]. balling phenomenon in metallic SLM process, to better understand the multiple physical phenomena occurring in the material and to study the influence of each parameter on the quality of the manufactured parts. This will extend the areas of application of this technology, which promises to be very innovative, especially if we succeed in making structurally improved parts of higher mechanical and thermal characteristics. A comprehensive model is developed coupling multiple phenomena of the full SLM process including radiation transfer, thermal conduction, phase change, coalescence and air exhaust together with a 3D numerical model based on the discrete element method, Cundall and 2 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Fig. 2. Operational process of the integrated model for the SLM process. Fig. 4. Conduction between two elastic spheres in contact. Fig. 3. Illustration of the luminance within the homogeneous absorbing scattering medium. 3. Radiation and heat transfer in metallic powder bed I(s) = Iλ0 e−αs (2) Idepth (z) = Isurface e−αz (4) Therefore, the intensity of the laser beam conforms nearly to Gauss distribution on the surface of the powder bed and attenuates following the Beer-Lambert law in depth, Defauchy [19], ] [ 2(x2 +y2 ) − 2P RL w2 Isurface = (1 − Re )Iλ0 e , Iλ0 = 2 w = (3) 2.146 πw 3.1. Radiation transfer in metallic powder bed A powerful fiber laser beam either of the CO2 or the Fiber laser type is used as the input energy source in the SLM process. The CO2 type is generally used with polymeric materials, and the Fiber laser and sometimes Chrysler laser (Nd:YAG) are more suitable in metallic applications, Yu et al. [22], Martinez et al. [23] and Sing et al. [24]. Although metallic grains are opaque, the metallic powder bed is not opaque due to porosity. A powder bed with opaque particles can be approximated by an equivalent homogeneous absorbing scattering medium, Gusarov and Smurov [25]. During a transient radiative heat transfer in a two-dimensional slab, the distribution of the luminance within the homogeneous absorbing scattering medium involves three mechanisms: emission, absorption and diffusion, Fig. 3. If emission is negligibly small, the radiation transfer equation can be simplified into the Beer-Lambert Law, Gusarov and Smurov [25], describing laser metal interaction: ∫ I(s) = Iλ0 e−αλ s dλ (1) where Re is the reflective coefficient on the surface, r is the radial distance from the center of the laser beam, P is the power of the laser beam, RL is the radius of the laser beam, α is the extinction coefficient, z the depth location and w the correction coefficient in the Beer-Lambert law. 3.2. Thermal conduction in granular systems and the DEM Unlike heat transfer in homogenous media, thermal conduction in granular media like powder beds is defined as transfer of energy by diffusion between objects in physical contact, Watson et al. [26]. The traditional continuum conduction model is not suitable for the laser melting process. A discrete model is needed to describe the thermal behavior of the powder bed. Heat flow by conduction between two particles i and j in a granular system is illustrated in Fig. 4. It consists of two components: conduction through the contact area Qc and conduction through air Qe . Total heat conduction between two particles is then given by: λ where αλ is the attenuation coefficient in the wave length λ, I(s) is the radiation energy intensity at the given depth s and Iλ0 is the initial radiation energy intensity. For the laser heat source, the radiation wave length is usually unique. Then equation (1) can be written as: 3 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Table 1 Thermo-physical properties and other parameters used in the simulation, Jodhpur [20]. Qi,j = Qc;i,j + Qe;i,j Qc could be estimated based on the Fourier equation: Qc;i,j = − kc Ac dTi,j dx (5) 2k k i j where kc = ki +k is the harmonic mean of the conductivity of the particles j [J/(K⋅s⋅m)] and Ac = πa2 is the contact area between particles [m2 ]. Because the size of the particles i and j is very small, usually less than 100μm, the thickness of the contact region d is assumed to be the same as the thickness of the thermal conduction distance, so the thermal gradient between two particles could be approximated by: dT ΔTi,j ≈ dx d (6) kc Ac ΔTi,j = −Hc ΔTi,j , d Hc = kc Ac π kc a2 = d d (7) where ΔTi,j = Ti − Tj [K] and Hc is the heat transfer coefficient [J/(K⋅ √̅̅̅̅̅̅ s)]. The radius of the contact area is defined as a = Rd based on the Hertz contact theory with d representing the thickness of the contact region, R = 1 +1 1 is the effective radius and R1 and R2 are the radii of the R1 R2 Ri Rj Ri + Rj (8) where Ri and Rj are the radii of particles i and j, respectively. Heat conduction from particle i to j via air Qe;i,j is given by, ⎡ [ ⎤ ( )2 ] 2π 1 − 12 ar (r − a) ⎥ ⎢ ⎥ Qe;i,j = −He ΔTi,j , He = kair ⎢ (9) ⎣ ⎦ 1 − π4 where kair is the conductivity of air and He is the thermal conductance for two particles in contact. In a multiple contact model, if the particle i is in contact with N particles, considering all the contact areas, heat flow between the particle i and neighboring j is given by: )⎤ ( )2 ]( ⎡ [ π 2 − N2 ar r−a ⎢ ⎥ H ′e = kair ⎣ (10) ⎦ 1 − π4 Tit+Δt = Tit + ∑( ) dTp,i Qc;i,j + Qe;i,j + Qp,i source =− dt Qti Δt, mi Cpi Qti = − ) ∑( Qtc;i,j + Qte;i,j + Qtp,isource (15) 3.3. Thermal boundary conditions Energy lost by radiation and convection at the upper surface of the powder bed is given by (16)1. The bottom of the powder bed is insulated as represented by (16)2: ⃒ ( ) ) ( ∂T ∂T ⃒ −ke |surf = h Ta − T|surf + εR σ Ta4 − T|4surf , − ke ⃒⃒ =0 (16) ∂z ∂z bottom (11) where Ta is the ambient temperature, h is the convective heat transfer coefficient, assumed as constant h = 10 w/m2K, εR is the surface emissivity of the material, σ is the Stefan-Boltzmann constant and ke is the effective thermal conductivity. Thus, using equations (5) and (11), the conductive heat transfer equation becomes: ρp C p (14) where the superscript t means at time t with the assumption that the temperature within each particle is uniform, thermal conduction between particles in contact is calculated as: Qe;i,j = − H ′e ΔTi,j 1673.0 K 285.0 kJ. kg−1 500.0 J.kg-1.K −1 7800.0 kg.m−3 40.0 W.m−1. K −1 0.2 mono-dispersed 30 μm 140 μm where the volumetric enthalpy Hp,i is related to temperature T by the thermal equation of phase state. Csp,i and Clp,i are the specific heats of the solid and liquid phases, respectively, and ρp is the particle density. Tm is the melting temperature and Hm is the latent heat of melting, Qp,isource is given by the Beer-Lambert law (4). DEM allows following the evolution in time of each particle in a batch of particles initially randomly distributed. The number of neighboring particles to each particle is known at each time step, and the associated temperature is calculated assuming it is uniformly distributed within each particle. Several integration schemes have been developed for DEM. We use the classic Euler explicit integration scheme. At each time step, the force, displacement and heat flux are calculated by submodels introduced in previous sections. Detailed description of the sub-models is given in Xin et al. [27]. The update scheme applied for the temperature is: spheres in contact, respectively. The heat transfer coefficient can then be modified as: Hc = π kc Value Melting point (Tm) Enthalpy of fusion (Hm) Specific heat (Cp) Density (ρ) Thermal conductivity (kc) Emissivity (ε) Size distribution Grain size Laser beam size ⎧ H p,i ⎪ : Hp,i ≤ ρp Csp,i *Tm ⎪ ⎪ ⎪ ρp Csp,i ⎪ ⎪ ⎨ Tpi = Tm : ρp Csp,i *Tm < Hp,i < ρp Csp,i *Tm + Hm ⎪ ⎪ ⎪ ⎪ Hp,i − Csp,i *Tm − Hm ⎪ ⎪ : Hp,i ≥ ρp Csp,i *Tm + Hm ⎩ Tm + ρp Clp,i Then (5) can be modified as: Qc;i,j = − Property (12) where Cp is the specific thermal capacity [J/(kg⋅K)] and ρp is the particle 3.4. Validation of thermal conduction approach in granular systems ∑( ) dHp,i =− Qc;i,j + Qe;i,j + Qp,i source dt In this section, the discrete thermal conduction model developed in this paper is validated by comparing the results with the published data from Jodhpur [20], who developed a similar approach, a 3D discrete thermal conduction model, and numerically simulated the temperature distribution in the powder bed using a Discrete Element Method. The simulations for validation are done under the same initial and boundary conditions used by Jodhpur [20]. The powder bed is made of stainless-steel grains. The properties of powder material are listed in Table .1. density [kg.m−3 ]. To account for the phase change phenomena during the SLM process, the conductive heat transfer equation (12) is modified as: (13) 4 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 4.1. Viscous coalescence model Metallic melt flow can be regarded as a viscous liquid. Therefore, the viscous coalescence model is valid in modeling of the SLM process. The coalescence described as the overlapping of spherical particles and neck growth between contacting particles is an important aspect of sintering, Fig. 7. Particles are assumed to be single crystals and they remain spherical throughout the coalescence process. The sintering rate equation is derived by Frenkel from the energy balance equation assuming the surface energy reduction rate equal to the viscous dissipation rate during the deformation, Smoluchowski [29]. Pokluda et al. [30] derived a first order equation for the sintered angle through a modification of the Frenkel’s model: 5 dθ Γ 2−3 cosθ sinθ (2 − cosθ)1/3 = dt ηr0 (1 − cosθ)(1 + cosθ)1/3 , θ(0) = 0 (17) where Γ, η and r0 represent the surface tension, the dynamic viscosity and the initial radius of the grains (spheres). The evolution of the sintering neck radius in time is given by Fig. 5. Temperature distribution in the powder bed for increasing scan speed at P = 50 W: (a) (c) Results from Jodhpur [20]; (b) (d) Results from our simulations. The top view of temperature distribution in the powder bed with different scanning velocities is illustrated in Fig. 5. The temperature history of a given particle in the laser scan path is shown in Fig. 6. Figs. 5 and 6 show that simulations are in good agreement with those from published literature, Jodhpur [20]. In Fig. 5, the scan velocity of 0.6 m/s with a power of 50 W is enough to melt the particles in the laser scan path to form a continuous melted track. The peak temperature in powder bed is about 2000 K, which is significantly above the melting point. Increasing the scan velocity up to 1.0 m/s and keeping laser power constant decreases interaction time and few particles in the laser scan path seem to undergo melting. In this case, the peak temperature is barely beyond the melting point. Thus, energy absorbed is not enough to generate a continuous molten track. Temperature history of a particle in the scan path with different powers is shown in Fig. 6. Clearly increasing power raises the peak temperature of particles, which is opposite of the observed trends in Fig. 5 where scan velocity is increased. This suggests that the ratio between the power and scan speed can play an important role in characterizing thermal behavior of heated particles in powder beds. Fig. 7. The neck geometry applied to the sintering of two spheres. 4. Sintering model Fig. 8. Illustration of the liquid menisci at the specimen surface and around a pore containing a gas of pressure ΔPp during liquid phase sintering, Cho et al. [31]. The sintering process mainly consists of two phenomena: coalescence and densification, Suk-Joong [28]. Fig. 6. Temperature history of a particle in the laser scan path: (a) Results from Jodhpur [19]; (b) Results from our simulations. 5 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 h = sinθ a (18) Thus, yielding an equation to trace out the evolution of the grain equivalent radius, a, in time as the grains are coalescing. 4.2. Entrapped gases and pore filling theory Solid and liquid particles coexist at the interface between the molten and solid regions. In this region, molten fluid flows into interstices between solid grains pushed by gravity. Substantial volume of gas remains entrapped in this region. The filling of the pores roughly corresponds to the escaping air because of the difference between external and internal pressure of entrapped gases. When the gas pressure in an isolated pore is different from that outside the compact area, the pore filling is either delayed with an excess internal pressure or accelerated with an excess external pressure. Fig. 8 shows schematically the compact surface and the internal surface of a pore containing insoluble gases, Cho et al. [31], Park et al. [32]. Densification is mainly caused by escaping entrapped gases in the powder bed. Thus, the pore filling theory is suitable in modeling densification in metallic SLM process. Since hydrostatic pressure is maintained in the liquid, the bulk liquid pressure at the surface is the same as that at the pore surface, Suk-Joong [28], 2Γl Pl = Ps − , ρs Pl = ΔPp + Ps − 2Γl Fig. 9. Original powder bed before laser treatment. (19) ρp where Pl is the liquid pressure, Ps is the sintering atmospheric pressure, ΔPp is the difference in gas pressure between the pore and the atmosphere, ρs and ρp are the radii of the liquid menisci at the pore and at the compact surface, respectively. ρs is linearly proportional to the grain radius a (20) ρs (t)∝a(t) = 0; the critical condition for the wetting of a ρp is equal to rp when ΔPp ∕ pore surface leading to a spherical pore is reached, Park et al. [32]. Based on this hypothesis of spherical pores, let a(ΔPp ) and a(0) be the critical grain sizes under ΔPp ∕ = 0 and ΔPp = 0, respectively. Then following Cho et al. [31] and Park et al. [32], ) ) ( ) ( ) ( ( a ΔPp ρ ΔPp ρ ΔPp a ΔPp 1 = s = , (21) = s r a(0) a(0) rp 1 − 2Γp l ΔPp ρs (0) Fig. 10. Heat diffusion and sintering process in a powder bed with the laser power and the scanning speed set at 50W and 0.25 m/s, respectively. (a) Time = 0.0001s; (b) Time = 0.001s; (c) Time = 0.002s. each grain, their surface energy Γ and the evolution of the viscosity η versus temperature via an Arrhenius law. Runge-Kutta method is used to solve Eq. (17) coupled with Eqs. (19) and (22) to update the grain radius at each time step. The evolution of the neck radius of the joined grains during coalescence gives the evolution of the shape of the metal bulls formed on the surface. The temperature decrease in time after the laser sweep and the growth of the viscosity as the temperature decreases at the limits of the melted zone fix the size of the metallic bulls. In this study, to start the calculation, the initial radius a(ΔPp ) and rp are taken constant for all the powder bed and evaluated, respectively, from the initial mean porosity of the powder bed, and the initial radius of the solid grains, Fig. 8. Considering that rp remains constant, as the cooling process following the melting and coalescence phenomena is very fast in the case of the SLM process, and as it is established that porosity remains during powder sintering, then the rate of change of the grain radius in time ȧ can be written as: ȧ = a(0) [ rp 2Γl ΔṖp r 1 − 2Γp l ΔPp ]2 = a(0) 1 r rp 2Γl ΔṖp r 1 − 2Γpl ΔPp 1 − 2Γp l ΔPp ) ( = a ΔPp rp 2Γl 5. Results and discussion To validate the numerical model, simulation results are compared to the experimental data from published literature, Johnson and Rahaman [33]. 13,909 particles of diameter 130 μm are deposited in a box with dimensions of 8mm × 4mm × 4mm, Fig. 9. For solid particles, the density is 8470 kg/m3 , specific heat is 444 J/kg⋅K and conductivity is 14.9 W/m⋅K. For molten particles, the density is 7880 kg/m3 , specific heat is 611 J/kg⋅K and conductivity is 27. 5 W/m⋅K. The melting point of Ni-alloy is 1475 K. The latent heat of melting is 2. 516 GJ/m3 . The surface tension and viscosity of Ni-alloy at the melting point are 1850 mN/m and 5 mPa⋅s, respectively. The power of input heat flux is 50 W and the radius of laser beam is 0.65 mm. In the SLM process, the laser beam scans the powder bed in the longitudinal direction with various scanning speeds. The entire numerical simulation of the laser sintering process in Ni-alloy powder bed is calculated using self-developed ΔṖp r 1 − 2Γp l ΔPp (22) Equation (22) gives a relationship between the pressure evolution in the pore zone and the radius of the grains. Its solution needs the calculation of the evolution of the grain radius, given by the sintering theory, equations (17) and (18). Hence, Eq. (22) coupled with the coalescence Eqs. (17) and (18), which determine the evolution of the radius of the metal bulls, form a complete set to define the kinetics of the balling phenomenon on the surface of the grain bed. The initial grain radius is fixed for each test, and the formation of metallic bulls due to coalescence and pore evolution are governed by the thermal state of 6 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Fig. 11. Effect of scanning speed on the balling phenomenon: (a) Conclusion from Guo & Shen [13]; (b) Simulation results with the power set at 50W and various scanning speeds: 0.15 m/s, 0.25 m/s, 0.65 m/s; (c) Experimental results from Tolochko et al. [6] and Yadroitsev and Smurov [16]. Fig. 12. Numerical estimation of the effect of scanning speed on the width of the molten track. in-house code based on Fortran 90 software. Details on the Discrete Element method and all the couplings are already presented in our previous paper, Xin et al. [27]. Fig. 10 illustrates the numerical results of heat diffusion and the sintering process in a powder bed with laser treatment. The top view of the molten tracks and the calculated temperature distribution on the top of the powder surface are presented. There is no molten particle at the beginning of the sintering process because of insufficient input heat flux, Fig. 10 (a). Particles begin melting with increasing input laser energy, Fig. 10 (b), and molten particles combine with each other and grow into larger grains through coalescence, Fig. 10 (c). The temperature of the molten region decreases because of convection cooling at the surface after laser spot has passed. The effect of the scanning speed on the balling phenomenon is presented in Fig. 11. The width of the molten track is in a highly unstable state when the scanning speed is low because the amount of molten particles generated is excessive, Figs. 11 (b-1). The surface energy of molten particles will keep decreasing to get a final equilibrium state as explained by Gu and Shen [13], and as represented in Fig. 11 (a). The absorbed heat flux decreases leading to the shrinkage of the molten region with increasing scanning speed. If the scanning speed is too high, the molten region becomes unstable resulting in the break-up of the molten track as illustrated in Figs. 11 (b-3). Fig. 11 provides the evidence that the simulation methodology presented in this paper is quite good as confirmed by comparison with experimental findings in the literature [6–13]. We conclude that the discrete numerical model of the 7 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Fig. 13. Numerical estimation of the effect of the laser power on the width of the molten track. metallic laser sintering developed in this paper is useful in predicting the suitable input power and scanning speed for the laser melting process to avoid the triggering of strong balling. The calculated width of molten track is presented in Fig. 12 to quantitatively analyze the effect of the scanning speed on the balling. The lines represent the limits of the melted zones. Note that the variations are because in DEM we consider each grain at homogeneous temperature, and the variation around the diameter of the grains appears in the estimation of the melting temperature location. The average width of molten track is largest when the scanning speed is too low (0.15 m/s), and the shape of the molten track is distorted. The average width of the molten track is smallest, and break-ups of the molten track may occur (width is zero) when the scanning speed is too high (0.65 m/ s). The laser power is also a very important parameter in the SLM process. We simulated the SLM process with constant scanning speed (0.25 m/s) and different laser powers (20 W, 50W and 80 W) to study the effect of the laser power on the balling phenomenon. The coalescence of molten grains is directly controlled by surface tension and viscosity according to Frenkel (Eq. (17)). To study the influence of these two material properties on the balling phenomenon, we simulated the SLM process with constant process parameters (laser power 50 W and scanning speed 0.25 m/s) and different material properties (surface tension 1350 mN/m, 1850 mN/m, 2350 mN/m and viscosity 3.75 mPa⋅s, 5 mPa⋅s, 6.25 mPa⋅s ). As shown in Fig. 13, the average width of the molten track is largest when laser power is too high (80 W), and the shape of the molten track is highly irregular. The average width of the molten track is smallest, and the molten track breaks up when the laser power is too low (20 W). Clearly scanning speed and laser power produce opposite effects. The interactive relationship between these two process parameters is embedded in the laser energy density (ED) parameter (ED = P/vϕ) commonly used in the literature to characterize the SLM process in energetic terms. In (ED) P, v and ϕ represent the laser power, the scanning speed and the diameter of the laser beam, respectively. Too many grains melt resulting in a state of high distortion and irregularity if (ED) is too high. The driving mechanism behind this state of high distortion is the Fig. 14. Effect of the surface tension on the width of the molten track. 8 M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Fig. 15. Effect of the viscosity on the width of the molten track. Data availability decreasing surface energy of the liquid molten track in search of a final equilibrium. If (ED) is too low, the formation of molten grains is limited resulting in an unstable state and the occurrence of break-ups. The width of the molten track with different properties is presented in Figs. 14 and 15. If we consider the variance of the dimension of the molten track to the mean value as a criterion, it turns out that the average widths of the molten track with different surface tension and viscosity values are nearly the same. In other words, the variation of surface tension and viscosity has little influence on the balling phenomenon in the SLM process. This is because the coalescence process of molten metallic grains is too fast. It only takes less than 0.001s for two molten Ni-alloy grains with a diameter of 130 μm to join as one larger grain according to the coalescence model of Frenkel developed in Pokluda et al. [30]. Therefore, process parameters have much larger influence than material properties in the metallic SLM process. No data was used for the research described in the article. References [1] L.E. Loh, C.K. Chua, W.Y. Yeong, J. Song, M. Mapar, S.L. Sing, Z.H. Liu, D. Q. Zhang, Numerical investigation and an effective modeling on the selective laser melting process with aluminum alloy 6061, Int. J. Heat Mass Tran. 80 (2015) 288–300. [2] H. Hu, X. Ding, L. Wang, Numerical analysis of heat transfer during multi-layer selective laser melting of AlSi10Mg, Optik 127 (2016) 8883–8891. [3] J.Y. Ho, K.K. Wong, K.C. Leong, Saturated pool boiling of FC-72 from enhanced surfaces produced by selective laser melting, Int. J. Heat Mass Tran. 99 (2016) 107–121. [4] H. Schwab, F. Palm, U. Kühn, J. 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In this work, a discrete element method is developed to model the coupled phenomena of radiative and conductive heat transfer in a granular medium, coalescence and densification and the moving laser heat source. The model is validated by comparison with findings from the literature. The laser heat source scanning speed and the melting power needed by the material are well captured by the model to avoid the balling phenomenon, an undesirable consequence of the sintering process. The findings in this paper represent a crucial step for the optimization of the process of laser sintering for additive manufacturing. We determine that the variation of surface tension and viscosity has little influence on the balling phenomenon, and that process parameters have much larger influence than material properties in the metallic SLM process. 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