Thermofluid field of molten pool and its effects during selective laser melting (SLM) of Inconel 718 alloy

Accepted Manuscript Title: Thermofluid field of molten pool and its effects during selective laser melting (SLM) of Inconel 718 alloy Authors: Dongyun Zhang, Pudan Zhang, Zhen Liu, Zhe Feng, Chengjie Wang, Yanwu Guo PII: DOI: Reference:

S2214-8604(17)30096-9 https://doi.org/10.1016/j.addma.2018.03.031 ADDMA 327

To appear in: Received date: Revised date: Accepted date:

4-3-2017 2-3-2018 31-3-2018

Please cite this article as: Zhang D, Zhang P, Liu Z, Feng Z, Wang C, Guo Y, Thermofluid field of molten pool and its effects during selective laser melting (SLM) of Inconel 718 alloy, Additive Manufacturing (2010), https://doi.org/10.1016/j.addma.2018.03.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermofluid field of molten pool and its effects during selective laser melting (SLM) of Inconel 718 alloy

Dongyun Zhang*a,b, Pudan Zhanga,b, Zhen Liua,b, Zhe Fenga,b, Chengjie Wanga,b ,

Institute for laser engineering, Beijing University of Technology, Pingleyuan No.100,

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a

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Yanwu Guoa,b

Beijing Engineering Research Center of 3D Printing for Digital Medical Health, Beijing

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b

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Chaoyang Dist, Beijing, 100124,P.R.China

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University of Technology, Pingleyuan No.100, Chaoyang Dist, Beijing, 100124,P.R.China

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* Corresponding author: Dongyun Zhang, Tel: 86 10 67396557, Fax: 86 10 67391524,

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E-mail: [email protected].

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Highlights 

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 

The optical penetration depth of the laser beam into the powder bed is taken into account in this model. The convective heat flux dominate the heat tranfer in the molten pool, and further decides the shape of molten pool.. Heat accumulation can significantly change the size of the molten pool, but has little effect on the molten pool shape.

Abstract A physical model coupled with heat transfer and fluid flow was developed to investigate 1

the thermofluid field of molten pool and its effects on SLM process of Inconel 718 alloy, in which a heat source considering the porous properties of powder bed and its reflection to laser beam is used. The simulation results showed that surface tension caused by temperature gradient on the surface of molten pool drives to Marangoni convection, which makes fluid flow

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state mainly an outward convection during SLM process. Marangoni convection includes convective and conductive heat flux, both of them have effects of on molten pool shape, but the

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effect of convective heat flux is dominant because its magnitude is one order larger than that of

conductive heat flux. The convective heat flux accelerates the flow rate of the molten metal,

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benefits to heat dissipation. The convective heat flux makes the molten pool wider, while the

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conductive heat flux makes comparably the molten pool deeper and wider. Furthermore, heat

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accumulation caused by multiple scanning increases convection and conduction heat flux

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resulting in the increase of the width and depth of the molten pool, but no change of dominant

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role of convective heat flux to the shape of the molten pool.

Keywords: Selective laser melting(SLM); Finite element model; Marangoni effect; Heat

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flux; Inconel 718 alloy

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Nomenclature Cp

Dp hc ΔΗ L

specific heat at constant pressure, J/(kg K) average diameter of the powder particles, m convective heat transfer coefficient, W/(m2 K) latent heat of the phase change, J/kg layer thickness, m 2

u, v, w x, y, z θ γ ε κ κeff

velocity magnitude, m/s coordinates, m volume fraction of solid phase surface tension, N/m radiation emissivity thermal conductivity of powder bed, W/(m K) effective thermal conductivity of

We V ⃗ 𝒗 u, v, w

κf κr

κs 𝝁 𝝆 𝝆𝒉 𝝈𝒆 𝝎

powder system, W/(m K) thermal conductivity of the ambient gas, W/(m K) thermal conductivity due to the radiation among particles, W/(m K) thermal conductivity of the solid, W/(m K) dynamic viscosity, Pa•s density, kg/m3 reflectivity Stefan-Boltzman constant, W/(m2 K4) radius of the Gaussian laser beam, m

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t T Tp

mass source, kg volume force pressure, Pa incident power density, W/m2 source item of the energy conservation equation time, s temperature, K temperature of the powder particles, K total laser power, W scan speed, m/s overall velocity vector, m/s velocity magnitude, m/s

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Ms F p Q0 SH

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1. Introduction

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Inconel 718 alloy, an extensively developed Ni–Cr–Fe austenite (γ) superalloy, has

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attracted enormous attention over the past four decades[1-3]. This superalloy has been used in

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aviation, aerospace, and energy industries owing to its excellent high-temperature strength,

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wear resistance, chemical stability, and corrosion resistance. However, its high hardness and low thermal conductivity make it difficult to be processed using traditional casting and

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forging[4-6], limiting its application. Meanwhile, the shape and performance of modern parts

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are becoming more complex, prompting the need for a processing technology that can produce parts with complex features and excellent mechanical properties.

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Selective laser melting (SLM), a powder bed based additive manufacturing method, can

fabricate complex three-dimensional parts directly from a CAD model. In SLM, a recoater spreads powder particles over a building platform, then a high-intensity laser beam scans over the powder layer according to the CAD data, fabricating the part by locally consolidating the powder bed in successive layers[7]. To prevent the metal powder from oxidizing at high 3

temperature, SLM process is usually performed in a closed chamber filled with pumped nitrogen or argon[8, 9]. Although SLM technology has many advantages, it is difficult to create high-quality parts. Its physical metallurgical process is very complex, schematically shown in Fig. 1. In SLM, laser

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energy was absorbed by the powder, which melts and forms a molten pool. The heat dissipation in the molten pool occurs normally by conduction, radiation, and convection[10]. Driven by

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temperature gradient on its surface, ‘Marangoni’ convection in the molten pool occurs and becomes one of main heat dissipation methods[11]. The heat flux in the molten pool promotes

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epitaxial growth and further lead to anisotropy of performances[12]. The final microstructure of

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a part produced by SLM depends largely on the thermofluid field in the molten pool[13]. To

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control and improve the mechanical properties of these parts, the thermofluid field in the molten

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pool should be studied. But it is difficult to understand such a complex physical metallurgical

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process using conventional experiments because of ultra-fast heating and cooling rates, tiny molten pool with the dimension of 100-300μm，ultra-short existence time of the molten pool

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with the order of μs and other factors. Numerical simulation provides the possibility to

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reproduce the ultra-fast laser-material process. Yadroitsev[14] studied the effects of process parameters on final product quality of SLM

AISI 420 stainless steel with a 3D finite element model(FEM), revealing the numerical

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simulation in the temperature field and the shape of the molten pool could help optimize processing parameters. Using FEM, Lin et al.[15] studied the heat transfer from powders to solid, and explored how process parameters would affect the temperature distribution and the dimensions of the molten pool. They found the dimensions of the molten pool strongly depend 4

on the process parameters. Li and Katakam[16, 17] used a multiphysics heat transfer model to analyze how process parameters affect the temperature field, combining these simulations with experimental results to explore how the temperature distribution would affect the microstructure. The results revealed that the thermal history during SLM process causes the

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formation of inhomogeneous microstructure. Özel T[18] et al. found that the process parameters and rotating scan strategy could affect the size of the molten pool and its temperature gradients

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using 3D FEM and thermal camera. Li C J[19] used Computational Fluid Dynamics (CFD) to

analyze the heat transfer behavior of Ti-6Al-4V powder particles during SLM process and

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predicted the cross-section shape of the weld. The results showed that heat transfer can affect

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the shape of the molten pool and a higher laser scanning speed can lead to bubble formation in

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the final microstructure. However, previous studies mainly reported the effects of process

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parameters and heat accumulation on the shape of the molten pool and surface appearance of

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final parts in the SLM process. Only a few researchers examined the effect of thermofluid field on the shape of the molten pool and surface quality of the final parts, especially the researches

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on heat and mass transfer in the molten pool and their affecting factors.

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In this paper, a three-dimensional finite element model considering Marangoni convection and laser optical penetration was developed to explore the thermofluid field in molten pool and its influence on the shape and dimensions of the molten pool during selective laser melting of

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Inconel 718 alloy.

Model description It is known that the interaction between laser and powder is a very complicated process, which contains physical phenomenon and metallurgical change such as energy absorption and 5

transfer, evaporation and melting of powder, phase transformation, convection of molten metal and solidification as well. That can be simulated with COMSOL Multi physicsTM 5.0 software characterized with coupling with multi-physical field, in which molten metal flow, temperature distribution, and heat flux are considered. To simplify the simulation process, the following

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assumptions are made in this study: (1) The powder particles are spherical particles with same diameter, uniformly distributed in

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the powder bed;

(2) The melt in the molten pool is incompressible homogeneous Newtonian fluid and the flow

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state is considered to be laminar;

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(3) In addition to surface tension, thermal conductivity and heat capacity, the other thermal

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physical parameters are constant;

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(4) The metal vaporization during SLM is ignored.

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2.1 Physical model

The three-dimensional finite element model was depicted in Fig. 2. The simulation domain

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has the dimensions of 2×1×0.33 mm, in which the top layer with the thickness 0.03 mm is a

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single-layer powder, and the lower part is a substrate. In order to reduce the computational complexity and time, and ensure the accuracy of calculation, the simulation domain is divided into different regions with different mesh sizes in terms of its importance. The mesh size in

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powder layer is refined, while the mesh size in the substrate area is relatively coarser. The minimum mesh size in the powder layer is 6 μm, grows gradually along the positive direction of z-axis, with a growth factor of 1.12. The laser beam is defined as function q (x, y, z, t) and scans over the surface of the powder bed in the x or y direction. In this paper, free meshing 6

method is used for the FEM. The scan strategy, namely a zig-zag scanning path, is shown also in Fig. 2, in which a continuous laser scanning tracks with five-channel is depicted. 2.2 Governing equation Selective Laser Melting is a typical process of nonlinear transient heat transfer, which

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involves the transformation of mass, momentum and energy. The governing equations which

three-dimensional Cartesian coordinate system as follows[20]: Mass conservation equation ⃗ ) = 𝑴𝒔 + 𝜵 ∙ (𝝆𝑽

⑴

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𝝏𝝆 𝝏𝒕

⃗ ∙ 𝜵𝑽 ⃗ ) = 𝝁𝜵𝟐 𝑽 ⃗ − 𝜵𝑷 + 𝑴𝒔 ∙ 𝑽 ⃗ +𝑭∙ 𝑽

⑵

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⃗ 𝝏𝑽 + 𝝏𝒕

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Momentum conservation equation 𝝆(

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comply with the mass, momentum and energy conservation equation can be expressed in a

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Energy conservation equation 𝝏𝑻

⑶

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𝝆𝑪𝑷 𝝏𝒕 + 𝝆𝑪𝑷 𝝁 ∙ 𝜵𝑻 = 𝜵 ∙ (𝜿𝜵𝑻) + 𝑺𝑯

where ρ, κ, μ, and P represent density, thermal conductivity, dynamic viscosity, and pressure,

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⃗ is the motion velocity of the melt; respectively. 𝐶𝑃 is the specific heat at constant pressure, 𝑉

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F is the body force, Ms is a mass source, and SH is the source item of the energy equation, which can be defined as follows: 𝝏 ⃗ ∆𝑯)] 𝑺𝑯 = −𝝆 [ ∆𝑯 + 𝜵 ∙ (𝑽 𝝏𝒕

⑷

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where ∆𝐻 is the latent heat of phase change. Liquid–solid phase transition is taken into account in this model, which begins at the solidus temperature (Ts) and ends at the liquidus temperature (Tm). In this phase change, κ, 𝜌, and CP can be obtained from the following equations[21]: 7

𝜿 = 𝜽𝜿𝒑𝒉𝒂𝒔𝒆𝟏 + (𝟏 − 𝜽)𝜿𝒑𝒉𝒂𝒔𝒆𝟐

⑸ 𝒅𝜶

𝑪𝑷 = 𝜽𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟏 + (𝟏 − 𝜽)𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟐 + 𝑳𝒇 /𝒗 𝒅𝑻 𝝆=

𝜽𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟏 +(𝟏−𝜽)𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟐 𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟐

⑹ ⑺

𝜽𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟏 +(𝟏−𝜽)𝑪𝑷∙𝒑𝒉𝒂𝒔𝒆𝟐

where phase1 and phase2 denote the solid and liquid phases, respectively. θ is the volume of

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the solid phase, and α is a smoothing function in the COMSOL software describing the phase ratio in the phase transition.

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2.3 Powder bed and heat source

An ideal model of powder packing with same particle size, namely hexagonal close packing, with a maximum packing density of 67%[22], is shown in Fig. 3(a). As we can see, the

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powder bed is not dense and there exist many gaps among particles although powder particles

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pack closely. In fact, powder with continuous particle size distribution is spread stochastic by

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recoater, the gaps among particles are much more complex than that described here. In order to reduce the computational complexity in the simulation, the ideal model of powder packing with

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same particle size in simulation is used. From the determination of apparent density, the porosity

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of naturally powder packing is normally 45% because of the existence of gaps among spherical powder particles.

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The existence of the gaps will not only affect the absorption of powder to laser energy, but

also the thermal conductivity on the powder bed. Here we discuss only the effect of the gaps

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among powder particles on energy absorption. When the laser beam irradiates the surface of the powder bed, the light can penetrate deeply the powder layer with the thickness of several particle-diameter with multiple reflections[23]. In several early studies (cite those papers), laser penetration with multiple reflections was not taken into account in the simulation and a simple surface heat source was applied. Whereby the laser source is assumed to be a Gaussian, given 8

by[24]: 𝒓 𝟐

𝒓 𝟐

𝑸𝟎 = 𝑸𝒎 (𝟏 − 𝝎) (𝒂 + 𝝎) , 0
⑻

where 𝜔 is the radius of the Gaussian laser beam, and Qm is related to the total laser power We as: 𝟑𝑾

𝑸𝒎 = 𝝅𝝎𝟐𝒆

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⑼

Eq. (8) gives the energy irradiated on the top surface of powder bed. To obtain the energy

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absorbed into powder material, a pure powder bed model with an unlimited thickness of powder is assumed, in which laser energy is totally absorbed by powder layer due to laser beam

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penetration with multi-reflection. The absorbed energy flux through the powder bed q is given

𝝆𝟐𝒉 )𝒆−𝝀 [(𝟏 − 𝒂)𝒆−𝟐𝒂𝝃 + (𝟏 + 𝒂)𝒆𝟐𝒂𝝃 ] − (𝟑 + 𝝆𝒉 𝒆−𝟐𝝀 ){[𝟏 + 𝒂 −

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𝝆𝒉 𝒂 {(𝟏 − 𝒉 −𝟑)𝑫

𝒒 = (𝟒𝝆

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by:

𝟑(𝟏−𝝆𝒉 )(𝒆−𝝃 −𝝆𝒉 𝒆𝝃−𝟐𝝀 )

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𝝆𝒉 (𝟏 − 𝒂)]𝒆𝟐𝒂(𝝃−𝝀) + [𝟏 − 𝒂 − 𝝆𝒉 (𝟏 + 𝒂)𝒆𝟐𝒂(𝝃−𝝀) ]}} −

𝟒𝝆𝒉 −𝟑

⑽

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where 𝜌ℎ is the reflectivity, 𝜆 = 𝛽𝐿 is the optical thickness of the powder bed, 𝑎 = √1 − 𝜌ℎ ; and D are given as follows:

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𝑫 = (𝟏 − 𝒂)[𝟏 − 𝒂 − 𝝆𝒉 (𝟏 + 𝒂)]𝒆−𝟐𝒂𝝀 − (𝟏 + 𝒂)[𝟏 + 𝒂 − 𝝆𝒉 (𝟏 − 𝒂)]𝒆𝟐𝒂𝝀

⑾

The extinction coefficient is estimated as follows: 𝜷 = 𝑺/𝟒

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⑿

where S is the specific powder surface per unit pore volume.

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A model with powder layer thickness of 30 μm similar to the powder bed during SLM

process was established and simulated. Some of laser energy irradiating was absorbed by powder materials on the powder bed, and some of them were absorbed by the substrate through penetrating into the powder bed. In this model, we assumed that the total absorption rate of both powder particles and substrate of Inconel 718 alloy is more than 80% [25]. When the rest 20% 9

reflected laser energy meets the other powder particles, who would absorb 80% and reflect 20% of them, multi-reflection would take place several times. Absorption of materials to laser beam is thus significantly improved. The energy absorbed by the substrate is given by q at z=30 μm (Eq. (10)).

𝑸 = −𝜷𝑸𝟎

𝒅𝒒 𝒅𝝃

⒀

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Ultimately, this model gives an expression for the volumetric heating Q as:

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where 𝛽 is the extinction coefficient, and 𝜉 = 𝛽𝑧 represents dimensionless coordinates. In

this paper, Eq. 13 is used in the simulation in heat flux and heat accumulation. Its movement in

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the form of a fixed-point heat source in heat flux and a moving heat source in heat accumulation

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was used in the simulation. The energy distribution of heat source is shown in Fig. 3(b). It can

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be seen that the energy of heat source attenuates with the increasing thickness of the powder

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layer along the Z direction, which describes also the laser energy distribution into the powder

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bed. 2.4 Boundary conditions

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During SLM process, the initial temperature of powder bed and substrate was set at

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ambient temperature (T0=300 K). On the top surface of powder bed, heat transfer is allowed between the powder bed and the surrounding environment. The powder bed absorbs the energy of laser beam while dissipating energy outwardly in the form of radiation, and convection. The

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boundary conditions can be represented as follows[26]: 𝝏𝑻

−𝜿𝒆𝒇𝒇 ( 𝝏𝒛 )

𝒛=𝟎

= 𝑸 − 𝒉𝒄 (𝑻 − 𝑻𝟎 ) − 𝝈𝒆 𝜺(𝑻𝟒 − 𝑻𝟒𝟎 )

⒁

where 𝜅𝑒𝑓𝑓 is the effective thermal conductivity of the powder bed, hc is the convective heat transfer coefficient, 𝜎𝑒 is the Stefan–Boltzmann constant and the value, which is 5.67×10−8 10

W/(m2 K4), and 𝜀 is the radiation emissivity. At the side of the powder bed, the boundary condition is defined as radiation, given by the last term of Eq. (14). In the molten pool, the Marangoni convection caused by temperature gradient can affect the mass and heat transfer, affecting temperature field, velocity field, and molten pool size[27].

𝝏𝒖

𝝏𝜸 𝝏𝑻

𝝏𝒗

𝝏𝜸 𝝏𝑻

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As such, the model considers Marangoni effect as follows[28]: −𝝁 𝝏𝒛 = 𝝏𝑻 𝝏𝒙

⒂

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−𝝁 𝝏𝒛 = 𝝏𝑻 𝝏𝒚

⒃

where γ is the surface tension and 𝜕𝛾/𝜕𝑇 is the surface tension gradient, also known as the

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Marangoni coefficient.

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2.5 Powder material properties

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The thermal conductivity and heat capacity of powder bed plays an important role in the

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simulation in cooling rate and temperature gradient in the molten pool. Just as mentioned above,

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the effect of gaps among powder particles on absorption of powder bed to the laser beam is already in consideration by using heat source (Eq. (13)). In nature, the existence of air in the

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gaps has possible effect on thermal conductivity and heat capacity of the powder bed. Fig. 5

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shows the temperature-dependent properties of bulk Inconel 718 alloy[29]. But the thermal conductivity of the powder bed becomes significantly lower due to the existence of gaps among powder particles and shielding gas in them. Therefore, a separate calculation in the thermal

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conductivity of the powder bed is necessary[30]. To simplify the calculations, we assume that the powder particles are spherical and that the contact surface is undeformed. Therefore, the thermal conductivity of the powder bed can be represented as follows[31]: 𝜿 𝜿𝒇

= (𝟏 − √𝟏 − ∅) (𝟏 +

∅𝜿𝒓 )+ 𝜿𝒇

√𝟏 − ∅ {

𝟐

𝟏−

𝜿𝒇 𝜿𝒔

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[

𝟏

𝜿𝒇

𝟏−

𝜿𝒔

𝜿

𝜿

𝒍𝒏 (𝜿𝒔 ) − 𝟏] + 𝜿𝒓 } 𝒇

𝒇

⒄

where ∅ is the porosity of the powder bed, 𝜅𝑓 is the thermal conductivity of the ambient gas, 𝜅𝑠 is the thermal conductivity of the solid, and 𝜅𝑟 is the thermal conductivity caused by radiation among particles, which can be represented as follows: 𝜿𝒓 = 𝟒𝑩𝝈𝒆 𝑻𝟑𝑷 𝑫𝑷

⒅

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where Dp is the average diameter of powder particles, TP is the temperature of powder particles, and B is an apparent coefficient, typically 1/3.

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Fig. 5 shows the thermal conductivity of the powder bed, calculated from Eq. 17, revealing that the thermal conductivity of the powder bed is two orders of magnitude lower than that of

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the bulk alloy. According to previous researches, the gaps among powder particles do not have

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a significant effect on the heat capacity of the powder bed[32], so no curve of heat capacity on

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the powder bed is schematized separately in this paper.

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2.6 Numerical simulation

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Recent researches in welding technology demonstrated that fluid flow, heat transfer and the resulting weld shape depend significantly on Marangoni convection[33-35]. Due to the

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similarity between SLM and welding process, Marangoni convection in the molten pool also

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has an effect on the SLM. Marangoni coefficient affects mainly the magnitude and direction of the Marangoni convection, and further the fluid flow, the heat transfer of molten pool and the resulting weld shape as well[31]. In addition, the content of the surface active elements such as

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O and S in the molten pool is also an important affecting factor[36]. Because SLM is a lasematerial interacting process with ultra-fast heating and cooling rate, numerical simulation is a good way to investigate the mechanism of the effect of Marangoni convection on SLM process. The flow field and temperature field during SLM were simulated using COMSOL

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MultiphysicsTM software. In order to reduce the amount of calculation and avoid the influence of the movement of the heat source on the flow of the molten metal, a fixed-point heat source was used to simulate the effects of Marangoni coefficients on the convective state, and the duration of the transient

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calculation is 0.0000625s. Marangoni coefficients of different vector directions have different effects on the magnitude and direction of Marangoni convection. In order to compare the

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changes in the shape of the molten pool, two convective states including positive and negative

Marangoni coefficients of 4×10−4 N/(m K) and −4×10−4 N/(m K) were selected from empirical

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value, a nonconvective state at ∂γ/∂T=0 N/(m K) as reference was simulated also. Then, the

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influence of Marangoni convection on the shape of the molten pool during SLM, namely five

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continuous tracks scanning of each track with the length of 1.5mm during the multiple tracks

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scanning process with an overlap of 30% was simulated. Here a moving heat source is used.

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Table 1 lists the thermal physical properties of Inconel 718 alloy[37, 38] and SLM processing

Table 1

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parameters used in the simulation.

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The thermal physical properties of Inconel 718 alloy and SLM processing parameters from EOSINT

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M280 used in the simulation

Thermal physical properties of Inconel 718 alloy

Value

Convective heat transfer coefficient, hc (W/(m2 K)) The Stefan-Boltzman constant, 𝜎𝑒 (W/(m2 K4)) Radiation emissivity, 𝜀 Melting point of Inconel 718, T (K) Marangoni coefficient, 𝜕𝛾/𝜕𝑇 (N/(m K))

80 5.67x10-8 0.8 1571 ±4x10^-4、0

SLM processing parameters from EOSINT M280

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Initial temperature, T0 (K) Laser power, We (W) Powder layer thickness, L (μm) Radius of laser beam, 𝜔 (μm) Scan speed, v (mm/s)

300 190 30 50 1200

3. Experimental procedures

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3.1 Inconel 718 powder material The 99.7% purity Inconel 718 alloy powder with a spherical particle shape and an average

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particle diameter of 30 μm is used in this paper. 3.2 SLM Processing and characterization

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The investigation for SLM was performed on an EOSINT M280, which consisted mainly

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of an YLR-400 fiber laser with a maximum output power of 400W and a spot size of 100 μm,

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an automatic powder delivery apparatus, a building platform, and a computer system for process

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control. Argon is used as the protective gas to avoid molten pool contamination. The oxygen

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content in the chamber during SLM process is less than 0.1%[39]. Specimens for microstructural characterization were prepared according to standard

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procedure, etched for a few seconds using Kalling’s etchant. The microstructure was observed

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with an OLYPMUS DP72 optical microscope(OM).

4. Results and discussion

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4.1 Marangoni coefficients and its effects Fig. 6 shows the velocity vector plots of convective flow in the molten pool with different

Marangoni coefficients. As we seen from Fig. 6a, for 𝜕𝛾/𝜕𝑇 of −4×10−4 N/(m K), the molten metal flows from the bottom to the upper surface through the center of the molten pool. On the upper surface of the molten pool, the molten metal flows from the center to the edge (Fig. 6b).

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While at the edge of the molten pool the molten metal flows from upper surface to the bottom(Fig. 6a). This fluid flow state, namely a circulation of center- upper surface- bottom of molten pool, is called outward convection. The flow rates in the center and on the surface of the molten pool are greater than that in others, and the maximum flow rate is 0.78 m/s. For

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𝜕𝛾/𝜕𝑇 of 4×10−4 N/(m K), an inverse fluid flow state forms, namely a circulation of bottomupper surface-center of molten pool, which is called inward convection (Figs. 6c,6d). Same as

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in outward convection, the fluid flows faster in the center and on the surface of the molten pool.

For 𝜕𝛾/𝜕𝑇 of 0 N/(m K), there is no Marangoni convection in the molten pool, and no

U

convective flow is plotted.

N

With a negative Marangoni coefficient, the surface tension of molten pool decreases with

A

increasing temperature. The hot molten metal in the center of the molten pool has lower surface

M

tension than that at the edge, and the molten metal on the surface is driven by the surface tension

ED

flows from the center to the edge. While the Marangoni coefficient is positive, the surface tension increases with increasing temperature and therefor the molten metal on the surface

PT

driven by surface tension flows on the contrary from the edge to the center.

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In nature, Marangoni effect in the molten pool is driven by surface tension variation due to temperature gradient. Any factors affecting surface tension can cause the altering of Marangoni effect. The content of the surface active element causes the altering of the surface

A

tension of the molten metal, what even changes the Marangoni coefficient from negative to positive and resulting in an inversion of fluid flowing state in molten pool, namely from an outward convection to an inward convection. In general, the content of the elements such as O, S in powder materials is already controlled before delivery, and the content of the O element in 15

building chamber is interchanged by shielding gas argon, the fluid flowing state in molten pool during SLM is outward convection[40].

4.2 Molten pool shape with a fixed-point heat source

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In general, the shape of the molten pool is determined by the heat flux in the molten pool, which consists of convective and conductive heat flux and causes heat transfer within the

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molten pool[41]. In order to understand the effects of Marangoni effect on the shape of the molten pool, the heat flux in the molten pool should be analyzed.

The effect of Marangoni effect on the shape of the molten pool is investigated

U

quantitatively. Fig. 7 shows the effect of Marangoni coefficient on the values of width, depth

A

N

and depth-to-width ratio of the molten pool with a fixed-point heat source. It can be seen, with

M

the increase of the Marangoni coefficient, the depth of the molten pool increased from 34 μm

from 117 μm to 92 μm.

ED

to 48 μm and the depth-to-width ratio increased from 0.29 to 0.52, while the width decreased

PT

Fig.8 shows the heat flux, namely convective and conductive heat flux in the molten pool at various Marangoni coefficients with a fixed-point heat source. It can be seen, there is no

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significant difference in the magnitude of the conductive heat flux in the case of 𝜕𝛾/𝜕𝑇=-4 and 4×10−4 N/(m K), and they are of same order of magnitude of 109 W/m^2. In addition, there is

A

no significant difference in the magnitude of the convective heat flux in the case of 𝜕𝛾/𝜕𝑇=-4 and 4×10−4 N/(m K), while the convective heat flux (1010 W/m^2) is one order larger than the conductive one. Fig. 8a showed also that the maximum convective heat flux is concentrated on the surface of the molten pool, its flowing direction is from the center to the edge. For 𝜕𝛾/𝜕𝑇 of −4×10−4 16

N/(m K), the flow of the molten metal is outward convection (Fig. 6a). Under outward convection, the hot molten metal on the surface of the molten pool flows to the edge first. This behavior promotes lateral heat conduction and restrains longitudinal heat conduction. There is no obvious difference in all directions of heat conduction (Fig. 8b). In such a heat flow state,

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the melting speed of the molten pool edge is accelerated and the melting rate of the molten pool bottom is slowed, so that the depth-to-width ratio is reduced relative to the convection-free state.

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For 𝜕𝛾/𝜕𝑇 of 0 N/(m K)，the molten metal does not flow, and there is no convective heat flux in the pool, so there is no vector diagram of the convective heat flux. At this point, the heat in

U

the molten pool is transferred only by conduction (Fig. 8c). For 𝜕𝛾/𝜕𝑇 of 4×10−4 N/(m K),

N

the flow of the molten metal is inward convection (Fig. 6c). In this case, the convective heat

A

flux in the molten pool is opposite to that in the outward convection, and the conductive heat

M

flux is similar to the convection-free state (Figs. 8d, 8e). Thus, the depth-to-width ratio is larger

ED

than that of the convection-free state. From the analysis above, the Marangoni effect can significantly affect the molten pool shape.

PT

Driven by surface tension or Marangoni effect, the convective heat flux results in a

CC E

circulation of the flow of molten metal, the melt in high temperature in the center of molten pool is carried into the low temperature region at the edge. The flow velocity of molten metal is larger on the surface of the molten pool, reaching 0.6 m/s (Fig. 6), which can significantly

A

improve the convective heat flux in the molten pool, and speeding up the flow of melt and heat transfer inside the molten pool. Therefore, convective heat flux dominates the heat transfer in the molten pool. 4.3 Molten pool shape with a continuous multiple scanning 17

From above discussion, Marangoni effect can significantly affect the shape of the molten pool. In addition, SLM process is also a process of accumulation in mass and energy. Due to continuous heat input by laser beam accompanying scanning process, the substrate and its neighboring powder have a temperature increase. The increase in temperature will improve the absorption of powder bed to laser energy, while prevent heat dissipation occurs from the laser scanning area to the surrounding. The effects of heat accumulation on heat flux and molten pool

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shape are simulated and discussed in the following, in which continuous five-track scanning

process is simulated, the Marangoni coefficient of Inconel 718 alloy during SLM process is -

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5×10−4 N/(m K)[42].

Fig. 9a and b show the microstructures in upper surface and vertical section of the experimental molten pool. Fig. 9 c and d show a top view of temperature gradient, a combined

U

weld macrostructure (OM) and the side view of the temperature gradient in the simulation of

N

the first scanning track, respectively. The gray lines in Fig. 9 c and d are fusion line of the

A

molten pool, which outlines solid-liquid phase boundary. Fig. 10 sketches the simulated change of shape and size of the molten pool at various locations of continuous five-track scanning in

M

the powder bed. It can be seen that during the process of continuous heat input, the length of the molten pool changes more than the depth and width of the molten pool.

ED

The width and depth of the molten pool in Fig. 9a and b were about 102μm and 50μm by optical microscope observation, respectively.

Its shape and size in cross-section is similar to

PT

that of the simulated one, which is approximately semi-elliptical. The center of the cross sketched with a black dashed line in Fig. 9c is the center of the laser beam, in which the center

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of molten pool lags behind the center of the laser beam. It is because the laser source is moving, both the molten and solid metal have a much higher thermal conductivity than the powder bed. The difference in conductivity means the energy absorbed by the powder bed and molten metal

A

transmits more quickly in the rear than that in other directions on the contrary of the movement of the molten pool. The temperature gradient distribution is similar to the “comet tail” distribution reported in the literature[43]. The maximum temperature in the molten pool is 6470 K, far above the boiling point of Inconel 718 alloy. It is because the physical model ignores the metal evaporation in the molten pool when the laser beam irradiates the powder bed in this paper. The temperature of the part of molten metal reaches the boiling point, heat dissipation 18

can not occur through evaporation, certainly leading to the increase of temperature in the molten pool and the increase in depth. Thus, the simulated depth of the molten pool of 53μm (Fig.9d right) is bigger than experimental one of 50μm(Fig.9d left). The comparison between the simulated and experimental depth of molten pool verifies roughly the results of simulation. In view of this, the evaporation of molten metal should be considered for a more exact simulation

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in the future. From Fig. 10a, the molten pool is approximately hemispherical at the beginning of the first

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scanning track, after that it becomes a shape similar to “comet tail”. Combined with Fig. 10b

we know that the depth and length of the molten pool general gradually increase with scanning sequences (namely scanning number). The difference of the molten pool shape and size at each

N

U

scanning track is mainly caused by the difference of heat accumulation in each scanning

A

sequence. The amount of heat accumulation in the initial processing area is small, and as

M

processing progresses, the heat accumulation in the powder bed and the substrate increases more and more. The depth and length of the molten pool at point 1 are the smallest one because

ED

this point is the first laser scanning point, initiates from ambient temperature, and has no heat

PT

accumulation. Points 4, 7, 10, 13 are turning points in scanning path, where heat dissipation condition around the scanned point is changed. In which the effect of heat accumulation on the

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length of the molten pool is significant, while the effect on the length of the molten pool is less. The effect of heat accumulation on the width of the molten pool is different from that of

A

mentioned above. The width of the molten pool at points 3, 6, 9, 12, 15 are slightly smaller than other points. Because they are the last points of a scanning track, they are weakly affected by the heat accumulation of previous scanning tracks. Fig. 10c shows the depth-to-width ratio of the molten pool at the midpoint of each laser scanning tracks (corresponding to points 2, 5, 8, 11, 14 in Fig. 10a, respectively). It can be seen 19

as the number of scanning tracks increases, the depth-to-width ratio of the molten pool increases gradually, but the growth rate is very small. This is principally because the heat accumulation leads to the increase both of the depth and width of the molten pool. However, the typical outward convection in the molten pool during SLM causes the acceleration of the lateral heat

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transfer, which makes the molten pool width increasing faster than the depth. Fig. 11 shows the heat flux in the molten pool at the midpoint of each scanning tracks

SC R

(corresponding to points 2, 5, 8, 11, 14 in Fig. 10a, respectively). It can be seen that the convective heat flux of the molten pool is one order larger than the conductive heat flux at the

U

same time. With continuous heat input, both convective heat flux and conductive heat flux are

N

increasing. Similar to the change in the shape and size of the molten pool with scanning

A

sequences, the heat flux in the molten pool firstly increases and then tends to stabilize.

M

The temperature of the molten pool tends to stadily increase due to the presence of heat

ED

accumulation, leading to an increase in both convective heat flux and conductive heat flux. But it does not change the dominant role of the convective heat flux. Therefor, the shape of the

PT

molten pool is still largely dependent on the convective heat flux in the molten pool.

CC E

Through the above analysis and discussions, we can conclude that the surface tension caused by the surface temperature gradient of a molten pool drives the molten melt to generate convection. Controlled by the content of the surface active element in the molten pool, the

A

convective direction of molten metal is possible an outward convection or an inward convection. Because the content of the surface active element in the molten pool is well controlled during SLM process, the molten melt exhibits outward convection. The maximum flow rate of molten metal can reach 0.78m/s from Fig. 6. The heavy convection of molten metal makes convective 20

heat flux significantly larger than conductive heat flux, dominating the heat transfer in the molten pool, and further decides the shape of the molten pool. The heat accumulation during SLM simultaneously increases convective heat flux and conductive heat flux, and further increases the size of the molten pool. Seen from simulation results, the dimension of molten

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pool obviously increases, but the depth-to-width ratio of the molten pool is not significantly changed.

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5. Conclusions

In this paper, a three dimensional finite element model including laser penetration and

U

Marangoni effect has been established and used to study thermofluid field in the molten pool

A

alloy. The following conclusions can be drawn:

N

and its influence on the shape of the molten pool during selective laser melting of Inconel 718

M

(1) A heat source considering the characteristics of thermal physical properties of powder bed

ED

with porosity and multi-reflection of powder bed to laser beam was implemented in simulation, which results were in agreement with the practice;

PT

(2) Marangoni effect driven by surface tension during SLM process makes fluid flow state in

CC E

molten pool mainly an outward convection (namely Marangoni coefficient 𝜕𝛾/𝜕𝑇 is negative);

A

(3) The effects of convective and conductive heat flux on molten pool shape were investigated during SLM process with fixed-point heat source. The results showed that the convective heat flux in molten pool is dominant, which is one order magnitude larger than conductive one, and accelerates flow rate of the melt in the weld, benefits to heat transfer. The convective heat flux makes the molten pool wider and the conductive heat flux makes 21

comparably the molten pool deeper and wider; (4) The effects of convective and conductive heat flux on molten pool shape were investigated during SLM process with a moving heat source. The results showed that thermofluid field of molten pool and the effects of convective and conductive heat flux on molten pool shape

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were same as that with fixed-point heat sources. (5) The effects of heat accumulation on heat flux and molten pool shape were investigated

SC R

during SLM process with a moving heat source different comparing with fixed-point heat

source. The process of multiple scanning with moving heat source led to heat accumulation,

U

which increases the magnitude of convection and conduction heat flux, and the length,

N

width and depth of the weld.

A

In the future, the evaporation process will be taken into account in the new model and the

ED

scanning strategies will be explored.

M

effect of heat accumulation on the molten pool shape and grain morphology with different

Acknowledgments

A

CC E

PT

The authors are grateful for financial support from the important research special projects of Beijing Natural Science Foundation (Project no. Z140002) and general research project of national Natural Science Foundation (Project no. 51675012).

22

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Figure and Table Captions

25

Fig. 1. Schematic of the physical metallurgical phenomenon in laser-material interaction zone during SLM Fig. 2. The established three-dimensional finite element model during the SLM process. Fig. 3. (a) Schematic of the top and side view of the ideal model of powder close packing. (b)The distribution of heat source energy. Fig. 4. The heat capacity ((a) at constant pressure) and thermal conductivity (b) of Inconel 718 Alloy. Fig. 5. The thermal conductivity on the powder bed. Fig. 6. Velocity vector plots of convection flow in the molten pool at various Marangoni coefficients with a fixed-point heat source: (a) 𝜕𝛾/𝜕𝑇=−4×10−4 N/(m K), vertical-section view; (b) 𝜕𝛾/𝜕𝑇=−4×10−4 view. The lengths and colors of the arrows show the intensity of fluid flow.

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N/(m K), top view, (c) 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), vertical-section view, (d) 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), top Fig. 7. The effect of Marangoni effect on the width, depth and depth-to-width ratio of the molten pool

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with a fixed-point heat source.

Fig. 8. Heat flux in the molten pool at various Marangoni coefficients with a fixed-point heat source: When 𝜕𝛾/𝜕𝑇=−4×10−4 N/(m K), (a) convective heat flux; (b) conductive heat flux; when 𝜕𝛾/𝜕𝑇=0 N/(m K), (c)conductive heat flux; and when 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), (d) convective heat flux; (e) conductive heat flux. The length and colors of the arrows characterize the intensity of the heat flux.

U

Fig. 9. The experimental and simulated molten pool size, with a moving heat source: (a) microstructure in upper surface of the experimental molten pool; (b) microstructure in vertical section of the

N

experimental molten pool; (c) temperature distribution in cross-section at 0.003125 s; (d) temperature distribution and experimental sample in vertical section. The gray line is the solid–liquid boundary.

A

Fig. 10. Molten pool shape and size at various locations in the powder bed: (a) molten pool shape in

M

various position; (b) molten pool size in various position; (c) the depth-to-width ratio of the molten pool at the midpoint of each laser scanning tracks. The gray line is the solid–liquid boundary. Fig. 11. Heat flux in the molten pool at the midpoint of scanning tracks: (a), (c), (e), (g) and (i) describe

ED

the convective heat flux from the first scanning track to the fifth, respectively; and (b), (d), (f), (h) and (j) describe the conductive heat flux from the first scanning track to the fifth, respectively. Table 1 The thermal physical properties of Inconel 718 alloy and SLM processing parameters from

A

CC E

PT

EOSINT M280 used in the simulation

Fig. 1. Schematic of the physical metallurgical phenomenon in laser-material interaction zone during SLM.

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IP T

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U

SC R

Fig. 2. The established three-dimensional finite element model during the SLM process.

A

Fig. 3. (a) Schematic of the top and side view of the ideal model of powder close packing. (b) The

CC E

PT

ED

M

distribution of heat source energy.

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Fig. 4. The heat capacity ((a) at constant pressure) and thermal conductivity (b) of Inconel 718 Alloy.

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A

CC E

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ED

M

A

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SC R

IP T

Fig. 5. The thermal conductivity on the powder bed.

Fig. 6. Velocity vector plots of convection flow in the molten pool at various Marangoni coefficients with a fixed-point heat source: (a) 𝜕𝛾/𝜕𝑇=−4×10−4 N/(m K), vertical-section view; (b) 𝜕𝛾/𝜕𝑇=−4×10−4 N/(m K), top view, (c) 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), vertical-section view, (d) 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), top view. The lengths and colors of the arrows show the intensity of fluid flow.

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IP T

(um)

Fig. 7. The effect of Marangoni effect on the width, depth and depth-to-width ratio of the molten pool

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CC E

PT

ED

M

A

N

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SC R

with a fixed-point heat source.

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IP T SC R U N A M ED

Fig. 8. Heat flux in the molten pool at various Marangoni coefficients with a fixed-point heat source:

PT

When 𝜕𝛾/𝜕𝑇=−4×10−4 N/(m K), (a) convective heat flux; (b) conductive heat flux; when 𝜕𝛾/𝜕𝑇=0 N/(m K), (c)conductive heat flux; and when 𝜕𝛾/𝜕𝑇=4×10−4 N/(m K), (d) convective heat flux; (e)

A

CC E

conductive heat flux. The length and colors of the arrows characterize the intensity of the heat flux.

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Fig. 9. The experimental and simulated molten pool size, with a moving heat source: (a) microstructure in upper surface of the experimental molten pool; (b) microstructure in vertical section of the

IP T

experimental molten pool; (c) temperature distribution in cross-section at 0.003125 s; (d) temperature

CC E

PT

ED

M

A

N

U

SC R

distribution and experimental sample in vertical section. The gray line is the solid–liquid boundary.

Fig. 10. Molten pool shape and size at various locations in the powder bed: (a) molten pool shape in various position; (b) molten pool size in various position; (c) the depth-to-width ratio of the molten pool

A

at the midpoint of each laser scanning tracks. The gray line is the solid–liquid boundary.

31

IP T SC R U N A M ED PT CC E A Fig. 11. Heat flux in the molten pool at the midpoint of scanning tracks: (a), (c), (e), (g) and (i) describe 32

the convective heat flux from the first scanning track to the fifth, respectively; and (b), (d), (f), (h) and

A

CC E

PT

ED

M

A

N

U

SC R

IP T

(j) describe the conductive heat flux from the first scanning track to the fifth, respectively.

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