Abstract

Selective laser melting (SLM) builds parts by selectively melting metallic powders layer by layer with a high-energy laser beam. It has a variety of applications in aerospace, medical device, and other low-volume manufacturing. Nevertheless, the lack of fundamental understanding of the process-structure-property relationship for better quality control inhibits wider applications of SLM. Recently, a mesoscale simulation approach, called phase field and thermal lattice Boltzmann method (PF-TLBM), was developed to simulate microstructure evolution of alloys in SLM melt pool with simultaneous consideration of solute transport, heat transfer, phase transition, and latent heat effect. In this paper, a nucleation model is introduced in the PF-TLBM framework to simulate heterogeneous nucleation at the boundary of the melt pool in SLM. A new method is also developed to estimate the thermal flux out of the SLM melt pool model given a constant cooling rate. The effects of latent heat and cooling rate on dendritic morphology and solute distribution are studied. The simulation results of AlSi10Mg alloy suggest that the inclusion of latent heat is necessary because it reveals the details of the formation of secondary arms, reduces the overestimation of microsegregation, and provides more accurate kinetics of dendritic growth.

References

1.
Jaafar
,
M. A.
,
Rousse
,
D. R.
,
Gibout
,
S.
, and
Bédécarrats
,
J. P.
,
2017
, “
A Review of Dendritic Growth During Solidification: Mathematical Modeling and Numerical Simulations
,”
Renewable Sustainable Energy Rev.
,
74
, pp.
1064
1069
. 10.1016/j.rser.2017.02.050
2.
Steinbach
,
I.
,
2009
, “
Phase-Field Models in Materials Science
,”
Modell. Simul. Mater. Sci. Eng.
,
17
(
7
), p.
073001
. 10.1088/0965-0393/17/7/073001
3.
Steinbach
,
I.
,
2013
, “
Why Solidification? Why Phase-Field?
,”
JOM
,
65
(
9
), pp.
1096
1102
. 10.1007/s11837-013-0681-5
4.
Choudhury
,
A.
,
Reuther
,
K.
,
Wesner
,
E.
,
August
,
A.
,
Nestler
,
B.
, and
Rettenmayr
,
M.
,
2012
, “
Comparison of Phase-Field and Cellular Automaton Models for Dendritic Solidification in Al-Cu Alloy
,”
Comput. Mater. Sci.
,
55
, pp.
263
268
. 10.1016/j.commatsci.2011.12.019
5.
Boettinger
,
W. J.
,
Warren
,
J. A.
,
Beckermann
,
C.
, and
Karma
,
A.
,
2002
, “
Phase Field Simulation of Solidification
,”
Annu. Rev. Mater. Res.
,
32
(
1
), pp.
63
94
. 10.1146/annurev.matsci.32.101901.155803
6.
Chen
,
L.-Q.
,
2002
, “
Phase-Field Models for Microstructure Evolution
,”
Annu. Rev. Mater. Res.
,
32
(
1
), pp.
113
140
. 10.1146/annurev.matsci.32.112001.132041
7.
Moelans
,
N.
,
Blanpain
,
B.
, and
Wollants
,
P.
,
2008
, “
An Introduction to Phase-Field Modeling of Microstructure Evolution
,”
CALPHAD: Comput. Coupling Phase Diagrams Thermochem.
,
32
(
2
), pp.
268
294
. 10.1016/j.calphad.2007.11.003
8.
Böttger
,
B.
,
Eiken
,
J.
, and
Steinbach
,
I.
,
2006
, “
Phase Field Simulation of Equiaxed Solidification in Technical Alloys
,”
Acta Mater.
,
54
(
10
), pp.
2697
2704
. 10.1016/j.actamat.2006.02.008
9.
Fu
,
Y.
,
Michopoulos
,
J. G.
, and
Song
,
J. H.
,
2017
, “
Bridging the Multi Phase-Field and Molecular Dynamics Models for the Solidification of Nano-Crystals
,”
J. Comput. Sci.
,
20
, pp.
187
197
. 10.1016/j.jocs.2016.10.014
10.
Song
,
J. H.
,
Fu
,
Y.
,
Kim
,
T. Y.
,
Yoon
,
Y. C.
,
Michopoulos
,
J. G.
, and
Rabczuk
,
T.
,
2018
, “
Phase Field Simulations of Coupled Microstructure Solidification Problems via the Strong Form Particle Difference Method
,”
Int. J. Mech. Mater. Des.
,
14
(
4
), pp.
491
509
. 10.1007/s10999-017-9386-1
11.
Lian
,
Y.
,
Gan
,
Z.
,
Yu
,
C.
,
Kats
,
D.
,
Liu
,
W. K.
, and
Wagner
,
G. J.
,
2019
, “
A Cellular Automaton Finite Volume Method for Microstructure Evolution During Additive Manufacturing
,”
Mater. Des.
,
169
, p.
107672
. 10.1016/j.matdes.2019.107672
12.
Körner
,
C.
,
Attar
,
E.
, and
Heinl
,
P.
,
2011
, “
Mesoscopic Simulation of Selective Beam Melting Processes
,”
J. Mater. Process. Technol.
,
211
(
6
), pp.
978
987
. 10.1016/j.jmatprotec.2010.12.016
13.
Rai
,
A.
,
Markl
,
M.
, and
Körner
,
C.
,
2016
, “
A Coupled Cellular Automaton–Lattice Boltzmann Model for Grain Structure Simulation During Additive Manufacturing
,”
Comput. Mater. Sci.
,
124
, pp.
37
48
. 10.1016/j.commatsci.2016.07.005
14.
Liu
,
P. W.
,
Ji
,
Y. Z.
,
Wang
,
Z.
,
Qiu
,
C. L.
,
Antonysamy
,
A. A.
,
Chen
,
L. Q.
,
Cui
,
X. Y.
, and
Chen
,
L.
,
2018
, “
Investigation on Evolution Mechanisms of Site-Specific Grain Structures During Metal Additive Manufacturing
,”
J. Mater. Process. Technol.
,
257
, pp.
191
202
. 10.1016/j.jmatprotec.2018.02.042
15.
Wang
,
X.
, and
Chou
,
K.
,
2019
, “
Microstructure Simulations of Inconel 718 During Selective Laser Melting Using a Phase Field Model
,”
Int. J. Adv. Manuf. Technol.
,
100
(
9–12
) pp.
2147
2162
. 10.1007/s00170-018-2814-z
16.
Keller
,
T.
,
Lindwall
,
G.
,
Ghosh
,
S.
,
Ma
,
L.
,
Lane
,
B. M.
,
Zhang
,
F.
,
Kattner
,
U. R.
,
Lass
,
E. A.
,
Heigel
,
J. C.
,
Idell
,
Y.
,
Williams
,
M. E.
,
Allen
,
A. J.
,
Guyer
,
J. E.
, and
Levine
,
L. E.
,
2017
, “
Application of Finite Element, Phase-Field, and CALPHAD-Based Methods to Additive Manufacturing of Ni-Based Superalloys
,”
Acta Mater.
,
139
, pp.
244
253
. 10.1016/j.actamat.2017.05.003
17.
Liu
,
P.
,
Wang
,
Z.
,
Xiao
,
Y.
,
Horstemeyer
,
M. F.
,
Cui
,
X.
, and
Chen
,
L.
,
2019
, “
Insight Into the Mechanisms of Columnar to Equiaxed Grain Transition During Metallic Additive Manufacturing
,”
Addit. Manuf.
,
26
, pp.
22
29
. 10.1016/j.addma.2018.12.019
18.
Yang
,
Y.
,
Ragnvaldsen
,
O.
,
Bai
,
Y.
,
Yi
,
M.
, and
Xu
,
B. X.
,
2019
, “
3D Non-Isothermal Phase-Field Simulation of Microstructure Evolution During Selective Laser Sintering
,”
npj Comput. Mater.
,
5
(
1
), pp.
1
12
. 10.1038/s41524-019-0219-7
19.
Acharya
,
R.
,
Sharon
,
J. A.
, and
Staroselsky
,
A.
,
2017
, “
Prediction of Microstructure in Laser Powder Bed Fusion Process
,”
Acta Mater.
,
124
, pp.
360
371
. 10.1016/j.actamat.2016.11.018
20.
Medvedev
,
D.
, and
Kassner
,
K.
,
2005
, “
Lattice Boltzmann Scheme for Crystal Growth in External Flows
,”
Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
,
72
(
5
), pp.
1
10
. 10.1103/physreve.72.056703
21.
Medvedev
,
D.
,
Varnik
,
F.
, and
Steinbach
,
I.
,
2013
, “
Simulating Mobile Dendrites in a Flow
,”
Procedia Comput. Sci.
,
18
, pp.
2512
2520
. 10.1016/j.procs.2013.05.431
22.
Takaki
,
T.
,
Rojas
,
R.
,
Ohno
,
M.
,
Shimokawabe
,
T.
, and
Aoki
,
T.
,
2015
, “
GPU Phase-Field Lattice Boltzmann Simulations of Growth and Motion of a Binary Alloy Dendrite
,”
IOP Conference Series: Materials Science and Engineering
,
84
, p.
012066
.
23.
Rojas
,
R.
,
Takaki
,
T.
, and
Ohno
,
M.
,
2015
, “
A Phase-Field-Lattice Boltzmann Method for Modeling Motion and Growth of a Dendrite for Binary Alloy Solidification in the Presence of Melt Convection
,”
J. Comput. Phys.
,
298
, pp.
29
40
. 10.1016/j.jcp.2015.05.045
24.
Liu
,
D.
, and
Wang
,
Y.
,
2017
, “
Mesoscale Multi-Physics Simulation of Solidification in Selective Laser Melting Process Using a Phase Field and Thermal Lattice Boltzmann Model
,”
2017 ASME International Design Engineering Technical Conferences & The Computer and Information in Engineering Conference (IDETC/CIE2017)
,
Cleveland, OH
,
Aug. 6–9
, p.
DETC2017-67633
.
25.
Liu
,
D.
, and
Wang
,
Y.
,
2019
, “
Mesoscale Multi-Physics Simulation of Rapid Solidification of Ti-6Al-4V Alloy
,”
Addit. Manuf.
,
25
, pp.
551
562
. 10.1016/j.addma.2018.12.005
26.
Liu
,
D.
, and
Wang
,
Y.
,
2019
, “
Simulation of Nucleation and Grain Growth in Selective Laser Melting of Ti-6Al-4V Alloy
,”
2019 ASME International Design Engineering Technical Conferences & The Computer and Information in Engineering Conference (IDETC/CIE2019)
,
Anaheim, CA
,
ASME
, p.
DETC2019-97684
.
27.
Shimono
,
Y.
,
Oba
,
M.
,
Nomoto
,
S.
,
Koizumi
,
Y.
, and
Chiba
,
A.
,
2017
, “
Numerical Simulation of Solidification in Additive Manufacturing of Ti Alloy by Multi-Phase Field Method
,”
Solid Freeform Fabrication Symposium
,
Austin, TX
,
Aug. 7–9
, pp.
1048
1057
.
28.
Gránásy
,
L.
,
Börzsönyi
,
T.
, and
Pusztai
,
T.
,
2002
, “
Crystal Nucleation and Growth in Binary Phase-Field Theory
,”
J. Cryst. Growth
,
237–239
(
1–4
), pp.
1813
1817
. 10.1016/S0022-0248(01)02350-8
29.
Gránásy
,
L.
,
Börzsönyi
,
T.
,
Börzsönyi
,
T.
, and
Pusztai
,
T.
,
2002
, “
Nucleation and Bulk Crystallization in Binary Phase Field Theory
,”
Phys. Rev. Lett.
,
88
(
20
), p.
206105
. 10.1103/PhysRevLett.88.206105
30.
Gránásy
,
L.
,
Pusztai
,
T.
,
Saylor
,
D.
, and
Warren
,
J. A.
,
2007
, “
Phase Field Theory of Heterogeneous Crystal Nucleation
,”
Phys. Rev. Lett.
,
98
(
3
), p.
035703
. 10.1103/PhysRevLett.98.035703
31.
Pusztai
,
T.
,
Tegze
,
G.
,
Tóth
,
G. I.
,
Környei
,
Ĺ
,
Bansel
,
G.
,
Fan
,
Z.
, and
Gŕńsy
,
Ĺ
,
2008
, “
Phase-Field Approach to Polycrystalline Solidification Including Heterogeneous and Homogeneous Nucleation
,”
J. Phys. Condens. Matter
,
20
(
40
), p.
404205
. 10.1088/0953-8984/20/40/404205
32.
Simmons
,
J. P.
,
Wen
,
Y.
,
Shen
,
C.
, and
Wang
,
Y. Z.
,
2004
, “
Microstructural Development Involving Nucleation and Growth Phenomena Simulated With the Phase Field Method
,”
Mater. Sci. Eng. A
,
365
(
1–2
), pp.
136
143
. 10.1016/j.msea.2003.09.019
33.
Li
,
J.
,
Wang
,
J.
, and
Yang
,
G.
,
2007
, “
Phase-Field Simulation of Microstructure Development Involving Nucleation and Crystallographic Orientations in Alloy Solidification
,”
J. Cryst. Growth
,
309
(
1
), pp.
65
69
. 10.1016/j.jcrysgro.2007.08.025
34.
Aziz
,
M. J.
,
1982
, “
Model for Solute Redistribution During Rapid Solidification
,”
J. Appl. Phys.
,
53
(
2
), pp.
1158
1168
. 10.1063/1.329867
35.
Marola
,
S.
,
Manfredi
,
D.
,
Fiore
,
G.
,
Poletti
,
M. G.
,
Lombardi
,
M.
,
Fino
,
P.
, and
Battezzati
,
L.
,
2018
, “
A Comparison of Selective Laser Melting With Bulk Rapid Solidification of AlSi10Mg Alloy
,”
J. Alloys Compd.
,
742
, pp.
271
279
. 10.1016/j.jallcom.2018.01.309
36.
Chen
,
S.
, and
Doolen
,
G. D.
,
1998
, “
Lattice Boltzmann Method for Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
(
1
), pp.
329
364
. 10.1146/annurev.fluid.30.1.329
37.
Guo
,
Z.
,
Zheng
,
C.
,
Shi
,
B.
, and
Zhao
,
T. S.
,
2007
, “
Thermal Lattice Boltzmann Equation for Low Mach Number Flows: Decoupling Model
,”
Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
,
75
(
3
), p.
036704
. 10.1103/physreve.75.036704
38.
Zhang
,
T.
,
Shi
,
B.
,
Guo
,
Z.
,
Chai
,
Z.
, and
Lu
,
J.
,
2012
, “
General Bounce-Back Scheme for Concentration Boundary Condition in the Lattice-Boltzmann Method
,”
Phys. Rev. E—Stat. Nonlin. Soft Matter Phys.
,
85
(
1
), p.
016701
. 10.1103/physreve.85.016701
39.
Chen
,
Q.
,
Zhang
,
X.
, and
Zhang
,
J.
,
2013
, “
Improved Treatments for General Boundary Conditions in the Lattice Boltzmann Method for Convection-Diffusion and Heat Transfer Processes
,”
Phys. Rev. E
,
88
(
3
), p.
033304
. 10.1103/PhysRevE.88.033304
40.
Thijs
,
L.
,
Kempen
,
K.
,
Kruth
,
J. P.
, and
Van Humbeeck
,
J.
,
2013
, “
Fine-Structured Aluminium Products With Controllable Texture by Selective Laser Melting of Pre-Alloyed AlSi10Mg Powder
,”
Acta Mater.
,
61
(
5
), pp.
1809
1819
. 10.1016/j.actamat.2012.11.052
41.
Mukherjee
,
T.
,
Wei
,
H. L.
,
De
,
A.
, and
DebRoy
,
T.
,
2018
, “
Heat and Fluid Flow in Additive Manufacturing—Part II: Powder Bed Fusion of Stainless Steel, and Titanium, Nickel and Aluminum Base Alloys
,”
Comput. Mater. Sci.
,
150
, pp.
369
380
. 10.1016/j.commatsci.2018.04.027
42.
Napolitano
,
R. E.
,
Liu
,
S.
, and
Trivedi
,
R.
,
2002
, “
Experimental Measurement of Anisotropy in Crystal-Melt Interfacial Energy
,”
Interface Sci.
,
10
(
2–3
), pp.
217
232
. 10.1023/A:1015884415896
43.
Steinbach
,
I.
,
2008
, “
Effect of Interface Anisotropy on Spacing Selection in Constrained Dendrite Growth
,”
Acta Mater.
,
56
(
18
), pp.
4965
4971
. 10.1016/j.actamat.2008.06.009
44.
Hoyt
,
J. J.
,
Asta
,
M.
, and
Karma
,
A.
,
2003
, “
Atomistic and Continuum Modeling of Dendritic Solidification
,”
Mater. Sci. Eng. R: Reports
,
41
(
6
), pp.
121
164
. 10.1016/S0927-796X(03)00036-6
45.
Du
,
Y.
,
Chang
,
Y. A.
,
Huang
,
B.
,
Gong
,
W.
,
Jin
,
Z.
,
Xu
,
H.
,
Yuan
,
Z.
,
Liu
,
Y.
,
He
,
Y.
, and
Xie
,
F. Y.
,
2003
, “
Diffusion Coefficients of Some Solutes in Fcc and Liquid Al: Critical Evaluation and Correlation
,”
Mater. Sci. Eng. A
,
363
(
1–2
), pp.
140
151
. 10.1016/S0921-5093(03)00624-5
46.
Pei
,
W.
,
Zhengying
,
W.
,
Zhen
,
C.
,
Junfeng
,
L.
,
Shuzhe
,
Z.
, and
Jun
,
D.
,
2017
, “
Numerical Simulation and Parametric Analysis of Selective Laser Melting Process of AlSi10Mg Powder
,”
Appl. Phys. A: Mater. Sci. Process.
,
123
(
8
), pp.
1
15
. 10.1007/s00339-017-1143-7
47.
Loginova
,
I.
,
Amberg
,
G.
, and
Ågren
,
J.
,
2001
, “
Phase-Field Simulations of Non-Isothermal Binary Alloy Solidification
,”
Acta Mater.
,
49
(
4
), pp.
573
581
. 10.1016/S1359-6454(00)00360-8
48.
Bouchard
,
D.
, and
Kirkaldy
,
J. S.
,
1996
, “
Equations and Specification of Predictive Procedures
,”
Metall. Mater. Trans. B
,
28B
(
4
), pp.
651
663
. 10.1007/s11663-997-0039-x
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