Current Situation and Prospect of Computationally Assisted Design in High-Performance Additive Manufactured Aluminum Alloys: A Review
GAO Jianbao1, LI Zhicheng1, LIU Jia1, ZHANG Jinliang2, SONG Bo2(), ZHANG Lijun1()
1.State Key Lab of Powder Metallurgy, Central South University, Changsha 410083, China 2.State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Cite this article:
GAO Jianbao, LI Zhicheng, LIU Jia, ZHANG Jinliang, SONG Bo, ZHANG Lijun. Current Situation and Prospect of Computationally Assisted Design in High-Performance Additive Manufactured Aluminum Alloys: A Review. Acta Metall Sin, 2023, 59(1): 87-105.
Additive manufacturing technology has greatly increased opportunities in the production of high-strength aluminum alloy complex parts. However, current additive manufactured aluminum alloy systems are still limited to castable and weldable Al-Si alloys. This impedes the development of high-performance additive manufactured aluminum alloys. Recently, various computational techniques at different scales have been gradually used to promote the development of high-performance additive manufactured aluminum alloys. This paper summarizes the research achievements in the field of computationally-assisted design of additive manufactured aluminum alloys and their preparation from domestic and foreign scholars and presents representative cases from atomic, mesoscopic, and macroscopic scales and machine learning. The different calculation methods used to assist alloy designs are analyzed and their shortcomings are presented. Finally, the prospect on how to improve the application of multi-scale computation techniques in the development of high-performance additive manufactured aluminum alloys is presented, and some specific development directions are also clarified.
Fund: National Key Research and Development Program of China(2019YFB2006500);National Natural Science Foundation of China(51922044);Key Research and Development Program of Guangxi(AB21220028);Natural Science Foundation of Hunan Province(2021JJ10062);China Post-doctoral Science Foundation(2021M701293)
Fig.1 Plot of solid solution strengthening increment as a function of solute concentration (atomic fraction) in the matrix (a) and plot of diffusivity at 400oC vs maximum equilibrium solid solubility (atomic fraction) for selected solutes in Al (b)[37]
Fig.2 Finally solidified structures of the aluminum nano-powder bed processed by micro-selective laser melting (μ-SLM) model using molecular dynamics. Ten laser tracks have fused together a total of 453 nano-powders of average diameter 9.67 ?nm in three different layers shown in first layer (a), second layer (b), and third layer (c) (Dark semi-circles outline the contours of the melt-pool boundaries; the grains that span across the three layers are explicitly numbered in Fig.2c; the solidified nanostructure is dominated by epitaxially grown grains. Other important structural features such as equiaxed grains, nano-pores, twin boundaries, and stacking faults are labeled in Fig.2c)[41]
Fig.3 Strategic workflow of alloy design approach for additive manufacturing aluminum alloys driven by computational thermodynamics[53] (HSI—hot susceptibility index or crack susceptibility index (CSI), ΔTCTR—craitical temperature range, Qtrue—growth restriction factor for true alloy system)
Fig.4 Solidification structure with characteristic temperatures in hot tearing[60] (a), and Scheil-Gulliver solidification simulations (b) and comparison of the calculated brittle temperature range ΔTBTR (ΔTBTR = TZST - TZDT) (c) for AlSi10Mg, 6061, and 7075 aluminum alloys[54] (TZST—zero strength temperature, TZDT—zero ductility temperature)
Fig.5 Schematic diagram of the crack susceptibility index (CSI) in the Kou criterion[55,66] (a) and comparison of the calculated CSI (CSI = |dT / d(fS)1/2|, when (fS)1/2 near 1)[67] and experimental crack susceptibility[62,63] of wrought Al alloys (b) (t is time, R is the characteristic radius of grain)
Fig.6 Calculational results of Scheil solidification and CSI of Si-modified Al7075 alloys, and grain morphologies of SLM processed Al7075 alloy (Al-5.10Zn-2.67Mg-1.55Cu, mass fraction, %) without and with Si[58] (a) T vs (fS)1/2 curves of the Al7075 alloys with 0.17% to 8% Si additions (mass fraction), the dashed vertical line indicates (fS)1/2 = 0.99 (b) variation of crack susceptibility of Al7075 alloys as a function of Si additions (Insets show the defect morphologies of Si-modified SLM processed Al7075 alloy) (c-f) grain morphologies of SLM processed Al7075 with solidification cracks (c, e), and crack-free Si-modified Al7075 alloy (Al7075-3.74Si%) processed by SLM (d, f) (BD—building direction) (g, h) schematics of epitaxial growth of the Al7075 alloy (g) and the solidification cracking mitigation mechanism in the Si-modified Al7075 (h) (Tl is the liquidus temperature, Ts or Ts1 is the terminal temperature of solidification, Ts2 is the temperature of full columnar grains zone, ΔT is solidification temperature range (ΔT = Tl - Ts), //ΔGmax represents that the growth direction of columnar grains is preferentially oriented parallel to the direction of the maximum temperature gradient G)
Fig.7 A novel crack-free Ti-modified Al-Cu-Mg alloy design flow for SLM[21] (a) vertical section of Al-2.25Cu-1.8Mg-xTi alloys (mass fraction, %) (b) Tvs (fS)1/2 curves of Al-Cu-Mg-xTi alloys with Ti contents ranging from 0 to 2% (c) calculated Qtrue values in Ti/Al-Cu-Mg alloys for constrained L→α-Al solidification with Ti contents ranging from 0 to 2% (Metastable solidification conditions are used at higher values of Ti content to suppress the formation of intermetallic phases) (d) schematic of cracking mechanism in the Al-Cu-Mg alloy (e, f) SEM image (e) and inverse pole figure (IPF) (f) showing the microstructure in the cracked zone of Al-Cu-Mg alloy (g, h) SEM image (g) and IPF (h) of Ti/Al-Cu-Mg alloy consisting of fine equiaxed grains without cracks
Solute
Element
Equilibrium
Maximum extended solubility
Maximum solubility
Ce or Cp
Eutectic
Zn
66.4
88.5
38-43.5
Ag
23.8
37.0
25-40
Mg
16.3
36.4
36.8-40
Cu
2.5
17.5
17-18
Si
1.6
12.0
10-16
Mn
0.9
0.95
6-10
Fe
~0.02
0.9
4-6
Co
< 0.01
0.45
0.5-5
Ni
~0.02
2.8
1.2-7.7
Ce
~0.01
2.6
1.9
Peritectic
Ti
0.6
0.06
0.2-2
Cr
0.4
0.19
5-7
V
0.25
0.05
1.4-2
Zr
0.09
0.03
1.2-1.5
Mo
0.07
0.03
1.0-1.5
W
0.02
0.01
0.9-1.9
Table 1 Solubility limits of solutes in binary aluminum alloys under equilibrium and rapid solidification conditions (~106 K/s)[79]
Fig.8 Solute trapping and kinetic phase diagram of the Al-Cu system under rapid solidification conditions using phase-field model with finite interface dissipation[102] (a) phase-field simulated steady-state concentration profiles with three different interface moving velocities (or solidification rate) V in Al-Cu system (The red dash line denotes the phase field, the bule solid lines denote the overall concentrations, while the dotted lines denote the liquid concentrations) (b) phase-field simulated solute segregation coefficient and solidification temperature as a function of interface velocity (or solidification rate) in Al-1.1%Cu (atomic fraction) alloy (c) model-predicted kinetic phase diagrams at different interface velocities (or solidification rate) due to the 1-D phase-field simulation using the time-elimination relaxation scheme of the Al-Cu system
Fig.9 Evolutions of the grain structure during solidification process in the laser molten pool with time[98] (a) t = 0 ms (b) t = 25.0 ms (c) t = 50.0 ms
Fig.10 Crack formation mechanism of Al-Cu-Mg alloy[32] (a) simulated stress distribution of molten pool (b) grain morphology in experimental molten pool (c) schematic of solidification process and crack formation
Fig.11 A physics-informed machine learning towards crack-free printing[33]. Computed values of cooling rate and solidification morphology (indicated by the ratio of temperature gradient and solidification growth rate) at the trailing edge of the melt pool, the ratio of vulnerable and relaxation times, and solidification stress are used in a physics informed machine learning to accurately predict cracking during SLM of aluminum alloys. The combination of machine learning and mechanistic modeling gives a cracking susceptibility index, process maps for crack-free printing, the comparative influence of the important variables, and a decision tree to predict crack formation[33] (PBF-L—powder bed fusion- laser)
1
Li Q, Wang F D, Wang G Q, et al. Wire and arc additive manufacturing of lightweight metal components in aeronautics and astronautics [J]. Aeronaut. Manuf. Technol., 2018, 61(3): 74
Qin Y L, Sun B H, Zhang H, et al. Development of selective laser melted aluminum alloys and aluminum matrix composites in aerospace field [J]. Chin. J. Lasers, 2021, 48: 1402002
doi: 10.3788/CJL202148.1402002
Zhang J L, Song B, Yang L, et al. Microstructure evolution and mechanical properties of TiB/Ti6Al4V gradient-material lattice structure fabricated by laser powder bed fusion [J]. Composites, 2020, 202B: 108417
5
Zhang J L, Song B, Wei Q S, et al. A review of selective laser melting of aluminum alloys: Processing, microstructure, property and developing trends [J]. J. Mater. Sci. Technol., 2019, 35: 270
doi: 10.1016/j.jmst.2018.09.004
6
Kotadia H R, Gibbons G, Das A, et al. A review of laser powder bed fusion additive manufacturing of aluminium alloys: Microstructure and properties [J]. Addit. Manuf., 2021, 46: 102155
7
Kimura T, Nakamoto T. Microstructures and mechanical properties of A356 (AlSi7Mg0.3) aluminum alloy fabricated by selective laser melting [J]. Mater. Des., 2016, 89: 1294
doi: 10.1016/j.matdes.2015.10.065
8
Wang M, Song B, Wei Q S, et al. Improved mechanical properties of AlSi7Mg/nano-SiCp composites fabricated by selective laser melting [J]. J. Alloys Compd., 2019, 810: 151926
doi: 10.1016/j.jallcom.2019.151926
9
Yan Q, Song B, Shi Y S. Comparative study of performance comparison of AlSi10Mg alloy prepared by selective laser melting and casting [J]. J. Mater. Sci. Technol., 2020, 41: 199
doi: 10.1016/j.jmst.2019.08.049
10
Van Cauwenbergh P, Samaee V, Thijs L, et al. Unravelling the multi-scale structure-property relationship of laser powder bed fusion processed and heat-treated AlSi10Mg [J]. Sci. Rep., 2021, 11: 6423
doi: 10.1038/s41598-021-85047-2
pmid: 33742014
11
Li X P, Wang X J, Saunders M, et al. A selective laser melting and solution heat treatment refined Al-12Si alloy with a controllable ultrafine eutectic microstructure and 25% tensile ductility [J]. Acta Mater., 2015, 95: 74
doi: 10.1016/j.actamat.2015.05.017
12
Suryawanshi J, Prashanth K G, Scudino S, et al. Simultaneous enhancements of strength and toughness in an Al-12Si alloy synthesized using selective laser melting [J]. Acta Mater., 2016, 115: 285
doi: 10.1016/j.actamat.2016.06.009
13
Starke Jr E A, Staley J T. Application of modern aluminum alloys to aircraft [J]. Prog. Aerosp. Sci., 1996, 32: 131
doi: 10.1016/0376-0421(95)00004-6
14
Roberts C E, Bourell D, Watt T, et al. A novel processing approach for additive manufacturing of commercial aluminum alloys [J]. Phys. Procedia, 2016, 83: 909
doi: 10.1016/j.phpro.2016.08.095
15
Del Guercio G, McCartney D G, Aboulkhair N T, et al. Cracking behaviour of high-strength AA2024 aluminium alloy produced by laser powder bed fusion [J]. Addit. Manuf., 2022, 54: 102776
16
Panwisawas C, Tang Y T, Reed R C. Metal 3D printing as a disruptive technology for superalloys [J]. Nat. Commun., 2020, 11: 2327
doi: 10.1038/s41467-020-16188-7
pmid: 32393778
17
Yamasaki S, Okuhira T, Mitsuhara M, et al. Effect of Fe addition on heat-resistant aluminum alloys produced by selective laser melting [J]. Metals, 2019, 9: 468
doi: 10.3390/met9040468
18
Nalivaiko A Y, Arnautov A N, Zmanovsky S V, et al. Al-Si-Cu and Al-Si-Cu-Ni alloys for additive manufacturing: Composition, morphology and physical characteristics of powders [J]. Mater. Res. Express, 2019, 6: 086536
19
Zhang B, Wei W, Shi W, et al. Effect of heat treatment on the microstructure and mechanical properties of Er-containing Al-7Si-0.6Mg alloy by laser powder bed fusion [J]. J. Mater. Res. Technol., 2022, 18: 3073
doi: 10.1016/j.jmrt.2022.04.023
20
Tan Q Y, Zhang J Q, Sun Q, et al. Inoculation treatment of an additively manufactured 2024 aluminium alloy with titanium nanoparticles [J]. Acta Mater., 2020, 196: 1
doi: 10.1016/j.actamat.2020.06.026
21
Zhang J L, Gao J B, Song B, et al. A novel crack-free Ti-modified Al-Cu-Mg alloy designed for selective laser melting [J]. Addit. Manuf., 2021, 38: 101829
22
Martin J H, Yahata B D, Hundley J M, et al. 3D printing of high-strength aluminium alloys [J]. Nature, 2017, 549: 365
doi: 10.1038/nature23894
23
Nie X J, Zhang H, Zhu H H, et al. Effect of Zr content on formability, microstructure and mechanical properties of selective laser melted Zr modified Al-4.24Cu-1.97Mg-0.56Mn alloys [J]. J. Alloys Compd., 2018, 764: 977
doi: 10.1016/j.jallcom.2018.06.032
24
Li G C, Brodu E, Soete J, et al. Exploiting the rapid solidification potential of laser powder bed fusion in high strength and crack-free Al-Cu-Mg-Mn-Zr alloys [J]. Addit. Manuf., 2021, 47: 102210
25
Li R D, Wang M B, Li Z M, et al. Developing a high-strength Al-Mg-Si-Sc-Zr alloy for selective laser melting: Crack-inhibiting and multiple strengthening mechanisms [J]. Acta Mater., 2020, 193: 83
doi: 10.1016/j.actamat.2020.03.060
26
Minasyan T, Hussainova I. Laser powder-bed fusion of ceramic particulate reinforced aluminum alloys: A review [J]. Materials, 2022, 15: 2467
doi: 10.3390/ma15072467
27
Zhou S Y, Su Y, Wang H, et al. Selective laser melting additive manufacturing of 7xxx series Al-Zn-Mg-Cu alloy: Cracking elimination by co-incorporation of Si and TiB2 [J]. Addit. Manuf., 2020, 36: 101458
28
Plotkowski A, Rios O, Sridharan N, et al. Evaluation of an Al-Ce alloy for laser additive manufacturing [J]. Acta Mater., 2017, 126: 507
doi: 10.1016/j.actamat.2016.12.065
29
Lu Z, Zhang L J. Thermodynamic description of the quaternary Al-Si-Mg-Sc system and its application to the design of novel Sc-additional A356 alloys [J]. Mater. Des., 2017, 116: 427
doi: 10.1016/j.matdes.2016.12.034
30
Yi W, Liu G C, Lu Z, et al. Efficient alloy design of Sr-modified A356 alloys driven by computational thermodynamics and machine learning [J]. J. Mater. Sci. Technol., 2022, 112: 277
doi: 10.1016/j.jmst.2021.09.061
31
Wei M, Tang Y, Zhang L J, et al. Phase-field simulation of microstructure evolution in industrial A2214 alloy during solidification [J]. Metall. Mater. Trans., 2015, 46A: 3182
32
Zhang J L, Yuan W H, Song B, et al. Towards understanding metallurgical defect formation of selective laser melted wrought aluminum alloys [J]. Adv. Powder Mater., 2022, 1: 100035
33
Mondal B, Mukherjee T, DebRoy T. Crack free metal printing using physics informed machine learning [J]. Acta Mater., 2022, 226: 117612
doi: 10.1016/j.actamat.2021.117612
34
Park S, Kayani S H, Euh K, et al. High strength aluminum alloys design via explainable artificial intelligence [J]. J. Alloys Compd., 2022, 903: 163828
doi: 10.1016/j.jallcom.2022.163828
35
Van de Walle C G, Neugebauer J. First-principles calculations for defects and impurities: Applications to III-nitrides [J]. J. Appl. Phys., 2004, 95: 3851
doi: 10.1063/1.1682673
36
Uesugi T, Higashi K. First-principles studies on lattice constants and local lattice distortions in solid solution aluminum alloys [J]. Comput. Mater. Sci., 2013, 67: 1
37
Michi R A, Plotkowski A, Shyam A, et al. Towards high-temperature applications of aluminium alloys enabled by additive manufacturing [J]. Int. Mater. Rev., 2022, 67: 298
doi: 10.1080/09506608.2021.1951580
38
Andersen H C. Molecular dynamics simulations at constant pressure and/or temperature [J]. J. Chem. Phys., 1980, 72: 2384
39
Nandy J, Sahoo S, Yedla N, et al. Molecular dynamics simulation of coalescence kinetics and neck growth in laser additive manufacturing of aluminum alloy nanoparticles [J]. J. Mol. Model., 2020, 26: 125
doi: 10.1007/s00894-020-04395-4
pmid: 32388665
40
Mahata A, Zaeem M A, Baskes M I. Understanding homogeneous nucleation in solidification of aluminum by molecular dynamics simulations [J]. Modell. Simul. Mater. Sci. Eng., 2018, 26: 025007
41
Kurian S, Mirzaeifar R. Selective laser melting of aluminum nano-powder particles, a molecular dynamics study [J]. Addit. Manuf., 2020, 35: 101272
42
Zeng Q, Wang L J, Jiang W G. Molecular dynamics simulations of the tensile mechanical responses of selective laser-melted aluminum with different crystalline forms [J]. Crystals, 2021, 11: 1388
doi: 10.3390/cryst11111388
43
Chen H L, Chen Q, Engström A. Development and applications of the TCAL aluminum alloy database [J]. Calphad, 2018, 62: 154
doi: 10.1016/j.calphad.2018.05.010
44
Kaufman L, Bernstein H. Computer Calculation of Phase Diagrams[M]. New York: Academic Press Inc., 1970: 1
45
Ågren J. Numerical treatment of diffusional reactions in multicomponent alloys [J]. J. Phys. Chem. Solids, 1982, 43: 385
doi: 10.1016/0022-3697(82)90209-8
46
Zhang L J, Du Y, Steinbach I, et al. Diffusivities of an Al-Fe-Ni melt and their effects on the microstructure during solidification [J]. Acta Mater., 2010, 58: 3664
doi: 10.1016/j.actamat.2010.03.002
47
Zhong J, Chen L, Zhang L J. Automation of diffusion database development in multicomponent alloys from large number of experimental composition profiles [J]. npj Comput. Mater., 2021, 7: 35
doi: 10.1038/s41524-021-00500-0
48
Hallstedt B, Dupin N, Hillert M, et al. Thermodynamic models for crystalline phases. Composition dependent models for volume, bulk modulus and thermal expansion [J]. Calphad, 2007, 31: 28
doi: 10.1016/j.calphad.2006.02.008
49
Zhang C, Du Y, Liu S H, et al. Thermal conductivity of Al-Cu-Mg-Si alloys: Experimental measurement and CALPHAD modeling [J]. Thermochim. Acta, 2016, 635: 8
doi: 10.1016/j.tca.2016.04.019
50
Zhang F, Du Y, Liu S H, et al. Modeling of the viscosity in the Al-Cu-Mg-Si system: Database construction [J]. Calphad, 2015, 49: 79
doi: 10.1016/j.calphad.2015.04.001
51
Shang Y J, Yang S L, Zhang L J. Computational modeling of Young's modulus in polycrystal two-phase alloys: Application in γ + γ' Ni-Al alloys [J]. Materialia, 2019, 8: 100500
doi: 10.1016/j.mtla.2019.100500
52
Yang S L, Zhong J, Wang J, et al. A novel computational model for isotropic interfacial energies in multicomponent alloys and its coupling with phase-field model with finite interface dissipation [J]. J. Mater. Sci. Technol., 2023, 133: 111
doi: 10.1016/j.jmst.2022.04.057
53
Yi W, Liu G C, Gao J B, et al. Boosting for concept design of casting aluminum alloys driven by combining computational thermodynamics and machine learning techniques [J]. J. Mater. Inf., 2021, 1: 11
54
Dreano A, Favre J, Desrayaud C, et al. Computational design of a crack-free aluminum alloy for additive manufacturing [J]. Addit. Manuf., 2022, 55: 102876
55
Kou S. A criterion for cracking during solidification [J]. Acta Mater., 2015, 88: 366
doi: 10.1016/j.actamat.2015.01.034
56
Maxwell I, Hellawell A. A simple model for grain refinement during solidification [J]. Acta Metall., 1975, 23: 229
doi: 10.1016/0001-6160(75)90188-1
57
Easton M A, StJohn D H. A model of grain refinement incorporating alloy constitution and potency of heterogeneous nucleant particles [J]. Acta Mater., 2001, 49: 1867
doi: 10.1016/S1359-6454(00)00368-2
58
Li G C, Jadhav S D, Martín A, et al. Investigation of solidification and precipitation behavior of Si-modified 7075 aluminum alloy fabricated by laser-based powder bed fusion [J]. Metall. Mater. Trans., 2021, 52A: 194
59
Sha J W, Li M X, Yang L Z, et al. Si-assisted solidification path and microstructure control of 7075 aluminum alloy with improved mechanical properties by selective laser melting [J]. Acta Metall. Sin. (Engl. Lett.), 2022, 35: 1424
doi: 10.1007/s40195-022-01419-1
60
Santillana B, Boom R, Eskin D, et al. High-temperature mechanical behavior and fracture analysis of a low-carbon steel related to cracking [J]. Metall. Mater. Trans., 2012, 43A: 5048
61
Scheil E. Bemerkungen zur schichtkristallbildung [J]. Int. J. Mater. Res., 1942, 34: 70
doi: 10.1515/ijmr-1942-340303
62
Dowd J D. Weld cracking of aluminum alloys [J]. Weld. J., 1952, 31: 448-s
63
Dudas J H, Collins F R. Preventing weld cracks in high-strength aluminum alloys [J]. Weld. J., 1966, 45: 241-s
64
Liu J W, Kou S. Susceptibility of ternary aluminum alloys to cracking during solidification [J]. Acta Mater., 2017, 125: 513
doi: 10.1016/j.actamat.2016.12.028
65
Soysal T, Kou S. A simple test for assessing solidification cracking susceptibility and checking validity of susceptibility prediction [J]. Acta Mater., 2018, 143: 181
doi: 10.1016/j.actamat.2017.09.065
66
Liu J W, Kou S. Crack susceptibility of binary aluminum alloys during solidification [J]. Acta Mater., 2016, 110: 84
doi: 10.1016/j.actamat.2016.03.030
67
Kou S. Predicting susceptibility to solidification cracking and liquation cracking by CALPHAD [J]. Metals, 2021, 11: 1442
doi: 10.3390/met11091442
68
Tang Z, Vollertsen F. Influence of grain refinement on hot cracking in laser welding of aluminum [J]. Weld. World, 2014, 58: 355
doi: 10.1007/s40194-014-0121-3
69
Greer A L, Bunn A M, Tronche A, et al. Modelling of inoculation of metallic melts: Application to grain refinement of aluminium by Al-Ti-B [J]. Acta Mater., 2000, 48: 2823
doi: 10.1016/S1359-6454(00)00094-X
70
StJohn D H, Qian M, Easton M A, et al. The interdependence theory: The relationship between grain formation and nucleant selection [J]. Acta Mater., 2011, 59: 4907
doi: 10.1016/j.actamat.2011.04.035
71
Gäumann M, Trivedi R, Kurz W. Nucleation ahead of the advancing interface in directional solidification [J]. Mater. Sci. Eng., 1997, A226-228: 763
72
Chai G, Bäackerud L, Arnberg L. Relation between grain size and coherency parameters in aluminium alloys [J]. Mater. Sci. Technol., 1995, 11: 1099
doi: 10.1179/mst.1995.11.11.1099
73
Quested T E, Dinsdale A T, Greer A L. Thermodynamic modelling of growth-restriction effects in aluminium alloys [J]. Acta Mater., 2005, 53: 1323
doi: 10.1016/j.actamat.2004.11.024
74
Men H, Fan Z. Effects of solute content on grain refinement in an isothermal melt [J]. Acta Mater., 2011, 59: 2704
doi: 10.1016/j.actamat.2011.01.008
75
Qi X B, Chen Y, Kang X H, et al. An analytical approach for predicting as-cast grain size of inoculated aluminum alloys [J]. Acta Mater., 2015, 99: 337
doi: 10.1016/j.actamat.2015.08.006
76
Schmid-Fetzer R, Kozlov A. Thermodynamic aspects of grain growth restriction in multicomponent alloy solidification [J]. Acta Mater., 2011, 59: 6133
doi: 10.1016/j.actamat.2011.06.026
77
Wu G H, Tong X, Jiang R, et al. Grain refinement of as-cast Mg-RE alloys: Research progress and future prospect [J]. Acta Metall. Sin., 2022, 58: 385
doi: 10.11900/0412.1961.2021.00519
Liu Z Y, Zhao D D, Wang P, et al. Additive manufacturing of metals: Microstructure evolution and multistage control [J]. J. Mater. Sci. Technol., 2022, 100: 224
doi: 10.1016/j.jmst.2021.06.011
79
Froes F H, Kim Y W, Hehmann F. Rapid solidification of Al, Mg and Ti [J]. JOM, 1987, 39(8): 14
80
Takata N, Liu M L, Kodaira H, et al. Anomalous strengthening by supersaturated solid solutions of selectively laser melted Al-Si-based alloys [J]. Addit. Manuf., 2020, 33: 101152
81
Ahmad N A, Wheeler A A, Boettinger W J, et al. Solute trapping and solute drag in a phase-field model of rapid solidification [J]. Phys. Rev., 1998, 58E: 3436
82
Aziz M J. An atomistic model of solute trapping [A]. Rapid Solidification Processing: Principles and Technologies III: Proceedings of the Third Conference on Rapid Solidification Processing Held at the National Bureau of Standards [C]. Gaithersburg, Maryland: The Bureau, 1982: 113
83
Aziz M J. Model for solute redistribution during rapid solidification [J]. J. Appl. Phys., 1982, 53: 1158
doi: 10.1063/1.329867
84
Aziz M J, Kaplan T. Continuous growth model for interface motion during alloy solidification [J]. Acta Metall., 1988, 36: 2335
doi: 10.1016/0001-6160(88)90333-1
85
Froes F H, Kim Y W, Krishnamurthy S. Rapid solidification of lightweight metal alloys [J]. Mater. Sci. Eng., 1989, A117: 19
86
Fiocchi J, Tuissi A, Biffi C A. Heat treatment of aluminium alloys produced by laser powder bed fusion: A review [J]. Mater. Des., 2021, 204: 109651
doi: 10.1016/j.matdes.2021.109651
87
Liu G C, Gao J B, Che C, et al. Optimization of casting means and heat treatment routines for improving mechanical and corrosion resistance properties of A356-0.54Sc casting alloy [J]. Mater. Today Commun., 2020, 24: 101227
88
Geng R W, Du J, Wei Z Y, et al. Current research status of phase field simulation for microstructures of additively manufactured metals [J]. Mater. Rep., 2018, 32: 1145
DebRoy T, Mukherjee T, Wei H L, et al. Metallurgy, mechanistic models and machine learning in metal printing [J]. Nat. Rev. Mater., 2020, 6: 48
doi: 10.1038/s41578-020-00236-1
90
Wheeler A A, Boettinger W J, McFadden G B. Phase-field model of solute trapping during solidification [J]. Phys. Rev., 1993, 47E: 1893
91
Kim S G, Kim W T, Suzuki T. Phase-field model for binary alloys [J]. Phys. Rev., 1999, 60E: 7186
92
Steinbach I, Pezzolla F, Nestler B, et al. A phase field concept for multiphase systems [J]. Physica, 1996, 94D: 135
93
Steinbach I, Zhang L J, Plapp M. Phase-field model with finite interface dissipation [J]. Acta Mater., 2012, 60: 2689
doi: 10.1016/j.actamat.2012.01.035
94
Zhang L J, Steinbach I. Phase-field model with finite interface dissipation: Extension to multi-component multi-phase alloys [J]. Acta Mater., 2012, 60: 2702
doi: 10.1016/j.actamat.2012.02.032
95
Zhang Z, Yao X X, Ge P. Phase-field-model-based analysis of the effects of powder particle on porosities and densities in selective laser sintering additive manufacturing [J]. Int. J. Mech. Sci., 2020, 166: 105230
doi: 10.1016/j.ijmecsci.2019.105230
96
Yang Y Y W, Ragnvaldsen O, Bai Y, et al. 3D non-isothermal phase-field simulation of microstructure evolution during selective laser sintering [J]. npj Comput. Mater., 2019, 5: 81
doi: 10.1038/s41524-019-0219-7
97
Yang M, Wang L, Yan W T. Phase-field modeling of grain evolution in additive manufacturing with addition of reinforcing particles [J]. Addit. Manuf., 2021, 47: 102286
98
Jiang P, Gao S, Geng S N, et al. Multi-physics multi-scale simulation of the solidification process in the molten pool during laser welding of aluminum alloys [J]. Int. J. Heat Mass Transfer, 2020, 161: 120316
doi: 10.1016/j.ijheatmasstransfer.2020.120316
99
Gunasegaram D R, Steinbach I. Modelling of microstructure formation in metal additive manufacturing: Recent progress, research gaps and perspectives [J]. Metals, 2021, 11: 1425
doi: 10.3390/met11091425
100
Karayagiz K, Johnson L, Seede R, et al. Finite interface dissipation phase field modeling of Ni-Nb under additive manufacturing conditions [J]. Acta Mater., 2020, 185: 320
doi: 10.1016/j.actamat.2019.11.057
101
O'Toole P I, Patel M J, Tang C, et al. Multiscale simulation of rapid solidification of an aluminium-silicon alloy under additive manufacturing conditions [J]. Addit. Manuf., 2021, 48: 102353
102
Yang X, Zhang L J, Sobolev S, et al. Kinetic phase diagrams of ternary Al-Cu-Li system during rapid solidification: A phase-field study [J]. Materials, 2018, 11: 260
doi: 10.3390/ma11020260
103
Li Y L, Gu D D. Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder [J]. Mater. Des., 2014, 63: 856
doi: 10.1016/j.matdes.2014.07.006
104
Geng R W, Du J, Wei Z Y, et al. Modelling and experimental observation of the deposition geometry and microstructure evolution of aluminum alloy fabricated by wire-arc additive manufacturing [J]. J. Manuf. Process., 2021, 64: 369
doi: 10.1016/j.jmapro.2021.01.037
105
Vastola G, Zhang G, Pei Q X, et al. Controlling of residual stress in additive manufacturing of Ti6Al4V by finite element modeling [J]. Addit. Manuf., 2016, 12: 231
106
Campoli G, Borleffs M S, Yavari S A, et al. Mechanical properties of open-cell metallic biomaterials manufactured using additive manufacturing [J]. Mater. Des., 2013, 49: 957
doi: 10.1016/j.matdes.2013.01.071
107
Jordan M I, Mitchell T M. Machine learning: Trends, perspectives, and prospects [J]. Science, 2015, 349: 255
doi: 10.1126/science.aaa8415
pmid: 26185243
108
Johnson N S, Vulimiri P S, To A C, et al. Invited review: Machine learning for materials developments in metals additive manufacturing [J]. Addit. Manuf., 2020, 36: 101641
109
Du Y, Mukherjee T, Mitra P, et al. Machine learning based hierarchy of causative variables for tool failure in friction stir welding [J]. Acta Mater., 2020, 192: 67
doi: 10.1016/j.actamat.2020.03.047
110
Silbernagel C, Aremu A, Ashcroft I. Using machine learning to aid in the parameter optimisation process for metal-based additive manufacturing [J]. Rapid Prototyp. J., 2020, 26: 625
doi: 10.1108/RPJ-08-2019-0213
111
Liu Q, Wu H K, Paul M J, et al. Machine-learning assisted laser powder bed fusion process optimization for AlSi10Mg: New microstructure description indices and fracture mechanisms [J]. Acta Mater., 2020, 201: 316
doi: 10.1016/j.actamat.2020.10.010
112
Caiazzo F, Caggiano A. Laser direct metal deposition of 2024 Al alloy: Trace geometry prediction via machine learning [J]. Materials, 2018, 11: 444
doi: 10.3390/ma11030444
113
Mishra R S, Thapliyal S. Design approaches for printability-performance synergy in Al alloys for laser-powder bed additive manufacturing [J]. Mater. Des., 2021, 204: 109640
doi: 10.1016/j.matdes.2021.109640
114
Gao J B, Zhong J, Liu G C, et al. A machine learning accelerated distributed task management system (Malac-Distmas) and its application in high-throughput CALPHAD computation aiming at efficient alloy design [J]. Adv. Powder Mater., 2022, 1: 100005
115
Xie J X, Su Y J, Xue D Z, et al. Machine learning for materials research and development [J]. Acta Metall. Sin., 2021, 57: 1343
doi: 10.11900/0412.1961.2021.00357
Dai R, Yang S L, Zhang T D, et al. High-throughput screening of optimal process parameters for PVD TiN coatings with best properties through a combination of 3-D quantitative phase-field simulation and hierarchical multi-objective optimization strategy [J]. Front. Mater., 2022, 9: 924294
doi: 10.3389/fmats.2022.924294
