Research progress in numerical simulation of vacuum arc remelting process
QU Jing-long1,2, YANG Shu-feng3, CHEN Zheng-yang1,2,4, DU Jin-hui1,2, BI Zhong-nan2,4, KONG Hao-hao3
1.High Temperature Materials Research Division, Central Iron and Steel Research Institute, Beijing 100081, China;
2.CISRI-GAONA Co., Ltd., Beijing 100081, China;
3.School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China;
4.Beijing Key Laboratory of Advanced High Temperature Materials, Central Iron and Steel Research Institute, Beijing 100081, China
To study the vacuum arc remelting process by means of computer simulation technology has gradually grown into a new trend. This method not only helps to ascertain the influences and mechanism of various technological parameters on the vacuum arc remelting process, but also can effectively predict the stability of the remelting process as well as the metallurgical quality of the ingot. Hence, the development history and the scientific research findings of the numerical simulation of the vacuum arc remelting process in the past 30 years were briefly introduced. Meanwhile, the research progress and the application status of the vacuum arc remelting model, the metal molten pool model and the microstructure model were reviewed in detail by taking the smelting process simulation, the macroscale simulation and the micro-scale simulation as the breakthrough point. Finally, a new development direction was proposed for the further development and application of numerical simulation of the vacuum arc remelting process in China.
曲敬龙, 杨树峰, 陈正阳, 杜金辉, 毕中南, 孔豪豪. 真空自耗冶炼过程数值仿真研究进展[J]. 中国冶金, 2020, 30(1): 1-9.
QU Jing-long, YANG Shu-feng, CHEN Zheng-yang, DU Jin-hui, BI Zhong-nan, KONG Hao-hao. Research progress in numerical simulation of vacuum arc remelting process[J]. China Metallurgy, 2020, 30(1): 1-9.
Patel A,Tripp D W,Fiore D.Application of a model for simulating the vacuum arc remelting process in titanium alloys[C]//Proceedings of the 2013 International Symposium on Liquid Metal Processing and Casting.Hoboken,NJ:John Wiley and Sons Inc,2013:241.
[7]
Woodside C R,King P E,Nordlund C.Arc distribution during the vacuum arc remelting of Ti-6Al-4V[J].Metall Mater Trans B,2013,44(1):154.
[8]
Kroll W J.Vacuum metallurgy:Its characteristics and its scope[J].Vacuum,1951,1(3):163.
[9]
Roberts R J.Automatic Melt Rate Control System for Consumable Electrode Remelting:American Patent,4131754[P].1978-12-26.
[10]
Beaman J J,Williamson R L,Melgaard D K,et al.A nonlinear reduced order model for estimation and control of vacuum arc remelting of metal alloys[C]//ASME 2005 International Mechanical Engineering Congress and Exposition.New York:ASME,2005:1059.
[11]
Flemings M C.Solidification processing[J].Metall Mater Trans B,1974,5(10):2121.
[12]
Zanner F J,Williamson R L,Harrison R P,et al.Vacuum arc remelting of alloy 718[C]//Superalloys 718 Metallurgy and Applications.Warrendale,Pa:Minerals,Metals and Materials Society,1989:17.
[13]
Zanner F J,Bertram L A.Vacuum arc remelting:An overview[C]//International Conference on Vacuum Metallurgy.Linz:Sandia National Labs.,Albuquerque,NM,1985:86.
[14]
Williamson R L,Melgaard D K,Shelmidine G J,et al.Model-based melt rate control during vacuum arc remelting of alloy 718[J].Metall Mater Trans B,2004,35(1):101.
[15]
Kelkar K,Patankar S,Mitchell A,et al.ASM Handbook[M].America:American Society for Metals International,2010.
[16]
Quatravaux T.volution De La Modélisation Du Procédé Var: Contribution à La Description De La Dispersion Inclusionnaire Dans Le Puits Liquide Et à La Prévention De Défauts De Solidification[D].Nancy,French:Institut National Polytechnique De Lorraine,2004.
[17]
YANG Z J,ZHAO X H,KOU H C,et al.Numerical simulation of temperature distribution and heat transfer during solidification of titanium alloy ingots in vacuum arc remelting process[J].Trans Nonferrous Met Soc China,2010,20(10):1957.
[18]
Stefanescu D M.Methodologies for modeling of solidification microstructure and their capabilities[J].ISIJ Int,1995,35(6):637.
[19]
ZHAO X H,LI J S,YANG Z J,et al.Numerical simulation of fluid flow caused by buoyancy forces during vacuum arc remelting process[J].Journal of Shanghai Jiao Tong University(Science),2011,16(3):272.
[20]
CHEN J T,CHEN K H.Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions[J].Appl Math Model,1998,22(9):703.
Reiter G,Maronnier V,Sommitsch C,et al.Numerical simulation of the VAR process with CALCOSOFT-2D and its validation[C]//International Symposium on Liquid Metal Processing and Casting (LMPC 2003).Norwell,Mass,Boston,Mass:Kluwer,2003:21.
[23]
Wu M,Ludwig A,Kharicha A.A four phase model for the macrosegregation and shrinkage cavity during solidification of steel ingot[J].Appl Math Model,2017,41:102.
[24]
Wang C Y,Beckermann C.Equiaxed dendritic solidification with convection:Part I.Multiscale/multiphase modeling[J].Metall Mater Trans A,1996,27(9):2754.
[25]
Ghazal G,Jardy A,Chapelle P,et al.On the dissolution of nitrided titanium defects during vacuum arc remelting of Ti alloys[J].Metall Mater Trans B,2010,41(3):646.
[26]
WANG Z,WANG N H,LI T.Computational analysis of a twin-electrode DC submerged arc furnace for MgO crystal production[J].J Mater Process Technol,2011,211(3):388.
[27]
Zalonik M,Combeau H.An operator splitting scheme for coupling macroscopic transport and grain growth in a two-phase multiscale solidification model:Part I-Model and solution scheme[J].Comput Mater Sci,2010,48(1):1.
[28]
Ballantyne A S.The development and application of an integrated var process model[J].BHM Berg-Huttenmann Monatsh,2016,161(1):12.
[29]
Williamson R L,Erdmann R G,Beaman J J,et al.Monitoring the vacuum arc remelting process[C]//Liquid Metal Processing and Casting Symposium.New York,NY:Springer,2007:1.
[30]
Kelkar K M,Patankar S V,Mitchell A,et al.Computational modeling of the vacuum arc remelting (VAR) process used for the production of ingots of titanium alloys[C]//11th World Conference on Titanium (Ti-2007).Kyoto:Japan Institute of Metals,2007:3.
[31]
Venkatesh V,Wilson A,Kamal M,et al.Computational modeling in the primary processing of titanium:A review[J].JOM,2009,61(5):45.
[32]
Hans S.Modélisation Des Transferts Couplés De Chaleur,De Soluté Et De Quantité De Mouvement Lors De La Refusion à L’Arc Sous Vide (Var)-Application Aux Alliages De Titane[D].French,Nancy:Institut National Polytechnique De Lorraine,1995.
Zhang W,Lee P D,McLean M.Numerical simulation of dendrite white spot formation during vacuum arc remelting of INCONEL718[J].Metall Mater Trans A,2002,33(2):443.
[36]
Beaman J J,Lopez L F,Williamson R L.Modeling of the vacuum arc remelting process for estimation and control of the liquid pool profile[J].J Dyn Syst Meas Control-Trans ASME,2014,136(3):031007.
[37]
Kondrashov E N,Musatov M I,Maksimov A Y,et al.Calculation of the molten pool depth in vacuum arc remelting of alloy Vt3-1[J].J Eng Thermophys,2007,16(1):19.
[38]
El Mir H,Jardy A,Bellot J P,et al.Thermal behaviour of the consumable electrode in the vacuum arc remelting process[J].J Mater Process Technol,2010,210(3):564.
[39]
Chapelle P,Ward R M,Jardy A,et al.Lateral boundary conditions for heat transfer and electrical current flow during vacuum arc remelting of a zirconium alloy[J].Metall Mater Trans B,2009,40(3):254.
[40]
Jardy A,Ablitzer D.Mathematical modelling of superalloy remelting operations[J].Mater Sci Technol,2009,25(2):163.
[41]
Kondrashov E N,Maksimov A Y,Konovalov L V.Quasi-steady-state characteristics of solidification of alloys made from VT3-1 alloy during vacuum arc remelting[J].Russ J Non-Ferrous Metals,2008,49(1):23.
[42]
Mitchell A.Solidification in remelting processes[J].Mat Sci Eng:A,2005(413/414):10.
[43]
杨永维.真空自耗电弧炉数学模型的实验研究及控制策略[D].重庆:重庆大学,2009.
[44]
Williamson R L,Schlienger M E,Hysinger C L,et al.Modern control strategies for vacuum arc remelting of segregation sensitive alloys[C]//Superalloys 718,625,706 and various derivatives.Warrendale,Pa:TMS,1997:37.
[45]
Kermanpur A,Evans D G,Siddall R J,et al.Effect of process parameters on grain structure formation during VAR of Inconel alloy 718[J].J Mater Sci,2004,39(24):7175.
[46]
Patel A,Fiore D.On the modeling of vacuum arc remelting process in titanium alloys[J].IOP Conf Ser:Mate Sci Eng,2016,143:012017.
[47]
龙洋.钛合金真空自耗重熔过程中温度场数值模拟[D].哈尔滨:哈尔滨工业大学,2008.
[48]
Nastac L.Solidification structure modeling in ingots processed through primary and secondary remelt operations[J].Int J Cast Metals Res,2003,15(3):279.
[49]
Warren J A,Boettinger W J.Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method[J].Acta Metall Mate,1995,43(2):689.
[50]
Spittle J A,Brown S G R.Computer simulation of the effects of alloy variables on the grain structures of castings[J].Acta Metall Mater,1989,37(7):1803.
[51]
Geiger J,Roosz A,Barkoczy P.Simulation of grain coarsening in two dimensions by cellular-automaton[J].Acta Mater,2001,49(4):623.
[52]
Jacot A,Rappaz M.A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys[J].Acta Mater,2002,50(8):1909.
Gao J,Thompson R G.Real time-temperature models for Monte Carlo simulations of normal grain growth[J].Acta Mater,1996,44(11):4565.
[55]
Porter D A,Easterling K E,Sherif M.Phase Transformations in Metals and Alloys(revised reprint) [M].3rd ed.Boca Raton:CRC Press,2009.
[56]
Thevoz P,Desbiolles J L,Rappaz M.Modeling of equiaxed microstructure formation in casting[J].Metall Mater Trans A,1989,20(2):311.
[57]
Kurz W,Giovanola B,Trivedi R.Theory of microstructural development during rapid solidification[J].Acta Metall Mater,1986,34(5):823.
[58]
Beltran-Sanchez L,Stefanescu D M.Growth of solutal dendrites:A cellular automaton model and its quantitative capabilities[J].Metall Mater Trans A,2003,34(2):367.
[59]
Nastac L.Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys[J].Acta Mater,1999,47(17):4253.
[60]
Nakajima K,Zhang H,Oikawa K,et al.Methodological progress for computer simulation of solidification and casting[J].ISIJ Int,2010,50(12):1724.
[61]
Gandin C A,Rappaz M.A 3D cellular automaton algorithm for the prediction of dendritic grain growth[J].Acta Mater,1997,45(5):2187.
[62]
ZHU M F,HONG C P.A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys[J].ISIJ Int,2001,41(5):436.
[63]
Zhu P P,Smith R W.Dynamic simulation of crystal growth by Monte Carlo method-Ⅰ:Model disription and kinetics[J].Acta Metall Mater,1992,40(4):683.
[64]
Rappaz M,Gandin C A.Probabilistic modelling of microstructure formation in solidification processes[J].Acta Metall Mater,1993,41(2):345.
[65]
Lee S M,Hong C P.Effects of Zr on microstructure and mechanical properties of Al-Cu base ribbons spun by planar flow casting[J].Met Mater-Int,1998,4(2):135.
[66]
Dilthley U,Pavlik V O.Numerical simulation of dendrite morphology and grain growth with modified cellular automata[C]//Modeling of Casting,Welding and Advanced Solidification Processes VIII.Warrendale,Pa:Minerals,Metals and Materials Society,1998:589.
Nastac L.Multiscale modeling of the solidification structure evolution of VAR-processed alloy 718 ingots[C]//8th International Symposium on Superalloy 718 and Derivatives.Red Hook,NY:Curran,2014:57.