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strue- steel.Mater Lett,2000,42(6):371 ture of 72A tire cord steel billet using CAFE method.China B1]Wang J,Fu P,Liu H,et al.Shrinkage porosity criteria and opti- Foundry,2012,9(1):53 mized design of a 100-on 30Cr2 Ni MoV forging ingot.Mater [9]Hou Z,Jiang F,Cheng G.Solidification structure and compact- De,2012,35:446 ness degree of central equiaxed grain zone in continuous casting B2]Li W S,Shen H F,Liu B C.Three-dimensional simulation of billet using cellular automaton-finite element method.IS//Int, thermosolutal convection and macrosegregation in Steel Ingots 2012,52(7):1301 Steel Res Int,2010,81(11):994 0]Rappaz M,Gandin CA.Probabilistic modelling of mierostructure B3]Lan P,Zhang J.Study on the mechanical behaviors of grey iron formation in solidification processes.Acta Metall Mater,1993, mould by simulation and experiment.Mater Des,2014,53:822北 京 科 技 大 学 学 报 第 36 卷 ［10］ Zhu P P，Smith Ｒ W． Dynamic simulation of crystal growth by Monte Carlo method: Ⅰ． Model description and kinetics． Acta Metall Mater，1992，40( 4) : 683 ［11］ Gandin C A，Ｒappaz M． A coupled finite element-cellular au￾tomaton model for the prediction of dendritic grain structures in solidification processes． Acta Metall Mater，1994，42( 7) : 2233 ［12］ Gandin C A，Desbiolles J L，Ｒappaz M，et al． A three-dimen￾sional cellular automation finite element model for the prediction of solidification grain structures． Metall Mater Trans A，1999，30 ( 12) : 3153 ［13］ Nastac L，Stefanescu D M． Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part Ⅰ． Model develop￾ment and discussion． Metall Mater Trans A，1996，27 ( 12 ) : 4061 ［14］ Nastac L，Stefanescu D M． Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part Ⅱ． Computation problems and validation on INCONEL 718 superalloy castings． Metall Mater Trans A，1996，27( 12) : 4075 ［15］ Yamazaki M，Natsume Y，Harada H，et al． Numerical simula￾tion of solidification structure formation during continuous casting in Fe-0. 7mass% C alloy using cellular automaton method． ISIJ Int，2006，46( 6) : 903 ［16］ Wang J，Wang F，Zhao Y，et al． Numerical simulation of 3D￾microstructures in solidification processes based on the CAFE method． Int J Miner Metall Mater，2009，16( 6) : 640 ［17］ Wang J，Wang F，Li C，et al． Simulation of 3D microstructure in free-cutting steel 9SMn28 under water cooling condition with con￾vection and porosity． ISIJ Int，2010，50( 2) : 222 ［18］ Jing C，Xu Z，Wang Y，et al． Simulation on solidification struc￾ture of 72A tire cord steel billet using CAFE method． China Foundry，2012，9( 1) : 53 ［19］ Hou Z，Jiang F，Cheng G． Solidification structure and compact￾ness degree of central equiaxed grain zone in continuous casting billet using cellular automaton-finite element method． ISIJ Int， 2012，52( 7) : 1301 ［20］ Ｒappaz M，Gandin C A． Probabilistic modelling of microstructure formation in solidification processes． Acta Metall Mater，1993， 41( 2) : 345 ［21］ Martorano M A，Beckermann C，Gandin C A． A solutal interac￾tion mechanism for the columnar-to-equiaxed transition in alloy solidification． Metall Mater Trans A，2003，34( 8) : 1657 ［22］ Kurz W，Fisher D J． Fundamentals of Solidification． Switzer￾land: Trans Tech Publications，1989 ［23］ Miettinen J． Thermodynamic-kinetic simulation of constrained dendrite growth in steels． Metall Mater Trans B，2000，31( 2) : 365 ［24］ Ishida H，Natsume Y，Ohsasa K． Numerical simulation of solidi￾fication structure formation in high Mn steel casting using cellular automaton method． ISIJ Int，2008，48( 12) : 1728 ［25］ Cornelissen M C M． Mathematical model for solidification of mul￾ticomponent alloys． Ironmaking Steelmaking，1986，13: 204 ［26］ Kubícek P ˇ ，Pepˇ rica T． Diffusion in molten metals and melts: ap￾plication to diffusion in molten iron． Int Met Ｒev，1983，28( 3) : 131 ［27］ Meng Y，Thomas B G． Heat-transfer and solidification model of continuous slab casting: CON1D． Metall Mater Trans B，2003， 34( 5) : 685 ［28］ Okane T，Umeda T． Eutectic growth of unidirectionally solidified Fe-Cr-Ni alloy． ISIJ Int，1998，38( 5) : 454 ［29］ Pequet C，Gremaud M，Ｒappaz M． Modeling of microporosity， macroporosity，and pipe-shrinkage formation during the solidifica￾tion of alloys using a mushy-zone refinement method: applications to aluminum alloys． Metall Mater Trans A，2002，33( 7) : 2095 ［30］ Moustafa I M，Moustafa M A，Nofal A A． Carbide formation mechanism during solidification and annealing of 17% Cr-ferritic steel． Mater Lett，2000，42( 6) : 371 ［31］ Wang J，Fu P，Liu H，et al． Shrinkage porosity criteria and opti￾mized design of a 100-ton 30Cr2Ni4MoV forging ingot． Mater Des，2012，35: 446 ［32］ Li W S，Shen H F，Liu B C． Three-dimensional simulation of thermosolutal convection and macrosegregation in Steel Ingots． Steel Ｒes Int，2010，81( 11) : 994 ［33］ Lan P，Zhang J． Study on the mechanical behaviors of grey iron mould by simulation and experiment． Mater Des，2014，53: 822 · 223 ·