·368· 工程科学学报，第39卷，第3期 (林均品，叶丰，陈国良，等.6.5wt%Si高硅钢冷轧薄板制备 Res1nt,2011,82(10):1173 工艺、结构和性能.前沿科学，2007(2)：13) [17]Wang J L,Wang F M,Zhao YY,et al.Numerical simulation of Spittle JA.Brown SG R.Computer simulation of the effects of 3D-microstructures in solidification processes based on the CAFE alloy variables on the grain structures of castings.Acta Metall, method.Int J Miner Metall Mater,2009,16(6):640 1989,37(7):1803 [18]Hou Z B,Jiang F,Cheng GG.Solidification structure and com- [8]Wang S L.Sekerka R F,Wheeler AA,et al.Thermodynamical- pactness degree of central equiaxed grain zone in continuous cast- ly-consistent phase-field models for solidification.Phys D,1993, ing billet using cellular automaton-finite element method.IS/ 69(12):189 ,2012,52(7):1301 9]Natsume Y,Ohsasa K,Narita T.Phase-field simulation of transi- [19]Kattner U R.The thermodynamic modeling of multicomponen ent liquid phase bonding process of Ni using Ni-P binary filler phase equilibria.JOM,1997,49(12)14 metal.Mater Trans,2003,44(5)819 [20] Thevoz P.Desbiolles JL Rappaz M.Modeling of equiaxed mi- [10]Zhao Y Z,Shi Y W,Shi L F.Current research status of comput- crostructure formation in casting.Metall Trans A.1989.20(2): er simulation of casting solidification structure.Met Form 311 Technol,2002,20(6):53 21] Kurz W,Giovanola B,Trivedi R.Theory of microstructural de- (赵玉珍，史耀武，史立丰.铸件凝固过程组织计算机模拟 velopment during rapid solidification.Acta Metall,1986,34 研究动态.金属成型工艺，2002,20(6)：53) (5):823 [11]Rappaz M,Gandin C A.Probabilistic modelling of microstructure 22] Gandin C A,Rappaz M.A coupled finite element-cellular au- formation in solidification processes.Acta Metall Mater,1993, tomaton model for the prediction of dendritic grain structures in 41(2):345 solidification processes.Acta Metall Mater,1994,42(7):2233 [2]Gandin CA,Rappaz M.A 3D cellular automaton algorithm for 3]Kovac F,Stoyka V,Petryshynets I.Strain-induced grain growth the prediction of dendritic grain growth.Acta Mater,1997,45 in non-oriented electrical steels.J MagnMagn Mater,2008, (5):2187 320(20):c627 [13]Gandin C A,Desbiolles J L,Rappaz M,et al.A three-dimen- 4]Zhang N.Yang P,Mao W M.Influence of columnar grains on sional cellular automation-finite element model for the prediction the recrystallization texture evolution in Fe-3%Si electrical of solidification grain structures.Metall Mater Trans A,1999,30 steel.Acta Metall Sin,2012,48(3):307 (12):3153 (张宁，杨平，毛卫民.柱状品对F©-3%Si电工钢再结晶织 [14]Pang R P,Wang F M,Zhang G Q,et al.Study of solidification 构演变规律的影响.金属学报，2012,48(3)：307) thermal parameters of 430 ferrite stainless steel based on 3D-CA- 25] Song W,Zhang J M,Liu Y,et al.Numerical simulation of so- FE method.Acta Metall Sin,2013,49(10):1234 lidification structure of 6.5 wt%Si steel ingot slab.lronmaking (庞瑞朋，王福明，张国庆，等.基于3D-CAFE法对430铁 Steelmaking,2015,42(9）:656 素体不锈钢凝固热参数的研究.金属学报，2013,49(10)： [26 Pickering EJ.Macrosegregation in steel ingots:the applicability 1234) of modelling and characterisation techniques.IS//Int,2013,53 [15]Lno YZ,Zhang J M,Wei X D,et al.Numerical simulation of (6):935 solidification structure of high carbon SWRH77B billet based on 27]Patil P,Nalawade R,Balachandran G,et al.Analysis of solidi- the CAFE method.Ironmaking Steelmaking,2012,39(1):26 fication behaviour of low alloy steel ingot casting-simulation and [6]Jing CL,Wang X H,Jiang M.Study on solidification structure experimental validation.fronmaking Steelmaking,2015,42 of wheel steel round billet using FE-CA coupling model.Steel (7):512工程科学学报，第 39 卷，第 3 期 ( 林均品，叶丰，陈国良，等． 6. 5wt% Si 高硅钢冷轧薄板制备 工艺、结构和性能． 前沿科学，2007( 2) : 13) ［7］ Spittle J A，Brown S G Ｒ． Computer simulation of the effects of alloy variables on the grain structures of castings． Acta Metall， 1989，37( 7) : 1803 ［8］ Wang S L，Sekerka Ｒ F，Wheeler A A，et al． Thermodynamical￾ly-consistent phase-field models for solidification． Phys D，1993， 69( 1-2) : 189 ［9］ Natsume Y，Ohsasa K，Narita T． Phase-field simulation of transi￾ent liquid phase bonding process of Ni using Ni--P binary filler metal． Mater Trans，2003，44( 5) : 819 ［10］ Zhao Y Z，Shi Y W，Shi L F． Current research status of comput￾er simulation of casting solidification structure． Met Form Technol，2002，20( 6) : 53 ( 赵玉珍，史耀武，史立丰． 铸件凝固过程组织计算机模拟 研究动态． 金属成型工艺，2002，20( 6) : 53) ［11］ Ｒappaz M，Gandin C A． Probabilistic modelling of microstructure formation in solidification processes． Acta Metall Mater，1993， 41( 2) : 345 ［12］ Gandin C A，Ｒappaz M． A 3D cellular automaton algorithm for the prediction of dendritic grain growth． Acta Mater，1997，45 ( 5) : 2187 ［13］ 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 ［14］ Pang Ｒ P，Wang F M，Zhang G Q，et al． Study of solidification thermal parameters of 430 ferrite stainless steel based on 3D--CA￾FE method． Acta Metall Sin，2013，49( 10) : 1234 ( 庞瑞朋，王福明，张国庆，等． 基于 3D--CAFE 法对 430 铁 素体不锈钢凝固热参数的研究． 金属学报，2013，49( 10) : 1234) ［15］ Luo Y Z，Zhang J M，Wei X D，et al． Numerical simulation of solidification structure of high carbon SWＲH77B billet based on the CAFE method． Ironmaking Steelmaking，2012，39( 1) : 26 ［16］ Jing C L，Wang X H，Jiang M． Study on solidification structure of wheel steel round billet using FE--CA coupling model． Steel Ｒes Int，2011，82( 10) : 1173 ［17］ Wang J L，Wang F M，Zhao Y 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 ［18］ Hou Z B，Jiang F，Cheng G G． Solidification structure and com￾pactness degree of central equiaxed grain zone in continuous cast￾ing billet using cellular automaton-finite element method． ISIJ Int，2012，52( 7) : 1301 ［19］ Kattner U Ｒ． The thermodynamic modeling of multicomponent phase equilibria． JOM，1997，49( 12) : 14 ［20］ Thevoz P，Desbiolles J L，Ｒappaz M． Modeling of equiaxed mi￾crostructure formation in casting． Metall Trans A，1989，20( 2) : 311 ［21］ Kurz W，Giovanola B，Trivedi Ｒ． Theory of microstructural de￾velopment during rapid solidification． Acta Metall，1986，34 ( 5) : 823 ［22］ 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 ［23］ Kovac F，Stoyka V，Petryshynets I． Strain-induced grain growth in non-oriented electrical steels． J Magn Magn Mater，2008， 320( 20) : e627 ［24］ Zhang N，Yang P，Mao W M． Influence of columnar grains on the recrystallization texture evolution in Fe-- 3% Si electrical steel． Acta Metall Sin，2012，48( 3) : 307 ( 张宁，杨平，毛卫民． 柱状晶对 Fe--3% Si 电工钢再结晶织 构演变规律的影响． 金属学报，2012，48( 3) : 307) ［25］ Song W，Zhang J M，Liu Y，et al． Numerical simulation of so￾lidification structure of 6. 5 wt-% Si steel ingot slab． Ironmaking Steelmaking，2015，42( 9) : 656 ［26］ Pickering E J． Macrosegregation in steel ingots: the applicability of modelling and characterisation techniques． ISIJ Int，2013，53 ( 6) : 935 ［27］ Patil P，Nalawade Ｒ，Balachandran G，et al． Analysis of solidi￾fication behaviour of low alloy steel ingot casting-simulation and experimental validation． Ironmaking Steelmaking， 2015， 42 ( 7) : 512 · 863 ·