奥氏体—铁素体相变的计算机模拟
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摘要
本文建立了碳钢二维等温奥氏体-铁素体相变的元胞自动机(2DCA)模型;应用所建立的等温相变模型,对含碳量分别为:0.1、0.15、0.2、0.25的四种钢在不同等温温度下奥氏体-铁素体相变进行了模拟,并对奥氏体-铁素体相变的形核、长大及粗化三个阶段进行讨论,提出铁素体生长的混合生长算法;最后,建立了三维等温奥氏体-铁素体相变的元胞自动机(3DCA)模型。
模拟结果显示:铁素体优先在奥氏体晶界形核,少量铁素体在奥氏体内部形核;随着保温时间的延长,铁素体优先在奥氏体晶界生长;相变温度一定时,等温奥氏体-铁素体相变过程,最终铁素体体积分数取决于相变初期铁素体的生长速度;生长速度大,铁素体最终体积分数大,而铁素体相的长大速度与奥氏体-铁素体相界处奥氏体相一侧碳原子浓度有关,碳原子浓度越大,铁素体相的长大速度越小;15SiMn钢奥氏体相的平衡碳浓度比25SiMn钢奥氏体相的低,15SiMn钢铁素体初始生长速度比25SiMn钢快,因而,最终铁素体体积分数较大。
混合生长算法的提出简化了模型,加快了计算的速度;3DCA模拟结果再现了相变过程中的组织演化过程,三维模型对于晶体相变过程中奥氏体初始状态的不规则性,晶粒形核的随机特性,铁素体长大和粗化等各方面都作了充分地展现,进一步印证了本文的3DCA模型的正确性、可行性。
A two-dimensional musicales cellular automaton model (2DCA) is developed to simulate the microstructure formed during the austenite to ferrite transformation in steels. The austenite to ferrite transformation at different isothermal temperatures in two low carbon steels of 0.1、0.15、0.2、0.25 is simulated using the present mode. Especially the grain from austenitic changes to the ferrite of the three stages: nuclear, Growth and coarse mixture of growth and proposed algorithm. Finally, a three-dimensional cellular automaton model (3DCA) is developed to simulate the microstructure formed during the austenite to ferrite transformation.
The simulations show: Priority ferrites nucleate in austenite-ferrite interface, and while a small amount of ferrite grain within the austenite nucleation. With the extended holding time, Priority ferrites grow in austenite-ferrite interface. The simulations show: At a given isothermal temperature, the final volume fraction of ferrite grain is determinated by the average original growth rate of ferrite grain during the austenite to ferrite transformation in steels. The mean growth rate of ferrite grain increases and the simulated final ferrite volume fraction also increases. And the mean growth rate of ferrite grain is affected by percentage composition of carbon in steels during the austenite to ferrite transformation in steels. Percentage composition of carbon in steels increases and the mean growth rate of ferrite grain reduce. Because the percentage composition of carbon in 15SiMn steel is lower than 25SiMn steel, and the mean growth rate of ferrite grain in 15SiMn steel is faster than 25SiMn steel, the simulated final ferrite volume fraction increases.
The simulation of mixed growth algorithm show: model is simplified and speed of the calculation is accelerated. The simulations of 3DCA show: Organizational evolution during the austenite to ferrite transformation. The initial irregular nature of austenite, grain nucleation of random features, and length large coarse ferrite for three- dimensional cellular automata 3DCA model are externalized. And three- dimensional cellular automata 3DCA model is exact.
模拟结果显示:铁素体优先在奥氏体晶界形核,少量铁素体在奥氏体内部形核;随着保温时间的延长,铁素体优先在奥氏体晶界生长;相变温度一定时,等温奥氏体-铁素体相变过程,最终铁素体体积分数取决于相变初期铁素体的生长速度;生长速度大,铁素体最终体积分数大,而铁素体相的长大速度与奥氏体-铁素体相界处奥氏体相一侧碳原子浓度有关,碳原子浓度越大,铁素体相的长大速度越小;15SiMn钢奥氏体相的平衡碳浓度比25SiMn钢奥氏体相的低,15SiMn钢铁素体初始生长速度比25SiMn钢快,因而,最终铁素体体积分数较大。
混合生长算法的提出简化了模型,加快了计算的速度;3DCA模拟结果再现了相变过程中的组织演化过程,三维模型对于晶体相变过程中奥氏体初始状态的不规则性,晶粒形核的随机特性,铁素体长大和粗化等各方面都作了充分地展现,进一步印证了本文的3DCA模型的正确性、可行性。
A two-dimensional musicales cellular automaton model (2DCA) is developed to simulate the microstructure formed during the austenite to ferrite transformation in steels. The austenite to ferrite transformation at different isothermal temperatures in two low carbon steels of 0.1、0.15、0.2、0.25 is simulated using the present mode. Especially the grain from austenitic changes to the ferrite of the three stages: nuclear, Growth and coarse mixture of growth and proposed algorithm. Finally, a three-dimensional cellular automaton model (3DCA) is developed to simulate the microstructure formed during the austenite to ferrite transformation.
The simulations show: Priority ferrites nucleate in austenite-ferrite interface, and while a small amount of ferrite grain within the austenite nucleation. With the extended holding time, Priority ferrites grow in austenite-ferrite interface. The simulations show: At a given isothermal temperature, the final volume fraction of ferrite grain is determinated by the average original growth rate of ferrite grain during the austenite to ferrite transformation in steels. The mean growth rate of ferrite grain increases and the simulated final ferrite volume fraction also increases. And the mean growth rate of ferrite grain is affected by percentage composition of carbon in steels during the austenite to ferrite transformation in steels. Percentage composition of carbon in steels increases and the mean growth rate of ferrite grain reduce. Because the percentage composition of carbon in 15SiMn steel is lower than 25SiMn steel, and the mean growth rate of ferrite grain in 15SiMn steel is faster than 25SiMn steel, the simulated final ferrite volume fraction increases.
The simulation of mixed growth algorithm show: model is simplified and speed of the calculation is accelerated. The simulations of 3DCA show: Organizational evolution during the austenite to ferrite transformation. The initial irregular nature of austenite, grain nucleation of random features, and length large coarse ferrite for three- dimensional cellular automata 3DCA model are externalized. And three- dimensional cellular automata 3DCA model is exact.
引文
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[3] Reed R C, Bhadeshia H K. Kinetics of reconstructive austenite to ferrite transforma-tion in low alloy steels [J]. Material Science and Engineering, 1992, 170(8): 421-433
[4] Krielaart G P, Sietsma J, Zwaag S. Ferrite formation in Fe-C alloys during austenite position under non-equilibrium interface conditions [J]. Material Science and Engineering: A, 1997, 237A: 216-223
[5] Leeuwen Y, Onink M, Sietsma J. The transformation kinetics of low carbon steels under ultra-fast cooling conditions [J]. ISIJ International, 2001, 41(3): 1037-1046
[6]王平吉,周晓光,吴迪.连续冷却过程中铁素体相变温度的模拟[J].材料与冶金学报,2006,5(1):57-60
[7]吕凯.CA法的研究及模型的建立[D].哈尔滨:哈尔滨理工大学,2007
[8]赵连城,徐洲.金属固态相变原理[M].北京:科技出版社,2004
[9]申孝民,关小军,张继祥等.有限元与Monte Ca rlo方法耦合的冷轧纯铝板再结晶模拟[J].中国有色金属学报,2007,17(1):124-130
[10]关小军,焦宪友,周家娟等.单一晶粒长大过程的CA法模拟[J].中国有色金属学报,2007,17(5):699-703
[11] Geiger J, Roosz A, Barkoczy P. Simulation of grain coarsening in two dimensions by cellular-automaton [J]. Acta Materialia, 2001, 49(4): 623-629
[12]焦宪友,关小军,刘运腾等.基于CA法的晶粒长大模拟[J].山东大学学报:工学版,2005,35(6):24-28
[13] Ding H L, He Y Z, Liu L F, Ding W L. Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle [J].Journal of Crystal Growth, 2006, 293(2): 489-497
[14]林国顺,黄梯云,邢月华.计算机模拟发展综进[J].交通与计算机,1998,16(5):1-6
[15]张维丽,朱有兰,李瑜岦.计算机模拟技术在材料科学中的应用[J].冶金丛刊,1999,(2):17-19
[16] D Raabe著.项金钟,吴兴惠译.计算材料学[M].北京:化学工业出版社, 2002
[17]卢渝.纯铜及纯镍动态再结晶过程的二维CA法模拟[D].大连:大连理工大学,2007
[18] Hesselbarth H W, Gobel I R. Simulation of recrystallization by cellular automata. Acat Metarialia, 1991, 39(6): 2135-2143
[19] Davies C H J. The effect of neighbourhood on the kinetics of a cellular automaton recrystallisation model [J]. Scripta Metallurgica Materialia, 1995, 33(7): 1139-1143
[20]李殿中,杜强,胡志勇等.金属成形过程中组织演变的Cellular Automaton模拟技术[J].金属学报,1999,35(11):1201-1205
[21] Marx V, Reher F R, Gottstein G. Simulation of primary recrystallization using a modified three-dimensional cellular automaton [J]. Acat Materialia, 1999, 47(5): 12-19
[22] Raabe D, Becker R C. Coupling a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium [J]. Material Science and Engineering, 2000, 56(8): 445-462
[23] Ding R, Guo Z X. Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization [J]. Acta Materialia, 2001, 49(16): 3163-3175
[24] Rappaz M, Gandin Ch A. Probabilistic modelling of microstructure formation in solidification processes [J]. Acta Metallurgica et Materialia, 1993, 41(2): 345-360
[25] Gandin A, Rappaz M. A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes [J]. Acta Metallurgica et Materialia, 1994, 42(7): 2233-2246
[26] Gandin Ch A, Rappaz M. 3D Cellular Automaton algorithm for the prediction of dendritic grain growth [J]. Acta Materialia, 1997, 45(5): 2187-2195
[27] Kremeyer K. Cellular automata investigations of binary solidification [J]. Comput Phys, 1998, 14(2): 243-262
[28] Kumar M, Sasikumar R, Nair P K. Competition between nucleation and early growth of ferrite from austenite-Studies using cellular automaton simulations [J]. Acta Materialia, 1998, 46(17): 6291-6303
[29] Militzer M, Pandi R, Hawbolt EB. Ferrite nucleation and growth during continuous cooling [J]. Metall Mater Trans A, 1996, 27A: 1547-1555
[30] Varma M R, Sasikumar R, Pillai SG K. Cellular automaton simulation of microstructure evolution during austenite decomposition under continuous cooling conditions [J]. Bull MaterScience, 2001, 56(3): 305-312
[31] Zhang L, Zhang C B, Wang Y M. Cellular automaton model to simulate nucleation and growth of ferrite grains for low-carbon steels [J]. Mater Res, 2002, 17(6): 2251-2259
[32] Zhang L, Wang Y M, Zhang C B. A cellular automaton model of the transformation from austenite to ferrite in low carbon steels [J]. Model Simulation Mater Science and Engineering, 2003, 34(11): 791-802
[33] Zhang L, Zhang C B, Wang Y M. A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling [J]. Acta Materialia, 2003, 51(5): 5519-5527
[34] Saurabh Kundu, Monojit Dutta, Suvankar Ganguly, Sanjay Chandra.Prediction of phase transformation and microstructure in steel using cellular automaton technique[J]. Scripta Materialia, 2004, 50(6): 891-895
[35]张林,张彩碚.连续冷却过程中低碳钢奥氏体-铁素体相变的CA法模拟[J].金属学报,2004,40(17):8-13
[36]兰勇军.低碳钢奥氏体-铁素体相变介观模拟计算[D].沈阳:中国科学院金属研究所,2005
[37]郑成武.热变形低碳钢中奥氏体静态再结晶介观尺度模拟[J].金属学报,2006,42(5):474-480
[38]王玉琨,刘启平.微观晶体三维相变模拟的研究[J].科技资讯,2008,(35):3-5
[39]和平鸽工作室.OpenGL三维图形系统开发与实用技术[M].北京:清华大学出版社,2003
[40] Kumar M. Modelling of microstructure evolution during transformation of austenite to ferrite and pearlite [M]. Madras: Indian Institute of Technology, 2000
[41] Bastien Chopard, MichelDroz. Cellular Automata Modeling of Physical Systems [M]. Cambridge Univ Press, 1998: 245-263
[42] Minsky M. Computation: finite and infinite machines [M]. NJ: Prentice-Hall, 1967
[43] Li Xia, Anthony Gar-Onyeh. A Cellular Automata Model to simulate Deve1opment Density for Urban Planning [J]. Environment and Planning, 2002, 29(5): 431-450
[44]唐小兵.CA法加速度技术初探[J].武汉交通科技大学学报,2000,24(6):602-605
[45]唐小兵,沈成武.平面桁架力学分析中的CA法初探[J].武汉交通科技大学学报,2000,24(2):105-108
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