为了获得合金静态再结晶前的变形晶粒组织, 应用网格畸变模型与相场模型结合, 生成变形合金再结晶前的初始晶粒组织; 针对合金不同变形区域的特征和体系储存能分布不均匀的特点, 分别引入反映不同变形区域的储存能分布的权重因子和变形区域的特征状态因子, 构造多状态的非均匀自由能密度函数. 在此基础上,应用相场动力学方程模拟了AZ31镁合金的静态再结晶过程的微结构演化,系统地分析了再结晶转变动力学曲线和Avrami曲线, 以及储存能释放规律和再结晶晶粒尺度分布. 模拟得到的动力学规律符合JMAK理论, 所得的Avrami曲线可近似看成一条直线, 对应于真应变ε=0.25, 0.50, 0.75和1.00,该直线的平均斜率分别为2.45, 2.35, 2.19和2.15. Avrami时间指数随变形量的增加而降低. 变形程度大的合金, 储存能释放的速度快, 完成静态再结晶所需的时间短.基于本文提出的模型, 结合相场方法计算模拟所得的结果与已有的理论结果和实验结果符合良好.
[1] Mordike B L, Ebert T. Magnesium: Properties-applications-potential[J]. Mater Sci Eng, 2001; A302:37-45
[2] Hakamada M, Furuta T, Chino Y, Chen Y Q, Kusuda H, Mabuchi M, Mamoru Mabuchi. Life cycle inventory study on magnesium alloy substitution in
vehicles[J]. Energy, 2007; 32(8):1352-1360
[3] Kancko T, Suzuki M. Automotive Applications of Magnesium Alloys[J]. Mater Sci Forum, 2003; 419-422: 67-72
[4] Agnew S R, Senn J W, andHorton J . Mg Sheet Metal Forming: Lessons Learned from Deep Drawing Li and Y Solid-Solution Alloys[J]. JOM, 2006;
58(5):62-69
[5] Humphreys F J, Hatherly M. Recrystallization and Related Annealing Phenomena[M], Elsevier Science, Oxford, UK, 1995
[6] Doherty R D, Hughes D A, Humphreys F J, Jonas J J, Jensen D J. Current issues in recrystallization: a review[J]. Mater Sci Eng, 1997; A238:219-274
[7] Liss K D, Garbe U, Li H J, Thomas S, Jonathan D A,Yan K. Adv Eng Mater, 2009; 11(8): 637-640
[8] Song X Y, Rettenmayr M. Modelling study on recrystallization,recovery and their temperature dependence in inhomogeneously deformed materials[J]. Mater Sci Eng, 2002; A332:153-160
[9] Walasek T A. Experimental verification of Monte Carlo recrystallization model[J]. J Mater Process Technol, 2004; 157-158:262-267
[10] Chun Y B, Semiatin S L, Hwang S K. Monte Carlo modeling of microstructure evolution during the static recrystallization of cold-rolled, commercial-purity titanium[J]. Acta Mater, 2006; 54(14):3673-3689
[11] Guan X J, Zhang J X and Sun S. Computer Simulation for Recrystallization of Deformed Metal[J]. Special Steel. 2004; 25(3): 34-37
(关小军, 张继详, 孙胜. 变形金属再结晶过程计算机模拟. 特殊钢, 2004,25(3):34-37)
[12] Zhang J X. PhD Dissertation, Shandong University, Jinan, 2006
(张继详. 基于Monte Carlo方法的材料退火过程模拟模型及计算机仿真关键技术研究[D]. 山东大学博士学位论文,济南,2006 )
[13] Kazeminezhad M. On the modeling of the static recrystallization considering the initial grain size effects[J]. Mater Sci Eng, 2008; A486:202-207
[14] Lu Y, Zhang L W, Deng X H, Pei J B, Wang S, Zhang G L. Modeling Dynamic Recrystalization of Pure Copper Using Cellular Automaton
Method[J]. Acta Metall Sin, 2008; 44(3):292-296
(卢瑀, 张立文, 邓小虎, 裴继斌, 王赛, 张国梁. 纯铜动态再结晶过程的元胞自动机模拟[J]. 金属学报, 2008; 44(3): 292-296)
[15] Mukhopadhyay P, Loeck M, Gottstein G. A cellular operator model for the simulation of static recrystallization. Acta Mater, 2007,55(2):551-564
[16] Zheng C W, Xiao N M, Li D Z, Li Y Y. Microstructure prediction of the austenite recrystallization during multi-pass steel strip hot rolling: A cellular automaton modeling[J]. Comput Maters Sci, 2008; 44(2): 507-514.
[17] Xiao N M, Zheng C W, Li D Z, Li Y Y. A simulation of dynamic recrystallization by coupling a cellular automaton method with a topology deformation
technique[J]. Comput Maters Sci, 2008,41(3):366-374.
[18] Guo J, Wang Y M, Li W, Wu D, Zhao X M. Cellular Automaton Simulation (I) in Static Recrystallization Process Microstructure Evolution and Dynamics Research[J]. Heavy Casting and Forging, 2009; 1(1) :20-24.
(郭娟, 王艳梅, 李卫, 吴迪, 赵宪明. 静态再结晶过程的元胞自动机模拟(I)——微观组织演化和动力学研究[J]. 大型铸锻件, 2009; 1(1):20-24).
[19] Chen L Q, Yang W. Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics[J]. Phys Rev B, 1994; 50(21):15752-15756
[20] Fan D,Chen L Q. Computer simulation of grain growth using a continuum field model[J]. Acta Mater,1997; 45(2): 611-622
[21] Moelans N, Blanpain B, Wollants P. Phase field simulations of grain growth in two-dimensional systems containing finely dispersed second-phase particles[J]. Acta Mater, 2006; 54(4):1175-1184.
[22] Suwa Y, Saito Y. Phase field simulation of grain growth containing finely dispersed second-phase particle[J]. Scr Mater, 2006; 55(4): 407-410
[23] Gao Y J, Zhang H L, Jin X, Huang C G, Luo Z R. Phase-field simulation of two-phase grain growth with hard particles[J]. Acta Metall Sin, 2009; 45(10):1190-1198
(高英俊, 张海林, 金星, 黄创高, 罗志荣. 相场方法研究硬质粒子钉扎的两相晶粒长大过程[J]. 金属学报, 2009; 45(10): 1190-1198)
[24] Vedantam S, Mallick A. Phase-field theory of grain growth in the presence of mobile second-phase particles[J]. Acta Mater, 2010; 58 (1):272–281
[25] Suwa Y, Saito Y, Onodera H. Phase field simulation of stored energy driven interface migration at a recrystallization front[J]. Mater Sci Eng, 2007; A457:132-138
[26] Suwa Y, Saito Y, Onodera H. Phase-field simulation of recrystallization based on the unified subgrain growth theory[J]. Comput Maters Sci, 2008; 44(2): 286-295
[27] Takaki T, Yamanaka A, Higa Y, Tomita Y. Phase-field model during static recrystallization based on crystal-plasticity theory[J]. J Computer-Aided Mater. Des, 2007; 14: 75-84
[28] Wang M T, Zong B Y, Wang G. Grain growth in AZ31 Mg alloy during recrystallization at different temperatures by phase field simulation. Comput Maters Sci, 2009; 45(2): 217-222
[29] Takaki T, Hirouchi T, Hisakuni Y, Yamanaka A and Tomita Y. J Crystal Growth, 2008; 310: 2248
[30] Li Y L and Chen L Q. Appl Phys Lett, 2006; 88: 072905
[31] Wang Y U. Acta Mater, 2006; 54: 953
[32] Li W, Gao L. Scr Mater, 2001; 44: 2269
[33] Guyer J E, Boittinger W J. Phys Rev, 2004; 69E: 021603
[34] Ramanarayan H, Abinandanan T A. Acta Mater, 2004; 52: 921
[35] Sreekala S, Haataja M. Phys Rev, 2007; 76B: 094109
[36] Cahn R W, Materials Science and Technology, Vol.15. Beijing: Science Press, 1999: 360
(R W 卡恩 主编. 材料科学与技术丛书(第15卷),北京: 科学出版社,1999: 360)
[37] Oono Y, Pori S. Phys Rev Lett, 1987; 58(8): 836
[38] Zheng C W, Lan Y J, Xiao N M, Li D Z, Li Y Y. Acta Metall Sin, 2006; 42(5):474-480
(郑成武,兰永军,肖纳敏,李殿中,李依依. 热变形低碳钢中奥氏体静态再结晶模拟[J]. 金属学报, 2006; 42(5): 474-480)
[39] Ye W P, Gell R L, Saindrenan G. A study of the recrystallization of an IF steel by kinetics models. Mater Sci Eng, 2002; A332: 41-47
[40] Liu R C, Wang L Y, Gu L G, Huang G S. Light Alloy Fabric Technol, 2004; 32: 22-25
(刘饶川,汪凌云,辜蕾钢,黄光胜. 轻合金加工技术,2004; 32: 22-25)