Ti-6.62Al-5.14Sn-1.82Zr钛合金高温变形行为及模型研究
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摘要
金属的塑性变形过程是一个十分复杂的物理过程，材料在高温变形时不仅宏观力学性能会发生变化，内部微观组织也会经历一系列变化，而金属内部的微观组织演变不仅对变形过程本身产生作用，而且在很大程度上直接决定了材料的宏观力学行为。因此，在正确理解金属塑性变形机理的基础上，建立精确的微观组织模型和反映微观组织参数影响的流动应力模型是实现材料变形过程的变形-传热-微观组织耦合数值模拟的基础，而且对于揭示金属塑性成形规律，优化工艺参数，提高产品质量及性能，促进先进塑性加工技术的发展具有重要意义。
Ti-6.62Al-5.14Sn-1.82Zr钛合金是一种近α型高温钛合金，具有优良的热强性和热稳定性，最高工作温度可达600℃。本文在热模拟压缩实验和定量金相实验的基础上，研究了变形工艺参数对Ti-6.62Al-5.14Sn-1.82Zr钛合金微观组织的影响，运用模糊神经网络理论建立了Ti-6.62Al-5.14Sn-1.82Zr钛合金在高温变形过程中的微观组织模型，并在微观组织模型的基础上，建立了反映微观组织参数影响的流动应力模型，考虑变形过程中的传热，将建立的流动应力模型耦合到有限元程序中，建立了变形-传热-微观组织的有限元耦合模拟系统，应用此系统实现了Ti-6.62Al-5.14Sn-1.82Zr钛合会镦粗过程的耦合数值模拟，研究了Ti-6.62Al-5.14Sn-1.82Zr钛合金镦粗过程的工艺参数对应变场、应力场、温度场和微观组织场的影响。
应用实验结果对微观组织模型和流动应力模型的有效性进行了验证。研究结果表明：模型的计算值与实验值吻合良好。Ti-6.62Al-5.14Sn-1.82Zr钛合金在高温变形过程中的微观组织模型和流动应力模型具有较高的预测精度。
Plastic deformation is a complicated process. At the high temperature deformation, both deformation behavior and microstructure undergo a series of dynamic changes. The microstructure evolution not only influences the deformation process, but also determines the deformation behavior of materials significantly. Therefore, based on understanding of deformation mechanism, to establish accurately the microstructure and flow stress models, which reflects the influence of microstructure evolution on the flow stress, is a basis for realizing the coupled simulation of deformation behavior, heat transfer and microstructure evolution. And it is very important to reveal the deformation principle, optimize the process parameters, improve the quality and mechanical properties of workpiece, and develop the advanced plastic processes.
Ti-6.62Al-5.14Sn-l.82Zr titanium alloy is a near alpha titanium alloy, which has good strength of high temperature and the thermostability, and the service temperature of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy can reach at 600℃. Effects of the process parameters, including deformation .temperature, strain and strain rate, on the microstructure during high temperature deformation have been investigated by the isothermal compression and quantitative metallography. At the high temperature deformation process of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy, the microstructure evolution model has been established in terms of the fuzzy-neural network theory. And the flow stress model has been proposed based on the microstructure model and the deformation mechanism of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy. Integrating the present flow stress model into the FE code, a coupled simulation of deformation with heat transfer and microstructure has been carried out for upsetting of Ti-6.62Al-5.14Sn-1.82Zr titanium alloy. Effects of the process parameters on the equivalent stress field, the equivalent strain field, the temperature rise and the grain size during the upsetting process have been studied.
Meanwhile, the models are verified through experimental results of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy. The calculated results are in a good agreement with the experimental results. Thus, the present models have high prediction accuracy.
Ti-6.62Al-5.14Sn-1.82Zr钛合金是一种近α型高温钛合金，具有优良的热强性和热稳定性，最高工作温度可达600℃。本文在热模拟压缩实验和定量金相实验的基础上，研究了变形工艺参数对Ti-6.62Al-5.14Sn-1.82Zr钛合金微观组织的影响，运用模糊神经网络理论建立了Ti-6.62Al-5.14Sn-1.82Zr钛合金在高温变形过程中的微观组织模型，并在微观组织模型的基础上，建立了反映微观组织参数影响的流动应力模型，考虑变形过程中的传热，将建立的流动应力模型耦合到有限元程序中，建立了变形-传热-微观组织的有限元耦合模拟系统，应用此系统实现了Ti-6.62Al-5.14Sn-1.82Zr钛合会镦粗过程的耦合数值模拟，研究了Ti-6.62Al-5.14Sn-1.82Zr钛合金镦粗过程的工艺参数对应变场、应力场、温度场和微观组织场的影响。
应用实验结果对微观组织模型和流动应力模型的有效性进行了验证。研究结果表明：模型的计算值与实验值吻合良好。Ti-6.62Al-5.14Sn-1.82Zr钛合金在高温变形过程中的微观组织模型和流动应力模型具有较高的预测精度。
Plastic deformation is a complicated process. At the high temperature deformation, both deformation behavior and microstructure undergo a series of dynamic changes. The microstructure evolution not only influences the deformation process, but also determines the deformation behavior of materials significantly. Therefore, based on understanding of deformation mechanism, to establish accurately the microstructure and flow stress models, which reflects the influence of microstructure evolution on the flow stress, is a basis for realizing the coupled simulation of deformation behavior, heat transfer and microstructure evolution. And it is very important to reveal the deformation principle, optimize the process parameters, improve the quality and mechanical properties of workpiece, and develop the advanced plastic processes.
Ti-6.62Al-5.14Sn-l.82Zr titanium alloy is a near alpha titanium alloy, which has good strength of high temperature and the thermostability, and the service temperature of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy can reach at 600℃. Effects of the process parameters, including deformation .temperature, strain and strain rate, on the microstructure during high temperature deformation have been investigated by the isothermal compression and quantitative metallography. At the high temperature deformation process of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy, the microstructure evolution model has been established in terms of the fuzzy-neural network theory. And the flow stress model has been proposed based on the microstructure model and the deformation mechanism of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy. Integrating the present flow stress model into the FE code, a coupled simulation of deformation with heat transfer and microstructure has been carried out for upsetting of Ti-6.62Al-5.14Sn-1.82Zr titanium alloy. Effects of the process parameters on the equivalent stress field, the equivalent strain field, the temperature rise and the grain size during the upsetting process have been studied.
Meanwhile, the models are verified through experimental results of Ti-6.62Al-5.14Sn-l.82Zr titanium alloy. The calculated results are in a good agreement with the experimental results. Thus, the present models have high prediction accuracy.
引文
1 张喜燕，赵永庆，白晨光编．钛合金及应用．北京：化学工业出版社，2004，3～17
2 钱九红．航空航天用新型钛合会的研究发展及应用．稀有金属，2000，24(3)：220～222
3 赵永庆，奚正平，曲恒磊．我国航空用钛合金材料研究现状．航空材料学报，2003，23：215～219
4 R. R. Boyer. Titanium Alloys. USA: ASM International, 1994, 1011
5 王金友，赖新锦，谢成木．高新技术新材料要览．北京：中国科学技术出版社，1993
6 李青．人工股关节用新型钛合会．上海钢研，2002，(1)：16～21
7 劳金海译．钛在生物医学中应用的新发展．上海钢研，2001，(4)：60～62
8 陈付时译．β-型钛合金Yi-29Nb-13Ta-4.6Zr的显微组织和机械性能．上海钢研，2002，(4)：62
9 王金友，葛志明，周彦邦．航空用钛合金．上海：上海科学技术出版社，1985
10 李梁，孙健科，孟祥军．钛合金的应用现状及发展前景．钛工业进展，2004，21(5)：19～24
11 Introduction to Alpha, Alpha+Beta, and Beta Alloys. Titanium Alloys for Aerospace. Advanced Materials & Processes, 1999, 155(3): 39～41
12 Lane Lineberger. Titanium Aerospace Alloy. Advanced Materials & Processes, 1998, 153(5): 45～46
13 The F-22 Story: Building Affordability. Flight International Supplement, 1997, (4): 9～11
14 孟祥军，汪汀．船用钛合金发展概况．钛工业进展，2000，(5)：7～8
15 周彦邦．钛合金铸造概论．北京：航空工业出版社，2000，307～314
16 西北工业大学有色金属锻造编写组．有色金属锻造．北京：国防工业出版社，1979，118～119
17 索朗宁娜著(张志方，葛志明译)．热强钛合金．北京：第三机械工业部第六二一研究所，1979，149～150
18 郭鸿镇编．合金钢与有色合金锻造．西安：西北工业大学出版社，1999
19 王芝英，邵仁兴．钛合金等温锻造进展．锻压技术，1997，(1)：12～18
20 曲银化，孙建科，孟祥军．钛合金等温锻造技术研究进展．钛工业进展，2006，23(1)：6～9
21 王勖成，邵敏．有限单元法基本原理与数值方法．北京：清华大学出版社，1988，37～38
22 R. W. Clough. The Finite Element Method in Plane Stress Analysis. J. Struct. Pic, ASCE, Proc. 2nd Conf. Electronic Computation, 1960, 345
23 C. H. Lee, S. Kobayashi. New Solutions to Rigid Plastic Deformation Problems using a Matrix Method. Transaction of ASME, Journal of Engineering for Industry, 1973, 95: 865～878
24 C. Zienkiewicz, P. N. Godbole. Flow of Plastic and Viscoplastic Solids with Special Reference to Extrusion and Forming Processes. International Journal for Numerical Methods in Engineering, 1974, 8: 3～15
25 N. Rebelo, H. Rydstad, G. Schroder. Simulation of Material Flow in Closed-Die Forging by Model Techniques and Rigid-plastic FEM. Num. Meth. Ind. Form, Proc, Swansea UK: Pineridge Press, 1982: 237～246
26 J. H. Argyris, J. S. Doltsinis, J. Luginsland. Three-dimension Thermomechanical Analysis of Metal Forming Processes. Proc. Int. Workshop Simulation of Metal Forming Processes by the Finite Element Method. (SIMOP-1), Stuttgart, 1985: 125～160
27 J. H. Yoon, D. Y. Yang. A Three-Dimensional Rigid-Plastic Finite Element Analysis of Bevel Gear Forging by using a Remeshing Technique. International Journal of Mechanical Science, 1990, 32(4): 277～291
28 J. W. Brooks, T. A. Dean, Z. M. Hu, E. Wey. Three-dimensional Finite Element Modelling of a Titanium Aluminide Aerofoil Forging. Journal of Materials Processing Technology,. 1998, 80-81: 149～155
29 杨宝付，张治民，王强，刘奎立．TC4合金等温挤压过程的有限元数值模拟．热加工工艺，2004，(1)：34～36
30 张麦仓，董建新，曾燕屏，谢锡善．PM Rene 95合金涡轮盘等温锻造工艺的模拟式设计．金属学报，2002，38(10)：1115～1120
31 刘建生，陈慧琴，郭会光．6160曲轴弯曲镦锻过程的有限元数值模拟．大型铸锻件，2002，(2)：8～11
32 洪慧平，康永林，冯长桃，陈溪强，韩畴．椭圆孔型连轧大圆钢三维热力耦合弹塑性有限元分析．特殊钢，2002，23(5)：5～8
33 洪慧平，康永林．椭圆孔型轧制合金钢方坯三维弹塑性有限元模拟．北京科技大学学报，2003，25(2)：171～173
34 洪慧平，康永林，冯长桃等．连轧大规格合金芯棒钢三维热力耦合模拟仿真．钢铁，2002，37(10)：23～26
35 颜建军，郑建荣，张海鹰，李勇．大型船用曲轴弯锻成形过程仿真和组织模拟研究．中国机械工程，2006，17(19)：2024～2028
36 李晓丽，陈胜晖，李淼泉．金属热念塑性成形过程中组织演变的模型化研究．中国机械工程，2004，15(1)：86～90
37 C. M. Sellars, J. A. Whiteman. Recrystallization and Grain Growth in Hot Rolling. Metal Science, 1979, 13(3): 187～194
38 C. M. Sellars. Modelling Microstructural Development during Hot Rolling. Materials Science and Technology, 1990, 6: 1072～1081
39 H. Yada, T. Senuma. Resistance to Hot Deformation of Steel. J. Jpn. Soc. Tech. Plasticity, 1988, 27: 33～44
40 R. Kopp, K. Karnhausen. Numerical Simulation Method for Designing Thermomechanical Treatment Illustrated by Bar Rolling scand. Journal of Metallurgy, 1991, 20: 351～363
41 G. S. Shen, S. L. Semiation, R. Shivpuri. Modeling Microstructural Development during the Forging of Waspaloy. Metallurgical and Materials Transactions A, 1995, 26A(7): 1795～1803
42 Z. M. Hu, J. W. Brooks, T. A. Dean. Experimental and Theoretical Analysis of Deformation and Microstructural Evolution in the Hot-die Forging of Titanium Alloy Aerofoil Sections. Journal of Materials Processing Technology, 1999, 88(1/3): 251～265
43 Y. S. Jang, D. C. Ko, B. M. Kim. Application of the Finite Element Method to Predict Microstructure Evolution in the Hot Forging of Steel. Journal of Materials Processing Technology, 2000, 101(1/3): 85～94
44 Y. S. Na, J. T. Yeom, N. K. Park, J. Y. Lee. Simulation of Microstructures for Alloy 718 Blade Forging using 3D FEM Simulator. Journal of Materials Procesing Technology, 2003, 141(3): 337～342
45 王芳，王作成．45#钢锻件热镦粗过程晶粒尺寸模拟．山东工业大学学报，2000，30(6)：569～574
46 李俊，李润方，游理华．热锻成型工件的微观组织模拟．塑性工程学报，1999，6(2)：8～12
47 王连生，曹起骧，许思广．三维热耦合刚粘塑性有限元数值模拟技术的开发和应用．塑性工程学报，1994，1(3)：34～41
48 王连生，马喜腾，曹起骧．三维热锻中动态再结晶过程的数值模拟及试验研究．机械工程学报，1996，32(6)：24～29
49 杨旗，罗子健，刘东．应用模糊数学预测变形高温合金锻件晶粒度．中国机械工程，1999，10(7)：832～834
50 熊爱明，林海，李淼泉．TC6钛合金盘等温锻造时晶粒尺寸的数值模拟．中国机械工程，2003，14(9)：791～794
51 M. Q. Li, X. M. Liu, A. M. Xiong. Modeling of Microstructure during Hot Working Process by ANN. Edited by Jiang Zhuangde, in: Proceedings of the International Conference on AMT'99, Science Press, New York, 1999: 1342～1345
52 M. Q. Li, D. J. Chen, A. M. Xiong, L. Long. An Adaptive Prediction Model of Grain Size for the Forging of Ti-6Al-4V Alloy Based on Fuzzy Neural Networks. Journal of Materials Processing Technology, 2002, 123(3): 377～381
53 熊爱明，薛善坤，李淼泉．TC4钛合金高温变形时微观组织变化的计算．塑性工程学报，2002，9(1)：14～16． Isothermal Forging of Ti-6Al-4V Alloy. Materials Science and Technology, 2002, 18(2): 212～214
55 孙惠学，胡金华，史艳国，周维智．大型锻件镦粗弹塑性有限元分析．钢铁，1998，33(4)：31～34
56 李萍，许沂，吕炎．Ti-15-3热镦粗变形的数值模拟及实验研究．金属成形工艺，2000，18(3)：15～17
57 高军，赵新海，宋立彬，赵国群．厚壁管闭式镦粗有限元分析及实验研究．锻压技术，2001，(3)：6～8
58 张宝红，张治民．双环形件塑性成形数值模拟研究．华北工学院学报，1999，20(4)：363～365
59 胡忠，朱利华，李家庆．圆环压缩过程的有限元模拟—一种标定摩擦系数理论曲线的新方法．金属学报，1997，33(4)：337～344
60 陈军，舒其复．一种采用圆环压缩测定材料应力—应变函数关系的方法．金属成形工艺，1996，14(3)：41～43
61 刘国权，刘胜新，黄启今，钟云龙，钟声，秦湘阁．金相学和材料显微组织定量分析技术．中国体视学与图像分析，2002，7(1)：248～251
62 余永宁，刘国权．体视学一组织定量分析的原理和应用．北京：冶金工业出版社，1989
63 潘洪泗．Ti-6.62A1-5.14Sn-1.82Zr合金的塑性变形机理及热处理工艺研究．西安：西北工业大学硕士学位论文．2005，15
64 熊爱明，陈胜晖，黄维超，林海，李淼泉．TC6钛合金的高温变形行为及组织演变．稀有金属材料与工程，2003，32(6)：447～450
65 吕炎．锻件组织性能控制．北京：国防工业出版社，1988
66 黄光胜，汪凌云，黄光杰，卢志文，宋美娟．AZ31镁合金高温本构方程．金属成形工艺，2004，22(2)：41～44
67 J. Langkruis, W. H. Kool, S. Zwaag. Assessment of Constitutive Equations in Modelling the Hot Deformability of Some Overaged Al-Mg-Si Alloys With Varying Solute Contents. Materials Science and Engineering, 1999, A266(1/2): 135～145
68 J. Langkruis, R. Bergwerf, S. Zwaag. Linking Plane Strain Compression Tests on AA6063 to Laboratory Scale Extrusion via Constitutive Equations. Materials Science Forum, 2000, 331(2): 565～570
69 Z. Gronostajski. The Constitutive Equations for FEM Analysis. Journal of Material s Processing Technology, 2000, 106(1/3): 40～44
70 周纪华，管克智．高温高速下合金结构钢的流动应力研究．金属学报，1986，22(1)：B31～B38
71 A. Wahlen, U. Feurer, J. Reissner. Computer Controlled Measurement and Analytical Modeling of Flow Stresses During Hot Deformation of the Copper Alloy CuZn42Mn2. Journal of Materials Processing Technology, 1997, 63(1/3): 233～237
72 L. X. Kong, P. D. Hodgson, B. Wang. Development of Constitutive Models for Metal Forming with Cyclic Strain Softening. Journal of Materials Processing Technology, 1999, 89/90(5): 44～50
73 D. G. Robertson, H. B. Mcshane. Analysis of High Temperature Flow Stress of Titanium Alloys IMI550 and Ti-10V-2Fe-3Al during Isothermal Forging. Materials Science and Technology, 1998, 14(4): 339～345
74 何宜柱，陈大宏，雷廷权．热变形动态软化本构模型．钢铁，1999，34(9)：29～33
75 J. Y. Cheng, S. Nemat-Nasser, W. G. Guo. A Unified Constitutive Model for Strain-rate and Temperature Dependent Behavior of Molybdenum. Mechanics of Materials, 2001, 33(11): 603～616
76 A. Laasraoui, J. J. Jonas. Prediction of Steel Flow Stress at High Temperatures and Strain Rates. Metallurgical and Materials Transactions A, 1991, 22A(7): 1545～1558
77 A. J. Beaudoin, A. Acharya, S. R. Chen, D. A. Karzekwa, M. G. Stout. Consideration of Grain-size Effect and Kinetics in the Plastic Deformation of Metal Polycrystals. Acta Materialia, 2000, 48(13): 3409～3423
78 P. F. Bariani, S. Bruschi, T. D. Negro. A New Constitutive Model for Hot Forging of Steels Taking into Account the Thermal and Mechanical History. Annals of the CIRP, 2000, 49(1): 195～198
79 T. Tsuta, Y. J. Yin, Z. C. Xie. Upper-bound rigid-plastic Constitutive Model for Mixed-hardening Materials with Micro Void Evolution Process. International Journal of Mechanical Science, 2000, 42(8): 1471～1498
80 熊爱明．钛合金锻造过程变形-传热-微观组织演化的耦合模拟．西安：西北工业大学博士学位论文．2003，44～46
81 S. Kobayashi, S. I. Oh, T. Altan. Metal Forming and the Finite Element Method. Oxford University Press, 1989, 74～75
82 陈火红编．Marc有限元实例分析教程．北京：机械工业出版社，2002，19～20
83 齐德新，刘冠权，马广锋．BT20钛合金切削加工性浅析．机械工程师．2002，10：28～30
84 张桂木，于超，高霁，施永臣．钛合金BT20端铣试验研究．机械设计与制造工程．2001，2：61～62
2 钱九红．航空航天用新型钛合会的研究发展及应用．稀有金属，2000，24(3)：220～222
3 赵永庆，奚正平，曲恒磊．我国航空用钛合金材料研究现状．航空材料学报，2003，23：215～219
4 R. R. Boyer. Titanium Alloys. USA: ASM International, 1994, 1011
5 王金友，赖新锦，谢成木．高新技术新材料要览．北京：中国科学技术出版社，1993
6 李青．人工股关节用新型钛合会．上海钢研，2002，(1)：16～21
7 劳金海译．钛在生物医学中应用的新发展．上海钢研，2001，(4)：60～62
8 陈付时译．β-型钛合金Yi-29Nb-13Ta-4.6Zr的显微组织和机械性能．上海钢研，2002，(4)：62
9 王金友，葛志明，周彦邦．航空用钛合金．上海：上海科学技术出版社，1985
10 李梁，孙健科，孟祥军．钛合金的应用现状及发展前景．钛工业进展，2004，21(5)：19～24
11 Introduction to Alpha, Alpha+Beta, and Beta Alloys. Titanium Alloys for Aerospace. Advanced Materials & Processes, 1999, 155(3): 39～41
12 Lane Lineberger. Titanium Aerospace Alloy. Advanced Materials & Processes, 1998, 153(5): 45～46
13 The F-22 Story: Building Affordability. Flight International Supplement, 1997, (4): 9～11
14 孟祥军，汪汀．船用钛合金发展概况．钛工业进展，2000，(5)：7～8
15 周彦邦．钛合金铸造概论．北京：航空工业出版社，2000，307～314
16 西北工业大学有色金属锻造编写组．有色金属锻造．北京：国防工业出版社，1979，118～119
17 索朗宁娜著(张志方，葛志明译)．热强钛合金．北京：第三机械工业部第六二一研究所，1979，149～150
18 郭鸿镇编．合金钢与有色合金锻造．西安：西北工业大学出版社，1999
19 王芝英，邵仁兴．钛合金等温锻造进展．锻压技术，1997，(1)：12～18
20 曲银化，孙建科，孟祥军．钛合金等温锻造技术研究进展．钛工业进展，2006，23(1)：6～9
21 王勖成，邵敏．有限单元法基本原理与数值方法．北京：清华大学出版社，1988，37～38
22 R. W. Clough. The Finite Element Method in Plane Stress Analysis. J. Struct. Pic, ASCE, Proc. 2nd Conf. Electronic Computation, 1960, 345
23 C. H. Lee, S. Kobayashi. New Solutions to Rigid Plastic Deformation Problems using a Matrix Method. Transaction of ASME, Journal of Engineering for Industry, 1973, 95: 865～878
24 C. Zienkiewicz, P. N. Godbole. Flow of Plastic and Viscoplastic Solids with Special Reference to Extrusion and Forming Processes. International Journal for Numerical Methods in Engineering, 1974, 8: 3～15
25 N. Rebelo, H. Rydstad, G. Schroder. Simulation of Material Flow in Closed-Die Forging by Model Techniques and Rigid-plastic FEM. Num. Meth. Ind. Form, Proc, Swansea UK: Pineridge Press, 1982: 237～246
26 J. H. Argyris, J. S. Doltsinis, J. Luginsland. Three-dimension Thermomechanical Analysis of Metal Forming Processes. Proc. Int. Workshop Simulation of Metal Forming Processes by the Finite Element Method. (SIMOP-1), Stuttgart, 1985: 125～160
27 J. H. Yoon, D. Y. Yang. A Three-Dimensional Rigid-Plastic Finite Element Analysis of Bevel Gear Forging by using a Remeshing Technique. International Journal of Mechanical Science, 1990, 32(4): 277～291
28 J. W. Brooks, T. A. Dean, Z. M. Hu, E. Wey. Three-dimensional Finite Element Modelling of a Titanium Aluminide Aerofoil Forging. Journal of Materials Processing Technology,. 1998, 80-81: 149～155
29 杨宝付，张治民，王强，刘奎立．TC4合金等温挤压过程的有限元数值模拟．热加工工艺，2004，(1)：34～36
30 张麦仓，董建新，曾燕屏，谢锡善．PM Rene 95合金涡轮盘等温锻造工艺的模拟式设计．金属学报，2002，38(10)：1115～1120
31 刘建生，陈慧琴，郭会光．6160曲轴弯曲镦锻过程的有限元数值模拟．大型铸锻件，2002，(2)：8～11
32 洪慧平，康永林，冯长桃，陈溪强，韩畴．椭圆孔型连轧大圆钢三维热力耦合弹塑性有限元分析．特殊钢，2002，23(5)：5～8
33 洪慧平，康永林．椭圆孔型轧制合金钢方坯三维弹塑性有限元模拟．北京科技大学学报，2003，25(2)：171～173
34 洪慧平，康永林，冯长桃等．连轧大规格合金芯棒钢三维热力耦合模拟仿真．钢铁，2002，37(10)：23～26
35 颜建军，郑建荣，张海鹰，李勇．大型船用曲轴弯锻成形过程仿真和组织模拟研究．中国机械工程，2006，17(19)：2024～2028
36 李晓丽，陈胜晖，李淼泉．金属热念塑性成形过程中组织演变的模型化研究．中国机械工程，2004，15(1)：86～90
37 C. M. Sellars, J. A. Whiteman. Recrystallization and Grain Growth in Hot Rolling. Metal Science, 1979, 13(3): 187～194
38 C. M. Sellars. Modelling Microstructural Development during Hot Rolling. Materials Science and Technology, 1990, 6: 1072～1081
39 H. Yada, T. Senuma. Resistance to Hot Deformation of Steel. J. Jpn. Soc. Tech. Plasticity, 1988, 27: 33～44
40 R. Kopp, K. Karnhausen. Numerical Simulation Method for Designing Thermomechanical Treatment Illustrated by Bar Rolling scand. Journal of Metallurgy, 1991, 20: 351～363
41 G. S. Shen, S. L. Semiation, R. Shivpuri. Modeling Microstructural Development during the Forging of Waspaloy. Metallurgical and Materials Transactions A, 1995, 26A(7): 1795～1803
42 Z. M. Hu, J. W. Brooks, T. A. Dean. Experimental and Theoretical Analysis of Deformation and Microstructural Evolution in the Hot-die Forging of Titanium Alloy Aerofoil Sections. Journal of Materials Processing Technology, 1999, 88(1/3): 251～265
43 Y. S. Jang, D. C. Ko, B. M. Kim. Application of the Finite Element Method to Predict Microstructure Evolution in the Hot Forging of Steel. Journal of Materials Processing Technology, 2000, 101(1/3): 85～94
44 Y. S. Na, J. T. Yeom, N. K. Park, J. Y. Lee. Simulation of Microstructures for Alloy 718 Blade Forging using 3D FEM Simulator. Journal of Materials Procesing Technology, 2003, 141(3): 337～342
45 王芳，王作成．45#钢锻件热镦粗过程晶粒尺寸模拟．山东工业大学学报，2000，30(6)：569～574
46 李俊，李润方，游理华．热锻成型工件的微观组织模拟．塑性工程学报，1999，6(2)：8～12
47 王连生，曹起骧，许思广．三维热耦合刚粘塑性有限元数值模拟技术的开发和应用．塑性工程学报，1994，1(3)：34～41
48 王连生，马喜腾，曹起骧．三维热锻中动态再结晶过程的数值模拟及试验研究．机械工程学报，1996，32(6)：24～29
49 杨旗，罗子健，刘东．应用模糊数学预测变形高温合金锻件晶粒度．中国机械工程，1999，10(7)：832～834
50 熊爱明，林海，李淼泉．TC6钛合金盘等温锻造时晶粒尺寸的数值模拟．中国机械工程，2003，14(9)：791～794
51 M. Q. Li, X. M. Liu, A. M. Xiong. Modeling of Microstructure during Hot Working Process by ANN. Edited by Jiang Zhuangde, in: Proceedings of the International Conference on AMT'99, Science Press, New York, 1999: 1342～1345
52 M. Q. Li, D. J. Chen, A. M. Xiong, L. Long. An Adaptive Prediction Model of Grain Size for the Forging of Ti-6Al-4V Alloy Based on Fuzzy Neural Networks. Journal of Materials Processing Technology, 2002, 123(3): 377～381
53 熊爱明，薛善坤，李淼泉．TC4钛合金高温变形时微观组织变化的计算．塑性工程学报，2002，9(1)：14～16． Isothermal Forging of Ti-6Al-4V Alloy. Materials Science and Technology, 2002, 18(2): 212～214
55 孙惠学，胡金华，史艳国，周维智．大型锻件镦粗弹塑性有限元分析．钢铁，1998，33(4)：31～34
56 李萍，许沂，吕炎．Ti-15-3热镦粗变形的数值模拟及实验研究．金属成形工艺，2000，18(3)：15～17
57 高军，赵新海，宋立彬，赵国群．厚壁管闭式镦粗有限元分析及实验研究．锻压技术，2001，(3)：6～8
58 张宝红，张治民．双环形件塑性成形数值模拟研究．华北工学院学报，1999，20(4)：363～365
59 胡忠，朱利华，李家庆．圆环压缩过程的有限元模拟—一种标定摩擦系数理论曲线的新方法．金属学报，1997，33(4)：337～344
60 陈军，舒其复．一种采用圆环压缩测定材料应力—应变函数关系的方法．金属成形工艺，1996，14(3)：41～43
61 刘国权，刘胜新，黄启今，钟云龙，钟声，秦湘阁．金相学和材料显微组织定量分析技术．中国体视学与图像分析，2002，7(1)：248～251
62 余永宁，刘国权．体视学一组织定量分析的原理和应用．北京：冶金工业出版社，1989
63 潘洪泗．Ti-6.62A1-5.14Sn-1.82Zr合金的塑性变形机理及热处理工艺研究．西安：西北工业大学硕士学位论文．2005，15
64 熊爱明，陈胜晖，黄维超，林海，李淼泉．TC6钛合金的高温变形行为及组织演变．稀有金属材料与工程，2003，32(6)：447～450
65 吕炎．锻件组织性能控制．北京：国防工业出版社，1988
66 黄光胜，汪凌云，黄光杰，卢志文，宋美娟．AZ31镁合金高温本构方程．金属成形工艺，2004，22(2)：41～44
67 J. Langkruis, W. H. Kool, S. Zwaag. Assessment of Constitutive Equations in Modelling the Hot Deformability of Some Overaged Al-Mg-Si Alloys With Varying Solute Contents. Materials Science and Engineering, 1999, A266(1/2): 135～145
68 J. Langkruis, R. Bergwerf, S. Zwaag. Linking Plane Strain Compression Tests on AA6063 to Laboratory Scale Extrusion via Constitutive Equations. Materials Science Forum, 2000, 331(2): 565～570
69 Z. Gronostajski. The Constitutive Equations for FEM Analysis. Journal of Material s Processing Technology, 2000, 106(1/3): 40～44
70 周纪华，管克智．高温高速下合金结构钢的流动应力研究．金属学报，1986，22(1)：B31～B38
71 A. Wahlen, U. Feurer, J. Reissner. Computer Controlled Measurement and Analytical Modeling of Flow Stresses During Hot Deformation of the Copper Alloy CuZn42Mn2. Journal of Materials Processing Technology, 1997, 63(1/3): 233～237
72 L. X. Kong, P. D. Hodgson, B. Wang. Development of Constitutive Models for Metal Forming with Cyclic Strain Softening. Journal of Materials Processing Technology, 1999, 89/90(5): 44～50
73 D. G. Robertson, H. B. Mcshane. Analysis of High Temperature Flow Stress of Titanium Alloys IMI550 and Ti-10V-2Fe-3Al during Isothermal Forging. Materials Science and Technology, 1998, 14(4): 339～345
74 何宜柱，陈大宏，雷廷权．热变形动态软化本构模型．钢铁，1999，34(9)：29～33
75 J. Y. Cheng, S. Nemat-Nasser, W. G. Guo. A Unified Constitutive Model for Strain-rate and Temperature Dependent Behavior of Molybdenum. Mechanics of Materials, 2001, 33(11): 603～616
76 A. Laasraoui, J. J. Jonas. Prediction of Steel Flow Stress at High Temperatures and Strain Rates. Metallurgical and Materials Transactions A, 1991, 22A(7): 1545～1558
77 A. J. Beaudoin, A. Acharya, S. R. Chen, D. A. Karzekwa, M. G. Stout. Consideration of Grain-size Effect and Kinetics in the Plastic Deformation of Metal Polycrystals. Acta Materialia, 2000, 48(13): 3409～3423
78 P. F. Bariani, S. Bruschi, T. D. Negro. A New Constitutive Model for Hot Forging of Steels Taking into Account the Thermal and Mechanical History. Annals of the CIRP, 2000, 49(1): 195～198
79 T. Tsuta, Y. J. Yin, Z. C. Xie. Upper-bound rigid-plastic Constitutive Model for Mixed-hardening Materials with Micro Void Evolution Process. International Journal of Mechanical Science, 2000, 42(8): 1471～1498
80 熊爱明．钛合金锻造过程变形-传热-微观组织演化的耦合模拟．西安：西北工业大学博士学位论文．2003，44～46
81 S. Kobayashi, S. I. Oh, T. Altan. Metal Forming and the Finite Element Method. Oxford University Press, 1989, 74～75
82 陈火红编．Marc有限元实例分析教程．北京：机械工业出版社，2002，19～20
83 齐德新，刘冠权，马广锋．BT20钛合金切削加工性浅析．机械工程师．2002，10：28～30
84 张桂木，于超，高霁，施永臣．钛合金BT20端铣试验研究．机械设计与制造工程．2001，2：61～62