高铬锻钢支承辊淬冷过程有限元分析
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摘要
高铬锻钢支承辊的淬冷过程因其影响因素繁多,边界条件复杂,一直是热处理数值模拟领域的重点与难点。因此对其展开研究,具有重要的理论和实际意义。
针对上述问题,本文以Cr5锻钢支承辊为研究对象,采用有限元法,重点研究了支承辊最终热处理尤其是喷雾淬火冷却过程中温度场、组织场及应力场的关系。
首先建立了计算支承辊喷雾淬火时温度场、组织场及应力场三场耦合的有限元仿真模型。在详细分析了支承辊喷雾淬火工艺特点的基础上,确定了模拟步骤、相应的边界条件以及计算温度场、组织场及应力场所需要的参数。
其次采用有限元分析软件DEFORM对Cr5锻钢支承辊的喷雾淬火冷却过程进行了模拟计算。考虑了支承辊从差温加热炉转移至喷雾淬火冷却设备过程中有无保温措施对于淬火冷却结果的影响,得到了淬火结束以后温度场、组织场及应力场的分布规律,详细分析了支承辊特殊位置节点的温度和应力变化曲线、淬火后沿中截面的组织及应力分布,经过对比分析后认为转移过程中不带保温措施更为合理。
最后根据有限元模拟计算结果,分析了马氏体相变对于淬火瞬时应力的影响,结果显示淬火时的瞬时拉应力峰值更容易出现在近表面,针对该问题提出了工艺改进方案;考虑了连续喷雾淬冷时间对于淬硬层深度、应力峰值及残余奥氏体含量等参数的影响,经过对比分析后认为在现有工艺及设备条件下,将连续喷淬时间减少至40分钟更为合理。
Because of various influence factors and complicated boundary conditions, the quenching process of high chromium forged backup rolls have been the key and difficult points of heat treatment numerical simulation domain. Therefore, the research has important theoretical and practical significance.
In view of the above questions, taking Cr5 forged backup rolls as investigated subject, this paper put emphasis on the relation of temperature , microstructure and stress field of final heat treatment especially the quenching process of backup rolls.
First, a finite element simulation model which can calculate the coupled temperature-microstructure-stress field is set up. On the base of analyzing the characteristics of spray quenching process of backup rolls, the simulation steps and the corresponding boundary conditions are determined and the parameters of calculating the coupled temperature-microstructure-stress field are given.
Then, the spray quenching process of Cr5 forged backup rolls is simulated using the Finite element software DEFORM. The influence of with insulation measures or not during transfer of backup rolls from differential temperature furnace to spray quenching equipment is taken into account. The distribution rules of temperature , microstructure and stress field can be obtained after quenching. The history curves of temperature and stress of special nodes on the backup rolls, the microstructure and residual stress distribution on middle section after quenching are analysed in detail. Through comparative analysis, it’s more reasonable without insulation measures during transfer process.
Finally, the influence of martensitic transformation for quenching instantaneous stress is analysed through the finite element simulation results. The results show that peak of instantaneous tensile stress easily appears in near surface. Besides, the improvement programs for subsistent problems are given. On the another hand, the influence of quenching time for continuous spray on the result is also considered. After comparative analysis, it’s more reasonable to reduce the continuous quenching time to 40 min in the existing technology and equipment conditions.
针对上述问题,本文以Cr5锻钢支承辊为研究对象,采用有限元法,重点研究了支承辊最终热处理尤其是喷雾淬火冷却过程中温度场、组织场及应力场的关系。
首先建立了计算支承辊喷雾淬火时温度场、组织场及应力场三场耦合的有限元仿真模型。在详细分析了支承辊喷雾淬火工艺特点的基础上,确定了模拟步骤、相应的边界条件以及计算温度场、组织场及应力场所需要的参数。
其次采用有限元分析软件DEFORM对Cr5锻钢支承辊的喷雾淬火冷却过程进行了模拟计算。考虑了支承辊从差温加热炉转移至喷雾淬火冷却设备过程中有无保温措施对于淬火冷却结果的影响,得到了淬火结束以后温度场、组织场及应力场的分布规律,详细分析了支承辊特殊位置节点的温度和应力变化曲线、淬火后沿中截面的组织及应力分布,经过对比分析后认为转移过程中不带保温措施更为合理。
最后根据有限元模拟计算结果,分析了马氏体相变对于淬火瞬时应力的影响,结果显示淬火时的瞬时拉应力峰值更容易出现在近表面,针对该问题提出了工艺改进方案;考虑了连续喷雾淬冷时间对于淬硬层深度、应力峰值及残余奥氏体含量等参数的影响,经过对比分析后认为在现有工艺及设备条件下,将连续喷淬时间减少至40分钟更为合理。
Because of various influence factors and complicated boundary conditions, the quenching process of high chromium forged backup rolls have been the key and difficult points of heat treatment numerical simulation domain. Therefore, the research has important theoretical and practical significance.
In view of the above questions, taking Cr5 forged backup rolls as investigated subject, this paper put emphasis on the relation of temperature , microstructure and stress field of final heat treatment especially the quenching process of backup rolls.
First, a finite element simulation model which can calculate the coupled temperature-microstructure-stress field is set up. On the base of analyzing the characteristics of spray quenching process of backup rolls, the simulation steps and the corresponding boundary conditions are determined and the parameters of calculating the coupled temperature-microstructure-stress field are given.
Then, the spray quenching process of Cr5 forged backup rolls is simulated using the Finite element software DEFORM. The influence of with insulation measures or not during transfer of backup rolls from differential temperature furnace to spray quenching equipment is taken into account. The distribution rules of temperature , microstructure and stress field can be obtained after quenching. The history curves of temperature and stress of special nodes on the backup rolls, the microstructure and residual stress distribution on middle section after quenching are analysed in detail. Through comparative analysis, it’s more reasonable without insulation measures during transfer process.
Finally, the influence of martensitic transformation for quenching instantaneous stress is analysed through the finite element simulation results. The results show that peak of instantaneous tensile stress easily appears in near surface. Besides, the improvement programs for subsistent problems are given. On the another hand, the influence of quenching time for continuous spray on the result is also considered. After comparative analysis, it’s more reasonable to reduce the continuous quenching time to 40 min in the existing technology and equipment conditions.
引文
1沈一鸣.宽带钢锻钢冷轧辊的材质与使用.轧钢, 2005, 22(3): 43-44
2 J.McCann. An overview of works rolls for cold rolling. Advance in mill roll technology, Birminghan, UK, 1982, (16): 441-450
3俞誓达,陈菡.我国轧辊业现状及发展中应重视的问题.钢铁, 2007, 42(7): 1-6
4康大韬,叶国斌.大型锻件材料及热处理.北京:龙门书局, 1998: 454464
5中国机械工程学会热处理学会编.热处理手册(第4卷).北京:机械工业出版社, 2001: 295-296
6刘时雨,王玉红,徐才. 1000 mm以下的45Cr4NiMoV支承辊最终热处理工艺的选择.大型铸锻件, 2006, (1): 22-26
7刘时雨,张晓辉,王东力.Φ2800冷轧机Cr5平整辊热处理工艺参数的制定.大型铸锻件, 2006, (4): 4-8
8武淑珍,陈敬超,冯晶,等.钢铁淬火过程模拟的研究进展.材料导报, 2008, (6): 75-78
9顾剑锋,潘键生,胡明娟.淬火过程的计算机模拟及其应用.金属热处理, 2000, (5): 35-44
10潘健生,胡明娟.计算机模拟与热处理智能化.金属热处理, 1998, (7): 21-23
11 E. S. Davenport, E. C. Bain. Transformation of austenite at constant sub-critical temperature. Trans AIME Iron and Steel Division, 1930, 90: 177-154
12 W. A. Johnson, F. R. Mehl. Reaction kinetics in processes of nucleation and growth. Trans AIME, 1939, 135: 416-425.
13 M. Avrami. Kinetics of phase change, Part I: General theory. Journal of Chemical Physics, 1939, (7): 1103-1112
14 M. Avrami. Kinetics of Phase Changes II, Transformation time relations for random distribution of nuclei. Journal of Chemical Physics, 1940, (8): 212-224
15 K. Grange, J. Kiefer. The transformation of austenite by continuous cooling. Trans ASM,1941, 29
16 C. L. Magee. Phase transformations: papers presented at a seminar of the American Society for Metals. Metals Park, 1968: 115-154
17 D. F. Koistien, R. E. Marburger. General equation prescribing the extent of the austensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall, 1959, (7): 50-60
18 B. Hildenwall, T. Ericsson. Prediction of residual stresses in case-hardening steels, hardenability concepts with application to steel. TMS-AIME, Warrendale, PA, 1978: 579-606
19 E. B. Hawbolt, B. Chau, J. K. Brimacomebe. Kinetics of austenite-pearlite transformation in eutectoid carbon steel. Metal. Trans. A, 1983, 14A: 1803-1815
20 S. Denis, A. Simon, G Beck.钢马氏体淬火过程中的热力学行为分析及内应力计算,第三届国际材料热处理大会论文选集,北京:机械工业出版社, 1985: 70-80
21 S. Denis, E. Gautier. A. Simon, et a1. Stress-phase-transformation interactions basic principles, modeling and calculation of internal stresses. Materials Science and Technology, 1985, 1(10): 805-814
22 T. Inoue, Z. Wang. Coupling between stress, temperature, and metallic structures during processes including creep and phase changes. Computers &Structures, 1981, 13: 771-779
23 T. Inoue, S. Nagaki, T. Kishino, et a1. Description of transformation kinetics, heat conduction and elastic-plastic stress in the course of quenching and tempering of some steels. Ing-Arch, 1981, 50: 315-327
24 Arif Sugianto, Michiharu Narazaki, Minoru Kogawara, Atsushi Shirayori. A comparative study on determination method of heat transfer coefficient using inverse heat transfer and iterative modification. Journal of Materials Processing Technology, 2009, 209: 4627-4632
25 Arif Sugianto, Michiharu Narazaki, Minoru Kogawara, Atsushi Shirayori. Failure analysis and prevention of quench crack of eccentric holed disk by experimental study and computer simulation. Engineering Failure Analysis, 2009, (16): 70-84
26 Caner Simsir, Cemil Hakan Gur. A FEM based framework for simulation of thermal treatments: Application to steel quenching. Computational Materials Science, 2008, (44):588-600
27 A. Murugaiyan, A. Saha Prodder, A. Pandit. Phase transformations in two C-Mn-Si-Cr dual phase steels. ISIJ International, 2006, 46(10): 1489-1494
28 J. Farijas, P. Roura. Modifacation of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution. Acta Materilia, 2006, 54: 5573-5579
29 Gaude-Fugarolas, Daniel, Jacques, Pascal J. A new physical model for the kinetics of the bainite transformation. ISIJ, 2006, 46(5): 712-717
30 Liu. F, Yang. C, Zhou. Y. Additivity rule ,isothermal and non-isothermal transformations on the basis of an analytical transformation model. Acta Material, 2007, 55(15): 5255-5267
31 Seong-Hoon Kang, Yong-Taek Im. Finite element investigation of multi-phase transformation within carburized carbon steel. Journal of Materials Processing Technology, 2007, 183: 241-248
32 D.Y. Ju, W.M. Zhang, Y. Zhang. Modeling and experimental verification of martensitic transformation plastic behavior in carbon steel for quenching process. Materials Science and Engineering A, 2006, 438-440: 246-250
33 R. Mukai, T. Matsumoto, JU Dong-ying. Modeling of numerical simulation and experimental verification for carburizing-nitriding quenching process. Transactions of Nonferrous Metals Society of China, 2006, 16: 566-571
34 H. Hoang, F. Barbe, R. Quey, L. Taleb. FE determination of the plasticity induced during diffusive transformation in the case of nucleation at random locations and instants. Computational Materials Science, 2008, 43: 101-107
35 A. Zehtab Yazdi, S.A. Sajjadi, S.M. Zebarjad, S.M. Moosavi Nezhad. Prediction of hardness at different points of Jominy specimen using quench factor analysis method. Journal of Materials Processing Technology, 2008, 199: 124-129
36樊东黎.美国热处理技术发展路线图概述.金属热处理, 2006, 31(1): 1-3
37姚善长, T. Ericsson.淬火过程的计算机模拟,金属热处理, 1987, (8): 25-32
38袁发荣.轴对称金属物体淬火过程中非定常的温度场与相变场的数值解.陕西机械学院学报, 1985, (18): 128-132
39袁发荣,伍尚礼.轴对称金属物体淬火过程中的瞬态温度场与残余应力场.机械工程学报, 1986, 22(3): 96-103
40吴景之.温度场计算机模拟在国外大锻件生产中的应用.大型铸锻件, 1993, (2)
41吴景之.大锻件加热.大型铸锻件, 1992, (3): 12-18
42石林.涡轮盘淬火的计算机模拟.航空制造工程, 1997, (3): 30-31
43许学军,陈国学,刘春成.钢的淬火过程的数值模拟.大型铸锻件, 1997, (2): 6-10
44许学军,陈国学,刘春成.钢的回火过程中应力演化的数值模拟.金属热处理, 1997, (3): 12-15
45 C.C. Liu, X.J. Xue, Z. Liu. A FEM model of quenching and tempering and its application in industrial engineering. Finite elements in analysis and design, 2003, 39: 1053-1070
46刘春成,刘庄,许学军.应力对核反应堆压力容器大型锻件用钢相变动力学和相变塑性影响的研究.大型铸锻件, 1998, (4): 6-13
47姚可夫,钱滨,石伟.应力对珠光体相变动力学及相变塑性的影响.材料热处理学报, 2002, 23(4): 1-6
48刘春成,姚可夫,高国峰.应力应变对马氏体相变动力学及相变塑性影响的研究.金属学报, 1999, 35(11): 1125-1129
49许学军,刘庄,吴肇基.应力应变相互作用对马氏体淬火残余应力的影响.塑性工程学报, 1996, 3(2): 60-66
50刘庄,吴肇基,吴景之.热处理过程的数值模拟.北京:科学出版社, 1996: 7-99
51李勇军,潘健生,顾剑锋. 70Cr3Mo钢大型支承辊淬火加热计算机模拟.金属热处理, 2000, (9): 34-35
52李勇军.扩散、相变热应力/应变非线性有限元分析中几个特殊问题的研究和应用.[上海交通大学工学博士学位论文]. 2000: 65-106
53胡明娟,潘健生,李兵.界面剧变的淬火过程三维温度场的计算机模拟.金属热处理学报, 1996, 17: 90-97
54顾剑锋,潘健生,胡明娟.冷轧辊淬冷过程数值模拟的研究.金属热处理学报, 1999, 20(2): 1-7
55顾剑锋,潘健生,胡明娟.淬火冷却过程中表面综合换热系数的反传热分析.上海交通大学学报, 1998, 32(2): 19-23
56顾剑锋,潘健生,胡明娟.淬火介质换热系数的计算机测算.热加工工艺, 1998, (5): 13-14
57 J.S.YE, T.Y. HSU. Modification of the additivity hypothesis with experiment. ISIJ International, 2004, 44(4): 777-779
58程赫明.热非弹性耦合理论及其在钢淬火中的应用. [西安交通大学工学博士论文]. 1999: 56-70
59程赫明,何天淳,黄协清.高压气体淬火过程中热传导方程逆问题的求解.材料热处理学报, 2001, 22(4): 81-84
60李强,王葛,陈乃录,等.淬火介质流场计算机模拟.科学通报, 2002, 47(24): 1861-1863
61王葛,李强,陈乃录,等.淬火槽内介质流场的计算机模拟.重型机械, 2002, (6): 31-34
62李强,王葛,陈乃录.淬冷过程工件温度场的计算机模拟与实验.燕山大学学报, 2002, 26(4): 297-300
63 Nailu Chen, Lizhan Han, Weimin Zhang, Xiaowei Hao. Enhancing mechanical properties and avoiding cracks by simulation of quenching connecting rods. Materials Letters, 2007, 61: 3021-3024
64 Jing Wang, Jianfeng Gu, Xuexiong Shan, Xiaowei Hao, Nailu Chen, Weimin Zhang. Numerical simulation of high pressure gas quenching of H13 steel. Journal of Materials Processing Technology, 2008, 202: 188-194
65 Huiping Li, Guoqun Zhao, Lianfang He. Finite element method based simulation of stress-strain field in the quenching process. Materials Science and Engineering A, 2008, 478: 276-290
66 Huiping Li, Guoqun Zhao, Chuanzhen Huang, Shanting Niu. Technological parameters evaluation of gas quenching based on the finite element method. Computational Materials Science, 2007, 40: 282-291
67 Li Huiping, Zhao Guoqun, He Lianfang, Mo Yue. Solution of non-linear thermal transient problems by a new adaptive time-step method in quenching process. Applied Mathematical Modeling, 2009, 33: 329-342
68 Li Huiping, Zhao Guoqun, Niu Shanting, Luan Yiguo. Technologic parameter optimization of gas quenching process using response surface method. Computational Materials Science, 2007, 38: 561-570
69 Li Huiping, Zhao Guoqun, Niu Shanting, Huang Chuanzhen. FEM simulation of quenching process and experimental verification of simulation results. Materials Science and Engineering A, 2007, 452-453: 705-714
70 Li Huiping, Zhao Guoqun, He Lianfang, Mu Yue. High-speed data acquisition of the cooling curves and evaluation of heat transfer coefficient in quenching process. Measurement, 2008, 41: 676-686
71李辉平.淬火过程有限元模拟关键技术及工艺参数优化的研究. [山东大学博士论文]. 2005: 12-14
72 Ligang Liu, Qiang Li, Bo Liao, Xuejun Ren, Qingxiang Yang. Stress field simulation of the specimen with multi-layer phase structure. Materials Science and Engineering A, 2006, 435-436: 484-490
73 Ligang Liu, Qiang Li, Xiaohei Liu, Yukui Gao, Xuejun Ren, Bo Liao, Qingxiang Yang. Stress field simulation of carburized specimens with different carbon content during quenching process. Materials Letters, 2007, 61: 1251-1255
74赵席春.宝钢2050轧机5%C r支承辊的制造.大型铸锻件, 2003, (2): 27-30
75《机械工程材料性能数据手册》编委会.机械工程材料性能数据手册.机械工业出版社, 1995: 703-704
76叶健松,李勇军,潘健生,等.大型支承辊热处理过程的数值模拟.机械工程材料, 2002, 26(6): 12-15
77杜凤山,张芳,黄华贵,等.大型锻件喷雾冷却过程数值模拟.金属热处理, 2008, 33(5): 35-38
78吕成.数值模拟技术在燃气轮机零部件锻造及热处理过程中的应用. [大连理工大学博士论文]. 2007: 118
79赵席春. Cr5型支承辊用钢的研究.金属热处理, 2003, 28(6): 26-28
80石伟,范洪涛,刘庄. Cr5支承辊用钢马氏体相变的相变塑性研究.材料热处理学报, 2006, 27(5): 122-125
2 J.McCann. An overview of works rolls for cold rolling. Advance in mill roll technology, Birminghan, UK, 1982, (16): 441-450
3俞誓达,陈菡.我国轧辊业现状及发展中应重视的问题.钢铁, 2007, 42(7): 1-6
4康大韬,叶国斌.大型锻件材料及热处理.北京:龙门书局, 1998: 454464
5中国机械工程学会热处理学会编.热处理手册(第4卷).北京:机械工业出版社, 2001: 295-296
6刘时雨,王玉红,徐才. 1000 mm以下的45Cr4NiMoV支承辊最终热处理工艺的选择.大型铸锻件, 2006, (1): 22-26
7刘时雨,张晓辉,王东力.Φ2800冷轧机Cr5平整辊热处理工艺参数的制定.大型铸锻件, 2006, (4): 4-8
8武淑珍,陈敬超,冯晶,等.钢铁淬火过程模拟的研究进展.材料导报, 2008, (6): 75-78
9顾剑锋,潘键生,胡明娟.淬火过程的计算机模拟及其应用.金属热处理, 2000, (5): 35-44
10潘健生,胡明娟.计算机模拟与热处理智能化.金属热处理, 1998, (7): 21-23
11 E. S. Davenport, E. C. Bain. Transformation of austenite at constant sub-critical temperature. Trans AIME Iron and Steel Division, 1930, 90: 177-154
12 W. A. Johnson, F. R. Mehl. Reaction kinetics in processes of nucleation and growth. Trans AIME, 1939, 135: 416-425.
13 M. Avrami. Kinetics of phase change, Part I: General theory. Journal of Chemical Physics, 1939, (7): 1103-1112
14 M. Avrami. Kinetics of Phase Changes II, Transformation time relations for random distribution of nuclei. Journal of Chemical Physics, 1940, (8): 212-224
15 K. Grange, J. Kiefer. The transformation of austenite by continuous cooling. Trans ASM,1941, 29
16 C. L. Magee. Phase transformations: papers presented at a seminar of the American Society for Metals. Metals Park, 1968: 115-154
17 D. F. Koistien, R. E. Marburger. General equation prescribing the extent of the austensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall, 1959, (7): 50-60
18 B. Hildenwall, T. Ericsson. Prediction of residual stresses in case-hardening steels, hardenability concepts with application to steel. TMS-AIME, Warrendale, PA, 1978: 579-606
19 E. B. Hawbolt, B. Chau, J. K. Brimacomebe. Kinetics of austenite-pearlite transformation in eutectoid carbon steel. Metal. Trans. A, 1983, 14A: 1803-1815
20 S. Denis, A. Simon, G Beck.钢马氏体淬火过程中的热力学行为分析及内应力计算,第三届国际材料热处理大会论文选集,北京:机械工业出版社, 1985: 70-80
21 S. Denis, E. Gautier. A. Simon, et a1. Stress-phase-transformation interactions basic principles, modeling and calculation of internal stresses. Materials Science and Technology, 1985, 1(10): 805-814
22 T. Inoue, Z. Wang. Coupling between stress, temperature, and metallic structures during processes including creep and phase changes. Computers &Structures, 1981, 13: 771-779
23 T. Inoue, S. Nagaki, T. Kishino, et a1. Description of transformation kinetics, heat conduction and elastic-plastic stress in the course of quenching and tempering of some steels. Ing-Arch, 1981, 50: 315-327
24 Arif Sugianto, Michiharu Narazaki, Minoru Kogawara, Atsushi Shirayori. A comparative study on determination method of heat transfer coefficient using inverse heat transfer and iterative modification. Journal of Materials Processing Technology, 2009, 209: 4627-4632
25 Arif Sugianto, Michiharu Narazaki, Minoru Kogawara, Atsushi Shirayori. Failure analysis and prevention of quench crack of eccentric holed disk by experimental study and computer simulation. Engineering Failure Analysis, 2009, (16): 70-84
26 Caner Simsir, Cemil Hakan Gur. A FEM based framework for simulation of thermal treatments: Application to steel quenching. Computational Materials Science, 2008, (44):588-600
27 A. Murugaiyan, A. Saha Prodder, A. Pandit. Phase transformations in two C-Mn-Si-Cr dual phase steels. ISIJ International, 2006, 46(10): 1489-1494
28 J. Farijas, P. Roura. Modifacation of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution. Acta Materilia, 2006, 54: 5573-5579
29 Gaude-Fugarolas, Daniel, Jacques, Pascal J. A new physical model for the kinetics of the bainite transformation. ISIJ, 2006, 46(5): 712-717
30 Liu. F, Yang. C, Zhou. Y. Additivity rule ,isothermal and non-isothermal transformations on the basis of an analytical transformation model. Acta Material, 2007, 55(15): 5255-5267
31 Seong-Hoon Kang, Yong-Taek Im. Finite element investigation of multi-phase transformation within carburized carbon steel. Journal of Materials Processing Technology, 2007, 183: 241-248
32 D.Y. Ju, W.M. Zhang, Y. Zhang. Modeling and experimental verification of martensitic transformation plastic behavior in carbon steel for quenching process. Materials Science and Engineering A, 2006, 438-440: 246-250
33 R. Mukai, T. Matsumoto, JU Dong-ying. Modeling of numerical simulation and experimental verification for carburizing-nitriding quenching process. Transactions of Nonferrous Metals Society of China, 2006, 16: 566-571
34 H. Hoang, F. Barbe, R. Quey, L. Taleb. FE determination of the plasticity induced during diffusive transformation in the case of nucleation at random locations and instants. Computational Materials Science, 2008, 43: 101-107
35 A. Zehtab Yazdi, S.A. Sajjadi, S.M. Zebarjad, S.M. Moosavi Nezhad. Prediction of hardness at different points of Jominy specimen using quench factor analysis method. Journal of Materials Processing Technology, 2008, 199: 124-129
36樊东黎.美国热处理技术发展路线图概述.金属热处理, 2006, 31(1): 1-3
37姚善长, T. Ericsson.淬火过程的计算机模拟,金属热处理, 1987, (8): 25-32
38袁发荣.轴对称金属物体淬火过程中非定常的温度场与相变场的数值解.陕西机械学院学报, 1985, (18): 128-132
39袁发荣,伍尚礼.轴对称金属物体淬火过程中的瞬态温度场与残余应力场.机械工程学报, 1986, 22(3): 96-103
40吴景之.温度场计算机模拟在国外大锻件生产中的应用.大型铸锻件, 1993, (2)
41吴景之.大锻件加热.大型铸锻件, 1992, (3): 12-18
42石林.涡轮盘淬火的计算机模拟.航空制造工程, 1997, (3): 30-31
43许学军,陈国学,刘春成.钢的淬火过程的数值模拟.大型铸锻件, 1997, (2): 6-10
44许学军,陈国学,刘春成.钢的回火过程中应力演化的数值模拟.金属热处理, 1997, (3): 12-15
45 C.C. Liu, X.J. Xue, Z. Liu. A FEM model of quenching and tempering and its application in industrial engineering. Finite elements in analysis and design, 2003, 39: 1053-1070
46刘春成,刘庄,许学军.应力对核反应堆压力容器大型锻件用钢相变动力学和相变塑性影响的研究.大型铸锻件, 1998, (4): 6-13
47姚可夫,钱滨,石伟.应力对珠光体相变动力学及相变塑性的影响.材料热处理学报, 2002, 23(4): 1-6
48刘春成,姚可夫,高国峰.应力应变对马氏体相变动力学及相变塑性影响的研究.金属学报, 1999, 35(11): 1125-1129
49许学军,刘庄,吴肇基.应力应变相互作用对马氏体淬火残余应力的影响.塑性工程学报, 1996, 3(2): 60-66
50刘庄,吴肇基,吴景之.热处理过程的数值模拟.北京:科学出版社, 1996: 7-99
51李勇军,潘健生,顾剑锋. 70Cr3Mo钢大型支承辊淬火加热计算机模拟.金属热处理, 2000, (9): 34-35
52李勇军.扩散、相变热应力/应变非线性有限元分析中几个特殊问题的研究和应用.[上海交通大学工学博士学位论文]. 2000: 65-106
53胡明娟,潘健生,李兵.界面剧变的淬火过程三维温度场的计算机模拟.金属热处理学报, 1996, 17: 90-97
54顾剑锋,潘健生,胡明娟.冷轧辊淬冷过程数值模拟的研究.金属热处理学报, 1999, 20(2): 1-7
55顾剑锋,潘健生,胡明娟.淬火冷却过程中表面综合换热系数的反传热分析.上海交通大学学报, 1998, 32(2): 19-23
56顾剑锋,潘健生,胡明娟.淬火介质换热系数的计算机测算.热加工工艺, 1998, (5): 13-14
57 J.S.YE, T.Y. HSU. Modification of the additivity hypothesis with experiment. ISIJ International, 2004, 44(4): 777-779
58程赫明.热非弹性耦合理论及其在钢淬火中的应用. [西安交通大学工学博士论文]. 1999: 56-70
59程赫明,何天淳,黄协清.高压气体淬火过程中热传导方程逆问题的求解.材料热处理学报, 2001, 22(4): 81-84
60李强,王葛,陈乃录,等.淬火介质流场计算机模拟.科学通报, 2002, 47(24): 1861-1863
61王葛,李强,陈乃录,等.淬火槽内介质流场的计算机模拟.重型机械, 2002, (6): 31-34
62李强,王葛,陈乃录.淬冷过程工件温度场的计算机模拟与实验.燕山大学学报, 2002, 26(4): 297-300
63 Nailu Chen, Lizhan Han, Weimin Zhang, Xiaowei Hao. Enhancing mechanical properties and avoiding cracks by simulation of quenching connecting rods. Materials Letters, 2007, 61: 3021-3024
64 Jing Wang, Jianfeng Gu, Xuexiong Shan, Xiaowei Hao, Nailu Chen, Weimin Zhang. Numerical simulation of high pressure gas quenching of H13 steel. Journal of Materials Processing Technology, 2008, 202: 188-194
65 Huiping Li, Guoqun Zhao, Lianfang He. Finite element method based simulation of stress-strain field in the quenching process. Materials Science and Engineering A, 2008, 478: 276-290
66 Huiping Li, Guoqun Zhao, Chuanzhen Huang, Shanting Niu. Technological parameters evaluation of gas quenching based on the finite element method. Computational Materials Science, 2007, 40: 282-291
67 Li Huiping, Zhao Guoqun, He Lianfang, Mo Yue. Solution of non-linear thermal transient problems by a new adaptive time-step method in quenching process. Applied Mathematical Modeling, 2009, 33: 329-342
68 Li Huiping, Zhao Guoqun, Niu Shanting, Luan Yiguo. Technologic parameter optimization of gas quenching process using response surface method. Computational Materials Science, 2007, 38: 561-570
69 Li Huiping, Zhao Guoqun, Niu Shanting, Huang Chuanzhen. FEM simulation of quenching process and experimental verification of simulation results. Materials Science and Engineering A, 2007, 452-453: 705-714
70 Li Huiping, Zhao Guoqun, He Lianfang, Mu Yue. High-speed data acquisition of the cooling curves and evaluation of heat transfer coefficient in quenching process. Measurement, 2008, 41: 676-686
71李辉平.淬火过程有限元模拟关键技术及工艺参数优化的研究. [山东大学博士论文]. 2005: 12-14
72 Ligang Liu, Qiang Li, Bo Liao, Xuejun Ren, Qingxiang Yang. Stress field simulation of the specimen with multi-layer phase structure. Materials Science and Engineering A, 2006, 435-436: 484-490
73 Ligang Liu, Qiang Li, Xiaohei Liu, Yukui Gao, Xuejun Ren, Bo Liao, Qingxiang Yang. Stress field simulation of carburized specimens with different carbon content during quenching process. Materials Letters, 2007, 61: 1251-1255
74赵席春.宝钢2050轧机5%C r支承辊的制造.大型铸锻件, 2003, (2): 27-30
75《机械工程材料性能数据手册》编委会.机械工程材料性能数据手册.机械工业出版社, 1995: 703-704
76叶健松,李勇军,潘健生,等.大型支承辊热处理过程的数值模拟.机械工程材料, 2002, 26(6): 12-15
77杜凤山,张芳,黄华贵,等.大型锻件喷雾冷却过程数值模拟.金属热处理, 2008, 33(5): 35-38
78吕成.数值模拟技术在燃气轮机零部件锻造及热处理过程中的应用. [大连理工大学博士论文]. 2007: 118
79赵席春. Cr5型支承辊用钢的研究.金属热处理, 2003, 28(6): 26-28
80石伟,范洪涛,刘庄. Cr5支承辊用钢马氏体相变的相变塑性研究.材料热处理学报, 2006, 27(5): 122-125