大锻件镦粗成形中内部空洞型缺陷的演化规律研究
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摘要
大锻件作为大型成套设备的核心零件,在国民经济建设、国防装备发展中发挥着举足轻重的作用。大锻件的锻造过程研究不仅仅着眼于如何生产出满足要求、具有一定形状尺寸的锻件,更重要的是研究如何修复缺陷、改善微观组织和创造有利的力学条件使锻造过程中不出现新的裂纹或夹杂性裂纹。镦粗成形作为最基本的锻造工艺,可以锻合锻件的先天性空洞缺陷,改善材料的力学性能,从而提高锻件的内在质量及承载能力。本文通过深入分析大锻件内部空洞型缺陷在镦粗过程中的变化,得到了空洞的演化规律、影响空洞闭合的因素和提高空洞闭合效果的条件。本文的主要工作和研究成果如下:
1)基于细观损伤力学的Gurson模型,对空洞的演化规律和影响空洞闭合的因素进行分析,得到材料内部空洞闭合的力学条件。
2)通过对Gurson模型的本构关系及更新计算的研究,对Marc进行二次开发,将包含空洞的本构模型嵌入到Hypela子程序中,实现了空洞演化的数值模拟运算。
3)通过比较包含Gurson本构模型和人工空洞模型的数值模拟结果,发现Gurson模型实现空洞闭合的条件是材料的静水应力或等效应变无穷大。由于这一条件并不符合实际情况,本文又基于正交试验设计,模拟了不同试验参数下的空洞体积变化,从而获得了修正的Gurson模型参数。修正后的Gurson模型给出的空洞体积比接近直接设置人工空洞的模拟结果。研究表明,空洞位于锻件心部时闭合最容易,其位置越接近端面越难于闭合;空洞的闭合程度随基体材料硬化程度的增高而变差。
4)以铅作为模拟大锻件成形的材料并在试件上设置微小空洞,进行镦粗成形物理试验模拟,验证了空洞的闭合准则。对比发现,空洞体积变化规律与数值模拟结果基本一致。
As key parts of large complete sets of equipment, heavy forgings have played important roles in national economic constructions and defense development. In addition to producing dimensional satisfactory forgings, the research on upsetting process pays greater attention on modification of inner defects, improvement of material tissue as well as creating favorable mechanical conditions which is able to prevent new fractures or inclusion-induced cracks. As basic forging techniques, upsetting can eliminate void defects so that the mechanical performance, inner quality and carrying ability of materials will be greatly improved. The law of void evolution, criterion of void closure and factors which affect void closure are revealed in this paper. The main work is as follows:
1) The law of void evolution and factors which affect void closure were investigated based on Gurson model which comes from Meso-mechanics. The criterion of void closure was also put forward.
2) The constitutive relationship of Gurson model and the update algorithm were studied and implemented through subroutine Hypela which defines the material property of porous material and facilitates the numerical simulation.
3) The simulation results of artificial model and Gurson model were compared. It is found that infinite hydraulic stress or equivalent strain is required when Gurson Model is employed to realize void closure of materials. However, such condition does not conform to reality. This paper obtained modified parameters of Gurson Model by Orthogonal experimental design and simulation under different sampling parameters through embedded subroutine. The modified Gurson model can be applied to simulate void volume variation in heavy forgings. The results demonstrate that the void volume change ratios are quite close to those obtained by artificial models, which implies that the predictions of void closure are greatly improved. It is also found that void closure in the center is the easiest one to achieve while the difficulty increases as it approaches the surface. The harder the matrix material, the worse the void closure degree will be.
4) By setting tiny artificial voids inside lead samples whose recrystallization temperature equates to room temperature, the criterion of void closure is verified by upsetting experiment. The void volume change ratios obtained from physical experiments are in agreement with those from numerical simulations.
1)基于细观损伤力学的Gurson模型,对空洞的演化规律和影响空洞闭合的因素进行分析,得到材料内部空洞闭合的力学条件。
2)通过对Gurson模型的本构关系及更新计算的研究,对Marc进行二次开发,将包含空洞的本构模型嵌入到Hypela子程序中,实现了空洞演化的数值模拟运算。
3)通过比较包含Gurson本构模型和人工空洞模型的数值模拟结果,发现Gurson模型实现空洞闭合的条件是材料的静水应力或等效应变无穷大。由于这一条件并不符合实际情况,本文又基于正交试验设计,模拟了不同试验参数下的空洞体积变化,从而获得了修正的Gurson模型参数。修正后的Gurson模型给出的空洞体积比接近直接设置人工空洞的模拟结果。研究表明,空洞位于锻件心部时闭合最容易,其位置越接近端面越难于闭合;空洞的闭合程度随基体材料硬化程度的增高而变差。
4)以铅作为模拟大锻件成形的材料并在试件上设置微小空洞,进行镦粗成形物理试验模拟,验证了空洞的闭合准则。对比发现,空洞体积变化规律与数值模拟结果基本一致。
As key parts of large complete sets of equipment, heavy forgings have played important roles in national economic constructions and defense development. In addition to producing dimensional satisfactory forgings, the research on upsetting process pays greater attention on modification of inner defects, improvement of material tissue as well as creating favorable mechanical conditions which is able to prevent new fractures or inclusion-induced cracks. As basic forging techniques, upsetting can eliminate void defects so that the mechanical performance, inner quality and carrying ability of materials will be greatly improved. The law of void evolution, criterion of void closure and factors which affect void closure are revealed in this paper. The main work is as follows:
1) The law of void evolution and factors which affect void closure were investigated based on Gurson model which comes from Meso-mechanics. The criterion of void closure was also put forward.
2) The constitutive relationship of Gurson model and the update algorithm were studied and implemented through subroutine Hypela which defines the material property of porous material and facilitates the numerical simulation.
3) The simulation results of artificial model and Gurson model were compared. It is found that infinite hydraulic stress or equivalent strain is required when Gurson Model is employed to realize void closure of materials. However, such condition does not conform to reality. This paper obtained modified parameters of Gurson Model by Orthogonal experimental design and simulation under different sampling parameters through embedded subroutine. The modified Gurson model can be applied to simulate void volume variation in heavy forgings. The results demonstrate that the void volume change ratios are quite close to those obtained by artificial models, which implies that the predictions of void closure are greatly improved. It is also found that void closure in the center is the easiest one to achieve while the difficulty increases as it approaches the surface. The harder the matrix material, the worse the void closure degree will be.
4) By setting tiny artificial voids inside lead samples whose recrystallization temperature equates to room temperature, the criterion of void closure is verified by upsetting experiment. The void volume change ratios obtained from physical experiments are in agreement with those from numerical simulations.
引文
[1]郭会光.着力提高我国大型锻造的现代化水平[J].大型铸锻件, 2003, (2):1-2.
[2]卢志辉,赖曾美.大锻件坯料拔长锻造时的应变分析[J].锻压技术,2001, (1):32-35.
[3] Shiro.W. Development of a New Forging Process to Manufacture Sound Heavy Forgings[C]. International Forging Conference, Dusseldorf, 1994, (5):4-9.
[4]吕炎.锻件缺陷分析与对策.北京:机械工业出版社.1999.
[5]马庆贤,钟约先,曹起骧.高温塑性加工过程中缺陷修复规律[J].清华大学学报,1999, 39(11):94-96.
[6]马庆贤,钟约先,曹起骧.高温塑性加工过程中裂纹损伤与修复特性研究[J].塑性工程学报, 2000,7(2):58-61.
[7]韦东滨,韩静涛,谢建新等.金属材料内部裂纹高温愈合实验研究[J].北京科技大学学报.2000.22(3):245-248.
[8]任运来.大型锻件内部缺陷修复条件和修复方法研究[D].燕山大学博士学位论文,2003.
[9]钟杰.大型轴类锻件锻造工艺的云纹法模拟研究[D].北京:清华大学图书馆,1989.
[10]金宁.大锻件孔隙性缺陷的压合与焊合规律的研究及高温栅的研究[D].北京:清华大学. 1990.
[11] Roberts S M, Kuaiak J, Liu Y L. Prediction of damage evolution in forged aluminium metal matrix composites using a neural network approach[J]. Mater. Process. Technol. 1998, (1):507–512.
[12] St?hlberg U, Keife H, Lundber A. A study of void closure during plastic deformation[J]. J.Mech.Work.Technol.1980, (4):51-63.
[13] Chaaban M A, Alexander J M. A study of the closure of cavities in swing forging[C]. Proc.17th int. Mach. Tool. Des. Res. Conf. Birmingham Sept.1976, Macmilan, London, 1977, (1):633-645.
[14] Keife H, St?hlberg U. Influence of pressure on the closure during plastic deformation [J]. J. Mech. Work. Technol., 1980, (4):133-145.
[15] Tanaka M, Ono S, Tsuneno M. A numerical analysis on void crushing during side compression of round bar by flat dies [J]. JSTP, 1987, 28 (314):238-244.
[16]王祖唐,刘庄,任猛.大钢锭内部空洞锻合过程的数值模拟[J].机械工程学报.1989, 25(3):51-55.
[17]王祖唐,任猛.大钢锭内部空洞性缺陷锻合过程的实验研究[J].机械工程学报.1989,25(4):47-53.
[18]韩静涛.有效控制夹杂性裂纹的大型锻件锻造技术及处理方法[J].塑性工程学报.1996, 3(1): 20-26.
[19]韩静涛.大型饼类锻件变形规律及夹杂性裂纹产生过程研究[J].塑性工程学报.1994, 1(3): 41-46.
[20]刘助柏.平砧拉长矩形截面毛坯的新理论[J].机械工程学报.1994, 30(5):47-49.
[21]朱明,金泉林.大型锻件内部孔隙缺陷闭合过程的理论探讨[C].第二次全国塑性力学学术交流会论文.1988.
[22]朱明,金泉林.一种考虑孔洞形状变化的损伤细观模型及其在孔洞闭合过程中的应用[J].应用数学和力学.1992,13(8):1-5.
[23]朱明,金泉林.材料内部孔洞压实机理的研究[J].兵工学报.1992, (1):1-3.
[24] Zhu Ming and Jin Quan-lin. A constitutive relation for material containing voids and application in closing of voids [J]. Advances in Constitutive Laws for Engineering Matericals. Ed. Fan Jing-hong and Sumio Murakami.Pergamon Press. Oxford (1989),542.
[25]任运来.大型锻件内部缺陷修复条件和修复方法研究[D].博士学位论文.燕山大学.2003.
[26] Henot J L. Recent contributions to the finite element modeling of mental forming process[J]. Journal of materials Processing Tech., 2000, (34):9-18.
[27] Hartley P P, Sturgess C E. Numerical modeling of material deformation processes[M]. Springer-Verlag London Limited, 1998, (2):22-28.
[28] Shah K N, Kiefer B V. Finite element simulation of void closure in open-die press forging [J]. Advanced manufacturing processes. 1999, (1):501-516.
[29] Sun J X. Analysis of special forging processes for heavy ingots by finite element method [J]. International journal of machine tools & manufacture.1988, (2):173-179.
[30] Sun H X, Hu J H. Elastic-plastic FEM analysis of cylinder upsetting between two flat platens. Chin.Mech.Eng.Soc, 1999, (12):45-49.
[31] Li.Y L. Recent development and application of three dimensional finite element modeling in buck forming process [J]. Journal of materials processing technology.2001, (113):40-49.
[32] Duan X, Sheppard T. Shape optimization using FEA software: a V-shaped anvil as an example [J]. Journal of materials processing technology.2002, (20):426-431.
[33] Queen M C, Ryan H J.N.D. Constitutive analysis in hot working[J]. Journal of materials processing technology. 2002, 322(1-2):42-63.
[34]肖景容,李尚健.塑性成型模拟理论.武汉:华中理工大学出版社,1994.
[35]任广升,谭红,李运兴等.镦粗过程中锻件内孔洞缺陷邻域应变分布的模拟研究[J].塑性工程学报.1994, 1(3):14-19.
[36] Hamzah S. A study of pore closure in the manufacturing of heavy rings[J]. J. Mater .Processing Technol.2001, (110):324-333.
[37] Wang A. A study of pore closure and welding in hot rolling process[J]. Journal of materials processing technology.1996, (60):95-120.
[38]崔振山,任广升,徐秉业等.圆柱体内部空洞的热锻闭合条件[J].清华大学学报, 2003, 43(2):227-229,233.
[39]崔振山,任广升等.圆柱体内部空洞热锻闭合过程的数值模拟[J].塑性工程学报, 2002,9 (1):49～52.
[40]崔振山,徐秉业,任广升.大锻件内部空洞的锻合压下率[J].塑性工程学报, 2002, 9 (3) : 6-8.
[41]崔振山,任广升,徐秉业等.大锻件空洞的局部效应与锻合压下率研究[J].工程力学, 2003 ,20 (2):55～59.
[42]蒋智,任广升等.圆柱体热锻件内部单空洞闭合的模拟分析[J].塑性工程学报. 2005, 12(1):47-49,57.
[43]蒋智.三维变形过程中空洞闭合的模拟研究[D].机械科学研究院.2003
[44]潘维国.定向凝固锭核电管板锻造工艺及内部质量控制[D].清华大学博士学位论文. 1996:20-58.
[45]马喜腾,钟志平.定向凝固锭管板凸砧锻造工艺高温纭文法模拟研究[J].塑性工程学报. 1998, 5(2):55-60.
[46]张艳妹.大锻件空洞锻合的光塑性研究与数值模拟[D].燕山大学硕士学位论文. 2002.32-63.
[47] Pertence A E M, Cetlin P R. Analysis of a new model material for the physical simulation of metal forming [J]. Journal of materials processing technology. 1998, (84):261-267.
[48] Arentoft M. Prevention of defects in forging by numerical and physical simulation [D]. PHD Dissertation of Technical University of Denmark, October 1999.
[49] Wanheim T. Physical modeling of metal processing[C]. Internal report of Technical University of Denmark, 1988.
[50] Danckert J, Wanheim T. Slipline The Physical Modeling of Plastic Working Processes [J].Mech.1976, (16):318-327.
[51] Blaes N, Bokelmann D, Poppenhager J and Wagner H. Optimization of the forging process of heavy forgings for power generation[C]. The Korea Institute of Meta and Materials. 13th international forge masters meeting. Pusan, Korea, 1997, (1):93-102.
[52] Tsukada H.超大型整体低压转子和超纯净转子轴的生产.周云松.第十一届国际锻造会议论文集,意大利,1991.四川德阳,中国二重集团,1995:207-211.
[53] Hideki Takamor, Yoshiaki Suzuki, Takaya Kawai. Manufacture of a shaft with flange using the upsetter[C].German Iron and Steel Institute. 14th international forgemaster meeting. Wiesbaden. Germany, 2000,(1):73-78.
[54] Steiner J E. Heavy forgings process technology[C]. The 13th IFM,1997, (1):83-93.
[55]张艳妹.砧宽比对孔洞闭合影响的光塑性研究[J].大型铸锻件.2002, (1):1-3,9.
[56]袁朝龙.大型锻件内部孔隙性缺陷修复规律的研究[J].锻压技术.2002, (3):3-6.
[57]杜学刚.大型支承辊类锻件锻造工艺优化的云纹法模拟[D].北京:清华大学图书馆,1989.
[58]任猛.大型钢锭内部孔洞性缺陷锻合过程的数值模拟和实验研究[D].北京:清华大学. 1986.
[59] McCLintock A criterion for ductile fracture by the growth of holes[J]. F.M.J., Appl. Mech., 1968,(35):363.
[60] Rice J.R, Tracey D.M. On the ductile enlargement of voids in triaxial stress fields [J].Mech.phys.Solids.1969, (17):201.
[61] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth [J]. ASME Journal of Engineering Materials and Technology, 1977, 99(1): 2 -15.
[62] Aravas N. On the numerical integration of a class of pressure-dependent plasticity model [J].International Journal for Numerical Methods in Engineering, 1987, (24):1395-1416.
[63] M.Ortiz and E.P.Popov. Accuracy and stability of integration algorithms for elasto-plasticconstitutive relations[J]. Int J Numer Meth Energy, 1985, (2):1561-1576.
[64] Krieg, R.D., Krieg, B.D. Accuracies of numerical solution methods for the elastic perfectly plastic model [J]. ASME. Pressure Vessel Tech., 1977, (99):510-15.
[65] Nagtegaal, J.C., Rebelo, N. On the development of a general purpose finite element program for analysis of forming processes [J]. Int.Num. Meth. in Eng., 1988, (25):113-31.
[66] Simo JC,Hughes TJR[C]. Computational Inelasticity,Springer-Verlag,New York,1998.
[67]伍爱著.质量管理学.广州:暨南大学出版社, 2002.
[68]陈火红MSC.Marc二次开发指南.北京:科学出版社, 2004:1-5.
[69]王勖成有限单元法.北京:清华大学出版社, 2003.
[2]卢志辉,赖曾美.大锻件坯料拔长锻造时的应变分析[J].锻压技术,2001, (1):32-35.
[3] Shiro.W. Development of a New Forging Process to Manufacture Sound Heavy Forgings[C]. International Forging Conference, Dusseldorf, 1994, (5):4-9.
[4]吕炎.锻件缺陷分析与对策.北京:机械工业出版社.1999.
[5]马庆贤,钟约先,曹起骧.高温塑性加工过程中缺陷修复规律[J].清华大学学报,1999, 39(11):94-96.
[6]马庆贤,钟约先,曹起骧.高温塑性加工过程中裂纹损伤与修复特性研究[J].塑性工程学报, 2000,7(2):58-61.
[7]韦东滨,韩静涛,谢建新等.金属材料内部裂纹高温愈合实验研究[J].北京科技大学学报.2000.22(3):245-248.
[8]任运来.大型锻件内部缺陷修复条件和修复方法研究[D].燕山大学博士学位论文,2003.
[9]钟杰.大型轴类锻件锻造工艺的云纹法模拟研究[D].北京:清华大学图书馆,1989.
[10]金宁.大锻件孔隙性缺陷的压合与焊合规律的研究及高温栅的研究[D].北京:清华大学. 1990.
[11] Roberts S M, Kuaiak J, Liu Y L. Prediction of damage evolution in forged aluminium metal matrix composites using a neural network approach[J]. Mater. Process. Technol. 1998, (1):507–512.
[12] St?hlberg U, Keife H, Lundber A. A study of void closure during plastic deformation[J]. J.Mech.Work.Technol.1980, (4):51-63.
[13] Chaaban M A, Alexander J M. A study of the closure of cavities in swing forging[C]. Proc.17th int. Mach. Tool. Des. Res. Conf. Birmingham Sept.1976, Macmilan, London, 1977, (1):633-645.
[14] Keife H, St?hlberg U. Influence of pressure on the closure during plastic deformation [J]. J. Mech. Work. Technol., 1980, (4):133-145.
[15] Tanaka M, Ono S, Tsuneno M. A numerical analysis on void crushing during side compression of round bar by flat dies [J]. JSTP, 1987, 28 (314):238-244.
[16]王祖唐,刘庄,任猛.大钢锭内部空洞锻合过程的数值模拟[J].机械工程学报.1989, 25(3):51-55.
[17]王祖唐,任猛.大钢锭内部空洞性缺陷锻合过程的实验研究[J].机械工程学报.1989,25(4):47-53.
[18]韩静涛.有效控制夹杂性裂纹的大型锻件锻造技术及处理方法[J].塑性工程学报.1996, 3(1): 20-26.
[19]韩静涛.大型饼类锻件变形规律及夹杂性裂纹产生过程研究[J].塑性工程学报.1994, 1(3): 41-46.
[20]刘助柏.平砧拉长矩形截面毛坯的新理论[J].机械工程学报.1994, 30(5):47-49.
[21]朱明,金泉林.大型锻件内部孔隙缺陷闭合过程的理论探讨[C].第二次全国塑性力学学术交流会论文.1988.
[22]朱明,金泉林.一种考虑孔洞形状变化的损伤细观模型及其在孔洞闭合过程中的应用[J].应用数学和力学.1992,13(8):1-5.
[23]朱明,金泉林.材料内部孔洞压实机理的研究[J].兵工学报.1992, (1):1-3.
[24] Zhu Ming and Jin Quan-lin. A constitutive relation for material containing voids and application in closing of voids [J]. Advances in Constitutive Laws for Engineering Matericals. Ed. Fan Jing-hong and Sumio Murakami.Pergamon Press. Oxford (1989),542.
[25]任运来.大型锻件内部缺陷修复条件和修复方法研究[D].博士学位论文.燕山大学.2003.
[26] Henot J L. Recent contributions to the finite element modeling of mental forming process[J]. Journal of materials Processing Tech., 2000, (34):9-18.
[27] Hartley P P, Sturgess C E. Numerical modeling of material deformation processes[M]. Springer-Verlag London Limited, 1998, (2):22-28.
[28] Shah K N, Kiefer B V. Finite element simulation of void closure in open-die press forging [J]. Advanced manufacturing processes. 1999, (1):501-516.
[29] Sun J X. Analysis of special forging processes for heavy ingots by finite element method [J]. International journal of machine tools & manufacture.1988, (2):173-179.
[30] Sun H X, Hu J H. Elastic-plastic FEM analysis of cylinder upsetting between two flat platens. Chin.Mech.Eng.Soc, 1999, (12):45-49.
[31] Li.Y L. Recent development and application of three dimensional finite element modeling in buck forming process [J]. Journal of materials processing technology.2001, (113):40-49.
[32] Duan X, Sheppard T. Shape optimization using FEA software: a V-shaped anvil as an example [J]. Journal of materials processing technology.2002, (20):426-431.
[33] Queen M C, Ryan H J.N.D. Constitutive analysis in hot working[J]. Journal of materials processing technology. 2002, 322(1-2):42-63.
[34]肖景容,李尚健.塑性成型模拟理论.武汉:华中理工大学出版社,1994.
[35]任广升,谭红,李运兴等.镦粗过程中锻件内孔洞缺陷邻域应变分布的模拟研究[J].塑性工程学报.1994, 1(3):14-19.
[36] Hamzah S. A study of pore closure in the manufacturing of heavy rings[J]. J. Mater .Processing Technol.2001, (110):324-333.
[37] Wang A. A study of pore closure and welding in hot rolling process[J]. Journal of materials processing technology.1996, (60):95-120.
[38]崔振山,任广升,徐秉业等.圆柱体内部空洞的热锻闭合条件[J].清华大学学报, 2003, 43(2):227-229,233.
[39]崔振山,任广升等.圆柱体内部空洞热锻闭合过程的数值模拟[J].塑性工程学报, 2002,9 (1):49～52.
[40]崔振山,徐秉业,任广升.大锻件内部空洞的锻合压下率[J].塑性工程学报, 2002, 9 (3) : 6-8.
[41]崔振山,任广升,徐秉业等.大锻件空洞的局部效应与锻合压下率研究[J].工程力学, 2003 ,20 (2):55～59.
[42]蒋智,任广升等.圆柱体热锻件内部单空洞闭合的模拟分析[J].塑性工程学报. 2005, 12(1):47-49,57.
[43]蒋智.三维变形过程中空洞闭合的模拟研究[D].机械科学研究院.2003
[44]潘维国.定向凝固锭核电管板锻造工艺及内部质量控制[D].清华大学博士学位论文. 1996:20-58.
[45]马喜腾,钟志平.定向凝固锭管板凸砧锻造工艺高温纭文法模拟研究[J].塑性工程学报. 1998, 5(2):55-60.
[46]张艳妹.大锻件空洞锻合的光塑性研究与数值模拟[D].燕山大学硕士学位论文. 2002.32-63.
[47] Pertence A E M, Cetlin P R. Analysis of a new model material for the physical simulation of metal forming [J]. Journal of materials processing technology. 1998, (84):261-267.
[48] Arentoft M. Prevention of defects in forging by numerical and physical simulation [D]. PHD Dissertation of Technical University of Denmark, October 1999.
[49] Wanheim T. Physical modeling of metal processing[C]. Internal report of Technical University of Denmark, 1988.
[50] Danckert J, Wanheim T. Slipline The Physical Modeling of Plastic Working Processes [J].Mech.1976, (16):318-327.
[51] Blaes N, Bokelmann D, Poppenhager J and Wagner H. Optimization of the forging process of heavy forgings for power generation[C]. The Korea Institute of Meta and Materials. 13th international forge masters meeting. Pusan, Korea, 1997, (1):93-102.
[52] Tsukada H.超大型整体低压转子和超纯净转子轴的生产.周云松.第十一届国际锻造会议论文集,意大利,1991.四川德阳,中国二重集团,1995:207-211.
[53] Hideki Takamor, Yoshiaki Suzuki, Takaya Kawai. Manufacture of a shaft with flange using the upsetter[C].German Iron and Steel Institute. 14th international forgemaster meeting. Wiesbaden. Germany, 2000,(1):73-78.
[54] Steiner J E. Heavy forgings process technology[C]. The 13th IFM,1997, (1):83-93.
[55]张艳妹.砧宽比对孔洞闭合影响的光塑性研究[J].大型铸锻件.2002, (1):1-3,9.
[56]袁朝龙.大型锻件内部孔隙性缺陷修复规律的研究[J].锻压技术.2002, (3):3-6.
[57]杜学刚.大型支承辊类锻件锻造工艺优化的云纹法模拟[D].北京:清华大学图书馆,1989.
[58]任猛.大型钢锭内部孔洞性缺陷锻合过程的数值模拟和实验研究[D].北京:清华大学. 1986.
[59] McCLintock A criterion for ductile fracture by the growth of holes[J]. F.M.J., Appl. Mech., 1968,(35):363.
[60] Rice J.R, Tracey D.M. On the ductile enlargement of voids in triaxial stress fields [J].Mech.phys.Solids.1969, (17):201.
[61] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth [J]. ASME Journal of Engineering Materials and Technology, 1977, 99(1): 2 -15.
[62] Aravas N. On the numerical integration of a class of pressure-dependent plasticity model [J].International Journal for Numerical Methods in Engineering, 1987, (24):1395-1416.
[63] M.Ortiz and E.P.Popov. Accuracy and stability of integration algorithms for elasto-plasticconstitutive relations[J]. Int J Numer Meth Energy, 1985, (2):1561-1576.
[64] Krieg, R.D., Krieg, B.D. Accuracies of numerical solution methods for the elastic perfectly plastic model [J]. ASME. Pressure Vessel Tech., 1977, (99):510-15.
[65] Nagtegaal, J.C., Rebelo, N. On the development of a general purpose finite element program for analysis of forming processes [J]. Int.Num. Meth. in Eng., 1988, (25):113-31.
[66] Simo JC,Hughes TJR[C]. Computational Inelasticity,Springer-Verlag,New York,1998.
[67]伍爱著.质量管理学.广州:暨南大学出版社, 2002.
[68]陈火红MSC.Marc二次开发指南.北京:科学出版社, 2004:1-5.
[69]王勖成有限单元法.北京:清华大学出版社, 2003.