金属成形过程的细观损伤力学模型及韧性断裂准则研究
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摘要
金属塑性成形技术具有生产效率高、材料利用率高、产品质量稳定等优点,而且还能有效改善工件的力学性能,在金属零件制造过程中占据了重要的地位。在金属塑性成形领域内,金属材料的成形性能(可加工性能)的研究一直是人们关注的课题,而金属的损伤和韧性断裂是影响成形性能的重要因素。随着计算机硬件和软件技术的发展以及金属塑性流动理论的日臻完善,利用数值模拟技术,可以准确计算金属成形过程中的应力、应变等物理量的分布,但对成形过程中断裂等缺陷的预测尚不够成熟,这是塑性成形过程模拟技术推广应用的一个瓶颈问题。
金属韧性断裂是损伤累积的结果。金属成形中工件的破裂通常要经历以下的过程:微孔洞的形核、长大、聚合直至产生塑性变形局部化,最终产生宏观裂纹。细观损伤力学模型以孔洞演化理论为基础,从物理本质上反映了材料微观结构的劣化最终导致材料失效断裂过程。但是细观损伤力学模型本身存在一些理想化的假设,引入了一些试验难以测定的模型参数,因此没有在工程中得到广泛应用。合理地确定这些模型参数是将细观损伤模型正确地应用于工程分析的必要条件。韧性断裂准则是预测金属材料发生断裂的判据,已有的韧性断裂准则还只能针对特定加工工艺中的破裂进行预测。金属成形工艺的多样性要求韧性断裂准则应该具有宽阔的适用范围。本文针对细观损伤力学模型和韧性断裂准则及其在金属成形有限元模拟中的应用进行了较为深入的研究,主要研究内容和结果如下:
提出了一组误差评价函数来评价Gurson-Tvergaard-Needleman (GTN)细观损伤模型模拟工程金属材料宏观力学行为的准确度,从而合理地选取GTN模型参数,并进行了孔洞形核参数的优化。
根据能量最小原理,建立了孔洞聚合的分析模型,推导了三维孔洞体胞模型中临界断裂时的等效应变与孔洞体积分数之间的函数关系。对单向拉伸试件断口处的孔洞体积分数进行了测量,结果表明:本文提出的该函数关系比依据二维孔洞体胞模型推导的函数关系更接近于试验的结果。
比较和评价了工程中常用的六种韧性断裂准则的适用范围和准确度。依据试验观测结果,将金属成形过程中的韧性断裂机制分为拉伸型和剪切型两种类型,提出了一个适用于不同变形路径的统一形式的韧性断裂准则。数值模拟结果与拉伸、压缩、扭转、先扭转再拉伸等材料试验结果的对比验证了该准则在不同变形方式下都具有较高的准确性。
将新建立的韧性断裂准则应用于金属板料成形和体积成形工艺中的韧性断裂预测。采用经过单向拉伸预变形的板料进行拉深试验,结果表明采用本文提出的韧性断裂准则比成形极限图(FLD)能够更准确地预测非线性变形路径下的板料拉深过程中的破裂现象。采用不同断面缩减率进行了金属正挤压试验,结果表明新的韧性断裂准则能够很好地反映挤压件中同时存在拉伸型和剪切型两种韧性损伤的现象,并能准确预测挤压件表面裂纹的出现。
Metal forming technology plays an important role in the manufacturing industry. It has the merits of high productivity, stable quality and effective utilization of raw material. The mechanical properties of the metal are also improved in the forming processes. In metal forming, workability or formability of material is one of the focusing subjects, which is mainly controlled by damage and ductile fracture. With the development of computer technology and the plasticity, numerical simulation for metal forming process by finite element method (FEM) is more and more widely used. The distribution of stress and strain in metal forming process can be precisely obtained by the numerical simulation, but the prediction of ductile fracture in metal forming process is still immature, which is a bottleneck problem restraining the application of numerical simulation in metal forming process.
Ductile fracture in metal forming process is the cumulative result of damage, and usually follows a multi-step failure process involving nucleation of microscopic voids, growth of voids, localization of plastic flow, coalescence of voids and occurrence of macro-fracture. Meso-damage model physically reflects the phenomenon that microscopic structural deterioration leads to failure or fracture of metallic material. However, it is based on idealized hypotheses, and some parameters, which could not be directly determined by experiments, are involved, therefore it is not widely used in engineering field. To determine the reasonable value of the parameters is the precondition of utilization of the model in engineering analysis. On the other hand, in metal forming ductile fracture criteria are usually adopted to predict ductile fracture of the workpiece. Existing ductile fracture criterion is established for specific metal forming process, while the diversity of metal forming processes requires the wide application range of ductile fracture criterion. The research on meso-damage model and ductile fracture criterion and its application in finite element (FE) simulation of metal forming processes are carried out in the dissertation, the main contents are:
A set of error function is established to evaluate the accuracy of the simulation on deformation behavior of metal by Gurson-Tvergaard-Needleman (GTN) damage model, then the values of the parameters in the model are reasonably selected, void nucleation parameters are also introduced and optimized.
Based on the principle of minimum energy, an analytical model of voids coalescence is propoed, the relationship between the critical strain to fracture and the void volume fraction is derived. Void volume fraction in fracture area of specimens in uniaxial tension experiment is measured, and it is confirmed that the relationship between the critical strain to fracture and the void volume fraction, calculated by using the proposed model, agrees better with the experimental results than that calculated by two-dimensional model.
The applicable range and accuracy of six ductile fracture criteria often used in engineering analysis are compared and evaluated. The basic mechanisms of ductile fracture are divided into two modes (tension-type mode and shear-type mode) according to the observation of experimental results. A unified ductile fracture criterion is proposed for wide applicable range. The comparison of experimental results, including tension, compression, torsion, tension after torsion, with numerical analysis results confirms the validity of the newly proposed ductile fracture criterion on different deformation path.
The new ductile fracture criterion is then used on predicting ductile fracture in sheet metal and bulk metal forming processes. Deep drawing process of pre-strained sheet metal by uniaxial tension is carried out, which confirms that the newly proposed ductile fracture criterion more accurately predicts ductile fracture compared with forming limit diagram (FLD). Forward extrusion process with different rates of area reduction in cross-section is carried out, which shows that ductile damage of tension-type and shear-type mode simultaneously exist in the extruding samples, the new ductile fracture criterion also accurately predicts the occurrence of surface crack on the samples.
金属韧性断裂是损伤累积的结果。金属成形中工件的破裂通常要经历以下的过程:微孔洞的形核、长大、聚合直至产生塑性变形局部化,最终产生宏观裂纹。细观损伤力学模型以孔洞演化理论为基础,从物理本质上反映了材料微观结构的劣化最终导致材料失效断裂过程。但是细观损伤力学模型本身存在一些理想化的假设,引入了一些试验难以测定的模型参数,因此没有在工程中得到广泛应用。合理地确定这些模型参数是将细观损伤模型正确地应用于工程分析的必要条件。韧性断裂准则是预测金属材料发生断裂的判据,已有的韧性断裂准则还只能针对特定加工工艺中的破裂进行预测。金属成形工艺的多样性要求韧性断裂准则应该具有宽阔的适用范围。本文针对细观损伤力学模型和韧性断裂准则及其在金属成形有限元模拟中的应用进行了较为深入的研究,主要研究内容和结果如下:
提出了一组误差评价函数来评价Gurson-Tvergaard-Needleman (GTN)细观损伤模型模拟工程金属材料宏观力学行为的准确度,从而合理地选取GTN模型参数,并进行了孔洞形核参数的优化。
根据能量最小原理,建立了孔洞聚合的分析模型,推导了三维孔洞体胞模型中临界断裂时的等效应变与孔洞体积分数之间的函数关系。对单向拉伸试件断口处的孔洞体积分数进行了测量,结果表明:本文提出的该函数关系比依据二维孔洞体胞模型推导的函数关系更接近于试验的结果。
比较和评价了工程中常用的六种韧性断裂准则的适用范围和准确度。依据试验观测结果,将金属成形过程中的韧性断裂机制分为拉伸型和剪切型两种类型,提出了一个适用于不同变形路径的统一形式的韧性断裂准则。数值模拟结果与拉伸、压缩、扭转、先扭转再拉伸等材料试验结果的对比验证了该准则在不同变形方式下都具有较高的准确性。
将新建立的韧性断裂准则应用于金属板料成形和体积成形工艺中的韧性断裂预测。采用经过单向拉伸预变形的板料进行拉深试验,结果表明采用本文提出的韧性断裂准则比成形极限图(FLD)能够更准确地预测非线性变形路径下的板料拉深过程中的破裂现象。采用不同断面缩减率进行了金属正挤压试验,结果表明新的韧性断裂准则能够很好地反映挤压件中同时存在拉伸型和剪切型两种韧性损伤的现象,并能准确预测挤压件表面裂纹的出现。
Metal forming technology plays an important role in the manufacturing industry. It has the merits of high productivity, stable quality and effective utilization of raw material. The mechanical properties of the metal are also improved in the forming processes. In metal forming, workability or formability of material is one of the focusing subjects, which is mainly controlled by damage and ductile fracture. With the development of computer technology and the plasticity, numerical simulation for metal forming process by finite element method (FEM) is more and more widely used. The distribution of stress and strain in metal forming process can be precisely obtained by the numerical simulation, but the prediction of ductile fracture in metal forming process is still immature, which is a bottleneck problem restraining the application of numerical simulation in metal forming process.
Ductile fracture in metal forming process is the cumulative result of damage, and usually follows a multi-step failure process involving nucleation of microscopic voids, growth of voids, localization of plastic flow, coalescence of voids and occurrence of macro-fracture. Meso-damage model physically reflects the phenomenon that microscopic structural deterioration leads to failure or fracture of metallic material. However, it is based on idealized hypotheses, and some parameters, which could not be directly determined by experiments, are involved, therefore it is not widely used in engineering field. To determine the reasonable value of the parameters is the precondition of utilization of the model in engineering analysis. On the other hand, in metal forming ductile fracture criteria are usually adopted to predict ductile fracture of the workpiece. Existing ductile fracture criterion is established for specific metal forming process, while the diversity of metal forming processes requires the wide application range of ductile fracture criterion. The research on meso-damage model and ductile fracture criterion and its application in finite element (FE) simulation of metal forming processes are carried out in the dissertation, the main contents are:
A set of error function is established to evaluate the accuracy of the simulation on deformation behavior of metal by Gurson-Tvergaard-Needleman (GTN) damage model, then the values of the parameters in the model are reasonably selected, void nucleation parameters are also introduced and optimized.
Based on the principle of minimum energy, an analytical model of voids coalescence is propoed, the relationship between the critical strain to fracture and the void volume fraction is derived. Void volume fraction in fracture area of specimens in uniaxial tension experiment is measured, and it is confirmed that the relationship between the critical strain to fracture and the void volume fraction, calculated by using the proposed model, agrees better with the experimental results than that calculated by two-dimensional model.
The applicable range and accuracy of six ductile fracture criteria often used in engineering analysis are compared and evaluated. The basic mechanisms of ductile fracture are divided into two modes (tension-type mode and shear-type mode) according to the observation of experimental results. A unified ductile fracture criterion is proposed for wide applicable range. The comparison of experimental results, including tension, compression, torsion, tension after torsion, with numerical analysis results confirms the validity of the newly proposed ductile fracture criterion on different deformation path.
The new ductile fracture criterion is then used on predicting ductile fracture in sheet metal and bulk metal forming processes. Deep drawing process of pre-strained sheet metal by uniaxial tension is carried out, which confirms that the newly proposed ductile fracture criterion more accurately predicts ductile fracture compared with forming limit diagram (FLD). Forward extrusion process with different rates of area reduction in cross-section is carried out, which shows that ductile damage of tension-type and shear-type mode simultaneously exist in the extruding samples, the new ductile fracture criterion also accurately predicts the occurrence of surface crack on the samples.
引文
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[5] Koplik J, Needleman A. Void growth and failure in notched bars. Journal of the Mechanics and Physics of Solids, 1988, 36(3):317-351
[6] Hancock J W, Thomson R D. Strain and stress concentrations in ductile fracture by void nucleation growth and coalescence. Materials Science and Technology, 1985, 1(9):684-690
[7] Kim J, Gao X S, Srivatsan T S. Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Engineering Fracture Mechanics, 2004, 71(3):379-400
[8] Komori K. Proposal and use of a void model for the simulation of shearing. Materials Science and Engineering, 2006, 421(1-2):226-237
[9] Aravas N. On the numerical integration of a class of pressure-dependent plasticity models. International Journal for Numerical Methods in Engineering, 1987, 24(7):1395-1416
[10]郑长卿,周利,张克实.金属韧性破坏的细观力学及其研究应用.北京:国防工业出版社,1995
[11] Thomason P F. A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. Acta Metallurgica, 1985, 33(6):1087-1095
[12] Thomason P F. Ductile fracture by the growth and coalescence of microvoids of non-uniform size and spacing. Acta Metallurgica, 1993, 41(7):2127-2134
[13] Komori K. Proposal and use of a void model for the simulation of ductile fracture behavior. Acta Metallurgica, 1999, 47(10):3069-3077
[14] (美)彼里西阿G E,浦迪S M.体视学和定量金相学.孙惠林,马继畬译.北京:机械工业出版社,1980
[15] Moussy F H, Lefebure P. Critical damage and ductile fracture: quantitative experimental determination. In Proc. Int. Symp on Computational Methods for Predicting Material Processing Defects, eds. M. Predeleanu, Amsterdam: Elsevier, 1987,275
[1]嵇国金.金属成形中的韧性损伤理论和缺陷预测研究.上海交通大学博士学位论文,1999
[2] Boisse P, Altan T, Luttervelt K. Friction and flow stress in forming and cutting. London: Sterling, VA, 2003
[3] Goijaerts A M, Govaert L E. Evaluation of ductile fracture model for different metals in blanking. Journal of Materials Processing Technology, 2001, 110 (3):312-323
[4] Devaux J, Gelin J C, Oudin J. Theoretical analysis and experimental applications of barrelling and folding in cylinder upsetting tests. International Journal of Mechanical Sciences, 1984, 26 (11-12):555-572
[5] Alberti N. Central bursting defects in drawing and extrusion numerical and uitrasonnic evaluation. Annals of the CIRP, 1993, 42 (1):269-272
[6] Freudenthal A M. The inelastic behavior of engineering materials and structures. New York, Wiley, 1950
[7] Cockroft M, Latham D. Ductility and workability of metals. Journal Institute of Metals, 1968,96:33-39
[8] Oh S I, Chen C C, Kobayashi S. Ductile fracture in ax-symmetric extrusion and drawing. Journal of Engineering for Industry, Transaction of the ASME, 1979, 101 (1):23-44
[9] Brozzo P, Deluca B. A new method for the prediction of formability limits in metal sheets. Proceeding of the 7th Biennial Conference of the International Deep Drawing Research, 1972
[10] Rice J R, Tracey D. On the ductile fracture by the growth of holes. Journal of the Mechanics and Physics of Solids, 1969, 17:201-217
[11] Oyane M, Sato T, Okimoto K. Criteria for ductile fracture and their applications. Journal of Mechanical Working Technology, 1980, 4:66-81
[12] McClintock F A. A criterion for ductile fracture by the growth of holes subjected to multi-axial stress states. Journal of Applied Mechanics, 1968, 35:363-371
[13] Roy G L, Embury J D. Model of ductile fracture based on the nucleation and growth of voids. Acta Metalllurgica, 1981, 29 (8):1509-1522
[14]谢晓龙.精冲成形延性损伤断裂与数值模拟研究.上海交通大学博士学位论文,2006
[1]胡平,柳玉起,李运兴.板料成形缺陷及其数值仿真.应用基础与工程科学学报,1999,7(1):39-54
[2] Keeler S P, Backofen W A. Plastic instability and fracture in sheets stretched over rigid punches. American Society of Mechanical Engineers, 1965, 56:25-48
[3] Goodwin G M. Application of strain analysis to sheet metal forming problems in the press shop. SAE Report, 1968
[4] Huang Y M, Chien K H. The formability limitation of the hole-flanging process. Journal of Materials Processing Technology, 2001, 117(1-2):43-51
[5]万敏,周贤宾.复杂加载路径下板材屈服强化与成形极限的研究进展.塑性工程学报,2000,7(2):35-39
[6] Takuda H, Mori K, Hatta N. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals. Journal of Materials Processing Technology, 1999, 95(1-3):116-121
[7]吴建军,周维贤.板料成形性基础.西安:西北工业大学出版社,2004
[8]张东娟.板料冲压成形回弹理论及有限元数值模拟.上海交通大学博士学位论文,2006
[9] Keeler S P, Brazier W G. Relationship between laboratory material characterization and press shop formability. Proceedings of Microalloying, 1975, 517-528
[10] Comette D C. High strength steels for automotive safety parts. SAE Paper, 2001
[11] Bleck W. Microstructure and tensile properties in dual phase and TRIP steels. Steel Research, 2004, 75:11
[1]谢建新,刘静安.金属挤压理论与技术.北京:冶金工业出版社,2001
[2]吴诗惇.挤压理论.北京:国防工业出版社,1994
[3]吴诗惇.冷温挤压技术.北京:国防工业出版社,1995
[4]赵震,陈军,吴公明.冷温热挤压技术.北京:电子工业出版社,2008
[5]一机部机电研究所,上海交通大学等.常用冷挤压钢材冷挤压件机械性能研究.锻压技术,1980,5(5):8-20
[6]杨长顺.冷挤压模具设计.北京:国防工业出版社,1994
[7]王学文,刘汉贵.挤压组合凹模设计.北京:国防工业出版社,1988
[8]洪深泽.冷挤压工艺及模具设计.合肥:安徽科学技术出版社,1985
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[27] Thomason P F. Ductile fracture by the growth and coalescence of microvoids of non-uniformsize and spacing. Acta Metallurgica, 1993, 41(7):2127-2134
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[38]郑长卿,张克实.含孔洞材料细观韧性损伤的体胞模型分析.内蒙古工业大学学报,1999,31(5):534-541
[39]李昱明.基于空穴损伤和韧性断裂的精冲成形过程的三维有限元仿真技术研究.上海交通大学博士学位论文,2001
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[41] Vujovic V, Shabaik A H. A new workability criterion for ductile metals. Journal of Engineering materials and Technology, Transactions of the ASME, 1986, 108 (3):245-249
[42] Cockroft M, Latham D. Ductility and workability of metals. Journal Institute of Metals, 1968,96:33-39
[43] Oh S I, Chen C C, Kobayashi S. Ductile fracture in ax-symmetric extrusion and drawing. Journal of Engineering for Industry, Transaction of the ASME, 1979, 101 (1):23-44
[44] Brozzo P, Deluca B. A new method for the prediction of formability limits in metal sheets. Proceeding of the 7th Biennial Conference of the International Deep Drawing Research, 1972
[45] Atkins A G. Possible explanation for unexpected departures in hydrostatic tension-fracture strain relations. Metal Science, 1981, 15(2):81-83
[46] Takuda H, Mori K. Prediction of forming limit in deep drawing of Fe/Al laminated composite sheet using ductile fracture criterion. Journal of Materials Processing Technology, 1996, 60(1-4) :291-296
[47] Takuda H, Mori K. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals. Journal of Materials Processing Technology, 1999, 95(1-3) :116-121
[48] Oyane M, Sato T, Okimoto K. Criteria for ductile fracture and their applications. Journal of Mechanical Working Technology, 1980, 4:66-81
[49]于忠奇.基于Lemaitre损伤理论的韧性断裂准则建立及板料成形极限预测.哈尔滨工业大学博士学位论文,2003
[50] Freudenthal A M. The inelastic behavior of engineering materials and structures. New York, Wiley, 1950
[51]周士能,陈志明,李江平.钢材冷锻的破裂准则研究.华中理工大学学报,1990,18(2):79-84
[52] McClintock F A. A criterion for ductile fracture by the growth of holes subjected to multi-axial stress state. Journal of Applied Mechanics, 1968, 35:363-371
[53] Wu S C, Liang H, Li M Q. Microvoid growth in metals during plastic deformation. Journal of Materials Processing Technology, 1992, 32(3):627-631
[54] Goijaerts A M, Govaert L E. Evaluation of ductile fracture model for different metals in blanking. Journal of Materials Processing Technology, 2001, 110 (3):312-323
[55] Devaux J, Gelin J C, Oudin J. Theoretical analysis and experimental applications of barrelling and folding in cylinder upsetting tests. International Journal of Mechanical Sciences, 1984, 26 (11-12):555-572
[56] Alberti N. Central bursting defects in drawing and extrusion numerical and uitrasonnic evaluation. Annals of the CIRP, 1993, 42 (1):269-272
[57] Goijaerts A M, Govaert L E. Prediction of ductile fracture in metal blanking. Journal of Manufacturing Science and Engineering, 2000, 122 (1):476-483
[58] Takuda H, Mori K. Finite element analysis of limits strains in biaxial stretching of sheet metals allowing for ductile fracture. International Journal of Mechanical Sciences, 2000, 42 (4):785-798
[59] Takuda H, Mori K. Prediction of forming limit in deep drawing using finite element simulationand ductile fracture criterion. Journal of the Japan Society for Technology of Plasticity, 1995, 36 (416):985-990
[60] Takuda H, Mori K. Prediction of forming limit in axisymmetric deep drawing of steel/aluminium alloy laminated sheet using a simple criterion for ductile fracture. Journal of the Japan Society for Technology of Plasticity, 1996, 37 (424):509-514
[61] Takuda H, Mori K. Finite element analysis of bore-expending processes with ductile fracture criterion. Journal of the Iron and Steel Institute of Japan, 1998, 84 (3):182-187
[62] Takuda H, Hatta N. Numerical analysis of formability of a commercially pure zirconium sheet in some sheet forming processes. Materials Science and Engineering A, 1998, 242 (1-2):15-21
[63] Takuda H, Yoshii T. Finite-element analysis of the formability of a magnesium-based alloy AZ31 sheet. Journal of Materials Processing Technology, 1999, 89-90:135-140
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[65] Lei L P, Kang B S. Prediction of the forming limit in hydroforming processes using the finite element method and a ductile fracture criterion. Journal of Materials Processing Technology, 2001, 113(1-3):673-679
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[1]郑长卿,周利,张克实.金属韧性破坏的细观力学及其研究应用.北京:国防工业出版社,1995
[2] Tang C Y, Lee T C, Rao B. An experimental study of shear damage using in-situ single shear test. International Journal of Damage Mechanics, 2002, 11 (4):335-353
[1]万建松,岳珠峰.金属韧性断裂的细观研究.计算力学学报,2002,19(3):320-323
[2] Gurson A L.Continuum theory of ductile rupture by void nucleation and growth: part I dash yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, Transaction of the ASME, 1977, 99(1):2-15
[3] Tvergaard V. Material failure by void coalescence in localized shear bands. International Journal of Solids and Structures, 1982, 18(8):659-672
[4] Needleman A, Triantafyllidis N. Void growth and local necking in biaxially stretched sheets. Journal of Engineering Materials and Technology, Transactions of the ASME, 1978, 100(2):164-169
[5] Koplik J, Needleman A. Void growth and failure in notched bars. Journal of the Mechanics and Physics of Solids, 1988, 36(3):317-351
[6] Hancock J W, Thomson R D. Strain and stress concentrations in ductile fracture by void nucleation growth and coalescence. Materials Science and Technology, 1985, 1(9):684-690
[7] Kim J, Gao X S, Srivatsan T S. Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Engineering Fracture Mechanics, 2004, 71(3):379-400
[8] Komori K. Proposal and use of a void model for the simulation of shearing. Materials Science and Engineering, 2006, 421(1-2):226-237
[9] Aravas N. On the numerical integration of a class of pressure-dependent plasticity models. International Journal for Numerical Methods in Engineering, 1987, 24(7):1395-1416
[10]郑长卿,周利,张克实.金属韧性破坏的细观力学及其研究应用.北京:国防工业出版社,1995
[11] Thomason P F. A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. Acta Metallurgica, 1985, 33(6):1087-1095
[12] Thomason P F. Ductile fracture by the growth and coalescence of microvoids of non-uniform size and spacing. Acta Metallurgica, 1993, 41(7):2127-2134
[13] Komori K. Proposal and use of a void model for the simulation of ductile fracture behavior. Acta Metallurgica, 1999, 47(10):3069-3077
[14] (美)彼里西阿G E,浦迪S M.体视学和定量金相学.孙惠林,马继畬译.北京:机械工业出版社,1980
[15] Moussy F H, Lefebure P. Critical damage and ductile fracture: quantitative experimental determination. In Proc. Int. Symp on Computational Methods for Predicting Material Processing Defects, eds. M. Predeleanu, Amsterdam: Elsevier, 1987,275
[1]嵇国金.金属成形中的韧性损伤理论和缺陷预测研究.上海交通大学博士学位论文,1999
[2] Boisse P, Altan T, Luttervelt K. Friction and flow stress in forming and cutting. London: Sterling, VA, 2003
[3] Goijaerts A M, Govaert L E. Evaluation of ductile fracture model for different metals in blanking. Journal of Materials Processing Technology, 2001, 110 (3):312-323
[4] Devaux J, Gelin J C, Oudin J. Theoretical analysis and experimental applications of barrelling and folding in cylinder upsetting tests. International Journal of Mechanical Sciences, 1984, 26 (11-12):555-572
[5] Alberti N. Central bursting defects in drawing and extrusion numerical and uitrasonnic evaluation. Annals of the CIRP, 1993, 42 (1):269-272
[6] Freudenthal A M. The inelastic behavior of engineering materials and structures. New York, Wiley, 1950
[7] Cockroft M, Latham D. Ductility and workability of metals. Journal Institute of Metals, 1968,96:33-39
[8] Oh S I, Chen C C, Kobayashi S. Ductile fracture in ax-symmetric extrusion and drawing. Journal of Engineering for Industry, Transaction of the ASME, 1979, 101 (1):23-44
[9] Brozzo P, Deluca B. A new method for the prediction of formability limits in metal sheets. Proceeding of the 7th Biennial Conference of the International Deep Drawing Research, 1972
[10] Rice J R, Tracey D. On the ductile fracture by the growth of holes. Journal of the Mechanics and Physics of Solids, 1969, 17:201-217
[11] Oyane M, Sato T, Okimoto K. Criteria for ductile fracture and their applications. Journal of Mechanical Working Technology, 1980, 4:66-81
[12] McClintock F A. A criterion for ductile fracture by the growth of holes subjected to multi-axial stress states. Journal of Applied Mechanics, 1968, 35:363-371
[13] Roy G L, Embury J D. Model of ductile fracture based on the nucleation and growth of voids. Acta Metalllurgica, 1981, 29 (8):1509-1522
[14]谢晓龙.精冲成形延性损伤断裂与数值模拟研究.上海交通大学博士学位论文,2006
[1]胡平,柳玉起,李运兴.板料成形缺陷及其数值仿真.应用基础与工程科学学报,1999,7(1):39-54
[2] Keeler S P, Backofen W A. Plastic instability and fracture in sheets stretched over rigid punches. American Society of Mechanical Engineers, 1965, 56:25-48
[3] Goodwin G M. Application of strain analysis to sheet metal forming problems in the press shop. SAE Report, 1968
[4] Huang Y M, Chien K H. The formability limitation of the hole-flanging process. Journal of Materials Processing Technology, 2001, 117(1-2):43-51
[5]万敏,周贤宾.复杂加载路径下板材屈服强化与成形极限的研究进展.塑性工程学报,2000,7(2):35-39
[6] Takuda H, Mori K, Hatta N. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals. Journal of Materials Processing Technology, 1999, 95(1-3):116-121
[7]吴建军,周维贤.板料成形性基础.西安:西北工业大学出版社,2004
[8]张东娟.板料冲压成形回弹理论及有限元数值模拟.上海交通大学博士学位论文,2006
[9] Keeler S P, Brazier W G. Relationship between laboratory material characterization and press shop formability. Proceedings of Microalloying, 1975, 517-528
[10] Comette D C. High strength steels for automotive safety parts. SAE Paper, 2001
[11] Bleck W. Microstructure and tensile properties in dual phase and TRIP steels. Steel Research, 2004, 75:11
[1]谢建新,刘静安.金属挤压理论与技术.北京:冶金工业出版社,2001
[2]吴诗惇.挤压理论.北京:国防工业出版社,1994
[3]吴诗惇.冷温挤压技术.北京:国防工业出版社,1995
[4]赵震,陈军,吴公明.冷温热挤压技术.北京:电子工业出版社,2008
[5]一机部机电研究所,上海交通大学等.常用冷挤压钢材冷挤压件机械性能研究.锻压技术,1980,5(5):8-20
[6]杨长顺.冷挤压模具设计.北京:国防工业出版社,1994
[7]王学文,刘汉贵.挤压组合凹模设计.北京:国防工业出版社,1988
[8]洪深泽.冷挤压工艺及模具设计.合肥:安徽科学技术出版社,1985
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