摘要
板料冲压成形技术在制造业中占有极其重要的地位,被广泛应用于航空航天、汽车、船舶、电器等工业领域。但由于变形条件、工艺参数及材料选择等因素,常产生破裂、回弹和起皱等缺陷,使得零件的废品率和试错次数显著增加。在板料成形工艺分析中,引入数值模拟技术是解决上述问题的有效手段,但目前对破裂和回弹缺陷的预测精度仍不可靠。如何准确而又迅速地预测冲压成形中可能出现的这两种缺陷,对有效控制产品质量,降低成本,缩短产品开发周期,提高产品的竞争力有重要意义。
本构模型是影响数值模拟可靠性一个重要方面。实际材料由于内部存在微缺陷,因而在变形过程中其力学性能是逐渐劣化的,但目前数值模拟分析少有考虑该因素,为了提高数值模拟预测精度,将损伤引入本构模型显得十分必要。为此,本文基于GTN细观损伤理论,考虑了板料的塑性各向异性性能和包申格效应,建立了符合冲压成形特点的损伤模型,并对数值实现方法进行了改进。将新的本构模型应用于成形和回弹分析,提出了与应变路径无关的韧性失稳判据和韧性断裂判据。本文的主要研究内容如下:
针对板料冲压成形问题,提出并建立了Hill’48-GTN和Barlat’89-GTN细观损伤模型。对原来GTN细观损伤模型进行了改进,将Hill’48和Barlat’89各向异性屈服准则表示的宏观等效应力引入到模型中,反映了材料的各向异性性能,推导了相应的本构方程及数值实现表达式。通过数值算例表明,新模型Hill’48-GTN和Barlart’89-GTN相对原来的GTN模型可以同时反映板料成形中的塑性各向异性行为和损伤发展过程。
针对原有本构方程数值算法在求解板料成形,尤其是破裂问题时计算效率低、收敛困难的问题,改进了本构积分算法的数值实现方法。将完全隐式的向后Euler本构积分算法与显式有限元法相结合,既保证了算法的准确性和稳定性,又提高了计算效率。基于有限元软件ABAQUS编写了几种GTN损伤模型的VUMAT材料子程序,实现了对板料成形过程中损伤演化的可视化。通过圆杯拉深成形试验验证了GTN损伤模型的可靠性。
研究比较了目前板料成形中3种常用流动应力模型:Hollomon、Swift和Voce方程的描述准确性。为了对韧性损伤机理有更深入直观的理解,利用扫描电镜观测了拉断试样断口形貌并进行了微观分析。采用逆向方法,将单向拉伸试验与有限元数值模拟相结合来确定GTN模型损伤参数。由于GTN模型中各损伤参数的组合不是固定不变的,而是在一定范围内变化的。基于正交试验设计和有限元数值模拟,研究了各参数变化对板料损伤行为的影响。
为了准确预测板料回弹,提出建立了遵循线性随动强化、非线性随动强化和混合强化法则的几种GTN模型,通过在模型中考虑了背应力的影响来反映回弹中的包申格效应。将几种遵循不同强化法则的GTN模型采用显隐式有限元求解相结合的方法来分析板料回弹,为准确预测回弹提供了理论方法和计算依据。分析比较了几种GTN损伤模型在采用不同强化法则时对板料回弹量的影响规律。考察了本构模型在考虑损伤因素前后的回弹量变化。
从工程应用角度考虑,提出了以GTN模型中损伤变量孔洞体积分数作为判别板料冲压成形中韧性失稳和破裂的依据。由于孔洞体积分数自然而然地考虑了材料的成形历史,为判断缩颈现象不明显的韧性较差板材(如铝合金板)或非线性应变路径条件下板料的成形性能提供了另一条途径。结合有限元数值模拟计算,分析了镀锌钢板和AA5052-O铝合金板圆杯件拉深的成形极限,并与试验比较。
Stamping plays a very important role in manufacturing industry. It is widely used in aviation, aerospace, automobile and other areas of industry. Fracture, springback and wrinkling are three main defects occurred in sheet metal forming because of some factors, such as forming condition, process parameters and material selection. These defects increase the reject ratio and try and error. Numerical simulation technology is a valid means to solve the above problems. But the prediction precision of the fracture and springback defects is still unreliable. Predicting the two defects accurately and rapidly is very important to the product quality control, cost reduction, product development cycle shortening and competitive power improving.
Constitutive model is a crucial factor affecting the reliability of numerical simulation. Owing to internal micro defects existing in actual metallic materials, the material mechanical property degrades gradually during the forming process. But up to present, which is seldom considered in numerical simulation analysis. Therefore, to improve the numerical simulation accuracy, introducing the damage factor into the constitutive relationship is very essential. In this paper, on the basis of GTN mesotropic damage theory, the damage model considering the plastic anisotropy and Bauschinger effect is established suitable for the sheet metal forming. The numerical realization of the damage model is improved. The model is applied to analyze forming process and springback. The ductile instability and fracture criteria are proposed. The main work in this paper is as follows.
Hill’48-GTN and Barlat’89-GTN mesotropic damage models are proposed and established based on the initial GTN model. The macroscopic equivalent stresses denoted by Hill’48 and Barlat’89 yield criteria take the place of the original von Mises equivalent stress to reflect the plastic anisotropy. The constitutive equations and numerical realization equations are derived. The results of numerical example show that the Hill’48-GTN and Barlat’89-GTN models can describe both the damage evolution and plastic anisotropy in sheet metal forming.
Because the original method is inefficient and converge difficultly when dealing with sheet metal forming, especially fracture problem. The constitutive numerical realization method is improved. Implicit back Euler constitutive integration algorithm is introduced into the explicit dynamic solver. The computational efficiency of the algorithm is improved and the accuracy is ensured. The corresponding GTN models user-defined subroutines VUMAT are developed based on the commercial software ABAQUS. The damage parameter, void volume fraction is displayed clearly in the sheet metal forming simulation. The reliability of the above damage models is validated through the circular cup drawing experiment.
The precision of three main flow stress models: Hollomon, Swift and Voce equations are studied and compared. To comprehending the mechanism of ductile damage intuitively and thoroughly, the fracture sections of cracked specimens are analyzed using SEM. Combining the experimental tensile test and finite element simulation, the inverse method is carried out to identify the GTN damage parameters. No matter which method is used, the parameters of GTN model are variational. The effect of parameters variation on damage behavior is analyzed based on orthogonal experimental design and FEM numerical simulation.
Several hardening laws are proposed based on GTN damage model. The back stress is considered into the model to reflect the Bauschinger effect. Springback analysis are simulated using the explicit-implicit algorithm using the above GTN models. The effects of different material hardening rules on springback are studied and compared. The effect of damage on the springback is also investigated.
From the engineering point of view, the ductile instability criterion and ductile fracture criterion are proposed based on the damage variable, void volume fraction in GTN model. Because the void volume fraction can take account of the material forming history, these criteria can deal with the forming limit of worse ductile sheet, for example, the alumimum alloy, and the sheet forming limit under the non-proportional loading strain path. The forming limits of steel and AA5052-O cup drawing processes are analyzed. The simulation results agree with the experimental data well.
引文
[1] Hua JG, Ishikawa T, Jonas JJ. Finite element analysis of damage evolution and the prediction of the limiting draw ratio in textured aluminum sheets [J]. Journal of Materials Processing Technology, 2000, 103(3): 374-382.
[2] Kuroda M, Tvergaard V. Forming limit diagrams for anisotropic metal sheets with different yield criteria [J]. International Journal of Solids and Structures, 2000, 37(37): 5037-5059.
[3] Butuc MC, Gracio JJ, da Rocha AB. A theoretical study on forming limit diagrams prediction [J]. Journal of Materials Processing Technology, 2003, 142(3): 714-724.
[4] Hora P, Tong L. Numerical prediction of FLC using the enhanced modified maximum force criterion (EMMFC) [C]. Proceedings of the FLC Zurich 2006. ETH Zurich, Switzerland, 2006: 31-36.
[5] Chow CL, Jie M. Forming limits of AL 6022 sheets with material damage consideration-theory and experimental validation [J]. International Journal of Mechanical Sciences, 2004, 46(1): 99-122.
[6] Brunet M, Morestin F. Experimental and analytical necking studies of anisotropic sheet metals [J]. Journal of Materials Processing Technology, 2001, 112: 214-226.
[7] Takuda H, Morib K, Hatta N. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals [J]. Journal of Materials Processing Technology, 1999, 95: 116-121.
[8] Mkaddem A, Hambli R, Potiron A. Comparison between Gurson and Lemaitre damage models in wiping die bending processes [J]. International Journal of Advanced Manufacturing Technology, 2004, 23: 451-461.
[9]王自强,段祝平.塑性细观力学[M].北京:科学出版社, 1995.
[10]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社, 1997.
[11]余天庆,钱济成.损伤理论及其应用[M].北京:国防工业出版社, 1993.
[12]楼志文.损伤力学基础[M].西安:西安交通大学出版社, 1991.
[13] Lemaitre J.损伤力学教程[M].北京:科学出版社, 1996.
[14] Kachanov LM. On the time to failure under creep condition [J]. Izv.Akad.Nauk.USSR.Otd.Tekhn.Nauk, 1958, 8: 26-31.
[15] Rabtnov YN. On the equations of state for creep [C]. Progress in Applied Mechanics, the Prager Anniversary 8. Amsterdam, North-Holland, 1963: 307-315.
[16] Lemaitre J. Evaluation of dissipation and damage in metals submitted to dynamic loading [C]. In: I.C.M. Proc. Vol. 1, Kyoto, Japan. 1971
[17] Andrade Pires FM, Cesar de Sa JMA, Costa Sousa L, et al. Numerical modelling of ductile plastic damage in bulk metal forming [J]. International Journal of Mechanical Sciences, 2003, 45(2): 273-294.
[18] Bahloul R, Mkaddem A, Dal Santo Ph, et al. Sheet metal bending optimisation using response surface method, numerical simulation and design of experiments [J]. International Journal of Mechanical Sciences, 2006, 48(9): 991-1003.
[19] Bonora N, Gentile D, Pirondi A, et al. Ductile damage evolution under triaxial state of stress: theory and experiments [J]. International Journal of Plasticity, 2005, 21(5): 981-1007.
[20]沈为.损伤力学[M].武汉:华中理工大学出版社, 1995.
[21] McClintock FA. A criterion for ductile fracture by growth of holes [J]. Journal of Applied Mechanics, 1968, 35: 363-371.
[22] Rice JR, Tracey DM. On the ductile enlargement of voids in triaxial stress fields [J]. Journal of the Mechanics and Physics of Solids, 1969, 17(3): 201-217.
[23] Gurson AL. Continuum theory of ductile rupture by void nucleation and growth: part 1-yield criteria and flow rules for porous ductile media [J]. Journal of Engineering Materials and Technology, 1977, 99(1): 2-15.
[24] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions [J]. International Journal of Fracture, 1981, 17(4): 398-407.
[25] Tvergaard V. On localization in ductile materials containing spherical voids [J]. International Journal of Fracture, 1982, 18(4): 237-252.
[26] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile test bar [J]. Acta Metallurgica, 1984, 32: 157-169.
[27] Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars [J]. Journal of the Mechanics and Physics of Solids, 1984, 32: 461-490.
[28] Tvergaard V. Studies of void growth in a thin ductile layer between ceramics [J]. Computational Mechanics, 1997, 20(1-2): 186-191.
[29] Becker R, Needleman A, Suresh S, Tvergaard V, et al. An analysis of ductile failure by grain boundary void growth [J] Acta Metallurgica, 1989, 37(1): 99-120.
[30] Pan J, Saje M, Needleman A. Localization of deformation in rate sensitive porous plastic solids [J]. International Journal of Fracture, 1983, 21(4): 261-278.
[31] Needleman A, Kushner AS. An analysis of void distribution effects on plastic flow in porous solids [J]. European Journal of Mechanics A-Solids, 1990, 9(3): 193-206.
[32] Fleck NA, Hutchinson JW, Tvergaard V. Softening by void nucleation and growth in tension and shear [J]. Journal of the Mechanics and Physics of Solids, 1989, 37(4): 515-540.
[33] Becker R, Smelser RE, Richmond O. The effect of void shape on the development of damage and fracture in plane-strain tension[J]. Journal of the Mechanics and Physics of Solids, 1989, 37(1): 111-129.
[34] Michel JC, Suquet P. The constitutive law of nonlinear viscous and porous materials [J]. Journal of the Mechanics and Physics of Solids, 1992, 40(4): 783-812.
[35] Thomason PF. Ductile fracture by the growth and coalescence of microvoids of non-uniform size and spacing [J]. Acta Metallurgica et Materialia, 1993, 41(7): 2127-2134.
[36] Doege E, Eldsoki T, Seibert D. Prediction of necking and wrinkling in sheet-metal forming [J]. Journal of Materials Processing Technology, 1995, 50(1-4): 197-206.
[37] Wang ZP, Lam KY, Cotterell B. An approximate yield criterion for voided nonlinear materials [J]. Mechanics of Materials, 1996, 22(4): 291-300.
[38] Kuna M, Sun DZ. Three-dimensional cell model analyses of void growth in ductile materials [J].International Journal of Fracture, 1996, 81(3): 235-258.
[39] Liao KC, Pan J, Tang SC. Approximate yield criteria for anisotropic porous ductile sheet metals [J]. Mechanics of Materials, 1997, 26: 213-226.
[40] Tvergaard V. Interaction of very small voids with larger voids [J]. International Journal of Solids and Structures, 1998, 35(30): 3989-4000.
[41] Chien WY, Pan J, Tang SC. Modified anisotropic Gurson yield criterion for porous ductile sheet metals [J]. Journal of Engineering Materials and Technology, 2001, 123: 409-416.
[42] Pardoen T, Hutchinson JW. An extended model for void growth and coalescence [J]. Journal of the Mechanics and Physics of Solids, 2000, 48: 2467-2512.
[43] Gologanu M, Leblond JB, Perrin G, et al. Theoretical models for void coalescence in porous ductile solids. I. Coalescence in layers [J]. International Journal of Solids and Structures, 2001, 38: 5581-5594.
[44] Benzerga AA. Micromechanics of coalescence in ductile fracture [J]. Journal of the Mechanics and Physics of Solids, 2002, 50: 1331-1362.
[45]李国琛,耶纳M.塑性大应变微结构力学[M].北京:科学出版社, 2003.
[46] Li GC, Ling XW, Shen H. On the mechanism of void growth and the effect of straining mode in ductile materials [J]. International Journal of Plasticity, 2000, 16: 39-57.
[47]郑长卿,雷登,周利等.韧性断裂细观力学的初步研究及其应用[M].西安:西北工业大学出版社, 1988.
[48]李振环,张克实.不同应力三维度条件下孔洞的演变及修正的Gurson模型[J].上海力学, 1997, 18(1): 50-58.
[49] Zhang KS, Bai JB, Francois D. Ductile fracture of materials with high void volume fraction [J]. International Journal of Solids and Structures, 1999, 36: 3407-3425.
[50]李晓红,张克实,赵泽茂.考虑孔洞大小及分布非均匀性的材料细观损伤[J].西安石油学院学报(自然科学版), 2002, 17(4): 62-65.
[51]李晓红,张克实.延性材料损伤演化及材料软化的孔洞尺寸影响[J].机械强度, 2003, 25(1): 81-84.
[52]李晓红.金属材料细观损伤非均匀性研究[D].西安:西北工业大学博士学位论文, 2001.
[53]文洁.考虑尺寸效应的Gurson模型[D].北京:清华大学博士学位论文, 2003.
[54] Needleman A, Triantafyllidis N. Void growth and local necking in biaxially stretched sheets [J]. Journal of Engineering Materials and Technology-Transactions of the ASME, 1978, 100(2): 164-169.
[55] Brunet M, Mguil, S, F.Morestin. Analytical and experimental studies of necking in sheet metal forming processes [J]. Journal of Materials Processing Technology 1998, 80-81: 40-46.
[56] Brunet M, Morestin F; Walter-Leberre H. Failure analysis of anisotropic sheet-metals using a non-local plastic damage model [J]. Journal of Materials Processing Technology, 2005, 170(1-2): 457-470.
[57] Huang HM, Pan J, Tang SC. Failure prediction in anisotropic sheet metals under forming operations with consideration of rotating principal stretch directions [J]. International Journal of Plasticity, 2000, 16(6): 611-633.
[58] Chow CL, Yu LG, Tai WH, et al. Prediction of forming limit diagrams for AL6111-T4 under non-proportional loading [J]. International Journal of Mechanical Sciences, 2001, 43: 471-486.
[59] Chow CL, Yang XJ, Chu E. Prediction of forming limit diagram based on damage coupled kinematic-isotropic hardening model under nonproportional loading [J]. Journal of Engineering Materials and Technology-Transactions of the ASME, 2002, 124(2): 259-265.
[60] Chow CL, Jie M. Anisotropic Damage-coupled Sheet Metal Forming Limit Analysis [J]. International Journal of Damage Mechanics, 2009, 18(4): 371-392.
[61] Hambli R, Mkaddem A, Potiron A. Damage prediction in L-bending processes using FEM [J].International Journal of Advanced Manufacturing Technology, 2003, 22: 12-19.
[62] Guo YQ, Li YM, Bogard F, et al. An efficient pseudo-inverse approach for damage modeling in the sheet forming process [J]. Journal of Materials Processing Technology, 2004, 151(1-3): 88-97.
[63] Chan LC, Cheng CH, Jie M, et al. Damage-based formability analysis for TWBs [J]. International Journal of Damage Mechanics, 2005, 14(1): 83-96.
[64] Teixeira P, Santos AD, Pires FMA, et al. Finite element prediction of ductile fracture in sheet metal forming processes [J]. Journal of Materials Processing Technology, 2006, 177(1-3): 278-281.
[65] Khelifa M, Oudjene M, Khennane A. Fracture in sheet metal forming: Effect of ductile damage evolution [J]. Computers and Structures, 2007, 85(3-4): 205-212.
[66]林忠钦,李淑慧,于忠奇,等.车身覆盖件冲压成形仿真[M].北京:机械工业出版社, 2005.
[67] Hill R. The Mathematical Theory of Plasticity [M]. London: Oxford University Press, 1950.
[68] Wenner ML. On work hardening and springback in plane strain draw forming [J]. Journal Applied Metal Working, 1983, 2(4): 277–286.
[69] Wang C, Kinzel G, Altan T. Mathematical modeling of plane-strain bending of sheet and plate [J]. Journal of Materials Processing Technology, 1993, 39(3-4): 279-304.
[70] Zhang DJ, Cui ZS, Ruan XY, et al. An analytical model for predicting springback and side wall curl of sheet after U-bending [J]. Computational Materials Science, 2007, 38(4): 707-715.
[71] Lee MG, Kim JH, Chung K, et al. Analytical springback model for lightweight hexagonal close-packed sheet metal [J]. International Journal of Plasticity, 2009, 25(3): 399-419.
[72] Oliveira MC, Alves JL, Chaparro BM, et al. Study on the influence of work-hardening modeling in springback prediction [J]. International Journal of Plasticity, 2007, 23: 516-543.
[73] Gau JT, Kinzel GL. An experimental investigation of the influence of the Bauschinger effect on springback predictions [J]. Journal of Materials Processing Technology, 2001, 108: 369-375.
[74]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海:上海交通大学博士学位论文, 2006.
[75] Keeler SP, Backofen WA. Plastic instability and fracture in sheets stretched over rigid punches [J]. Transactions of American Society for Metals, 1963, 56: 25-48.
[76] Goodwin GM. Application of strain analysis to sheet metal forming problems in the press shop [J]. SAE Paper No. 680093, 1968: 380-387.
[77]陈劼实,周贤宾.板料成形极限的理论预测与数值模拟研究[J].塑性工程学报, 2004, 11(1): 13-17.
[78] Raghavan KS. A simple technique to generate inplane forming limit curves and selected applications [J]. Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science, 1995, 26(8): 2075-2084.
[79] Friebe H, Galanulis K, Erne O, et al. FLC determination and forming analysis by optical measurement systems [C]. Proceedings of the FLC Zurich 2006. ETH Zurich, Switzerland, 2006.
[80] Swift HW. Plastic instability under plane stress [J]. Journal of the Mechanics and Physics of Solids, 1952, 1(1): 1-18.
[81] Hill R. On discontinuous plastic state with special reference to localized necking in thin sheets [J]. Journal of the Mechanics and Physics of Solids, 1952, 1(1): 19-30.
[82]肖景容,姜奎华.冲压工艺学[M].北京:机械工业出版社, 1999.
[83] Marcinia Z, Kuczynski K. Limit strains in the processes of stretch-forming sheet metal [J]. International Journal of Mechanical Sciences, 1967, 9: 609-620.
[84]苑世剑,何祝斌.板料成形性理论评价与深入研究[J].塑性工程学报, 2003, 10(3): 6-11.
[85] Kleemola HJ, Pelkkikangas MT. Effect of predeformation and strain path on the forming limits of steel,copper and brass [J]. Sheet Metal Industries, 1977, 63: 591-599.
[86] Arrieux R. Determination and use of the forming limit stress diagrams in sheet metal forming [J]. Journal of Materials Processing Technology, 1995, 53(1-2): 47-56.
[87] Storen S, Rice JR. Localized necking in thin sheets [J]. Journal of the Mechanics and Physics of Solids, 1975, 23(6): 421-441.
[88] Stoughton TB, Zhu XH. Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD [J]. International Journal of Plasticity 2004, 20(8-9): 1463-1486.
[89] Han HN, Kim KH. A ductile fracture criterion in sheet metal forming process [J]. Journal of Materials Processing Technology, 2003, 142(1): 231-238.
[90] Ozturk F, Lee D. Analysis of forming limits using ductile fracture criteria [J]. Journal of Materials Processing Technology, 2004, 147(3): 397-404.
[91] Yu ZQ, Lin ZQ, Zhao YX. Evaluation of fracture limit in automotive aluminium alloy sheet forming [J]. Materials and Design [J]. 2007, 28(1): 203-207.
[92] Vallellano C, Guzmán C, García-Lomas FJ. Prediction of ductile failure in the stretch-forming of AA2024 sheets [C]. NUMIFORM’2007, Materials Processing and Design: Modeling, Simulation and Applications. Porto, Portugal, 2007.
[93] Ozturk F, Lee D. A new methodology for ductile fracture criteria to predict the forming limits [J]. Journal of Materials Engineering and Performance, 2007, 16(2): 224-228.
[94] Freudenthal AM. The inelastic behavior of engineering materials and structures [M]. New York: John Wiley & Sons, 1950.
[95] Cockcroft MG, Latham DJ. Ductility and the workability of metals [J]. Journal of the Institute of Metals, 1968, 96: 33-39.
[96] Brozzo P, Deluca B, Rendina R. A new method for the prediction of formability in metal sheets [C]. Proceedings of the Seventh Biennial Conference on Sheet Metal Forming and Formability. International Deep Drawing Research Group, 1972.
[97] Norris DM, Reaugh JE, Moran B, et al. A plastic-strain, mean-stress criterion for ductile fracture [J]. Journal of Engineering Materials and Technology-Transactions of the ASME, 1978, 100: 279-286.
[98] Oyane M, Sato T, Okimoto K, et al. Criteria for ductile fracture and their applications [J]. Journal of Mechanical working and Technology, 1980, 4: 65-81.
[99] Jain M, Allin J, Lloyd DJ. Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet [J]. International Journal of Mechanical Sciences, 1999, 41: 1273-1288.
[100] Ragab AR. A model for ductile fracture based on internal necking of spheroidal voids [J]. Acta Materialia, 2004, 52: 3997-4009.
[101] Komori K. Ductile fracture criteria for simulating shear by node separation method [J]. Theoretical and Applied Fracture Mechanics, 2005, 43: 101-114.
[102]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[J].哈尔滨:哈尔滨工业大学博士学位论文, 2003.
[103] Takuda H, Tanaka Y, Hatta N. Finite element analysis of forming limit in bore expanding of aluminium alloy sheets [J]. Archive of Applied Mechanics, 1998, 68(7-8): 566-576.
[104] Takuda H, Hatta N. Numerical analysis of the formability of an aluminum 2024 alloy sheet and its alloy sheet and its laminates with steel sheets [J]. Metallurgical and Materials Transactions A, 1998, 29A(11): 2829-2834.
[105] Takuda H, Yoshii T, Hatta N. Finite-element analysis of the formability of a magnesium-based alloy AZ31 sheet [J]. Journal of Materials Processing Technology, 1999, 89-90: 135-140.
[106] Takuda H, Hatta N. Numerical analysis of formability of a commercially pure zirconium sheet in some sheet forming processes [J]. Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 1998, 242(1-2): 15-21.
[107] Takuda H, Mori K, Hatta N. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals [J]. Journal of Materials Processing Technology, 1999, 95(1-3): 116-121.
[108] Hambli R, Reszka M. Fracture criteria identification using an inverse technique method and blanking experiment [J]. International Journal of Mechanical Sciences, 2002, 44: 1349-1361.
[1]余寿文,冯西桥.损伤力学[M]. 1997,北京:清华大学出版社.
[2] Gurson AL. Continuum theory of ductile rupture by void nucleation and growth: part I-Yield criteria and flow rules for porous ductile media [J]. Journal of Engineering Materials and Technology-Transactions of the ASME, 1977, 99: 2-15.
[3] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions [J]. International Journal of Fracture, 1981, 17: 389-407.
[4] Tvergaard V. On localization in ductile materials containing spherical voids [J]. International Journal of Fracture, 1982, 18: 237-252.
[5] Prat F, Grange M, Besson J, et al. Behavior and rupture of hydrided ZIRCALOY-4 tubes and sheets [J]. Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science, 1998, 29(6): 1643-1651.
[6] Besson J, Devillers-Guerville L, Pineau A. Modeling of scatter and size effect in ductile fracture: application to thermal embrittlement of duplex stainless steels [J]. Engineering Fracture Mechanics, 2000, 67(2): 169-190.
[7] Berdin C, Dong MJ, Prioul C. Local approach of damage and fracture toughness for nodular cast iron [J]. Engineering Fracture Mechanics, 2001, 68: 1107-1117.
[8] Rachik M, Roelandt JM, Maillard A. Some phenomenological and computational aspects of sheet metal blanking simulation [J]. Journal of Materials Processing Technology, 2002, 128(1-3): 256-265.
[9]于忠奇,杨玉英,王永志,等.基于韧性断裂准则的铝合金板材成形极限预测[J].中国有色金属学报, 2003, 13(5): 1223-1226.
[10] NUMISHEET'2002. Proceedings of the 5th international conference and workshop on numerical simulation of 3D sheet metal forming processes [C]. Jeju island, Korea, 2002.
[11]吴永礼.计算固体力学方法[M].北京:科学出版社, 2003.
[12]林忠钦,李淑慧,于忠奇,等.车身覆盖件冲压成形仿真[M].北京:机械工业出版社, 2005.
[13] Hosford WF. Comments on anisotropic yield criteria [J]. International Journal of Mechanical Sciences, 1985, 27(7-8): 423-427.
[14]倪向贵.板料成形过程力学行为及数值模拟技术的研究[D].合肥:中国科学技术大学博士学位论文, 2000.
[15] Barlat F, Lian J. Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions [J]. International Journal of Plasticity, 1989, 5: 51-66.
[16] Barlat F, Lege DJ, Brem JC. A six-component yield function for anisotropic materials [J]. International Journal of Plasticity, 1991, 7(7): 693-712.
[17] Barlat F, Becker RC, Hayashida Y, et al. Yielding description of solution strengthened aluminum alloys [J]. International Journal of Plasticity, 1997, 13(4): 385-401.
[18] Barlat F, Maeda Y, Chung K, et al. Yield function development for aluminum alloy sheets [J]. Journal of the Mechanics and Physics of Solids, 1997, 45(11-12): 1727-1763.
[19] Barlat F, Brem JC, Yoon JW, et al. Plane stress yield function for aluminum alloy sheets-Part I: theory [J]. International Journal of Plasticity, 2003, 19(9): 1297-1319.
[20] Hill R. The Mathematical Theory of Plasticity [M]. London: Oxford University Press, 1950.
[21]北川浩.塑性力学基础[M].北京:高等教育出版社, 1986.
[22] ABAQUS User's Manual Version6.6, Hibbitt, Karlsson & Sorenson, Inc., 2006.
[23]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海:上海交通大学博士学位论文, 2006.
[24] Hill R. Theoretical plasticity of textured aggregates [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1979. 75: 179-191.
[25] Hill R. Constitutive modeling of orthotropic plasticity in sheet metals [J]. Journal of the Mechanics and Physics of Solids, 1990, 38(3): 405-417.
[26] Hill R. A user-friendly theory of orthotropic plasticity in sheet metals [J]. International Journal of Mechanical Sciences, 1993, 35(1): 19-25.
[27] Hosford WF. A generalized isotropic yield criterion [J]. Journal of Applied Mechanics-Transactions of the ASME, 1972, 39: 607-609.
[28] Hosford WF. The plasticity of crystal and polycrystals [M]. Oxford: Oxford university press, 1992.
[29] Hosford WF. On the crystallographic basis of yield criteria [J]. Textures and Microstructures, 1996. 26-27: 479-493.
[30]王自强,段祝平.塑性细观力学[M].北京:科学出版社, 1995.
[31] McClintock FA. A criterion for ductile fracture by growth of holes [J]. Journal of Applied Mechanics-Transactions of the ASME, 1968, 35: 363-371.
[32] Rice JR, Tracey DM. On the ductile enlargement of voids in triaxial stress fields [J]. Journal of the Mechanics and Physics of Solids, 1969, 17(3): 201-217.
[33] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile test bar [J]. Acta Metallurgica, 1984, 32: 157-169.
[34] Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars [J]. Journal of the Mechanics and Physics of Solids, 1984, 32(6): 461-490.
[35] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids [J]. International Journal of Solids and Structures, 1988, 24(8): 835-853.
[36] Chu CC, Needleman A. Void nucleation effects in biaxially stretched sheets [J]. Journal of Engineering and Materials Technology, 1980, 102: 249-256.
[37] Doege E, Eldsoki T, Seibert D. Prediction of necking and wrinkling in sheet-metal forming [J]. Journal of Materials Processing Technology, 1995, 50(1-4): 197-206.
[38] Chen ZT, Worswick MJ, Pilkey AK, et al. Damage percolation during stretch flange forming of aluminum alloy sheet [J]. Journal of the Mechanics and Physics of Solids 2005, 53(12): 2692-2717.
[39] Betegon C, del Coz JJ, Penuelas I. Implicit integration procedure for viscoplastic Gurson materials [J].Computer Methods in Applied Mechanics and Engineering, 2006, 195(44-47): 6146-6157.
[40] Aravas N. On the numerical integration of a class of pressure-dependent plasticity models [J]. International Journal for Numerical Methods in Engineering, 1987, 24: 1395-1416.
[41] Zhang ZL. Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models [J]. Computer Methods in Applied Mechanics and Engineering, 1995, 121(1-4): 29-44.
[42] Simo JC, Taylor RL. Consistent tangent operators for rate independent elastoplasticity [J]. Computer Methods in Applied Mechanics and Engineering, 1985, 48: 101-119.
[43] Simo JC, Hughes TJR. Computational Inelasticity [M]. New York: Springer-Verlag, 1998.
[44] Belytschko T, Liu WK, Moran B.连续体和结构的非线性有限元[M].北京:清华大学出版社2002.
[45] Tang CY, Fan JP, Lee TC. Simulation of necking using a damage coupled finite element method [J]. Journal of Materials Processing Technology, 2003, 139(1-3): 510-513.
[46] Lievers WB, Pilkey AK, Lloyd DJ. Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys [J]. Acta Materialia, 2004, 52(10): 3001-3007.
[47] NUMISHEET'2005. Proceedings of the 6th international conference and workshop on numerical simulation of 3D sheet metal forming processes [C]. Detroit MI, USA, 2005.
[48] NUMISHEET'93. Proceedings of the 2nd international conference and numerical simulation of 3D sheet metal forming processes [C]. Isehara, Japan, 1993.
[49] Bernauer G, Brocks W. Micro-mechanical modelling of ductile damage and tearing-results of a European numerical round robin [J]. Fatigue & Fracture of Engineering Materials & Structures, 2002, 25: 363-384.
[50] Danckert J. Experimental investigation of a square-cup deep-drawing process [J]. Journal of Materials Processing Technology, 1995, 50(1-4): 375-384.
[1] Hollomon JH. Tensile deformation [J]. Transacions of the American Institute of Mining and Metallurgical Engineers, 1945, 162: 268-290.
[2] Voce E. The relationship between stress and strain for homogeneous deformation [J]. Journal of the Institute of Metals, 1948, 74: 537-562.
[3] Swift HW. Plastic instability under plane stress [J]. Journal of the Mechanics and Physics of Solids, 1952, 1: 1-18.
[4]中华人民共和国国家标准.金属薄板和薄带塑性应变比(r值)试验方法,理化检验-物理分册, 2000, 36(11): 520-523.
[5]林忠钦,李淑慧,于忠奇,等.车身覆盖件冲压成形仿真[M].北京:机械工业出版社, 2005.
[6] Benallal A, Berstad T, B?rvik T, et al. An experimental and numerical investigation of the behaviour of AA5083 aluminium alloy in presence of the Portevin–Le Chatelier effect [J]. International Journal of Plasticity, 2008, 24(10): 1916-1945.
[7] B?hlke T, BondárG, Estrin Y, et al. Geometrically non-linear modeling of the Portevin-Le Chatelier effect [J]. Computational Materials Science, 2009, 44(4): 1076-1088.
[8]江慧丰,张青川,徐毅豪,等.时效对Al-Cu合金中锯齿形流动的影响[J].金属学报, 2006, 42(2): 139-142.
[9]钟群鹏,赵子华.断口学[M].北京:高等教育出版社, 2006.
[10]上海交通大学《金属断口分析》编写组.金属断口分析[M].北京:国防工业出版社, 1979.
[11]崔约贤.金属断口分析[M].哈尔滨:哈尔滨工业大学出版社, 1998.
[1]周储伟,杨卫,方岱宁.金属基复合材料的强度与损伤分析[J].固体力学学报, 2000, 21(2): 161-165.
[2] Steglich D, Brocks W. Micromechanical modelling of the behaviour of ductile materials including particles [J]. Computational Materials Science, 1997, 9(1-2): 7- 17.
[3] Mahnken R. Aspects on the finite-element implementation of the Gurson model including parameter identification [J]. International Journal of Plasticity 1999, 15(11): 1111-1137.
[4]黄西成,陈裕泽,陈勇梅,等. 2169钢细观损伤参数识别[J].材料工程, 2007(4): 50-52.
[5] Sun DZ, Siegele D, Voss B, et al. Application of local damage models to the numerical analysis of ductile rupture [J]. Fatigue & Fracture of Engineering Materials & Structures, 1989, 12(3): 201-212.
[6] Steglich D, Siegmund T, Brocks W. Micromechanical modeling of damage due to particle cracking in reinforced metals [J]. Computational Materials Science, 1999, 16(1-4): 404-413.
[7]车洪艳,朱亮,陈剑虹.有限元反推法评定AA6014铝合金的损伤参数[J].机械工程材料, 2007, 31(7): 57-59,68.
[8] Zhang ZL. A sensitivity analysis of material parameters for the Gurson constitutive model [J]. Fatigue & fracture of engineering materials & structures, 1996, 19(5): p. 561-570.
[9] Bonora N. Identification and measurement of ductile damage parameters [J]. Journal of Strain Analysis for Engineering Design, 1999, 34(6): 463-478.
[10] Brunet M, Morestin F, Walter-Leberre H. Failure analysis of anisotropic sheet-metals using a non-local plastic damage model [J]. Journal of Materials Processing Technology, 2005, 170(1-2): 457-470.
[11] Croix P, Lauro, F, Oudin J, et al. Improvement of damage prediction by anisotropy of microvoids [J].Journal of Materials Processing Technology, 2003, 143-144: 202-208.
[12] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile test bar [J]. Acta Materialia, 1984, 32: 157-169.
[13] Springmann M, Kuna M. Determination of ductile damage parameters by local deformation fields: measurement and simulation [J]. Archive of Applied Mechanics, 2006, 75(10-12): 775-797
[14] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids [J]. International Journal of Solids and Structures, 1988, 24(8): 835-853.
[15]梁瑞.损伤材料参数对16MnR钢断裂影响研究[D].兰州:兰州理工大学硕士学位论文, 2004.
[16] Abendroth M, Kuna M. Identification of ductile damage and fracture parameters from the small punch test using neural networks [J]. Engineering Fracture Mechanics, 2006, 73(6): 710-725.
[17] Corigliano A, Mariani S, Orsatti B. Identification of Gurson-Tvergaard material model parameters via Kalman filtering technique. I. theory [J]. International Journal of Fracture, 2000, 104(4): 349-373.
[18] Negre P, Steglich D, Brocks W. Crack extension in aluminium welds: a numerical approach using the Gurson-Tvergaard-Needleman model [J]. Engineering Fracture Mechanics, 2004, 71(16-17): 2365-2383.
[19] Lievers WB, Pilkey AK, Lloyd DJ. Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys [J]. Acta Materialia, 2004, 52: 3001-3007.
[20] Zhang ZL, Niemi E. Analyzing ductile fracture using dual dilational constitutive equations [J]. Fatigue & Fracture of Engineering Materials & Structures, 1994, 17(6): 695-707.
[21]夏伯忠.正交试验法[M].长春:吉林人民出版社, 1985.
[22]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海:上海交通大学博士学位论文, 2006.
[23]上海市科学技术交流站.正交试验设计法:多因素的试验方法[M].上海:上海人民出版社, 1975.
[24]王晓林.蒙皮拉形过程有限元数值模拟技术研究[D].北京:北京航空航天大学博士学位论文, 1999.
[25] Huang YM. The formability limitation of the hole-flanging process [J]. Journal of Materials Processing Technology, 2001, 117(1-2): 43-51.
[26]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[D].哈尔滨:哈尔滨工业大学博士学位论文, 2003.
[27]吴贵生.试验设计与数据处理[M].北京:冶金工业出版社, 1997.
[1] Roll K. Simulation of sheet metal forming-necessary developments in the future [C]. NUMISHEET’2008. Interlaken, Switzerland, 2008: 3-11.
[2] Taylor L, Cao J, Karafillis AP, et al. Numerical simulations of sheet-metal forming [J]. Journal of Materials Processing Technology, 1995, 50(1-4):168-179.
[3] Muhlich U, Brocks W. On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening [J]. Computational Mechanics, 2003, 31(6): 479-488.
[4] Aravas N. On the numerical integration of a class of pressure-dependent plasticity models [J]. International Journal for Numerical Methods in Engineering, 1987, 24: 1395-1416.
[5]焦明华,于军涛,解挺,等.板材冲压成形回弹模拟的评述[J].锻压技术, 2007, 32(6):1-6.
[6]朱东波,孙琨,李涤尘,等.板料成形回弹问题研究新进展[J].塑性工程学报, 2000, 7(1): 11-17.
[7]彭颖红.金属塑性成形仿真技术[M].上海:上海交通大学出版社, 1999.
[8]美国ABAQUS公司. ABAQUS有限元软件6.4版入门指南[M].北京:清华大学出版社, 2004.
[9] Liu GR, Quek SS.有限元法实用教程[M].长沙:湖南大学出版社, 2004.
[10]李尚健.金属塑性成形过程模拟[M].北京:机械工业出版社, 2002.
[11] Mughrabi H, Johann Bauschinger. Pioneer of modern materials testing [J]. Materials Forum, 1987, 10(1): 5-10.
[12] Abel A. Historical perspectives and some of the main features of the Bauschinger effect [J]. Materials Forum, 1987, 10(1): 11-26.
[13] Tvergaard V. Effect of kinematic hardening on localized necking in biaxially stretched sheets [J]. International Journal of Mechanical Sciences, 1978, 20: 651-658.
[14] Prager W. A new method of analyzing stresses and strains in work-hardening plastic solids [J]. Journal of Applied Mechanics-Transactions of the ASME, 1956, 23: 493-496.
[15] Ziegler H. A modification of Prager's hardening rule [J]. Quarterly of Applied Mathematics, 1959, 17: 55-65.
[16]张冬娟.板料冲压成形回弹理论及有限元数值模拟研究[D].上海:上海交通大学博士学位论文, 2006.
[17] Hodge P. Discussion of the Prager hardening law [J]. Journal of Applied Mechanics, 1957, 24: 482-484.
[18] Moroz Z. On the description of anisotropic work hardening [J]. Journal of Mechanics and Physics of Solids, 1967, 15: 163-175.
[19] Lemaitre J, Chaboche JL. Mechanics of Solid Materials [M] Cambridge: Cambridge University Press, 1990.
[20] Brunet M, Morestin F, Godereaux S. Nonlinear kinematic hardening identification for anisotropic sheet metals with bending-unbending tests [J]. Transactions of the ASME, Journal of Engineering Materials and Technology, 123: 378-383.
[21]林忠钦,李淑慧,于忠奇,等.车身覆盖件冲压成形仿真[M].北京:机械工业出版社, 2005.
[22] Sabourin F, Morestin F, Brunet M. Effect of non-linear kinematic hardening on spring-back analysis [C]. NUMISHEET'2002. Jeju island, Korea, 2002: 79-84
[23]张冬娟,崔振山,李玉强,等.材料强化模型对板料回弹量的影响[J].上海交通大学学报, 2006, 40(10): 1671-1674.
[1] Khelifa M, Oudjene M. Numerical damage prediction in deep-drawing of sheet metals [J]. Journal of Materials Processing Technology, 2008, 200(1-3): 71–76.
[2]梁炳文,陈孝戴,王志恒.板金成形性能[M].北京:机械工业出版社, 1999.
[3] Takuda H, Tanaka Y, Hatta N. Finite element analysis of forming limit in bore expanding of aluminium alloy sheets [J]. Archive of Applied Mechanics, 1998, 68(7-8): 566-576.
[4] Freudenthal AM. The inelastic behavior of engineering materials and structures [M]. New York: John Wiley & Sons, 1950.
[5] Cockcroft MG, Latham DJ. Ductility and the workability of metals [J]. Journal of the Institute of Metals, 1968, 96: 33-39.
[6] Brozzo P, Deluca B, Rendina R. A new method for the prediction of formability in metal sheets [C]. Proceedings of the Seventh Biennial Conference on Sheet Metal Forming and Formability. International Deep Drawing Research Group, 1972.
[7] Oh SI, Chen CC, Kobayashi S. Ductile fracture in axisymmetric extrusion and drawing [J]. Journal of Engineering for Industry-Transactions of the ASME, 1979, 101(2): 36-44.
[8] Norris DM, Reaugh JE, Moran B, et al. A plastic-strain, mean-stress criterion for ductile fracture [J]. Journal of Engineering Materials and Technology-Transactions of the ASME, 1978, 100: 279-286.
[9] Atkins AG. Possible explanation for unexpected departures in hydrostatic tension-fracture strain relations [J]. Metal Science, 1981, 15: 81-83.
[10] Oyane M, Sato T, Okimoto K, et al. Criteria for ductile fracture and their applications [J]. Journal of Mechanical working and Technology, 1980, 4: 65-81.
[11]郑长卿,雷登,周利等.韧性断裂细观力学的初步研究及其应用[M].西安:西北工业大学出版社, 1988.
[12]郑长卿,周利,张克实.金属韧性破坏的细观力学及其应用研究[M].北京:国防工业出版社, 1995.
[13]王晓春.金属材料韧性断裂模式的分析及其在压力容器中的应用[D].杭州:浙江大学博士学位论文, 2002.
[14]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[J].哈尔滨:哈尔滨工业大学博士学位论文, 2003.
[15] Takuda H, Mori K, Fujimoto H, et al. Prediction of forming limit in deep drawing of Fe/Al laminated composite sheets using ductile fracture criterion [J]. Journal of Materials Processing Technology, 1996, 60(1-4): 291-296.
[16] Takuda H, Hatta N. Numerical analysis of formability of a commercially pure zirconium sheet in some sheet forming processes [J]. Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 1998, 242(1-2): 15-21.
[17] Takuda H, Mori K, Fujimoto H, et al. Prediction of forming limit in bore-expanding of sheet metals usingductile fracture criterion [J]. Journal of Materials Processing Technology, 1999, 92-93: 433-438.
[18] Takuda H, Mori K, Hatta N. The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals [J]. Journal of Materials Processing Technology, 1999, 95(1-3): 116-121.
[19] Han HN, Kim KH. A ductile fracture criterion in sheet metal forming process [J]. Journal of Materials Processing Technology, 2003, 142(1): 231-238.
