面心立方多晶体塑性变形有限元模拟
|
摘要
本文以有限元理论和晶体塑性力学为基础,采用Voronoi图表模拟多晶体微观结构,并对建模过程中的两个主要因素:晶粒尺寸和晶粒取向以及计算过程中的两个主要因素:网格划分和晶粒数目对模型模拟计算结果的影响作了深入的讨论,最终建立了面心立方晶格的多晶体塑性变形模型。从细观层次(主要是指晶粒尺度)模拟研究了多晶体室温单向拉伸变形行为,以工业纯铜和GH4169为例,模拟计算了多晶体塑性变形过程的宏观应力应变响应,与实验结果进行比较,得到如下结论:
(1) Voronoi图表通过真实材料的几何学性质和拓扑性质,提供了平面晶格边界,在各向同性和稳定状态生长假设下,不同晶粒之间的边界可以用这些多面体很好的描述,而且它可以与晶核成形和随机生长过程作比较,在模拟多晶体材料中具有很好的可靠性和有效性;
(2)晶粒数目和网格划分的影响主要体现在计算精度要求上,晶粒数目的多少及网格划分的疏密代表了计算过程中模型离散点的数量多少,模型离散点数量越多,计算过程中对晶粒变形、转动情况的数学记录和描述数据点越多,模拟得到的结果也越精确,但相应的计算效率会大大降低。实际模拟计算时应综合考虑模拟计算的精度和效率,选取适当的晶粒数目和网格划分方法;
(3)晶粒取向对模拟计算的影响主要分为两种情况,对于理想条件下的材料,可选用完全随机分布的晶粒取向;对于含有较多织构的材料,选用织构取向。这两种情况得到的晶粒取向具有广泛的适应性,可用于不同加工状态下的真实材料中特殊晶粒取向的模拟;本文建立的Voronoi多晶体晶体结构模型重点关注于晶体结构对模型模拟结果的影响,而晶粒尺寸在本文模型中的影响很小,可以不考虑;
(4)综合上述主要的影响因素,建立面心立方多晶体塑性变形模型,并以纯铜多晶体和GH4169拉伸试验为例,对模拟计算结果进行了验证。验证结果表明,本文建立的面心立方多晶体模型具有较高的可靠性和有效性。
The poly-crystal plasticity finite element model at room temperature is set up in this thesis using the Voronoi diagram, based on finite element theories and crystal plasticity mechanics. During the modeling, three primary factors that maybe influence the model are discussed in details. Three primary influence factors are the number of the grains of the poly-crystal, the orientation of the grains and the density of the mesh partition. The model is established by taking into account these factors synthetically. By using the model, this thesis studies the macroscopic stress-strain responses of polycrystalline materials in a simple tensile test at room temperature in the meso-scale. Results of simulation are compared with experiments of the pure copper and GH4169. The following results can be concluded:
(i) The Voronoi diagram can be used to describe the microstructure of polycrystalline materials via the geometrical and topological properties in real materials. And it also can be used to compare with the form of crystal core and the growth of crystal randomly.
(ii) The influence of the size of the grains is not taken into account in this model. The number of the grains has a biggish influence on the results of the simulation. While increasing the number of the grains, results of the simulation go into better and better. The number of the grains in model should be chosen according to the requirement of the precision.
In this thesis, we chose universal type of the mesh and study the affection of the density of the mesh partition. Different density of the mesh partition reflects the amount of the elements that will be calculated during the calculation. Results will be more exact with more discrete elements in the crystal. For the responses of the macroscopic stress-strain, the effect of the density of the mesh partition is very small even if there is only one element for one grain.
(iii) Two types of the orientation of grains have been chosen to study the affection of the orientation, random and texture respectively. With different orientations of the grains, the macroscopic stress-strain responses of the poly-crystal have biggish difference. With the increment of the content of texture, the poly-crystal represents its anisotropies mightily. But the difference is not obvious if the orientation of the grains have been chosen random. The choice of the orientation of the grains should be determined by the materials accordingly.
(iv) It is showed that the model of this thesis is reliable and effective at simulation of the macroscopic stress-strain responses during plastic deformation of the poly-crystal by comparing with experiments for pure copper and GH4169.
(1) Voronoi图表通过真实材料的几何学性质和拓扑性质,提供了平面晶格边界,在各向同性和稳定状态生长假设下,不同晶粒之间的边界可以用这些多面体很好的描述,而且它可以与晶核成形和随机生长过程作比较,在模拟多晶体材料中具有很好的可靠性和有效性;
(2)晶粒数目和网格划分的影响主要体现在计算精度要求上,晶粒数目的多少及网格划分的疏密代表了计算过程中模型离散点的数量多少,模型离散点数量越多,计算过程中对晶粒变形、转动情况的数学记录和描述数据点越多,模拟得到的结果也越精确,但相应的计算效率会大大降低。实际模拟计算时应综合考虑模拟计算的精度和效率,选取适当的晶粒数目和网格划分方法;
(3)晶粒取向对模拟计算的影响主要分为两种情况,对于理想条件下的材料,可选用完全随机分布的晶粒取向;对于含有较多织构的材料,选用织构取向。这两种情况得到的晶粒取向具有广泛的适应性,可用于不同加工状态下的真实材料中特殊晶粒取向的模拟;本文建立的Voronoi多晶体晶体结构模型重点关注于晶体结构对模型模拟结果的影响,而晶粒尺寸在本文模型中的影响很小,可以不考虑;
(4)综合上述主要的影响因素,建立面心立方多晶体塑性变形模型,并以纯铜多晶体和GH4169拉伸试验为例,对模拟计算结果进行了验证。验证结果表明,本文建立的面心立方多晶体模型具有较高的可靠性和有效性。
The poly-crystal plasticity finite element model at room temperature is set up in this thesis using the Voronoi diagram, based on finite element theories and crystal plasticity mechanics. During the modeling, three primary factors that maybe influence the model are discussed in details. Three primary influence factors are the number of the grains of the poly-crystal, the orientation of the grains and the density of the mesh partition. The model is established by taking into account these factors synthetically. By using the model, this thesis studies the macroscopic stress-strain responses of polycrystalline materials in a simple tensile test at room temperature in the meso-scale. Results of simulation are compared with experiments of the pure copper and GH4169. The following results can be concluded:
(i) The Voronoi diagram can be used to describe the microstructure of polycrystalline materials via the geometrical and topological properties in real materials. And it also can be used to compare with the form of crystal core and the growth of crystal randomly.
(ii) The influence of the size of the grains is not taken into account in this model. The number of the grains has a biggish influence on the results of the simulation. While increasing the number of the grains, results of the simulation go into better and better. The number of the grains in model should be chosen according to the requirement of the precision.
In this thesis, we chose universal type of the mesh and study the affection of the density of the mesh partition. Different density of the mesh partition reflects the amount of the elements that will be calculated during the calculation. Results will be more exact with more discrete elements in the crystal. For the responses of the macroscopic stress-strain, the effect of the density of the mesh partition is very small even if there is only one element for one grain.
(iii) Two types of the orientation of grains have been chosen to study the affection of the orientation, random and texture respectively. With different orientations of the grains, the macroscopic stress-strain responses of the poly-crystal have biggish difference. With the increment of the content of texture, the poly-crystal represents its anisotropies mightily. But the difference is not obvious if the orientation of the grains have been chosen random. The choice of the orientation of the grains should be determined by the materials accordingly.
(iv) It is showed that the model of this thesis is reliable and effective at simulation of the macroscopic stress-strain responses during plastic deformation of the poly-crystal by comparing with experiments for pure copper and GH4169.
引文
1谢配良,盛伟,游庆.金属塑性成形过程的计算机模拟.锻压机械, 1997, 3(4): 45~48
2周思柱.金属成形的三维有限元模拟系统的发展及展望.锻压技术, 1998, 24(4): 46~50
3 G. L. Taylor. Plastic strain in metals. J. Inst. Metals, 1938,62(3): 307~324
4 R. Hill, J. R. Rice. Constitutive analysis of elastic-plastic crystal at arbitrary strain. J. Mech. Phys. Solids, 1972, 20(5): 401~413
5 Miyamoto. The design of finite element code for crystal plasticity. J. Inst. Metals, 1972, 2(11): 15~28
6 Asaro, R. J. Needleman. Texture development and strain hardening in rate dependent poly-crystals. Acta Metall. 1985, 33(8): 923~953
7 Veera Sundararaghavan, Nicholas Zabaras. Design of microsturcture-sensitive properties in elastic-viscoplastic poly-crystals using multi-scale homogenization. International Journal of Plasticity. 2006, 22(2): 1799~1824
8 J. Besson, R. Foerch. Large scale object-oriented finite element code design. Compute Methods Appl. Mech. Engrg. 1997, 142(2): 165~187
9 Barbe, F. Forest, S. Cailletaud. Intragranular behavior of polycrystalline aggregates. Int. J. Plasticity, 2001, 2(17): 537~563
10 Barbe, F. Decker, L. Jeulin, D. Cailletaud. Intergranular and intragranular behavior of polycrystalline aggregates. Int. J. Plasticity. 2002, 50(1): 133~148
11董湘怀.材料成型计算机模拟.机械工业出版社, 2002年1月第1版
12冯露,张克实,张光.延性单晶非均匀变形的三维有限元模拟.应用力学学报, 2002, 9(4): 5~9
13 O. Diard, S. Leclercq, G. Rousselier, G. Cailletaud. Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity Application to crystal plastivity model identification and the study of stress and strain fields near grain boundaries. International Journal of Plasticity. 2005, 21(1): 691~722
14宋晓艳,刘国权.基于计算机模拟的正常晶粒长大的三维特征和二维截面特征.材料研究学报, 1998, 12(3): 17~30
15 Asaro, J. R. Rice. Strain localization in ductile single crystals. J. Nech. Phys.Solids, 1977,25(5): 309~338
16 T. Alan, W. Thomas. Simulation of Metal Forming Process Application & Future Trends. Advanced Technology of Plasticity, 1999, 11(2): 23~40
17孙友松,刘天湖,肖小亭.面向新世纪的塑性加工技术.锻压机械, 2000, 15(2): 59~60
18溺向贵,林巨广.汽车覆盖件成形过程数值模拟技术研究发展.金属成形工艺, 1999, 3(6): 1~3
19李尚健主编.金属塑性成型过程模拟.机械工业出版社, 2002年4月第5版
20王勖成等编著.有限单元法基本原理和数值方法.清华大学出版社, 1997年5月第二版
21 E. R. Zen, J. H. Hollomon. Effect of Strain-Rate up on The Plastic Flow of Steel. Journal of App1ied Physics. 1994, 15(1): 22~28
22 K. P. Rao, E. B. Hawbolt. Development of Constitutive Relationship using Compression Testing of a Medium Carbon Steel. Journal of Materials Engineering Technology. 1992, 114(1): 116~123
23 L. X. Zhou, T. N. Baker. Effects of Dynamic and Metadynamic Recrystallization on Microstructures of Wrought IN718 due to Hot Deformation. Materials Science and Engineering A. 1995, 196(2): 89~95
24 J. M. Zhang, Z. Y. Gao, J. Y. Zhuang, Z. Y. Zhong, P. Janschek. Strain-rate Hardening Behavior of Superalloy IN718. Journal of Materials Processing Technology. 1997, 128(70): 252~257
25 G. Shen, S. L. Semiatin, R. Shivpuri. Modeling Microstructural Developing during the Forging of Waspaloy. Metallurgy and Materials Transaction A. 1995, 36(2): 1795~1804
26刘东,罗子健. GH4169合金热加工过程中的显微组织演化数学模型.中国有色金属学报. 2003, 13(1): 1211~1218
27 R. A. Jaramillo, F. S. Suarez, J. A. Plyburn, D. E. Camus. Evaluation of an IN718 Microstructure Evolution Model. Superalloys718, 625, 706 and various Derivatives. E. A. Loria, TMS. 1997, 18(23): 257~277
28刘文昌. Inconel 718合金在冷热变形条件下组织变化的研究.哈尔滨工业大学博士学位论文. 1997: 79~91
29 Y. S. Na, J. T. Yeom, N. K. Park, J. Y. Lee. Simulation of Microstructures for Alloy 718 Blade Forging using 3D FEM Simulator. Journal of MaterialsProcessing Technology. 2003, 141(3): 337~342
30 Serge Yefimov. Discrete dislocation and nonlocal crystal plasticity modeling. Netherlands Institute for Metals Research. 1997, 101(3): 201~325
31 J. L. Chaboche, G. Cailletaud. Integration methods for complex plastic constitutive equations. Compute Methods Appl. Mech. Engrg. 1996, 133(2): 125~155
32 R. Foerch, J. Besson, G.. Cailletaud, P. Pilvin. Polymorphic Constitutive Equations in Finite Element Codes. Comput Methods Appl. Mech. Engrg. 1997, 142(3): 204~322
33 L. P. Evers, W. A. M. Brekelmans, M. G.. D. Geers. Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. International Journal of Solids and Structures. 2004, 41(2): 5209~5230
34黄晓旭,蔡大勇,刘庆,姚枚.多晶与单晶铜塑性变形行为的相关性.中国有色金属学报. 2001, 2(11): 2002~2358
35王勖成编著.有限单元法.清华大学出版社, 2003年7月第1版
36 Zhigang Fan, Yugong Wu, Xuanhe Zhao,Yuzhu Lu. Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres. Computational Materials Science. 2004, 29(12): 301~308
37石亦平,周玉蓉. ABAQUS有限元分析实例详解.机械工业出版社. 2006年7月第1版
38刘卫国主编. MATLAB程序设计教程.中国水利水电出版社. 2005年3月第
1版
39刘国权.材料三维显微组织形态研究进展与展望. CT理论与应用研究. 2000, 5(9): 148~153
40黄乾尧,李汉康.高温合金.冶金工业出版社, 2000年6月第2版
41 J. L. Burger, R. R. Biederman and W. H. Couts. The Effects of starting Condition on the Aging Response of As-Forged Alloy 718.in“Superalloy 718-Metallurgy and Applications”, eds. E. A. Loria, TMS, 1989, 26(32): 207~217
42鲁凤鸣,金槿秀. GH4169合金涡轮盘件长期时效组织稳定性的研究.金属学报(增刊), 1995, 31(7): 14~16
43 B. Pieraggi and J. F. Uginet. Fatigue and Creep Properties in Relation with Alloy718 Microstructure. In“Superalloys718,625,706 and Various Derivatives”, eds. E. A. Loria, TMS, 1994, 18(3): 535~544
44杜金辉,庄景云,邓群等.应力集中及晶粒形态对GH4169合金性能的影响.金属学报(增刊), 1995, 31(7): 17~21
45冶军.美国镍基高温合金.北京科学出版社, 1979年8月第2版
46 M. Chang, P. Au, T. Terada and A.K. Koul. Damage Tolerance of Alloy Turbine Disc Material.“Superalloys 1992”, eds. S. D. Antolovich et al., TMS, 1992, 17(23): 447~456
47 A. W. Dix, J. M. Hyzak, R. P. Singh. Application of Ultra Fine Grain Alloy 718 Forging Billet.“Superalloys 1992”, eds. S. D. Antolovich et al., TMS, 1992, 13(4): 23~32
48凌斌,钟炳文,杨玉荣. GH169合金的相变研究.航空材料学报. 1994, 1(4): 1~7
49杨玉荣.变形GH4169(Inconel718)合金的发展与应用. GH4169合金应用研究文集. 1996, 2(13): 16~21
50 K. Resgect, I. E. Leomow, W. J. Roth et al. Ordered Mesoporous Molecular Sieves Synthesized by a Liquid-Crystal Template Mechanism. Nature. 1992, 13(359): 710~712
2周思柱.金属成形的三维有限元模拟系统的发展及展望.锻压技术, 1998, 24(4): 46~50
3 G. L. Taylor. Plastic strain in metals. J. Inst. Metals, 1938,62(3): 307~324
4 R. Hill, J. R. Rice. Constitutive analysis of elastic-plastic crystal at arbitrary strain. J. Mech. Phys. Solids, 1972, 20(5): 401~413
5 Miyamoto. The design of finite element code for crystal plasticity. J. Inst. Metals, 1972, 2(11): 15~28
6 Asaro, R. J. Needleman. Texture development and strain hardening in rate dependent poly-crystals. Acta Metall. 1985, 33(8): 923~953
7 Veera Sundararaghavan, Nicholas Zabaras. Design of microsturcture-sensitive properties in elastic-viscoplastic poly-crystals using multi-scale homogenization. International Journal of Plasticity. 2006, 22(2): 1799~1824
8 J. Besson, R. Foerch. Large scale object-oriented finite element code design. Compute Methods Appl. Mech. Engrg. 1997, 142(2): 165~187
9 Barbe, F. Forest, S. Cailletaud. Intragranular behavior of polycrystalline aggregates. Int. J. Plasticity, 2001, 2(17): 537~563
10 Barbe, F. Decker, L. Jeulin, D. Cailletaud. Intergranular and intragranular behavior of polycrystalline aggregates. Int. J. Plasticity. 2002, 50(1): 133~148
11董湘怀.材料成型计算机模拟.机械工业出版社, 2002年1月第1版
12冯露,张克实,张光.延性单晶非均匀变形的三维有限元模拟.应用力学学报, 2002, 9(4): 5~9
13 O. Diard, S. Leclercq, G. Rousselier, G. Cailletaud. Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity Application to crystal plastivity model identification and the study of stress and strain fields near grain boundaries. International Journal of Plasticity. 2005, 21(1): 691~722
14宋晓艳,刘国权.基于计算机模拟的正常晶粒长大的三维特征和二维截面特征.材料研究学报, 1998, 12(3): 17~30
15 Asaro, J. R. Rice. Strain localization in ductile single crystals. J. Nech. Phys.Solids, 1977,25(5): 309~338
16 T. Alan, W. Thomas. Simulation of Metal Forming Process Application & Future Trends. Advanced Technology of Plasticity, 1999, 11(2): 23~40
17孙友松,刘天湖,肖小亭.面向新世纪的塑性加工技术.锻压机械, 2000, 15(2): 59~60
18溺向贵,林巨广.汽车覆盖件成形过程数值模拟技术研究发展.金属成形工艺, 1999, 3(6): 1~3
19李尚健主编.金属塑性成型过程模拟.机械工业出版社, 2002年4月第5版
20王勖成等编著.有限单元法基本原理和数值方法.清华大学出版社, 1997年5月第二版
21 E. R. Zen, J. H. Hollomon. Effect of Strain-Rate up on The Plastic Flow of Steel. Journal of App1ied Physics. 1994, 15(1): 22~28
22 K. P. Rao, E. B. Hawbolt. Development of Constitutive Relationship using Compression Testing of a Medium Carbon Steel. Journal of Materials Engineering Technology. 1992, 114(1): 116~123
23 L. X. Zhou, T. N. Baker. Effects of Dynamic and Metadynamic Recrystallization on Microstructures of Wrought IN718 due to Hot Deformation. Materials Science and Engineering A. 1995, 196(2): 89~95
24 J. M. Zhang, Z. Y. Gao, J. Y. Zhuang, Z. Y. Zhong, P. Janschek. Strain-rate Hardening Behavior of Superalloy IN718. Journal of Materials Processing Technology. 1997, 128(70): 252~257
25 G. Shen, S. L. Semiatin, R. Shivpuri. Modeling Microstructural Developing during the Forging of Waspaloy. Metallurgy and Materials Transaction A. 1995, 36(2): 1795~1804
26刘东,罗子健. GH4169合金热加工过程中的显微组织演化数学模型.中国有色金属学报. 2003, 13(1): 1211~1218
27 R. A. Jaramillo, F. S. Suarez, J. A. Plyburn, D. E. Camus. Evaluation of an IN718 Microstructure Evolution Model. Superalloys718, 625, 706 and various Derivatives. E. A. Loria, TMS. 1997, 18(23): 257~277
28刘文昌. Inconel 718合金在冷热变形条件下组织变化的研究.哈尔滨工业大学博士学位论文. 1997: 79~91
29 Y. S. Na, J. T. Yeom, N. K. Park, J. Y. Lee. Simulation of Microstructures for Alloy 718 Blade Forging using 3D FEM Simulator. Journal of MaterialsProcessing Technology. 2003, 141(3): 337~342
30 Serge Yefimov. Discrete dislocation and nonlocal crystal plasticity modeling. Netherlands Institute for Metals Research. 1997, 101(3): 201~325
31 J. L. Chaboche, G. Cailletaud. Integration methods for complex plastic constitutive equations. Compute Methods Appl. Mech. Engrg. 1996, 133(2): 125~155
32 R. Foerch, J. Besson, G.. Cailletaud, P. Pilvin. Polymorphic Constitutive Equations in Finite Element Codes. Comput Methods Appl. Mech. Engrg. 1997, 142(3): 204~322
33 L. P. Evers, W. A. M. Brekelmans, M. G.. D. Geers. Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. International Journal of Solids and Structures. 2004, 41(2): 5209~5230
34黄晓旭,蔡大勇,刘庆,姚枚.多晶与单晶铜塑性变形行为的相关性.中国有色金属学报. 2001, 2(11): 2002~2358
35王勖成编著.有限单元法.清华大学出版社, 2003年7月第1版
36 Zhigang Fan, Yugong Wu, Xuanhe Zhao,Yuzhu Lu. Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres. Computational Materials Science. 2004, 29(12): 301~308
37石亦平,周玉蓉. ABAQUS有限元分析实例详解.机械工业出版社. 2006年7月第1版
38刘卫国主编. MATLAB程序设计教程.中国水利水电出版社. 2005年3月第
1版
39刘国权.材料三维显微组织形态研究进展与展望. CT理论与应用研究. 2000, 5(9): 148~153
40黄乾尧,李汉康.高温合金.冶金工业出版社, 2000年6月第2版
41 J. L. Burger, R. R. Biederman and W. H. Couts. The Effects of starting Condition on the Aging Response of As-Forged Alloy 718.in“Superalloy 718-Metallurgy and Applications”, eds. E. A. Loria, TMS, 1989, 26(32): 207~217
42鲁凤鸣,金槿秀. GH4169合金涡轮盘件长期时效组织稳定性的研究.金属学报(增刊), 1995, 31(7): 14~16
43 B. Pieraggi and J. F. Uginet. Fatigue and Creep Properties in Relation with Alloy718 Microstructure. In“Superalloys718,625,706 and Various Derivatives”, eds. E. A. Loria, TMS, 1994, 18(3): 535~544
44杜金辉,庄景云,邓群等.应力集中及晶粒形态对GH4169合金性能的影响.金属学报(增刊), 1995, 31(7): 17~21
45冶军.美国镍基高温合金.北京科学出版社, 1979年8月第2版
46 M. Chang, P. Au, T. Terada and A.K. Koul. Damage Tolerance of Alloy Turbine Disc Material.“Superalloys 1992”, eds. S. D. Antolovich et al., TMS, 1992, 17(23): 447~456
47 A. W. Dix, J. M. Hyzak, R. P. Singh. Application of Ultra Fine Grain Alloy 718 Forging Billet.“Superalloys 1992”, eds. S. D. Antolovich et al., TMS, 1992, 13(4): 23~32
48凌斌,钟炳文,杨玉荣. GH169合金的相变研究.航空材料学报. 1994, 1(4): 1~7
49杨玉荣.变形GH4169(Inconel718)合金的发展与应用. GH4169合金应用研究文集. 1996, 2(13): 16~21
50 K. Resgect, I. E. Leomow, W. J. Roth et al. Ordered Mesoporous Molecular Sieves Synthesized by a Liquid-Crystal Template Mechanism. Nature. 1992, 13(359): 710~712
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |