单晶Cu纳米线加工硬化现象的分子动力学研究
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摘要
加工硬化现象普遍存在于金属塑性加工过程中。长久以来,这种现象一直吸引着人们的注意力。当在低温(T<0.3Tm)条件下施加应力时,加工硬化可以在2个甚至3个数量级内改变韧性材料的强度,因此许多学者对它进行了大量研究,但其中大多数研究仅局限于宏观范畴。晶体是由大量的原子有序排列而成,材料的强度来源于原子间的相互作用,塑性来源于原子间的相互运动,因此,直接从原子尺度上对材料的微观力学行为进行研究非常有必要。分子动力学方法可以直接对原子的运动进行观察,从而分析材料的变形机理。
为了研究纳米单晶材料的加工硬化现象,本文以分子动力学为主要研究手段,模拟了单晶Cu的三维拉伸、压缩过程,分析微观塑性变形机制,并研究了缺陷对材料力学性能的影响。
本文模拟采用EAM势函数描述原子间的相互作用情况,共轭梯度算法用于求解运动方程,并采用中心对称参数表征晶体缺陷类型。
在此基础上研究了单晶Cu纳米线0K下的单向拉伸、压缩过程。分别从位错机制、硬化现象及拉、压不对称性三个方面对模型的微观变形过程进行分析。结果表明:单晶铜纳米线的屈服通过{111}<112>部分位错的形核和扩展实现,塑性变形由堆垛层错的形成所主导。位错交割及位错与层错的相互作用可以引起屈服应力升高。研究最终发现,单晶纳米线没有加工硬化现象发生。
带孔洞的单晶Cu拉伸模拟主要研究了缺陷对材料弹性模量和屈服应力的影响规律。结果表明:随孔洞体积分数的增大,材料的弹性模量和屈服应力近线性降低,塑性变形提前。
The phenomenon of work-hardening prevalently consists in metal plastic forming. This phenomenon has attracted people’s attention for a long time. Work-hardening can change the strength of ductile material by two or three orders of magnitude when given stress in low temperature conditions(T<0.3Tm). Therefore, extensive studies have been carried out on it. While most of the studies only confine to the microscopic category. As the strength of materials results from the interactions of dislocations, the plastic deformation results from the mutual movement of dislocations, it is important to investigate the microscopic mechanical behavior on atomic scale. While the molecular dynamics simulation method is able to observe the motion of atoms, it can be used to investigate the deformation mechanism.
In order to study the work-hardening phenomenon of single crystal nano-materials, molecular dynamics simulations are carried out on the tension and compression process of single crystal copper. The effects of crystal defects on the material mechanical properties were studied. Some analysises on the plastic forming mechanism were given.
Embedded atom method and conjugate gradient method are used in this simulation. The centrosymmetry parameter is used to characterize crystal defects. With the molecular dynamics simulation mentioned, we then study the uniaxial tension and compression processes of single crystal Cu nano-wire in three dimensions under absolute zero temperature condition. In this dissertation, the research focuses on three aspects around the microscopic deformation mechanism: stress-strain analysis, dislocation mechanism and the unsymmetry of tension and compression. The results indicate that, nanowires yield via the nucleation and propagation of the {111}<112> partial dislocations. Formation of stacking fault is the dominant mechanism in the microscopic deformation of single crystal. Interaction of stacking fault and dislocation is the principal factor leading to the rising of yield stress. But we find that, there is no work-hardening in single crystal nano-wire.
The tension simulation of single crystal copper with void is mainly to study the influence of void volume fraction on elastic modulus and yield stress. The results show that, elastic modulus and yield stress decrease with increasing void volume fraction, the plastic deformation occurs in advance.
为了研究纳米单晶材料的加工硬化现象,本文以分子动力学为主要研究手段,模拟了单晶Cu的三维拉伸、压缩过程,分析微观塑性变形机制,并研究了缺陷对材料力学性能的影响。
本文模拟采用EAM势函数描述原子间的相互作用情况,共轭梯度算法用于求解运动方程,并采用中心对称参数表征晶体缺陷类型。
在此基础上研究了单晶Cu纳米线0K下的单向拉伸、压缩过程。分别从位错机制、硬化现象及拉、压不对称性三个方面对模型的微观变形过程进行分析。结果表明:单晶铜纳米线的屈服通过{111}<112>部分位错的形核和扩展实现,塑性变形由堆垛层错的形成所主导。位错交割及位错与层错的相互作用可以引起屈服应力升高。研究最终发现,单晶纳米线没有加工硬化现象发生。
带孔洞的单晶Cu拉伸模拟主要研究了缺陷对材料弹性模量和屈服应力的影响规律。结果表明:随孔洞体积分数的增大,材料的弹性模量和屈服应力近线性降低,塑性变形提前。
The phenomenon of work-hardening prevalently consists in metal plastic forming. This phenomenon has attracted people’s attention for a long time. Work-hardening can change the strength of ductile material by two or three orders of magnitude when given stress in low temperature conditions(T<0.3Tm). Therefore, extensive studies have been carried out on it. While most of the studies only confine to the microscopic category. As the strength of materials results from the interactions of dislocations, the plastic deformation results from the mutual movement of dislocations, it is important to investigate the microscopic mechanical behavior on atomic scale. While the molecular dynamics simulation method is able to observe the motion of atoms, it can be used to investigate the deformation mechanism.
In order to study the work-hardening phenomenon of single crystal nano-materials, molecular dynamics simulations are carried out on the tension and compression process of single crystal copper. The effects of crystal defects on the material mechanical properties were studied. Some analysises on the plastic forming mechanism were given.
Embedded atom method and conjugate gradient method are used in this simulation. The centrosymmetry parameter is used to characterize crystal defects. With the molecular dynamics simulation mentioned, we then study the uniaxial tension and compression processes of single crystal Cu nano-wire in three dimensions under absolute zero temperature condition. In this dissertation, the research focuses on three aspects around the microscopic deformation mechanism: stress-strain analysis, dislocation mechanism and the unsymmetry of tension and compression. The results indicate that, nanowires yield via the nucleation and propagation of the {111}<112> partial dislocations. Formation of stacking fault is the dominant mechanism in the microscopic deformation of single crystal. Interaction of stacking fault and dislocation is the principal factor leading to the rising of yield stress. But we find that, there is no work-hardening in single crystal nano-wire.
The tension simulation of single crystal copper with void is mainly to study the influence of void volume fraction on elastic modulus and yield stress. The results show that, elastic modulus and yield stress decrease with increasing void volume fraction, the plastic deformation occurs in advance.
引文
1.黄克智,肖纪美.材料的损伤断裂机理和宏微观力学理论.清华大学出版社, 1999: 36-61
2.秦克诚译.理论物理学中的计算机模拟方法.北京大学出版社, 1996: 16-45
3.罗旋.β-SiC表面及Al/SiC界面结构的分子动力学模拟.哈尔滨工业大学博士论文. 1997
4.赵宇军,姜明,曹培林.从头计算分子动力学.物理学进展. 1998, 18(1): 47-75
5. B.J. Alder, T.E. Wainwright. Studies in Molecular Dynamics General Methed. The Journal of Chemical Physics. 1959, 31(2): 459-466
6.严六明,严琪良,等.模型溶液的分子动力学模拟及扩散系数计算.华东理工大学学报. 1997, 23(4): 477-483
7. J.P. Hirth, J. Lothe. Theory of Dislocations. Wiley-Interscience, 1982
8. D. Hull, D.J. Bacon. Introduction to Dislocations. Butterworth Heinemann, 2002
9. T.H. Courtney. Mechanical Behavior of Materials. McGraw-Hill, 1990
10 M. Rhee, H.M. Zbib, J.P. Hirth, et al. Models For Long-/Short-range Interactions and Cross Slip in 3D Dislocation Simulation of BCC Single Crystals. Modeling Simul. Mater. Sci. Eng. 1998, 6(4): 467-492
11 M. Wen, D.L. Lin. Atomistic Process of Dislocation Cross-slip in Ni3Al. Scripta Mater. 1997: 265-268
12 S.J. Zhou, D.L Preston, F. Louchet. Investigation of Vacancy Formation by a Jogged Dissociated Dislocation with Large-scale Molecular Dynamics and Dislocation Energetics. Acta Mater. 1999: 2695-2703
13 M. Li, S.J. Zhou. Investigation of Jog Motion in Gamma-TiAl via Molecular Dynamics. Phil. Mag. Lett. 1999: 773-784
14 M. Li, W.Y. Chu, C.F. Qian, et al. Molecular Dynamics Simulation of Dislocation Intersections in Aluminum. Mat. Sci. Eng. 2003: 234-241
15 V. Bulatov, L. Hsiung, M. Tang, et, al. Dislocation Multi-junctions and Strain Hardening. Nature, 2006, 440(27): 1174-1178
16 M. Buehler, A. Hartmaier, M. Duchaineau, et, al. The Dynamical Complexity of Work-hardening: A Large-scale Molecular Dynamics Simulation. Acta Mech Sinica. 2005: 103-111
17 M.P. Allen, D.J. Tildesley. Computer Simulation of Liquids. OxfordUniversity Press, 1989
18 N.F. Mott. The Work Hardening of Metals. AIME, 1960: 962
19 F. Abraham, R. Walkup, H. Gao, et al. Simulating Materials Failure by Using up to One Billion Atoms and the World’s Fastest Computer: Work-hardening. Proceedings of the National Academy of Sciences. 2002, 99(9): 5783-5787
20 R.G. Hoagland, M.S. Daw, J.P. Hirth. Some Aspects of Forces and Fields in Atomic Models of Crack Tips. Journal of Materials Research.1991: 2565
21 S. Li, K.W. Gao, L.J. Qiao, F.X. Zhou, W.Y. Chu. Comput Mater Sci, 2001, 20: 143
22 V. Bulator, F. Abraham, L. Kubin, B. Devincre, S. Yip. Nature. 1998: 391- 669
23袁子洲,匡毅,陈学定,仇珊. ZGMn18Cr2Mo超高锰钢加工硬化机理研究.机械工程材料. 2005, 29(5): 9-11
24王建华,任立军.高锰钢加工硬化机理研究.煤矿机械. 2003: 24-26
25陈富生.高锰钢爆炸硬化机实验研究.武汉钢铁学院学报. 1991: 32-34
26王兆昌.奥氏体锰钢的综合加工硬化机理.钢铁研究学报. 1994: 27 -32
27李树索,陈希杰.超高锰钢加工硬化及耐磨的研究.钢铁研究学报, 1997: 28–31
28 R. Selinger, Z. Wang, W. Gelbart. Statistical Thermodynamic Approach to Fracture. Physical Review A. 1991, 43(8): 4396-400
29 S. Hu, M. Ludwig, P. Kizler, S. Schmauder. Atomistic Simulation of Deformation and Fracture ofα-Fe. Modelling Simul. Mater. Sci. Eng. 1998, 6(5): 567-568
30 M. Doyama. Simulation of Plastic Deformation of Small Iron and Copper Single Crystals. Nuclear Instruments and Methods Physics Research B. 1995, 102(1-4): 102-107
31 R. Lynden-Bell. A Simulation Study of Induced Disorder, Failure and Fracture of Perfect Metal Cryatals under Uniaxial Tension. Journal of Physics: Condensation of Matter. 1995, 44(1): 295-298
32 R.M. Lynden-Bell. Computer Simulations of Fracture at the Atomic Level. Science. 1994, 12(4): 1704-1705
33 J. Diao. Yield Strength Asymmetry in Metal Nanowires. Nano Letters. 2004, 4(10): 1863-1867
34 R. Komanduri. Molecular. Dynamics Simulation of Uniaxial Tension of Some Single-Crystal Cubic Metals at Nanolevel. International Journal of Mechanical Sciences. 2001, 43(10): 2237-2260
35梁海弋.纳米铜单晶拉伸力学性能的分子动力学模拟.中国科学技术大学学报. 2001, 31(4): 454-458
36文玉华,朱如曾,周富信等.分子动力学模拟的主要技术.力学进展. 2003, 33(1): 65-73
37 D. Rapaport. Art of Molecular Dynamics Simulation. Cambridge UniversityPress, 1995: 1-3
38陈强,草红红,黄海波.分子动力学中势函数研究.天津理工学院学报. 2004, 20(2): 101-105
39罗熙淳.基于分子动力学的微纳米加工表面形成机理研究.哈尔滨工业大学博士学位论文. 2002: 18-22
40 M. Daw, M. Baskes. Embedded-atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Physical Review B. 1984, 29: 6443-6453
41 Masao Doyama, Y. Kogure. Embedded Atom Potentials in Fcc and Bcc Metals. Computational Materials Science, 1999, 14(6): 80-86
42 L.Verlet.Computer“Experiments”on Classical Fluids.I.Thermodynamical Properties of Lennard-Jones Molecules.Phys.Rev. 1967, 159: 98-103
43吴恒安.纳米尺度下结构和材料力学行为的分子动力学模拟研究.中国科学技术大学博士学位论文. 2002: 12-21
44 Hoffmann K H, Schreiber M. Computational Physics. Berlin Heidelberg Springer-Verlag. 1996: 268-326
45周富信.宏观力学性质的微观模拟方法及其应用.清华大学出版社, 1997.
46 D.赫尔, D.培根,著.丁树深,李齐,译.位错导论.科学出版社, 1990
47 Cynthia L. Kelchner, S.J. Plimpton, J.C. Hamilton. Dislocation nucleation and defect structure during surface indentation. Physical Review B. 1998: 11085-11087
48张永军,韩静涛,韦东滨.金属内部裂纹愈合内变量及其演化分析.钢铁研究学报. 2004, 16(2): 59-61
49 Y.Mishin, M. Mehl, D. PapaconstantoPoulos, A.F.Voter. Phys.Rev. 2001
50 J. Krystyn, V. Vliet, S. Yip. Quantifying the Early Stage of Plasticity through Nanoscale Experiments and Simulation. Physical Review B. 2003, 67(6): 104-105
51梁海弋,倪向贵,王秀喜.表面效应对纳米铜杆拉伸性能影响的原子模拟.金属学报. 2001, 37 (8): 833-836
52 W. Wunderlich, Y. Ishida, R. Maurer. Scripta Metall Mater. 1990, 24: 403
53 M. Nastasi, D. Parkin, H. Gleiter. Mechanical Properties and Deformation Behavior of Materials Having Ultra-fine Microstructures. Kluwer, 1993
54 R.W. Siegel. Mater Sci Forum. 1997: 235
55 J. Huang, Y. Wu, H. Ye. Acta Mater. 1996, 44: 1211
56 R. Islamgaliev, F. Chmelik, R. Kuzel. Mat Sci Eng A. 1997: 234-236
57 A. Cottrell. Dislocations and Plastic Flow in Crystals. Oxford Clarendon Press, 1961
58 H. Gleiter. Nanocrystalline Materials. Progress in Materials Science, 1989, 33(4): 223-315
59 Z. Chen, Q. Yuan, J. Ding. Molecular Dynamics Simulations on the Consolidation Process and Relaxed Structure of Nanocrystalline Alopha-iron.Chinese Physics Letters. 1993, 10(2): 103-106
60 D.T. Read, J.W. Dally. A New Method for Measuring the Constitutive Properties of Thin Films. J. Mater. Res. 1992, 8(5): 1542-1549
61 M.P. Osterberg, S.D. Senturia. A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures. Journal of MEMS. 1997, 6(2): 107-118
62 W.C. Oliver. An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments. Journal of materials research. 1992, 7(6): 1564
63 G.M. Pharr, W.C. Oliver. Nanoindentation of Silver-Relations Between Hardness and Dislocation Structure. Journal of Materials Research. 1989, 4(1): 94-99
64 S.E. Grillo. Nano Indentation of Si, Gap, Ga, As, and Zn Single Crystals. Journal of Physics D. 2003, 36(1): l5-l9
2.秦克诚译.理论物理学中的计算机模拟方法.北京大学出版社, 1996: 16-45
3.罗旋.β-SiC表面及Al/SiC界面结构的分子动力学模拟.哈尔滨工业大学博士论文. 1997
4.赵宇军,姜明,曹培林.从头计算分子动力学.物理学进展. 1998, 18(1): 47-75
5. B.J. Alder, T.E. Wainwright. Studies in Molecular Dynamics General Methed. The Journal of Chemical Physics. 1959, 31(2): 459-466
6.严六明,严琪良,等.模型溶液的分子动力学模拟及扩散系数计算.华东理工大学学报. 1997, 23(4): 477-483
7. J.P. Hirth, J. Lothe. Theory of Dislocations. Wiley-Interscience, 1982
8. D. Hull, D.J. Bacon. Introduction to Dislocations. Butterworth Heinemann, 2002
9. T.H. Courtney. Mechanical Behavior of Materials. McGraw-Hill, 1990
10 M. Rhee, H.M. Zbib, J.P. Hirth, et al. Models For Long-/Short-range Interactions and Cross Slip in 3D Dislocation Simulation of BCC Single Crystals. Modeling Simul. Mater. Sci. Eng. 1998, 6(4): 467-492
11 M. Wen, D.L. Lin. Atomistic Process of Dislocation Cross-slip in Ni3Al. Scripta Mater. 1997: 265-268
12 S.J. Zhou, D.L Preston, F. Louchet. Investigation of Vacancy Formation by a Jogged Dissociated Dislocation with Large-scale Molecular Dynamics and Dislocation Energetics. Acta Mater. 1999: 2695-2703
13 M. Li, S.J. Zhou. Investigation of Jog Motion in Gamma-TiAl via Molecular Dynamics. Phil. Mag. Lett. 1999: 773-784
14 M. Li, W.Y. Chu, C.F. Qian, et al. Molecular Dynamics Simulation of Dislocation Intersections in Aluminum. Mat. Sci. Eng. 2003: 234-241
15 V. Bulatov, L. Hsiung, M. Tang, et, al. Dislocation Multi-junctions and Strain Hardening. Nature, 2006, 440(27): 1174-1178
16 M. Buehler, A. Hartmaier, M. Duchaineau, et, al. The Dynamical Complexity of Work-hardening: A Large-scale Molecular Dynamics Simulation. Acta Mech Sinica. 2005: 103-111
17 M.P. Allen, D.J. Tildesley. Computer Simulation of Liquids. OxfordUniversity Press, 1989
18 N.F. Mott. The Work Hardening of Metals. AIME, 1960: 962
19 F. Abraham, R. Walkup, H. Gao, et al. Simulating Materials Failure by Using up to One Billion Atoms and the World’s Fastest Computer: Work-hardening. Proceedings of the National Academy of Sciences. 2002, 99(9): 5783-5787
20 R.G. Hoagland, M.S. Daw, J.P. Hirth. Some Aspects of Forces and Fields in Atomic Models of Crack Tips. Journal of Materials Research.1991: 2565
21 S. Li, K.W. Gao, L.J. Qiao, F.X. Zhou, W.Y. Chu. Comput Mater Sci, 2001, 20: 143
22 V. Bulator, F. Abraham, L. Kubin, B. Devincre, S. Yip. Nature. 1998: 391- 669
23袁子洲,匡毅,陈学定,仇珊. ZGMn18Cr2Mo超高锰钢加工硬化机理研究.机械工程材料. 2005, 29(5): 9-11
24王建华,任立军.高锰钢加工硬化机理研究.煤矿机械. 2003: 24-26
25陈富生.高锰钢爆炸硬化机实验研究.武汉钢铁学院学报. 1991: 32-34
26王兆昌.奥氏体锰钢的综合加工硬化机理.钢铁研究学报. 1994: 27 -32
27李树索,陈希杰.超高锰钢加工硬化及耐磨的研究.钢铁研究学报, 1997: 28–31
28 R. Selinger, Z. Wang, W. Gelbart. Statistical Thermodynamic Approach to Fracture. Physical Review A. 1991, 43(8): 4396-400
29 S. Hu, M. Ludwig, P. Kizler, S. Schmauder. Atomistic Simulation of Deformation and Fracture ofα-Fe. Modelling Simul. Mater. Sci. Eng. 1998, 6(5): 567-568
30 M. Doyama. Simulation of Plastic Deformation of Small Iron and Copper Single Crystals. Nuclear Instruments and Methods Physics Research B. 1995, 102(1-4): 102-107
31 R. Lynden-Bell. A Simulation Study of Induced Disorder, Failure and Fracture of Perfect Metal Cryatals under Uniaxial Tension. Journal of Physics: Condensation of Matter. 1995, 44(1): 295-298
32 R.M. Lynden-Bell. Computer Simulations of Fracture at the Atomic Level. Science. 1994, 12(4): 1704-1705
33 J. Diao. Yield Strength Asymmetry in Metal Nanowires. Nano Letters. 2004, 4(10): 1863-1867
34 R. Komanduri. Molecular. Dynamics Simulation of Uniaxial Tension of Some Single-Crystal Cubic Metals at Nanolevel. International Journal of Mechanical Sciences. 2001, 43(10): 2237-2260
35梁海弋.纳米铜单晶拉伸力学性能的分子动力学模拟.中国科学技术大学学报. 2001, 31(4): 454-458
36文玉华,朱如曾,周富信等.分子动力学模拟的主要技术.力学进展. 2003, 33(1): 65-73
37 D. Rapaport. Art of Molecular Dynamics Simulation. Cambridge UniversityPress, 1995: 1-3
38陈强,草红红,黄海波.分子动力学中势函数研究.天津理工学院学报. 2004, 20(2): 101-105
39罗熙淳.基于分子动力学的微纳米加工表面形成机理研究.哈尔滨工业大学博士学位论文. 2002: 18-22
40 M. Daw, M. Baskes. Embedded-atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Physical Review B. 1984, 29: 6443-6453
41 Masao Doyama, Y. Kogure. Embedded Atom Potentials in Fcc and Bcc Metals. Computational Materials Science, 1999, 14(6): 80-86
42 L.Verlet.Computer“Experiments”on Classical Fluids.I.Thermodynamical Properties of Lennard-Jones Molecules.Phys.Rev. 1967, 159: 98-103
43吴恒安.纳米尺度下结构和材料力学行为的分子动力学模拟研究.中国科学技术大学博士学位论文. 2002: 12-21
44 Hoffmann K H, Schreiber M. Computational Physics. Berlin Heidelberg Springer-Verlag. 1996: 268-326
45周富信.宏观力学性质的微观模拟方法及其应用.清华大学出版社, 1997.
46 D.赫尔, D.培根,著.丁树深,李齐,译.位错导论.科学出版社, 1990
47 Cynthia L. Kelchner, S.J. Plimpton, J.C. Hamilton. Dislocation nucleation and defect structure during surface indentation. Physical Review B. 1998: 11085-11087
48张永军,韩静涛,韦东滨.金属内部裂纹愈合内变量及其演化分析.钢铁研究学报. 2004, 16(2): 59-61
49 Y.Mishin, M. Mehl, D. PapaconstantoPoulos, A.F.Voter. Phys.Rev. 2001
50 J. Krystyn, V. Vliet, S. Yip. Quantifying the Early Stage of Plasticity through Nanoscale Experiments and Simulation. Physical Review B. 2003, 67(6): 104-105
51梁海弋,倪向贵,王秀喜.表面效应对纳米铜杆拉伸性能影响的原子模拟.金属学报. 2001, 37 (8): 833-836
52 W. Wunderlich, Y. Ishida, R. Maurer. Scripta Metall Mater. 1990, 24: 403
53 M. Nastasi, D. Parkin, H. Gleiter. Mechanical Properties and Deformation Behavior of Materials Having Ultra-fine Microstructures. Kluwer, 1993
54 R.W. Siegel. Mater Sci Forum. 1997: 235
55 J. Huang, Y. Wu, H. Ye. Acta Mater. 1996, 44: 1211
56 R. Islamgaliev, F. Chmelik, R. Kuzel. Mat Sci Eng A. 1997: 234-236
57 A. Cottrell. Dislocations and Plastic Flow in Crystals. Oxford Clarendon Press, 1961
58 H. Gleiter. Nanocrystalline Materials. Progress in Materials Science, 1989, 33(4): 223-315
59 Z. Chen, Q. Yuan, J. Ding. Molecular Dynamics Simulations on the Consolidation Process and Relaxed Structure of Nanocrystalline Alopha-iron.Chinese Physics Letters. 1993, 10(2): 103-106
60 D.T. Read, J.W. Dally. A New Method for Measuring the Constitutive Properties of Thin Films. J. Mater. Res. 1992, 8(5): 1542-1549
61 M.P. Osterberg, S.D. Senturia. A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures. Journal of MEMS. 1997, 6(2): 107-118
62 W.C. Oliver. An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments. Journal of materials research. 1992, 7(6): 1564
63 G.M. Pharr, W.C. Oliver. Nanoindentation of Silver-Relations Between Hardness and Dislocation Structure. Journal of Materials Research. 1989, 4(1): 94-99
64 S.E. Grillo. Nano Indentation of Si, Gap, Ga, As, and Zn Single Crystals. Journal of Physics D. 2003, 36(1): l5-l9
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