MEMS微结构力学性能的尺度效应研究
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摘要
随着科学技术的发展,微结构得到了广泛的应用。随之而来的微结构的设计和制造得到了大量的关注。越来越多的实验表明:当材料的本征长度为微米量级时,金属材料的力学性能呈现出很强的尺寸效应。经典的连续介质理论已经无法解释这些现象。因此,对微尺度下材料的力学性能研究将会对MEMS的发展带来巨大的影响。
经典弹性理论是建立在材料的均匀、连续等假设之上的,忽略了材料内部微结构对材料力学性能的影响。本文基于偶应力理论,在经典弹性理论基础上,引入偶应力和转动梯度,重新建立MEMS微结构的力学模型,推导其平衡方程、边界条件,并建立了在连续介质理论框架下基于偶应力理论的新的本构模型,和利用这个模型分析了细铜丝扭转和微薄板弯曲以及平板式电容加速度计的尺度效应行为。
应用高阶应变梯度理论分析微结构中孔边应力集中问题。在经典弹性理论基础上,引入高阶应力和其本构关系,推导出含有应变梯度效应的孔边应力集中问题的力学模型,并通过半逆解法,得出应力和高阶应力所对应的应力函数,从而获得其应力场,分析应力集中的尺度效应行为。
本文的结果,为MEMS微结构的设计和制造提供良好的参考价值。
There are extensive applications of micro-structures, along with the development of science and technology. Meantime, people focus their attentions on the design and manufacturing of micro-structures. A number of experiments are demonstrated that the mechanical properties of metal materials have intense size effects, when the length scale parameters of materials are at the level of micron dimension. The phenomenon can't explain by the traditional continuous medium theory. So, the research on mechanical properties of materials will accelerate the development of MEMS.
The traditional elastic theory, based on the hypothesis of material's continuity and uniformity, neglect the influence of inner micro-structure of the material. In this paper, the couple stress and rotation gradient are introduced, the mechanical model of micro-structure in MEMS is rebuild, the equilibrium equation and boundary condition are derived, the new constitutive relation based on the couple stress theory and elasticity theory is given. The size effect behaviors of thin brass-wire torsion, ultra-thin plate bending and plate-capacitive accelerometer are analyzed.
Using the high-order strain gradient theory, the stress concentration around a hole has been analyzed. The high-order stress and its constitutive relations are introduced, the stress fields of the stress and high-order stress are obtained. The size effect behavior of the stress concentration problem is investigated.
The results of this paper can provide a favorable referenced value for the design and manufacturing of micro-structure in MEMS.
经典弹性理论是建立在材料的均匀、连续等假设之上的,忽略了材料内部微结构对材料力学性能的影响。本文基于偶应力理论,在经典弹性理论基础上,引入偶应力和转动梯度,重新建立MEMS微结构的力学模型,推导其平衡方程、边界条件,并建立了在连续介质理论框架下基于偶应力理论的新的本构模型,和利用这个模型分析了细铜丝扭转和微薄板弯曲以及平板式电容加速度计的尺度效应行为。
应用高阶应变梯度理论分析微结构中孔边应力集中问题。在经典弹性理论基础上,引入高阶应力和其本构关系,推导出含有应变梯度效应的孔边应力集中问题的力学模型,并通过半逆解法,得出应力和高阶应力所对应的应力函数,从而获得其应力场,分析应力集中的尺度效应行为。
本文的结果,为MEMS微结构的设计和制造提供良好的参考价值。
There are extensive applications of micro-structures, along with the development of science and technology. Meantime, people focus their attentions on the design and manufacturing of micro-structures. A number of experiments are demonstrated that the mechanical properties of metal materials have intense size effects, when the length scale parameters of materials are at the level of micron dimension. The phenomenon can't explain by the traditional continuous medium theory. So, the research on mechanical properties of materials will accelerate the development of MEMS.
The traditional elastic theory, based on the hypothesis of material's continuity and uniformity, neglect the influence of inner micro-structure of the material. In this paper, the couple stress and rotation gradient are introduced, the mechanical model of micro-structure in MEMS is rebuild, the equilibrium equation and boundary condition are derived, the new constitutive relation based on the couple stress theory and elasticity theory is given. The size effect behaviors of thin brass-wire torsion, ultra-thin plate bending and plate-capacitive accelerometer are analyzed.
Using the high-order strain gradient theory, the stress concentration around a hole has been analyzed. The high-order stress and its constitutive relations are introduced, the stress fields of the stress and high-order stress are obtained. The size effect behavior of the stress concentration problem is investigated.
The results of this paper can provide a favorable referenced value for the design and manufacturing of micro-structure in MEMS.
引文
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[3]沈桂芬,张宏庆,韩宇,范军,付世,丁德宏,姚朋军.微机电系统的研究与分析,传感技术学报.2004,17(1):168-171
[4]李志坚.微电子机械系统(MEMS)发展展望[J].电子科技导报,1999(1):2-9
[5]李旭辉.MEMS发展应用现状.传感器与微系统,2006,25(5):7-9
[6]刘媛,邴志刚,刘景泰.MEMS及其在生物医学领域中的应用.天津工程师范学院学报,2005,15(4):40-42
[7]冯亚林,郝一龙.MEMS技术及其在军事中的应用.微电子学,2006,36(1):66-69
[8]马宝华,高世桥.抓住MEMS技术带来的机遇,实现我国引信技术大跨度发展.中国国防科研报告.1996
[9]黄志奇,杜平安,卢凉.微机电系统科学与技术的现状研究[J].机械设计,2003,20(11):4-6
[10]童志义,赵晓东.国内外MEMS器件现状及发展趋势[J].电子工业专用设备,2002,31(4):200-206
[11]梅涛,孔德义,张培强等.微电子机械系统的力学特性与尺度效应.机械强度,2001,23(4):373-379
[12]唐祯安,王立鼎.关于微尺度理论[J].光学精密工程,2001,9(6):493-498
[13]王琪民.微型机械导论[M].中国科学技术出版社,2003
[14]J W Judy.Micro-electro-mechanical systems(MEMS).Fabrication,design and application[J].Smart Materials and Structures.2001,10(6)
[15]Spring S M.Materials issues in micro electro mechanical systems(MEMS)[J].Acta Materialia.2000,48(1)
[16]Tang W C.Overview of micro electro mechanical systems and design process[C].Proceedings-Design Automation Conference.1997
[17]潘武,钟先信,巫正中.无线通信系统中的微尺度射频单元[J].光学精密工程,2001,9(4):304-309
[18]周兆英,叶雄英,崔天宏等.微米纳米技术及微型机电系统[J].光学精密工程,1998,6(1):1-7
[19]邵培革,王立鼎,任延同.微机械元件和仪器新进展[J].光学精密工程,1999,7(1):10-15
[20]魏悦广.机械微型化所面临的科学难题——尺度效应.世界科技研究与发展,2002, 22(2):57-61
[21]张泰华,杨业敏,赵亚溥等.MEMS材料力学性能的测试技术[J].力学进展,2002,32(4):545-562
[22]张广平,高岛和希,肥俊矢吉.微米尺寸不锈钢的变形与疲劳行为的尺寸效应.金属学报,2005,41(4):337-341
[23]Tien C L,Chen G.Challenges in microscale conductive and radiative heat transfer[J].ASME Journal of Heat Transfer,1994,166(11):799-807
[24]Dedkov G V.Experimental and Theoretical aspects of modem nanotribology[J].Phys Stat,2000,(A)179(3):3-75
[25]Fleck N A,Muller G M,Ashby M F,Hutchinson J W.Strain gradient plasticity:theory and experiment.Acta Meta Mater,1994,42:475-487
[26]Stolken J S,Evans A G.A microbend test method for measuring the plasticity length scale.Acta Mater,1998,46:5109-5115
[27]Lloyd D J.Particle reinforced aluminum and magnesium matrix composites.Int Master Rev,1994,39:1-23
[28]Yang J,Cady C,Hu M S.Effects of damage on the flow strength and ductility of a ductile Al-alloy reinforced with SiC particulates.Acta Metall Master,1990,38:2613-2619
[29]Ling Z.Deformation behavior and microstructure effect in 2124Al/SiCp composite.J Comp Master,2000,34:101-105
[30]Doemer M F,Nix W D.A method for interpreting the data from depth-sensing indentation instructures.J Master Res,1986,1:601-611
[31]Nix W D.Mechanical properties of tin flims.Metall Trans,1989,20A:2217-2245
[32]Stemashenko N A,Walls M G,Brown L M,Milman Y V.Microindentation on W and Mo oriental single crystals:an STM study.Acta Metall Master,1993,41:2855-2865
[33]Ma Q,Clarke D R.Size dependent hardness in silver single crystals.J Master Res,1995,10:853-863.
[34]McElhaney K W,Vlassak J J,Nix W D.Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments.J Master Res,1998,13:1300-1306
[35]Elssner G,Kom D,Ruehke M.The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramc bicrystals.Scripta Metall Master,1994,31:1037-1042
[36]陈少华,王自强.应变梯度理论进展.力学进展,2003,33(2):207-216
[37]Toupin R A.Elastic materials with couple-stresses.Arch Rational Mech Anal,1962,11:385-414
[38]Mindlin R D,Tiersten H F.Effect of couple-stresses in linear elasticity.Arch Rational Mech Anal,1962,11:415-448
[39]Mindlin R D.Micro-structrue in linear elasticity.Arch Ration Mech Anal,1964,16:51-78
[40]黄克智,邱信明,姜汉卿.应变梯度理论的新进展(一)——偶应力理论和SG理论.机械强度,1999,21(2):81-87
[41]黄克智,邱信明,姜汉卿.应变梯度理论的新进展(二)——基于细观机制的MSG 应变梯度塑性理论.机械强度,1999,21(3):161-165
[42]Fleck N A,Hutchinson J W.A phenomenological theory for strain gradient effects in plasticity.J Mech Phs Solids,1993,41:1825-1857
[43]黄克智,黄永刚.固体本构关系.清华大学出版社,1999
[44]邱信明.基于细观机制的应变梯度理论[D].北京:清华大学博士学位论文,2001
[45]陈少华.应变梯度理论及其应用[D].北京:中国科学院力学研究所博士后学位论文,2001
[46]余寿文.复杂微力——电系统的细微尺度力学.力学进展,1995,25(2):249-258
[47]Ho C M,Tai Y C.微电子机械系统和流体流动.力学进展,1998,28(2):250-272
[48]赵亚溥,王立森,孙克豪.Tabor数,黏着数与微尺度黏着弹性接触理论.力学进展,2000,30(4):529-537
[49]赵亚溥.微型飞行器中的关键力学和智能材料问题.中国科学基金,2000,1:11-14
[50]傅卫平,方宗德.微系统动力学中的若干非线性问题.力学进展,2002,32(1):17-25
[51]石庚辰.微机电系统技术[M].北京:国防工业出版社,2002
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