Torsion and bending of micron-scaled structures
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F. Yang Institute of Computational Engineering and Science, Southwest Jiaotong University, Chengdu 610031, Sichuan, People’s Republic of China and Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China
D.C.C. Lam and P. Tong Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China (Received 6 June 2000; accepted 25 January 2001)
Typical microelectromechanical systems (MEMS) devices and packages are composed of micron-scaled structures. Experimental investigations on the effect of size on the deformation behavior of simple structures have shown that the deformation behavior of metals and polymers is size dependent. The size dependence in small structures is attributed to the contribution of nonnegligible strain gradients. In this work, torsion and bending of micron-sized rods and plates were analyzed by using a two-parameter model of strain-gradient plasticity. Microrod torsion and microplate bending experimental data were analyzed to determine the magnitude of the strain-gradient material parameters. The parametric analyses showed that conventional analysis is applicable only when the size of the structure is significantly larger than the material parameters, which are typically in the micron range. Strain-gradient analysis of micron-sized rod revealed that the presence of strain gradient increased the torque by three to nine times at the same twist. For MEMS structures with micron-sized features, conventional structural analysis without strain gradient is potentially inadequate, and strain-gradient analysis must be conducted to determine the elastoplastic behavior in the micron scale. I. INTRODUCTION
Devices in microelectronics are routinely micronsized. They are fabricated by using combinations of resin deposition, patterning, etching, and material depositions in sequence to create structures that are several microns wide and submicron thick. Thin films are built on top of substrates and each other, resulting in planar micronscaled structures. Microelectromechanical systems (MEMS) with space structures are built by using similar processing technologies and new non-silicon techniques. Although microelectronic and MEMS devices are both micron-scaled structures, mechanical deformation is more critical in MEMS than in microelectronics because MEMS have space structures and moving parts. Experimental investigations on the effect of size on deformation behavior of simple structures have shown that the deformation behavior of metal1–6 and polymer7,8 is size dependent. In torsion of small rods, experimental results indicated that the normalized torque needed to achieve the same twist for a 12-m-diameter rod is a)
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J. Mater. Res., Vol. 16, No. 4, Apr 2001 Downloaded: 15 Feb 2015
approximately three times higher than that of
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