Effect of substrate deformation in the nanowire/nanotube bending test
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Effect of substrate deformation in the nanowire/nanotube bending test Wingkin Chan, Yong Wang, Jianrong Li, Tong-Yi Zhang* Department of Mechanical Engineering, Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong, China ABSTRACT The present work analyses the effect of substrate deformation during the nanowire/nanotube bending test. An individual nanowire or nanotube is treated as a linear isotropic continuum. The substrate deformation is modeled by two coupled springs and the spring compliances are functions of the nanowire/nanotube diameter, and the Young moduli of the nanowire/nanotube and the substrates. An atomic potential is used to determine the adhesion between the nanowire/nanotube and its substrate. Consequently, a simple three dimensional Finite Element (FE) model is built to calculate the spring compliances. The load-displacement relation, which takes into account of substrate deformation, is derived in a closed form, which can be reduced to the load-displacement relations based on the simply-supported ends and the built-in ends. The numerical results indicate that the substrate deformation has a great influence on the determination of the Young modulus of a nanowire/nanotube from the bending test. The nanobridge test on carbon nanotubes is taken as an example to demonstrate the feasibility of the developed method. INTRODUCTION The rapid development of nanomaterials has fueled activities in nanotechnology and nanomechanics [1]. Nanotechnology will enable the integration of mechanical, electrical, optical and magnetic functions into devices and/or systems on micron and smaller scales, such as sensors, actuators and micro/nano-machines [2]. The establishment of nanomechanics theories and experiments to understand and characterize the mechanical behavior and properties of nanomaterials is of critical importance in the development of nanotechnology. Nanomechanics studies the mechanical behavior of materials on the nanometer scale by coupling the conventional boundary-value solutions to the atomistic analysis. It is now possible to understand the origin of material properties by calculation and to tailor-make a material from the atomic scale upwards by artificially building up the material structure one atomic layer at a time from selected atoms. One can achieve the desired material structure and functional properties and control the material’s chemical composition and the size, shape, and the *
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crystalline orientation. It is essential now to be able to understand and predict the reliability and the performance of structures and devices made of nanomaterials. Typical nanomaterials are nanotubes and nanowires, which have extremely high Young’s modulus, elongation, ultimate fracture strength and length-to-diameter ratios. Thereby they are ideal reinforcing fibres for composites. However, it is a great challenge to characterize nanotubes and nanowires mechanically because t
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