On the Flexural Characteristics of Multi-walled Carbon Nanotubes
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On the Flexural Characteristics of Multi-walled Carbon Nanotubes Rong Bai, Justin Molenaur Polymer Engineering Department University of Akron Akron, OH 44236-0301 R. Byron Pipes, Schools of Materials Engineering, Aeronautics and Astronautics, and Chemical Engineering Purdue University ABSTRACT We use an analytical solution for bending of coaxial orthotropic cylinders to model the flexural deformation of multi-walled nanotubes with any number of layers. The simulation results show that the bending stiffness of the MWNT increases with the number of nanotube layers. For fixed number of layers, MWNT with larger inner radius has greater bending stiffness. The bending stiffness also increases with out layer radius. For certain outer radius, smaller inner radius results in a larger stiffness. The effective elastic modulus of the MWNT also increases with the number of layers and the outer radius. For the same value of the outer radius, the MWNT with smaller inner radius has a larger effective elastic modulus. As the number of layers increases, the effective modulus approaches the in-plane elastic modulus of graphene. In this work we find that the interface conditions, i.e., perfect bonding or no friction, do not affect the bending stiffness and effective elastic modulus of the MWNT. Furthermore, the cross-section of MWNT does not show any warping under bending, which suggest the classic beam theory is applicable in determining the flexural response of MWNT. INTRODUCTION The discovery of carbon nanotubes has led tremendous amount of research in scientific and engineering fields. Carbon nanotubes are anticipated to have elastic modulus of 1 TPa (1000GPa) with the strength around 30 GPa besides other remarkable physical properties. Due to its excellent mechanical properties [1, 2, 3, 4, 5], such as the highest strength and the highest stiffness, it possibly provides us the next generation of super strong, lightweight and highly elastic composite materials. Fundamental understanding of carbon nanotube mechanical properties at nano-scale is essential for us to fully utilize the potential of nanotubes to reinforce composites. Multiwall nanotubes can be considered as candidates to improve bending rigidity since it has higher stiffness compared to single wall nanotubes. In an earlier publication [6] one of the authors studied the effective properties of single-walled carbon nanotubes and their hexagonal arrays and developed relationships for the effective density and Young’s modulus as well as mixing rules for conversion of weight fraction to volume fraction. It was implied in these relationships that in mixtures, the effective engineering properties must account for the entire volume occupied. Since carbon nanotubes may be viewed as hollow cylindrical elements at the nanoscale, the volume occupied by the carbon atoms provides the stiffness and mass for the system. But in computing effective engineering properties the volume contained inside the hollow
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cylinder must also be considered when computing effective
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