A Model of the Mechanical Behavior of Vertically Aligned Carbon Nanotubes under Compression
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A carbon nanotube (CNT) turf is composed of an array of nominally parallel aligned nanotubes that are weakly bonded together by van der Waals (vdW) forces. The structure is very compliant in compression and tends to deform by a unique buckling mechanism whereby small-wavelength buckles form and collapse in sequence. Subsequent buckles form adjacent to the previous buckle such that the deformation propagates across the loading axis of the specimen. The deformation appears as a propagating front that separates a distinct unbuckled region from a region consisting of a regular array of small-wavelength buckles. This behavior is quite different from that of a single CNT which would exhibit beam-like buckling. An axial supported beam undergoes large-wavelength buckling, which implies that the buckle wavelength is determined by the size of the structure (length of the beam). Undoubtedly, the added constraint associated with interactions between nanotubes affects the characteristics of the deformation in CNT turfs. The purpose of this work is to propose a possible mechanism for the buckling behavior and test it with a mechanical model and computer simulations. From stress versus strain measurements during compression, a CNT turf exhibits clearly different loading and unloading paths that indicate energy dissipation. The dissipation may be the result of a microstructural transformation such as debonding/rebonding of tubes or due to internal friction that occurs as tubes slide relative to each other within the potential field of van der Waals interactions. This work will assess the role of internal friction in the deformation process and determine if it might lead to the observed deformation mechanism of buckle formation and propagation. For this analysis, internal friction is treated as viscous force on a CNT as it deforms through an effective medium which accounts for the interaction of a nanotube with surrounding tubes. Finite element analysis is used to calculate results of the model. It is found that the model exhibits progressive buckle formation from one end to the other end of the structure. The buckles form at a uniform size and propagate at a steady rate, which depend on the rate of compression. It is also found that buckling propagation occurs at a constant load such that the stress versus strain curve exhibits a distinct plateau. Buckle wavelength, plateau load and buckle forming rate are obtained as functions of the rate of compression, the bending stiffness of a nanotube and the viscosity of the effective medium. The bending stiffness characterizes elastic behavior of individual tubes in the turf and effective viscosity characterizes both the Vdw force between tubes and the density of tubes in the turf. The influences of nanotube geometry and material parameters on the deformation results are investigated.