Mechanics of deformation of carbon nanotubes

Abstract

The deformation mechanics of multi-walled carbon nanotubes (MWCNT) and vertically aligned carbon nanotube (VACNT) arrays were studied using analytical and numerical methods. An equivalent orthotropic representation (EOR) of the mechanical properties of MWCNTs was developed to model the anisotropic mechanical behavior of these tubes during various types of deformation. Analytical models of the micro-mechanical contact and deformation during nano-indentation and scratching of VACNTs were developed. The EOR model was developed based on finite element (FE) nested shell structural representation of MWCNTs. The EOR was used together with the FE method to simulate bending, axial compression and lateral compression. Results were compared with those of the nested shell model for 4-, 8-, 9-, 14-, and 19-walled carbon nanotubes. The comparison of axial and lateral compression results indicated that although MWCNTs have high strength and stiffness in the axial direction, they can exhibit significant radial deformability owing to their relatively compliant interwall normal and shear behaviors. The EOR results provide an improvement in computational efficiency as well as a successful replication of the overall deformation behavior including the initial linear elastic behavior and the onset of buckling of MWCNTs and the post-buckling compliance.

(cont.) The post-buckling progression in wavelength (a doubling of wavelength as deformation progresses) was not captured by the EOR model. Analytical predictions of the force-penetration depth during nano-indentation with a three-sided pyramidal shaped indentor tip were compared with results from macro-scale experiments, FE simulations and nano-indentation of VACNT forests. These comparisons indicated that the proposed nano-indentation micro-mechanical contact model captures effectively both the nonlinear deformation mechanics and buckling effects of MWCNTs. The effective bending modulus of two VACNT forest samples was found to be 1.10 TPa and 1.08 TPa. Similarly, results from the micro-mechanical contact model for nano-scratching were compared with the results from macro-scale experiments with a sharp tip and FE simulations with both sharp and Bekovich tips. The comparison of these results indicated that the proposed contact model is able to capture remarkably well the variation in vertical force with lateral indentor tip displacement. The proposed FE and analytical models offer computationally efficient methods for simulating large and complex systems of MWCNTs with a small penalty in precision.