Numerical and analytical modelling of strength and toughness of carbon nanotubes and carbon nanotube reinforced nanocomposites

The exceptional mechanical properties of carbon nanotubes (CNTs) make them highly attractive as potential reinforcing constituents in next generation composites. CNTs can be used as toughening agents in ceramic, metal or polymer matrices. However, a major drawback is the weak van der Waals forces between walls of multi-walled CNTs (MWCNTs) and CNTs and the matrix. This makes for easy sliding between CNT walls and little energy absorption during pullout from the matrix. This has major, negative implications for overall composite strength and toughness. This thesis discusses the potential for addressing this deficiency through the creation of inter-wall covalent bonds which can result spontaneously during certain manufacturing techniques, or can be added deliberately through irradiation with electrons or ions. The topic is addressed via a set of three studies: a molecular dynamics study of MWCNTs with variable amounts of inter-wall bonds as well as intra-wall defects (vacancies); an analytical shear-lag model of load transfer within a MWCNT with inter-wall bonds for optimisation of inter-wall bond arrangement; and a finite element study of MWCNT pullout from a ceramic matrix, where the MWCNT has variable inter-wall bond density, and a "wavy" surface due to intermittent "missing" outer walls. In the first study it is shown that MWCNTs with inter-wall bonding are less sensitive to defects than single-wall carbon nanotubes (SWCNTs). The scaling of failure strength with defect size in a MWCNT with inter-wall bonding exceeds that of SWCNTs containing the same size initial intra-wall defect. For structural composite materials, the scaling of failure strength with defect size is an important design factor. In the second study, the required length for full load transfer between walls of MWCNTs is calculated via an analytical shear lag model developed for this thesis, and validated via molecular dynamics simulations. The simulations show that load transfer is sensitive to natural statistical fluctuations in the spatial distribution of the inter-wall bonding between pairs of walls, and such fluctuations generally increase the net load transfer length needed to fully load a MWCNT. Optimal load transfer is achieved when bonding is uniformly distributed axially, and all inter-wall regions have the same shear stiffness. Finally, in the third study, MWCNT-matrix pullout is investigated via a parametric finite element study covering variable material properties and a rough or wavy interfacial geometry. The most influential factors in determining energy absorption during pullout are identified. Interfacial roughness resists pullout and aids push-out over different portions of the pullout process, so a cracked nanocomposite with multiple MWCNTs would experience both crack closing and opening stresses. The net average pullout stress due to fibre bundles is then quite low relative to peak values, reducing energy dissipation. During pullout, significant stress concentrations develop that can cause premature fibre fracture. Results indicate that utilising interface roughness is not an effective strategy to improve composite strength and toughness. Instead, utilization of interstitial atoms between fibre and matrix, which can increase surface adhesion and friction, appears to be a better strategy. The results and conclusions presented in this thesis show that inter-wall coupling of MWCNTs facilitates load transfer between walls and is beneficial to overall composite performance. Although methods used to increase inter-wall coupling also induce structural defects, the benefits can significantly outweigh the detrimental effects of these defects.