Sarah-Jane V. Frankland

THE STRESS-STRAIN BEHAVIOR OF POLYMER-NANOTUBE COMPOSITES FROM MOLECULAR DYNAMICS SIMULATION

Stress–strain curves of polymer–carbon nanotube composites generated from molecular dynamics simulations of a single-walled carbon nanotube embedded in polyethylene are presented. A comparison is made between the response to mechanical loading of a composite with a long, continuous nanotube (replicated via periodic boundary conditions) and the response of a composite with a short, discontinuous nanotube. Both composites are mechanically loaded in the direction of, and transverse to, the nanotube axis. The long-nanotube composite shows an increase in the stiffness relative to the polymer and behaves anisotropically under the different loading conditions considered. The short-nanotube composite shows no enhancement relative to the polymer, most probably because of its low aspect ratio. The stress–strain curves from molecular dynamics simulations are compared with corresponding rule-of-mixtures predictions. Published by Elsevier Ltd.

Effect of Nanotube Functionalization on the Elastic Properties of Polyethylene Nanotube Composites

The effects of the chemical functionalization of a single-wall carbon nanotube in nanotube/polyethylene composites on the bulk elastic properties are presented. Constitutive equations are established for composites containing both functionalized and nonfunctionalized nanotubes using an equivalent-continuum modeling technique. The elastic properties of both composite systems are predicted for amorphous and crystalline polyethylene matrices with various nanotube lengths, volume fractions, and orientations. The results indicate that for the specific composite materials considered in this study most of the elastic stiffness constants of the composite with functionalized nanotubes are either less than or equal to those of the composite without functionalized nanotubes.

Transverse mechanical properties of single-walled carbon nanotube crystals. Part I: determination of elastic moduli

Abstract Carbon nanotubes naturally tend to form crystals in the form of hexagonally packed bundles. An accurate determination of the effective mechanical properties of nanotube bundles is important in order to assess potential structural applications such as reinforcement in future composite material systems. Although the intratube axial stiffness is on the order of 1 TPa due to a strong network of carbon–carbon bonds, the intertube interactions are controlled by weaker, nonbonding van der Waals forces which are orders of magnitude less. A direct method for calculating effective material constants is implemented in the present study. The Lennard–Jones potential is used to model the nonbonding cohesive forces. A complete set of transverse moduli is obtained and shown to exhibit a transversely isotropic constitutive behavior. The predicted elastic constants obtained using the direct method are compared with available published results obtained from other methods.

Investigation of the effect of single wall carbon nanotubes on interlaminar fracture toughness of woven carbon fiber—epoxy composites:

Single wall carbon nanotubes (SWCNTs) were introduced in the interlaminar region of woven carbon fiber—epoxy composites and the mode-I delamination behavior was investigated. Pristine (P-SWCNT) and functionalized (F-SWCNT) nanotubes were sprayed in the mid-plane of these laminates and delamination was initiated using a teflon pre-crack insert. The composite laminates were produced using vacuum-assisted resin transfer molding process. The interlaminar fracture toughness (ILFT) represented by mode-I critical strain energy release rate (GIc) for the initiation of delamination was measured using double cantilever beam tests. The specimens with pristine nanotubes and functionalized nanotubes showed a small effect on the ILFT. The specimens with P-SWCNTs showed stable crack growth and the potential for enhanced crack bridging along with slightly higher GIc than F-SWCNT specimens. Scanning electron microscopy images showed enhanced fiber—matrix interfacial bonding in the specimens with F-SWCNTs. However, large unstable crack propagation was observed in these F-SWCNT specimens from load—displacement curves and crack propagation videos. This research helps in understanding the differences in mechanisms by addition of functionalized and unfunctionalized (pristine) nanotubes to the woven carbon fiber—epoxy matrix composite laminates.

THE EFFECT OF CHEMICAL FUNCTIONALIZATION ON MECHANICAL PROPERTIES OF NANOTUBE/POLYMER COMPOSITES

The effects of the chemical functionalization of a carbon nanotube embedded in a nanotube/polyethylene composite on the bulk elastic properties are presented. Constitutive equations are established for both functionalized and nonfunctionalized nanotube composites systems by using an equivalent-continuum modeling technique. The elastic properties of both composites systems are predicted for various nanotube lengths, volume fractions, and orientations. The results indicate that for the specific composite material considered in this study, most of the elastic stiffness constants of the functionalized composite are either less than or equal to those of the non-functionalized composite.

Multiscale Analysis of Delamination of Carbon Fiber-Epoxy Laminates with Carbon Nanotubes

A multi-scale analysis is presented to parametrically describe the Mode I delamination of a carbon fiber/epoxy laminate. In the midplane of the laminate, carbon nanotubes are included for the purposes of selectively enhancing the fracture toughness of the laminate. To analyze carbon fiber epoxy carbon nanotube laminate, the multi-scale methodology presented here links a series of parameterizations taken at various length scales ranging from the atomistic through the micromechanical to the structural level. At the atomistic scale molecular dynamics simulations are performed in conjunction with an equivalent continuum approach to develop constitutive properties for representative volume elements of the molecular structure of components of the laminate. The molecular-level constitutive results are then used in the Mori-Tanaka micromechanics to develop bulk properties for the epoxy-carbon nanotube matrix system. In order to demonstrate a possible application of this multi-scale methodology, a double cantilever beam specimen is modeled. An existing analysis is employed which uses discrete springs to model the fiber bridging affect during delamination propagation. In the absence of empirical data or a damage mechanics model describing the effect of CNTs on fracture toughness, several tractions laws are postulated, linking CNT volume fraction to fiber bridging in a DCB specimen. Results from this demonstration are presented in terms of DCB specimen load-displacement responses.

Calculation of Non-bonded Forces due to Sliding of Bundled Carbon Nanotubes

An important consideration for load transfer in bundles of single-walled carbon nanotubes is the nonbonded (van der Waals) forces between the nanotubes and their effect on axial sliding of the nanotubes relative to each other. In this research, the non-bonded forces in a bundle of seven hexagonally packed (10,10) single-walled carbon nanotubes are represented as an axial force applied to the central nanotube. A simple model, based on momentum balance, is developed to describe the velocity response of the central nanotube to the applied force. The model is verified by comparing its velocity predictions with molecular dynamics simulations that were performed on the bundle with different force histories applied to the central nanotube. The model was found to quantitatively predict the nanotube velocities obtained from the molecular dynamics simulations. Both the model and the simulations predict a threshold force at which the nanotube releases from the bundle. This force converts to a shear yield strength of 10.5-11.0 MPa for (10,10) nanotubes in a bundle.

Multi-scale Rule-of-Mixtures Model of Carbon Nanotube/Carbon Fiber/Epoxy Lamina

A unidirectional carbon fiber/epoxy lamina in which the carbon fibers are coated with single-walled carbon nanotubes is modeled with a multi-scale method, the atomistically informed rule-of-mixtures. This multi-scale model is designed to include the effect of the carbon nanotubes on the constitutive properties of the lamina. It included concepts from the molecular dynamics/equivalent continuum methods, micromechanics, and the strength of materials. Within the model both the nanotube volume fraction and nanotube distribution were varied. It was found that for a lamina with 60% carbon fiber volume fraction, the Youngs modulus in the fiber direction varied with changes in the nanotube distribution, from 138.8 to 140 GPa with nanotube volume fractions ranging from 0.0001 to 0.0125. The presence of nanotube near the surface of the carbon fiber is therefore expected to have a small, but positive, effect on the constitutive properties of the lamina.

Local Elastic Constants For Epoxy-Nanotube Composites From Molecular Dynamics Simulation

A method from molecular dynamics simulation is developed for determining local elastic constants of an epoxy/nanotube composite. The local values of C11, C33, K12, and K13 elastic constants are calculated for an epoxy/nanotube composite as a function of radial distance from the nanotube. While the results possess a significant amount of statistical uncertainty resulting from both the numerical analysis and the molecular fluctuations during the simulation, the following observations can be made. If the size of the region around the nanotube is increased from shells of 1 to 6 in thickness, then the scatter in the data reduces enough to observe trends. All the elastic constants determined are at a minimum 20 from the center of the nanotube. The C11, C33, and K12 follow similar trends as a function of radial distance from the nanotube. The K13 decreases greater distances from the nanotube and becomes negative which may be a symptom of the statistical averaging.

Predicting the Influence of Nano-scale Material Structure on the In-plane Buckling of Orthotropic Plates

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the nonfunctionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.