Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references. @DOI: 10.1115/1.1490129#

/pdf/mechanics-of-carbon-nanotubes-4eqt38eq4w.pdf

Mechanics of carbon nanotubes

Natural biological materials such as bone, teeth and nacre are nanocomposites of protein and mineral with superior strength. It is quite a marvel that nature produces hard and tough materials out of protein as soft as human skin and mineral as brittle as classroom chalk. What are the secrets of nature? Can we learn from this to produce bio-inspired materials in the laboratory? These questions have motivated us to investigate the mechanics of protein–mineral nanocomposite structure. Large aspect ratios and a staggered alignment of mineral platelets are found to be the key factors contributing to the large stiffness of biomaterials. A tension–shear chain (TSC) model of biological nanostructure reveals that the strength of biomaterials hinges upon optimizing the tensile strength of the mineral crystals. As the size of the mineral crystals is reduced to nanoscale, they become insensitive to flaws with strength approaching the theoretical strength of atomic bonds. The optimized tensile strength of mineral crystals thus allows a large amount of fracture energy to be dissipated in protein via shear deformation and consequently enhances the fracture toughness of biocomposites. We derive viscoelastic properties of the protein–mineral nanostructure and show that the toughness of biocomposite can be further enhanced by the viscoelastic properties of protein.

Mechanical properties of nanostructure of biological materials

Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotubereinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites. @DOI: 10.1115/1.1751182#

/pdf/the-effect-of-nanotube-waviness-and-agglomeration-on-the-2jdj6qqix2.pdf

The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites

https://utw10193.utweb.utexas.edu/Archive/RuoffsPDFs/117.pdf

Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements

Since the last decade, research activities in the area of nano-materials have been increased dramatically. More than a 1000 of journal articles in this area have been published within the last 3 years. Materials scientists and researchers have realized that the mechanical properties of materials can be altered at the fundamental level, i.e. the atomic-scale. Carbon nanotubes (hereafter called ‘nanotubes’) have been well recognized as nano-structural materials that can be used to alter mechanical, thermal and electrical properties of polymer-based composite materials, because of their superior properties and perfect atom arrangement. In general, scientific research related to the nanotubes and their co-related polymer based composites can be distinguished into four particular scopes: (i) production of high purity and controllable nanotubes, in terms of their size, length and chiral arrangement; (ii) enhancement of interfacial bonding strength between the nanotubes and their surrounding matrix; (iii) control of the dispersion properties and alignment of the nanotubes in nanotube/polymer composites and (iv) applications of the nanotubes in real life. Although, so many remarkable results in the above items have been obtained recently, no concluding results have so far been finalized. In this paper, a critical review on recent research related to nanotube/polymer composites is given. Newly-adopted coiled nanotubes used to enhance the interfacial bonding strength of nanocomposites are also discussed. Moreover, the growth of nanotubes from nanoclay substrates to form exfoliated nanotube/nanoclay polymer composites is also introduced in detail.

http://chem.rutgers.edu/~kyc/pdf/491/cuneo/cuneo%203.pdf

A critical review on nanotube and nanotube/nanoclay related polymer composite materials

The recently developed virtual-internal- bond (VIB) model has incorporated a cohesive-type law into the constitutive law of solids such that fracture and failure of solids become a coherent part of the consti- tutive law and no separate fracture or failure criteria are needed. A numerical algorithm is developed in this study for the VIB model under static loadings. The model is applied to study three examples, namely the crack nucle- ation and propagation from stress concentration, kinking and subsequent propagation of a mode II crack, and the buckling-driven delamination of a thin film from a sub- strate. The results have demonstrated that the VIB model provides an effective method to study crack nucleation and propagation in engineering materials and systems.

Numerical Simulation of Cohesive Fracture by the Virtual-Internal-Bond Model

Carbon nanotubes show great promise for applications ranging from nanocomposites, nanoelectronic components, nanosensors, to nanoscale mechanical probes. These materials exhibit very attractive mechanical properties with extraordinarily high stiffness and strength, and are of great interest to researchers from both atomistic and continuum points of view. In this paper, we intend to develop a continuum theory of fracture nucleation in single-walled carbon nanotubes by incorporating interatomic potentials between carbon atoms into a continuum constitutive model for the nanotube wall. In this theory, the fracture nucleation is viewed as a bifurcation instability of a homogeneously deformed nanotube at a critical strain. An eigenvalue problem is set up to determine the onset of fracture, with results in good agreement with those from atomistic studies. ©2002 ASME

Fracture Nucleation in Single-Wall Carbon Nanotubes Under Tension: A Continuum Analysis Incorporating Interatomic Potentials

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Numerical Simulation of Cohesive Fracture by the Virtual-Internal-Bond Model

Fracture Nucleation in Single-Wall Carbon Nanotubes Under Tension: A Continuum Analysis Incorporating Interatomic Potentials