J. Eng. Mater. Technol. 2004;126(3):221. doi:10.1115/1.1743410.
Commentary by Dr. Valentin Fuster


J. Eng. Mater. Technol. 2004;126(3):222-229. doi:10.1115/1.1743426.

Carbon nanotubes are a material system of increasing technological importance with superb mechanical and electrical properties. It is well known that depending on details of atomic structure, nanotubes may be electrically conducting, semiconducting, or insulating, so deformation is believed to have strong effects on nanotube electrical properties. In this paper, a combination of continuum, empirical atomistic, and quantum atomistic modeling methods are used to demonstrate the effect of homogeneous deformation—tension, compression, and torsion—on the electrical conductance and current versus voltage (I(V)) characteristics of a variety of single wall carbon nanotubes. The modeling methods are used in a coupled and efficient multiscale formulation that allows for computationally inexpensive analysis of a wide range of deformed nanotube configurations. Several important observations on the connection between mechanical and electrical behavior are made based on the transport calculations. First, based on the I(V) characteristics, electron transport in the nanotubes is evidently fairly insensitive to homogeneous deformation, though in some cases there is a moderate strain effect at either relatively low or high applied voltages. In particular, the conductance, or dI/dV behavior, shows interesting features for nanotubes deformed in torsion over small ranges of applied bias. Second, based on a survey of a range of nanotube geometries, the primary determining feature of the I(V) characteristics is simply the number of conduction electrons available per unit length of nanotube. In other words, when the current is normalized by the number of free electrons on the tube cross section per unit length, which itself is affected by extensional (but not torsional) strain, the I(V) curves of all single walled carbon nanotubes are nearly co-linear.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):230-237. doi:10.1115/1.1751180.

In this paper, we report on molecular dynamics (MD), continuum (based on linear and nonlinear beam theories) and combined molecular dynamics/continuum simulation of carbon nanotube based nanoelectromechanical switches. As a prototype device, we study the pull-in voltage characteristics of a nanoelectromechanical switch made of a suspended single wall nanotube over a ground plane. The various simulations (MD, continuum and combined MD/continuum) have been performed accounting for the electrostatic and van der Waals forces between the nanotube and the ground plane. The results from the nonlinear continuum theory compared well with the results from MD, except, for cases, where nanotube buckling was observed. When buckling occurs, the electromechanical behavior of the switch is simulated by employing a combined MD/continuum approach. The combined MD/continuum approach is computationally more efficient compared to the MD simulation of the entire device. Static and dynamic pull-in, pull-in time and fundamental frequency analysis is presented for fixed-fixed and cantilever carbon nanotube switches.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):238-244. doi:10.1115/1.1751179.

The fracture toughness of highly-ordered multi-wall carbon-nanotube-reinforced alumina composites is calculated from experimental data on nanoindentation cracking. A combined analytical and numerical model, using cohesive zone models for both matrix cracking and nanotube crack bridging and accounting for residual stresses, is developed to interpret the indentation results and evaluate the fracture toughness of the composite. Results show that residual stress and nanotube bridging play important roles in the nanocomposite fracture. The contribution to toughness from the nanotube bridging for cracking transverse to the axis of the nanotubes is calculated to be ∼5 MPa-m1/2 . From the nanotube bridging law, the nanotube strength and interfacial frictional stress are also estimated and range from 15–25 GPa and 40–200 MPa, respectively. These preliminary results demonstrate that nanotube-reinforced ceramics can exhibit the interfacial debonding/sliding and nanotube bridging necessary to induce nanoscale toughening, and suggest the feasibility of engineering residual stresses, nanotube structure, and composite geometry to obtain high-toughness nanocomposites.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):245-249. doi:10.1115/1.1751181.

We report atomistic studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. These long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios. We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rod-like buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a flexible macromolecule which tends to fold due to vdW interactions between different parts of the carbon nanotube. This suggests a shell-rod-wire transition of the mechanical behavior of carbon nanotubes with increasing aspect ratios. While continuum mechanics concepts can be used to describe the first two types of deformation, statistical methods will be necessary to describe the dynamics of wire-like long tubes.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):250-257. doi:10.1115/1.1751182.

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 nanotube-reinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):258-264. doi:10.1115/1.1752924.

An abnormal friction law refers to the case where the friction force does not increase monotonically with the normal pressure. We investigate the possibility of abnormal tribological behavior for two surfaces coated with aligned single-walled carbon nanotubes (SWCNTs). Detailed molecular dynamics simulations for aligned SWCNTs predict modulated variation between the kinetic friction force and the applied pressure. The interacting SWCNTs float with respect to each other at about the equilibrium separation of van der Waals interaction, and the wavy contact profile breaks the symmetry of the contacting cross-section. Cases treated by molecular dynamics simulation include two aligned (10,10) SWCNTs with periodic end conditions, and a stack of three aligned (10,10) SWCNTs with free end boundary conditions. A continuum theory based on the wall deflection under finite deformation, in combination with an adhesion criterion similar to the JKR theory, on the other hand, predicts a declining law between the frictional force and the pressure. The correlation of the data obtained through the atomistic and the continuum approaches relies on a deeper understanding on the friction process among SWCNTs.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):265-270. doi:10.1115/1.1752925.

We have developed an analytical method to determine the coefficient of thermal expansion (CTE) for single wall carbon nanotubes (CNTs). We have found that all CTEs are negative at low and room temperature and become positive at high temperature. As the CNT diameter decreases, the range of negative CTE shrinks. The CTE in radial direction of the CNT is less than that in the axial direction for armchair CNTs, but the opposite holds for zigzag CNTs. The radial CTE is independent of the CNT helicity, while the axial CTE shows a strong helicity dependence.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):271-278. doi:10.1115/1.1755245.

Representing a new class of nanoscale material, carbon nanotubes possess many extraordinary mechanical and electronic properties stemming essentially from their unique geometric and chemical structures. Through more than two decades of extensive theoretical and experimental investigations, our understanding on the mechanical properties of carbon nanotubes has greatly improved. The intrinsic mechanical properties of carbon nanotubes, such as their stiffness, strength and deformability, have been relatively well studied and understood; and other mechanics-related properties of carbon nanotubes, such as the defect formation, the fracture mechanism, the interface mechanics and the electromechanics, have also being broadly examined and a comprehensive knowledge of them begins to emerge. I review the current status of research on the mechanical study of carbon nanotubes, especially on the experimental study of their fundamental mechanical properties, such as Young’s modulus, tensile and shear strength, compressibility and deformability. Selected experimental methods and techniques used for the studies will also be introduced. I conclude the review by discussing the new challenges still facing the mechanical study of carbon nanotubes.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):279-284. doi:10.1115/1.1752926.

A recently developed procedure for modeling the deformation of single and multi-wall carbon nanotubes [13,14] is applied to nanotube buckling and post-buckling under axial compression. Critical features of the model, which is grounded in elastic shell theory, include identification of (a) an appropriate elastic modulus and thickness pair matching both the wall stretching and bending resistances of the single atomic layer nanotube walls, and (b) a sufficiently stiff interwall van der Waals potential to preserve interwall spacing in locally buckled MWNTs, as is experimentally observed. The first issue is illustrated by parametric buckling studies on a SWNT and comparisons to a corresponding MD simulation from the literature; results clearly indicating the inadequacy of arbitrarily assigning the shell thickness to be the equilibrium spacing of graphite planes. Details of the evolution of local buckling patterns in a nine-walled CNT are interpreted based on a complex interplay of local shell buckling and evolving interwall pressure distributions. The transition in local buckling wavelengths observed with increasing post-buckling deformation is driven by the lower energy of a longer-wavelength, multiwall deformation pattern, compared to the shorter initial wavelength set by local buckling in the outermost shell. This transition, however, is contingent on adopting a van der Waals interaction sufficiently stiff to preserve interlayer spacing in the post-buckled configuration.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):285-291. doi:10.1115/1.1753264.

A polycrystal plasticity model is used to conduct parametric studies of forming limit diagrams (FLD) and to compare with experimental data. The Marcinak and Kuczynski [13] method is applied. It is confirmed that the onset of necking is retarded by increases in the ratio of initial band to sheet thickness and material strain rate sensitivity. It was also demonstrated that initial texture plays an important role in FLD response, as has been shown in other recent studies [6,26,7]. It is shown that a texture resulting from plane strain compression to one-tenth of the initial thickness gives a predicted FLD that more closely matches measured data than that based on an initially isotropic texture. The influence of a relatively softer response in terms of effective stress in torsional shear than in compression (i.e., shear softening) on FLDs is investigated with the aid of a hardening surface formulation along with the polycrystal plasticity texture evolution model. It is shown that necking behavior can be significantly affected by shear softening, particularly for initially textured sheets. It is also demonstrated that the hardening surface formulation provides additional flexibility in modeling FLD behavior beyond that afforded by classical polycrystal plasticity.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):292-302. doi:10.1115/1.1752927.

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Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):303-313. doi:10.1115/1.1753265.

Excessive coil deformation can complicate normal handling of a wound or rolled coil, cause difficulties in mass production, and introduce undesirable variations in the subsequent manufacturing processes. Four critical factors for coil deformation have been identified, i.e., radial stiffness of the coil material, winding tension, stiffness of the core which supports the coil, and lubrication. In this paper, we advance the understanding of coil deformation by developing an equivalent material model based on the internal stress distribution obtained from a two-dimensional winding-analysis model. The proposed material model is then implemented in a multi-layer finite element model to study the coil deformation under gravitational loading. This proposed framework can quantify the contribution of each factor in the coil deformation and thereby provide more scientific base in the engineering design process. The approach is used to analyze the deformation of laminate sheet coils.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2004;126(3):314-324. doi:10.1115/1.1755244.

Various fracture criteria, based on different assumptions and different mechanical models, have been proposed in the past to predict ductile fracture. The objective of this study is to assess their effectiveness and accuracy in a wide range of process parameters. A series of tests on 2024-T351 aluminum alloy, including upsetting tests and tensile tests is carried out. It is found that none of the existing fracture criteria give consistent results. Two totally different fracture mechanisms are clearly observed from microfractographs of upsetting and tensile specimens. This observation confirms that it is impossible to capture all features of ductile crack formation in different stress states with a single criterion. It is shown that different functions are necessary to predict crack formation for different ranges of stress triaxiality. Weighting functions in a wide range of stress states can be obtained by determining the fracture locus in the space of equivalent strain to fracture and stress triaxiality.

Commentary by Dr. Valentin Fuster


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