Wet fiber shear flexibility and its contribution to the overall transverse deformation of fibers

A new method has been developed for measuring not only bending but also shear flexibility of pulp fibers by using confocal laser scanning microscopy. Based on the Steadman and Luner method, a two-stage wet pressing process was used which enabled both bending and shear flexibility and both bending and shear modulii of fibers to be determined with a single test. Three types of fibers, i.e., bleached spruce Kraft Pulp (BKP), aspen bleached chemi-themomechanical pulp (BCTMP), and aspen themomechanical pulp (CTMP), were tested. Results show that the longitudinal elastic modulii of the fibers are in a range of 3–37 GPa, and the transverse shear modulii of them are in a range of 27–103 MPa. It was also found that the shear contribution to the overall fiber deformation ranged from 60% to 90% for the fibers measured. This substantiates the concept of shear contribution to measured fiber flexibility as proposed by Waterhouse and Page.     

Effect of compressive strain on electric resistance of multi-wall carbon nanotube networks

The network of entangled multi-wall carbon nanotubes is shown as a conductor whose resistance is sensitive to compressive strain, both in the course of strain growth and when loading/unloading cycles are imposed. If the compression is applied, the resistance decrease is up to 25% at the maximum applied deformation. The experimental data are analysed using the Weibull distribution model and a contact network model to get an estimate of the contact resistance between carbon nanotubes and the formation of contacts in the course of compression.     

Radial mechanical properties of single-walled boron nitride nanotubes

The radial mechanical properties of single-walled boron nitride nanotubes (SW-BNNTs) are investigated by atomic force microscopy. Nanomechanical measurements reveal the radial deformation of individual SW-BNNTs in both elastic and plastic regimes. The measured effective radial elastic moduli of SW-BNNTs are found to follow a decreasing trend with an increase in tube diameter, ranging from 40.78 to 1.85 GPa for tube diameters of 0.58 to 2.38 nm. The results show that SW-BNNTs have relatively lower effective radial elastic moduli than single-walled carbon nanotubes (SWCNTs). The axially strong, but radially supple characteristics suggest that SW-BNNTs may be superior to SWCNTs as reinforcing additives for nanocomposite applications.     

Carbon nanotube-reinforced composites: frequency analysis theories based on the matrix stiffness

Strong and versatile carbon nanotubes are finding new applications in improving conventional polymer-based fibers and films. This paper studies the influence of matrix stiffness and the intertube radial displacements on free vibration of an individual double-walled carbon nanotube (DWNT). For this, a double elastic beam model is presented for frequency analysis in a DWNT embedded in an elastic matrix. The analysis is based on both Euler–Bernoulli and Timoshenko beam theories which considers shear deformation and rotary inertia and for both concentric and non-concentric assumptions considering intertube radial displacements and the related internal degrees of freedom. New intertube resonant frequencies and the associated non-coaxial vibrational modes are calculated. Detailed results are demonstrated for the dependence of resonant frequencies and mode shapes on the matrix stiffness. The results indicate that internal radial displacement and surrounding matrix stiffness could substantially affect resonant frequencies especially for longer double-walled carbon nanotubes of larger innermost radius at higher resonant frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. Therefore, depending on the matrix stiffness, for carbon nanotubes reinforced composites, different analysis techniques should be used while the aspect ratio of carbon nanotubes has a little effect on the analysis theory which should be selected.     

Elastic properties of As-Sb-Se glasses

Results of measurement of elastic modulii on As-Sb-Se glasses are reported and their composition dependence discussed. The Young’s and the shear modulii lie in the range of 170–210 and 65–80 kb respectively. These values are typical of chalcogenide glasses. For (As, Sb)₄₀Se₆₀ glasses, the modulii increase monotonically with increasing Sb₂Se₃ content. The observed composition dependence of the modulii for the As _x Sb₁₅Se_{85 −x} glasses is examined in terms of the chemically ordered structural units in the glasses.     

Investigation into cylinder-on-flat adhesion elastic–plastic micro-contact under repeated loading and unloading condition

The evolution of microcontact induced deformation and stress states under repeated loading and unloading condition is of great interest for the scientific understanding as well as from the engineering design considerations of microelectromechanical systems (MEMS) based switches and similar other devices since they operate under cyclic condition. This study, therefore, investigated the microcontact interaction between deformable smooth cylindrical segment and deformable smooth flat using the finite element analysis. Elastic and elastic–plastic material behaviors and adhesion interaction are considered. The detailed information about contact area, displacement and stress state in the contact region under cycling condition are presented. Contact area varies nonlinearly even when the applied load is varying linearly in a cycle. Additionally, contact areas during loading and unloading portions of a cycle are not equal at the same load level. The deformation and contact area increases in the presence of adhesion force and also with elastic–plastic material behavior. However, the adhesion force is reduced while the contact area is increased during the microcontact between elastic–plastic bodies in comparison to those between elastic bodies. The maximum increase in stress and deformation states occurs during the first cycle, and then slowly with increasing number of cycles. Further, the maximum stress state is not at the contact surface and also not at instant of the maximum applied external force. Finally, adhesion force during microcontact interaction can be of the same order as the applied external force. Therefore, design and analysis of microcontacts in micromechanical switches and similar other devices should include the effects of adhesion force and cyclic effects. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United State Air Force, Department of Defense, or the U.S. Government.     

Effects of Ti2448 half-pin with low elastic modulus on pin loosening in unilateral external fixation

The objective of this study was to compare the benefits of titanium 2448 (Ti2448) half-pin and titanium-6 aluminium-4 vanadium (TAV) half-pin on reducing pin loosening during external fracture fixation. Although having similar strength, Ti2448 half-pin had even lower elastic modules(33 GPa)when compared with TAV half-pin (110 GPa), which was similar to that of cortical bone (20 GPa). In the external fixation of tibial model fractures and canine cadaveric tibia fractures, Ti2448 half-pin had greater recoverable deformation and less stress concentration at the pin–bone interface in compression, torsion, and four-points bending test. Then, tibial fractures were created in 24 dogs and stabilized with four half-pins of either Ti2448 or TAV in each animal. At 4 and 8 weeks postoperatively, fracture healing and pin loosening was assessed by radiographic grading scale. The scores of Ti2448 group were significantly higher than those of TAV group. Micro-CT analysis also indicated larger quantity and higher quality of newly formed bone at pin–bone interface in Ti2448 group. Histology observation showed the newly formed bone integrated well into the threads of Ti2448 half-pins. In contrast, there was a layer of necrotic tissue between the bone tissue and TAV half-pin at pin–bone interface in TAV group. The extraction torque values of Ti2448 half-pins near the fracture line were significantly higher than those TAV pins. In conclusion, the Ti2448 half-pin with low elastic modulus could enhance osseointegration and reduce pin loosening when compared with TAV half-pin. It is a promising biomaterial for constructing external fixation system in clinical application.     

AFM indentation method used for elastic modulus characterization of interfaces and thin layers

Atomic force microscopy (AFM) is increasingly being used as a nanoindentation tool to measure local elastic properties of surfaces. In this article, a method based on AFM in force volume (force curve mapping) mode is employed to measure the elastic modulus distribution at the interface of a glass flake-reinforced polypropylene sample and at a lead-free Cu–solder joint. Indentation arrays are performed using a diamond AFM tip. The processing of experimental AFM indentation data is automated by customized software that can analyse and calibrate multiple force curves. The analysis algorithm corrects the obtained force curves by selecting the contact point, discarding the non-contact region and subtracting the cantilever deflection from the measured force curve in order to obtain true indentation curves. A Hertzian model is then applied to the resulting AFM indentation data. Reference materials are used to estimate the tip radius needed to extract the elastic modulus values. With the proposed AFM measurement method, we are able to obtain high-resolution maps showing elastic modulus variations around a composite interface and a Cu–solder joint. No distinct interphase region is detected in the composite case, whereas a separate intermetallic layer (1–2 μm thick) of much higher Young’s modulus (~131 GPa) than Cu and solder material is identified in the Cu–solder joint. Elastic modulus results obtained for the Cu (~72 GPa), solder (~50 GPa) and glass (~65 GPa) materials are comparable to the results obtained by instrumented indentation [~73, ~46 and ~61 GPa], which accentuates the potential of this method for applications requiring high lateral resolution.     

Energy absorption during compression and impact of dry elastic-plastic spherical granules

The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters (modulus of elasticity, stiffness, yield pressure, restitution coefficient and strength) of spherical granules (γ-Al₂O₃, zeolites 4A and 13X, sodium benzoate) with different mechanical behaviour have been measured by single particle compression and impact tests. Starting with the elastic compression behaviour of granules as described by Hertz theory, a new contact model was developed to describe the force-displacement behaviour of elastic-plastic granules. The aim of this work is to understand the energy absorption during compression (slow stressing velocity of 0.02 mm/s) and impact (the impact velocity of 0.5–4.5 m/s) of granules. For all examined granules the estimated energy absorption during the impact is found to be far lower than that during compression. Moreover, the measured restitution coefficient is independent of the impact velocity in the examined range and independent of the load intensity by compression (i.e. maximum compressive load). In the case of repeated loading with a constant load amplitude, the granules show cyclic hardening with increasing restitution coefficient up to a certain saturation in the plastic deformation. A model was proposed to describe the increase of the contact stiffness with the number of cycles. When the load amplitude is subsequently increased, further plastic deformation takes place and the restitution coefficient strongly decreases.     

Phase transformations of carbon-black in high-temperature shock compression

The carbon-black transformations into diamond and amorphous carbon phase having an intermediate density of 2.9 g/cm³ in high-temperature shock compression at 20–32 GPa and 2500–3500 K have been studied. The conditions of compression that ensure the maximum yield of these phases have been defined. The transformation regularities have been analyzed under the assumption that the amorphous phase is an intermediate structure on the way to the transformation of turbostratic carbon into diamond.     

An elastic shell model for characterizing single-walled carbon nanotubes

This paper proposes a two-dimensional elastic shell model to characterize the deformation of single-walled carbon nanotubes using the in-plane rigidity, Poisson ratio, bending rigidity and off-plane torsion rigidity as independent elastic constants. It was found that the off-plane torsion rigidity of a single-walled carbon nanotube is not zero due to the off-plane change in the π-orbital electron density on both sides of the nanotube. It was concluded that a three-dimensional elastic shell model of single-walled carbon nanotubes can be established with well-defined effective thickness.     

Characterizing the Structure and Properties of Individual Wire‐Like Nanoentities

A new approach to the characterization of the mechanical and electrical properties of individual nanowires and nanotubes is demonstrated by in‐situ transmission electron microscopy (TEM). The technique allows a one‐to‐one correlation between the structure and properties of the nanowires. Recent developments include the determination of the Young's modulii of carbon nanotubes and semiconductor nanowires, femtogram nanobalance of a single fine particle, field emission of carbon nanotubes, and quantum ballistic conductance in carbon nanotubes.     

Characterization of damping in carbon-nanotube filled fiberglass reinforced thermosetting-matrix composites

Use of carbon nanotubes as additives to composite parts for the purpose of increased damping has been the subject of much recent attention, owing to their large surface area per weight ratio which provides for frictional losses at the carbon nanotube–resin matrix interface. This article presents an experimental study to quantify the structural damping in composites due to the addition of carbon nanotubes to thermosetting resin systems with and without fiberglass reinforcement. Carbon nanotubes of varying quantity and morphology are ultrasonically dispersed in epoxy resin and are compression molded to form test samples that are used in forced vibration, free vibration with initial tip deflection, and tension tests to determine their damping ratio, specific damping capacity, and Young’s modulus. Results show increased stiffness and specific damping capacity with the addition of carbon nanotubes and particularly increased frictional loss with increasing surface area to weight ratio. The addition of fiberglass reinforcement to composite samples is shown to reduce the effective damping ratio over plain epoxy samples and carbon nanotube-filled epoxy samples.     

Micromechanical analysis of fuzzy fiber reinforced composites

A novel fuzzy fiber reinforced composite (FFRC) reinforced with zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is proposed. The distinct constructional feature of this composite is that the uniformly aligned CNTs are radially grown on the surface of carbon fibers. Analytical models based on the mechanics of materials approach and the Mori–Tanaka method are derived to estimate the effective elastic constants of this proposed FFRC. The values of the effective elastic properties of this composite are estimated with and without considering an interphase between the CNT and the polymer matrix. It has been found that the transverse effective properties of this composite are significantly improved due to the radial growing of CNTs on the surface of carbon fiber. The effective properties are also found to be sensitive to the CNT diameter.     

Eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix

This paper reports the results of an investigation on the eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix. Based on continuum modeling, a multilayer shell model is presented for the eccentric compression buckling of multi-walled carbon nanotubes embedded in an elastic matrix, in which the effect of van der Waals forces between two adjacent tubes is taken into account. The critical bending moment and the eccentric compression mode for three types of multi-walled carbon nanotubes with different layer numbers and ratios of radius to thickness are calculated. Results obtained show that the eccentric compression buckling mode corresponding the critical bending moment is unique, and is different from the purely axial compression buckling of an individual multi-walled carbon nanotube. For different types of multi-walled carbon nanotubes, the effect of matrix stiffness on the critical bending moment of multi-walled carbon nanotubes under eccentric compression loading is obviously different, and is dependent on the innermost radius and layer numbers of the multi-walled carbon nanotubes. The critical bending stress exerted on the center tubes of nearly solid multi-walled carbon nanotubes does not change as the ratio of the axial compression loading to the bending membrane force increases. The new features and meaningful numerical results in this paper are helpful for the application and the design of nanostructures in which multi-walled carbon nanotubes act as basic elements.     

Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments

In the present article, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed. In this regard, the governing equations are derived based on higher-order shear deformation plate theory and von Kármán geometrical nonlinearity. Three types of distributions of the temperature field and moisture concentrations, namely, uniformly, linearly, or nonlinearly through the thickness direction of the plates are considered. The effective material properties of the multiphase nanocomposite are calculated using fiber micromechanics and Halpin–Tsai equations in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the matrix. The contact force between the impactor and the plate is obtained with the aid of the modified nonlinear Hertzian contact law models. After examining the validity of the present work, the effects of the weight percentage of CNT, moisture concentration, temperature variations, distribution of temperature and moisture concentration, elastic foundation, and the eccentricity on the contact force, indentation, and central deflection of polymer-CNT-fiber multiscale nanocomposite plate are studied in details.     

Dynamical simulation of an abrasive wear process

A dynamic computer model was developed to simulate wear behavior of materials on micro-scales. In this model, a material system is discretized and mapped onto a lattice or grid. Each lattice site represents a small volume of the material. During a wear process, a lattice site may move under the influence of external force and the interaction between the site and its adjacent sites. The site–site interaction is a function of mechanical properties of the material such as the elastic modulus, yield strength, work hardening and the fracture strain. Newton's law of motion is used to determine the movement of lattice sites during a wear process. The strain between a pair of sites is recoverable if it is within the elastic deformation range; otherwise plastic deformation takes place. A bond between two adjacent sites is broken when its strain exceeds a critical value. A site or a cluster of sites is worn away if all bonds connecting the site or the cluster to its nearest neighbors are broken. The model well describes the strain distribution in a contact region, in consistence with a finite element analysis. This model was applied to several metallic materials abraded under the ASTM G65 abrasion condition, and the results were compared to experimental observations. Good agreement between the modeling and the experiment was found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of nanotube geometry on the elastic properties of nanocomposites

Many analytical models replace carbon nanotubes with “effective fibers” to bridge the gap between the nano and micro-scales and allow for the calculation of the elastic properties of nanocomposites using micromechanics. Although curvature of nanotubes can have a direct impact on these properties, it is typically ignored. In this work, the nanotube geometry in 3D is included in the calculation of the elastic properties of a modified effective fiber. The strain energy of the nanotube and the effective fiber are calculated using Castligiano’s theorem and constraints imposed by the matrix on the deformation are taken into consideration. Model results are compared to results from archived literature, and a reasonable agreement is observed. Results show that the effect of nanotube curvature on reducing the modulus of the effective fiber is not limited to in-plane curvature but also to curvature in 3D. The impact of the nanotube curvature on the elastic properties of nanocomposites is studied utilizing the modified fiber model and the approach developed by Mori–Tanaka. Analytical results show that for a low weight fraction of nanotubes the effect of curvature seems to be minor and as the weight fraction increases, the effect of nanotube curvature becomes critical.     

Finite Element Modeling of Compressive Deformation of Super-long Vertically Aligned Carbon Nanotubes

The super-long, vertically aligned carbon nanotubes (SL-VACNTs) are novel carbon nanomaterial produced from template-free synthesis. The mechanical responses of such material have been investigated by continuum finite element modeling and compared with experimental observations. The crushable foam model has been adequate in modeling the stress-strain curve and deformation of the SL-VACNTs under compression. SL-VACNTs are seen to exhibit transient elastic deformation at small displacement and then plastic deformation at large displacement. The deformation mostly occur at the position immediately beneath the compression platen (indenter face) due to the high stress/strain concentrations.     

Mechanical properties of cellular solids produced from hollow stainless steel spheres

Mechanical properties of cellular hollow sphere structures are studied in this work. The material was fabricated by coating the metallic powder slurry on expanded polystyrol (EPS) spheres, drying, forming under compression, debinding, and final sintering of the spheres to each other. Longitudinal elastic wave velocities were measured using ultrasound phase spectroscopy while compression tests were carried out up to a homologous temperature of 0.6. Dependence of the relative Young’s modulus on the relative density is similar to conventional open-cell foams. Compression stress–strain plots show the three stages of elastic deformation, plateau, and densification. With increasing temperature the overall level of the compressive stress–strain plots shifts to lower stresses. The hollow sphere solids show slightly better high temperature strength in comparison to the base metal. However, due to the considerable scatter in the experimental data points, this improvement seems to be insignificant. Structural observations on samples deformed to within the plateau region clearly show the heterogeneous progress of deformation.