Effective Properties Of Nanocomposites Research Articles

Free vibration and transient response of initially compressed CNT-reinforced composite plates

This paper investigates the linear free vibration and nonlinear transient response of carbon nanotube (CNT)-reinforced composite plates subjected to pre-existent compressive load in thermal environments. CNTs are reinforced into matrix according to uniform and functionally graded distributions. The properties of constitutive materials are assumed to be temperature-dependent while the effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations are established within the framework of classical plate theory incorporating von Kármán nonlinearity and initial geometrical imperfection. Analytical solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain a time differential equation including both quadratic and cubic nonlinear terms. Fourth-order Runge–Kutta numerical integration scheme is employed to determine dynamical deflection-time response of nanocomposite plates. Numerical analyses are presented to consider the influences of CNT volume fraction, CNT distribution, initial compressive load, geometrical imperfection, elevated temperature and plate geometry on the natural frequencies and nonlinear dynamical response of nanocomposite plates. The study reveals that the natural frequency and dynamical deflection are strongly decreased and increased when initial compressive load is increased, respectively. Numerical results also find that the natural frequencies are enhanced and dynamical deflection is dropped as a result of increase in volume percentage of CNTs, respectively.

Nonlinear dynamical characteristics of carbon nanotube-reinforced composite beams with piezoelectric actuators and elastically restrained ends under thermo-electro-mechanical loads

Nonlinear free vibration and dynamical responses of carbon nanotube (CNT) reinforced composite beams with surface-bonded piezoelectric layers and tangentially restrained ends under thermo-electro-mechanical loads are investigated in this paper. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are estimated using an extended rule of mixture. Unlike previous studies, the present work considers the effects of tangentially elastic constraints of two ends on the nonlinear dynamic characteristics of hybrid beams. Motion equation is established within the framework of Euler-Bernoulli beam theory taking into account von Kármán nonlinearity. Analytical solution is assumed to satisfy simply supported boundary conditions and Galerkin procedure is employed to obtain a time ordinary differential equation including both quadratic and cubic nonlinear terms. This differential equation is numerically solved employing fourth-order Runge-Kutta scheme to determine the frequencies of nonlinear free vibration and nonlinear transient response. Parametric studies are executed to examine numerous influences on the nonlinear dynamical characteristics of hybrid nanocomposite beams. The study reveals that tangential constraints of ends substantially effect the frequencies and dynamic response of the beam, especially at elevated temperatures. The results also indicate that nonlinear dynamic responses can be controlled effectively by means of piezoelectric actuators and elasticity of tangential constraints of ends should be considered in design of piezo-CNTRC beams.

Thermoelastic nonlinear vibration and dynamical response of geometrically imperfect carbon nanotube-reinforced composite plates on elastic foundations including tangential edge constraints

The combined influences of initial geometrical imperfection, elasticity of in-plane constraints of edges, elastic foundations and elevated temperature on the nonlinear vibration and dynamical response of carbon nanotube-reinforced composite rectangular plates are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix according to functionally graded distributions. The properties of CNTs and matrix are assumed to be temperature dependent and effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations in terms of deflection and stress function are established within the framework of thin plate theory including von Kármán nonlinearity, geometric imperfection and interactive pressure from elastic foundation. Analytical solutions are assumed for simply supported plates and Galerkin method is applied to result in nonlinear time differential equation. This nonlinear equation is solved using fourth-order Runge–Kutta scheme. Parametric studies are executed to examine numerous influences on the natural frequency, nonlinear to linear frequency ratio and nonlinear dynamical response of CNT-reinforced composite plates. The results reveal that increase in imperfection size results in increase and decrease in natural frequencies and the amplitude of forced vibration, respectively. In contrast, it is found that the elevated temperature reduces the natural frequencies and enhances the amplitude of forced vibration.

Thermally induced postbuckling of thin CNT-reinforced composite plates under nonuniform in-plane temperature distributions

This paper presents an analytical investigation on postbuckling behavior of thin plates reinforced by carbon nanotubes (CNTs) and subjected to nonuniform thermal loads. Unlike many previous works considered ideal case of thermal load is that uniform temperature rise, the present study considers more practical situations of thermal load are that sinusoidal and linear in-plane temperature distributions. CNTs are reinforced into matrix through functionally graded distributions and effective properties of nanocomposite are estimated according to extended rule of mixture. Basic equations are based on classical plate theory taking into account Von Karman nonlinearity, initial geometrical imperfection, interactive pressure from elastic foundations and elasticity of tangential constraints of simply supported boundary edges. Basic equations are solved by using analytical solutions and Galerkin method. From the obtained closed-form relations, thermal buckling and postbuckling behavior of nanocomposite plates are analyzed through numerical examples.

Thermal postbuckling behavior of CNT-reinforced composite sandwich plate models resting on elastic foundations with tangentially restrained edges and temperature-dependent properties

Buckling and postbuckling behaviors of sandwich plates reinforced by single-walled carbon nanotube (CNT), rested on elastic foundations and subjected to uniform temperature rise, are investigated in this article. CNT is embedded into matrix phase through uniform or functionally graded distributions. The properties of constituent materials are assumed to be temperature-dependent, and effective properties of nanocomposite are determined by extended rule of mixture. Two models of sandwich plates with face sheets and core layer reinforced by CNTs are presented. Formulations are based on the first-order shear deformation theory taking geometrical nonlinearity, initial geometrical imperfection, plate-foundation interaction, and elasticity of tangential edge constraints into consideration. Analytical solutions of deflection and stress function are assumed, and Galerkin method is applied to derive nonlinear temperature–deflection relation from which buckling temperatures and thermal postbuckling paths are obtained through an iteration algorithm. Numerical examples show the effects of CNT volume fraction, distribution patterns, in-plane edge constraint, elastic foundations, geometrical ratios, initial imperfection, and temperature dependence of properties on thermal postbuckling behavior of nanocomposite sandwich plates. The most important finding is that sandwich plate constructed from CNT-poor nanocomposite core layer and thin homogeneous face sheets with partially movable edges bring the best capacities of thermal buckling resistance and postbuckling load carrying.

Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells.

Thermal postbuckling of shear deformable CNT-reinforced composite plates with tangentially restrained edges and temperature-dependent properties

Buckling and postbuckling behaviors of moderately thick composite plates reinforced by single-walled carbon nanotubes (SWCNTs), rested on elastic foundations and subjected to two types of thermal loading are investigated in this article. Carbon nanotubes (CNTs) are reinforced into isotropic polymer matrix according to functional rules in which volume fractions of constituents are graded in the thickness direction. Material properties of constituents are assumed to be temperature-dependent and effective properties of nanocomposite are estimated by extended rule of mixture. Formulations are based on first-order shear deformation theory taking von Karman nonlinearity, initial geometrical imperfection, tangential constraints of edges, and two-parameter elastic foundation into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive nonlinear temperature–deflection relations from which buckling temperatures and postbuckling equilibrium paths are determined by an iteration algorithm. Novel findings of the present study are that deteriorative influences of temperature-dependent properties on the postbuckling behavior become more serious as plate edges are partially movable, CNT volume fraction is higher, elastic foundations are stiffer, plates are thicker, and/or temperature linearly changed across the thickness.

Finite element and micromechanical modeling for investigating effective material properties of polymer–matrix nanocomposites with microfiber, reinforced by CNT arrays

This paper is motivated by the lack of studies to investigate the effect of fiber reinforced CNT arrays on the material properties of nanocomposites. To make a comprehensive study, this research work is conducted in two ways. Firstly, the effect of microfiber as reinforcement on the effective material properties is investigated; secondly, the study is carried on as the microfibers reinforced by CNT arrays. In both above-mentioned approaches, the results are compared to the results of generalized mixture rule which is known as a widely used micro-mechanical model. The representative volume element (RVE) is considered as a well-known method to investigate the effect of adding CNT arrays on the skin of microfibers. The results show that Generalized Mixture Rule cannot properly predict the effects of changing the length and diameter of nanotubes on the effective properties of nanocomposites. The main objective of this research work is to determine the effects of increasing nanotubes on the elastic properties which are achieved using two aforementioned methods including FE and rule of mixture. It is also absorbed; effective properties of RVE can be improved by increasing the volume fraction, length and decreasing CNT arrays diameter.

MODELING THE HYGRO-THERMO-MECHANICAL AGGLOMERATION RELATIONS OF CARBON-EPOXY HYBRID NANOCOMPOSITES

In the present work, the hygro-thermo-mechanical properties of hybrid nanocomposites are presented under the agglomeration effects of carbon nanotubes in the polymer matrix. In order to study the composite behaviors, the Voigt and Reuss homogenization method is adopted to present new relations for a hybrid nanocomposite that contains micro carbon fibers as inclusions along with the nanotubes. The experimental findings have shown that the nanotube agglomerations have a significant impact on the effective thermo-mechanical and moisture properties of nanocomposites. Experimental works also prove that nanotube agglomerations further degrade the electrical and vibration characteristics. Additionally, the existing fabrication methods have shown that extensive deagglomeration process has resulted in considerable damage to the nanotubes. Therefore, in order to overcome the above problems the hybrid nanocomposite concept has been proposed and the effective elastic, thermal, and moisture properties are derived in terms of the nanotube agglomeration. The effective hygro-thermo-mechanical properties of hybrid nanocomposites as a function of nanotube agglomeration volume fraction have been presented. The results prove that the effective properties of nanocomposites are reduced under nanotube agglomerations but enhanced when carbon fibers are used as inclusions. Consequently it is concluded that the nanocomposite properties can be improved by using carbon fibers as hybrid inclusions although nanotube agglomerations may be present.

Atomistic–continuum interphase model for effective properties of composite materials containing nano-inhomogeneities

Classical micromechanics were revised to study the elastic properties of heterogeneous materials containing nano-inhomogeneities. Contrary to previous studies, this work introduces the concept of an interphase, in contrast to a sharp interface, to account for the interface excess stress effect at the nano-scale. The interphase's constitutive properties are derived from atomistic simulations within the continuum framework. These properties are then incorporated in a micromechanics-based interphase model to compute the effective properties of nano-composites. This scale transition approach bridges the gap between discrete systems (atomic level interactions) and continuum mechanics. An advantage of this approach is that it combines atomistic with continuum models that consider inhomogeneity and interphase morphology. It thereby enables us to account simultaneously for both the shape and the anisotropy of a nano-inhomogeneity and interphase at the continuum level when we compute a material's overall properties. In so doing, it frees us from making any assumptions about the interface characteristics between matrix and the nano-inhomogeneity.

Finite element modelling of nanoscale inhomogeneities in an elastic matrix

Nanoscale inhomogeneities in elastic matrix materials are encountered in the development of nanocomposites and various nanoscale structures. The overall effective properties of nanocomposites and nanostructures are controlled by the elastic field of the inhomogeneity–matrix system. As an alternative to analytical solution approaches that are confined to the solution of a single inhomogeneity of ideal shape, this study presents a two-dimensional finite element formulation for the analysis of multiple arbitrary shaped anisotropic inhomogeneities in an anisotropic matrix material. The Gurtin–Murdoch surface/interface elasticity model is used in the analysis. Instabilities of the elastic field are found under certain conditions. Selected numerical results are presented to show the influence of inhomogeneity geometry, multiple inhomogeneities, inhomogeneity eigenstrain and anisotropy on the stress and displacement fields.

Microstructure and effective properties of nanocomposites: ferrofluids as tunable model systems

We have studied the correlation between microstructure and effective material properties using colloidal dispersions of magnetic nanoparticles in a carrier liquid (ferrofluids). Their microstructure can be altered in a continuous and reversible way via an external magnetic field. Two-dimensional small angle x-ray scattering and Monte Carlo simulations show that field-induced structural anisotropy develops due to the formation of anisometric particle clusters having a preferred orientation parallel to the field. In this polydisperse system particles of all sizes take part in cluster formation. The structural data are compared with results of dielectric measurements in the frequency range from 5 Hz to 1 GHz. We show that dielectric anisotropy is correlated with the shape anisometry of oriented clusters.