Isotropic Polymer Matrix Research Articles

Vibration analysis of functionally graded carbon nanotubes reinforced composite nanoplates

This work presents the analytical analysis for free linear vibration behavior of functionally graded-carbon nanotubes reinforced composite (FG-CNTRC) nanoplates in the framework of nonlocal strain gradient theory (NSGT) and the first-order shear deformation plate theory (FSDPT). The nanoplate is considered made of a mixture of an isotropic polymer matrix and reinforced carbon nanotubes (CNTs). Four different distributions of CNTs are examined including uniformly distributed and FG reinforcements (FG-O, FG-X, and FG-V). The governing equations of motion are established based on the Hamilton’s principle. The closed-form analytical solution for the natural frequency of FG-CNTRC nanoplates with simply supported all edges is carried out by using the Navier-type solution. The impact of some key parameters on the natural frequencies of FG-CNTRC nanoplates is also studied and discussed. The result shows that FG-CNTRC nanoplates reveal the softening- or hardening-stiffness effects depending on the relationship between the nonlocal parameter and the material length scale parameter. The aspect ratios of FG-CNTRC nanoplates, the volume fraction, and the distribution pattern of CNTs have also an important impact on the vibration behavior of FG-CNTRC nanoplates.

Critical speed and frequency behavior of rotating joined FG-CNTRC conical-conical shells

This paper provides information on critical speed and frequency behavior of rotating joined functionally graded carbon nanotube reinforced (FG-CNTRC) conical-conical shells. Furthermore, frequency bifurcation as a consequence of rotational effects is investigated. The shell is assumed to be composed of an isotropic polymer matrix that is reinforced by uniformly or functionally distributions of carbon nanotubes (CNTs). The structure’s kinematics originates from the first order shear deformation theory (FSDT). To derive spin-based motion equations, Coriolis and centrifugal forces together with initial hoop tensions are propounded through the Hamilton’s principle. Moreover, matching and boundary conditions are ascertained to supplement the governing equations. To discretize the governing equations meridionally, the generalized differential quadrature (GDQ) technique is employed. After validity checking, some significant parameters like cones’ angles, rotation speed, edge supports, CNT volume fractions and dispersion patterns that play effective roles on the critical speed and vibration characteristics are examined. It is revealed that by enhancing spinning speed, frequencies of different FG patterns converge. In addition, difference between backward and forward frequencies decreases as the circumferential mode number increases.

On the free vibration behavior of nanocomposite laminated plates contained piece-wise functionally graded graphene-reinforced composite plies

The numerical answer to the free vibration behavior of laminated plate structure contained piece-wise carbon-based nanocomposites plies is investigated. Plies are made from a combination of an isotropic polymer matrix and a nanoscale carbon-based reinforcements namely graphene. The graphene reinforcements are dispersed across the plate thickness either in uniform or non-uniform fashion according to four different distribution patterns. To assess the effect of the grading graphene patterns five types of lay-up arrangements are comparatively investigated. The effective elastic moduli of the laminated nanocomposite including Young’s and shear moduli are obtained by using the so-called extended Halpin-Tsai model. Theoretical approaches are based on the first-order shear deformation theory (FSDT), while Lagrange's equation and a finite element formulation are employed to derive the natural frequencies. The accuracy of the results using the present framework model is examined with those available in previous attempts and an excellent agreement is achieved. A large range of parametric studies was carried out with a view to investigate the effect of several factors including lay-up arrangements, graphene distribution patterns, lamination sequence, plate geometric parameters, plate boundary conditions, and plate mode shapes on the free vibration behavior of functionally graded graphene-reinforced composite (FG-GRC) laminated plates. New suggestions are presented with the aim of providing useful remarks and new design criteria for future and innovative nanocomposite structures.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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.

Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates

The geometrically nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates with different edge conditions is examined. The considered plate with NL-layers is made from a mixture of an isotropic polymer matrix and graphene platelets (GPLs) in each layer. The weight fraction of GPLs changes in a layer-wise manner. The modified Halpin-Tsai model and rule of mixture are utilized to compute the effective material properties of FG-GPLRCs. To mathematically model the vibrations of FG-GPLRC plates, the displacement field, strain tensor and constitutive relations as well as the energy functional of system including strain and kinetic energies and external work are represented in matrix forms as a function of the displacement components. Then, by simultaneous use of Hamilton’s principle and an efficient numerical scheme namely, the variational differential quadrature (VDQ) technique, the weak form of discretized nonlinear equations of motion is obtained. The present model includes the influences of geometric nonlinearity, rotary inertia and transverse shear deformation. Furthermore, a multistep numerical approach based on the Galerkin method, time periodic discretization method and pseudo arc-length continuation technique in conjunction with the modified Newton-Raphson method is employed to solve the problem of nonlinear harmonically excited vibration of FG-GPLRC rectangular plates. Results are plotted in the form of frequency-response and force-response curves to indicate the effect of various parameters such as GPL distribution pattern, weight fraction, geometry of GPL nanofillers and boundary constraints of FG-GPLRC plates.

Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation

Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy, refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.

A novel diffuser sheet comprising nanosized birefringent fibers embedded within an isotropic polymer matrix

We fabricated a novel diffuser sheet that consisted of an isotropic polymer matrix and nanosized birefringent fibers. The nanosized birefringent fibers, which had two distinct refractive indices, i.e., an ordinary (no) and an extraordinary (ne) refractive index, were embedded within the isotropic polymer matrix and then orthogonally stacked between successive layers of the polymer. The matching/mismatching of the refractive index of the isotropic polymer matrix with those of the fibers gave rise to a one-dimensional diffusion effect, and the orthogonally piled-up structure promoted two-dimensional diffusion distributions. The results of our study confirmed that this diffuser sheet could be a feasible candidate for replacing conventional diffuser sheets.

Effect of fibre transverse isotropy on micro-residual stresses in polymeric composites

In this paper, the influence of transversely isotropic behaviour of the fibre on micro-residual stress fields is investigated. For this purpose, the energy method is utilized to predict the micro-structural stresses in polymer matrix composites under uniform thermal loads. The representative volume element (RVE) considered here includes a transversely isotropic fibre embedded in an isotropic polymer matrix. Based on the energy method, a three-dimensional closed-form solution for micro-residual stresses is obtained. The analytical results are evaluated with a finite element solution. The analysis shows that the transversely isotropic behaviour of the fibre greatly increases the fibre and matrix axial residual stresses in comparison with the isotropic fibre assumption. Fibre anisotropy has a significant effect on the interfacial shear stress distribution, in contrast with the interfacial radial stress field. Both the finite element solution and analytical method result in a similar behaviour for micro-residual stresses distribution along the fibre length. However, the finite element method cannot satisfy the stress-free condition for the residual shear stress at the fibre end due to the stress singularity.

Magnetic films of negative Poisson’s ratio in rotating magnetic fields

Mechanical properties of a thin magnetic film subjected to an external, rotating magnetic field have been studied by computer simulations. The film is modeled by a two-dimensional bead-spring model of a non-magnetic polymer matrix with inclusions of magnetic nanoparticles (nanograins) of uniaxial anisotropy. The isotropic polymer matrix is represented as a hexagonal structure with sites decorated with small hexagonal particles containing magnetic nanograins. The beads correspond to polymer segments and the springs between them imitate chemical bonds, approximated by harmonic interactions. The beads also interact by the Lennard–Jones potential whose role is to mimic the core of non-bonded polymer segments.The Poisson ratio of the constructed polymer matrix is negative, i.e. the system expands laterally under longitudinal stretching force. It is shown that the magneto-elastic coupling can be used to control the expansion and contraction of the polymer matrix. Depending on the applied magnetic field, the Poisson ratio of the magnetic film may assume positive or negative values.

The effect of applied stresses on the equilibrium moisture content in polymers

The relation between saturation moisture content in a polymer and applied stresses is derived as a function of the coefficient of moisture expansion. The model is applied to the equilibrium water uptake of an isotropic polymer matrix composite . It is shown that a composite has a nonlinear sorption isotherm even though the matrix has a linear one, because of the internal stresses induced by swelling.

The scattering of electro-elastic waves by a spherical piezoelectric particle in a polymer matrix

This paper is devoted to the study of scattering of plane harmonic waves by a piezoelectric sphere with spherical isotropy embedded in an unbounded isotropic polymer matrix. The scattered displacement field and the electric potential in the matrix are expressed in terms of spherical vector wave functions and spherical harmonic functions, respectively. For the field points inside the inhomogeneity, new displacement functions are introduced. Expansion of the new displacement functions and the electric potential in terms of spherical harmonic functions, the equations of motion and electrostatic lead to four second order ordinary differential equations (odes), where three of them are coupled. The coupled system of odes is solved by the generalized Frobenius series. This approach is readily used to handle low and high frequencies. Three different types of piezoelectric inhomogeneities, PZT-4, PZT-5H, and BaTiO 3 are considered and the associated piezoelectric effects on the electro-mechanical fields, differential and total scattering cross-sections are addressed.

Colloidal ordering from phase separation in a liquid-crystalline continuous phase

Some binary mixtures exist as a single phase at high temperatures and as two phases at lower temperatures; rapid cooling therefore induces phase separation that proceeds through the initial formation of small particles and subsequent growth and coarsening. In solid and liquid media, this process leads to growing particles with a range of sizes, which eventually separate to form a macroscopically distinct phase. Such behaviour is of particular interest in systems composed of an isotropic fluid and a liquid crystal, where the random distribution of liquid-crystal droplets in an isotropic polymer matrix may give rise to interesting electro-optical properties. Here we report that a binary mixture consisting of an isotropic fluid and a liquid crystal forming the continuous phase does not fully separate into two phases, but self-organizes into highly ordered arrays of monodisperse colloidal droplet chains. We find that the size and spatial organization of the droplets are controlled by the orientational elasticity of the liquid-crystal phase and the defects caused by droplets exceeding a critical size. We expect that our approach to forming monodisperse, spatially ordered droplets in liquid crystals will allow the controlled design of ordered composites that may have useful rheological and optical properties.

Constitutive Equations of Viscoelasticity and Estimation of Viscoelastic Parameters of Unidirectional Fibrous Polymeric Composites

A method for modelling viscoelastic properties of fibre reinforced polymeric composites, based on the original reinforcement theory as well as original description of viscoelasticity of the matrix [4}, is developed in the paper. The composite material consists of a viscoelastic isotropic polymer matrix and elastic monotropic fibres. In order to model arbitrary shear/bulk creep in the matrix, the Mittag-Leffler fractional exponential functions are used as the generating functions. Hence, the viscoelastic model of the polymer matrix is described with 2 elastic constants and 6 viscoelastic constants, while the elastic properties of the fibres are described with 5 well-known elastic constants. Both groups of the material constants can be estimated experimentally relatively easy. Coupled constitutive equations of linear viscoelasticity of a unidirectional fibrous polymeric composite, modeled as a homogeneous monotropic material are formulated in the study. The viscoelastic model of the composite is described using 5 elastic constants and 27 viscoelastic constants, i.e., 9 long-lasting compliance ratios, 9 retardation times, and 9 fractions defining an order of the fractional exponential functions. The elastic-viscoelastic analogy is used to predict theoretically the complex compliances of the composite [4]. An iterative optimization procedure for theoretical prediction of the viscoelastic constants of the composite is formulated, computerised and positively tested on the selected composite materials.

On the use of homogenization theory to design optimal piezocomposites for hydrophone applications

We consider an optimal design of composite hydrophones consisting of parallel piezoelectric PZT rods that are embedded in a porous polymer matrix. Given the material properties of the polymer and PZT ceramic, we have optimally designed the piezocomposite to maximize the hydrostatic coupling factor, hydrophone figure of merit, or electromechanical coupling factor, using the methods of homogenization theory. The optimal composite is obtained by using a two-step procedure: (i) first we find the ideal structure of the matrix material by weakening the polymer by an optimal arrangement of pores, and (ii) then we embed the PZT rods in this matrix. The design parameters are the shape, volume fraction, and spatial arrangement of the piezoceramic rods, and the structure of the matrix material. It turns out that the optimal matrix is highly anisotropic and is characterized by negative Poisson's ratios in certain directions. The optimal composites possess performance characteristics that are significantly higher than those of a piezocomposite with an isotropic polymer matrix. The results can be viewed as theoretical upper bounds on the hydrophone performance.

Optimal design of 1-3 composite piezoelectrics

An optimal design problem for piezoelectric composite hydrophones is considered. The hydrophone consists of parallel piezoelectric rods embedded in a poroustransversely isotropic polymer matrix. We find the shape, volume fraction, and spatial arrangement of the piezoceramic rods, and the structure of the matrix material that maximizes the hydrophone performance characteristics. We found that the optimal composite consists of a hexagonal array of rods with small volume fraction, in a highly anisotropic matrix that is characterized by negative Poisson's ratios in certain directions. The performance characteristics of hydrophones with such a matrix are significantly higher than those with anisotropic polymer matrix. The results can be viewed as theoretical upper bounds on the hydrophone performance.

Wide Viewing Angle Properties in Nematic Liquid Crystal/UV Curable Liquid Crystal Composite Films with Some Aligned-Modes.

Liquid crystal l polymer composite (LCPC) films can be electrically switched from a light scattering off-state to a transparent on-state due to the refractive index mismatch or match between the polymer matrix and LC. We have proposed novel LCPC films prepared using a UV curable liquid crystal (UVCLC) as a polymer matrix material, which has an anisotropic optical property in contrast with an isotropic polymer matrix of conventional LCPC films. We investigate the optical properties of nematic LC/UVCLC composite films with homogeneous-, twisted- and hybrid-modes. All of these films show a reverse mode property which have a transparent off-state and light scattering on-state, and wide viewing angle properties in both states. The refractive index match or mismatch is discussed through the relation between the incident light angle and optical axes of the LC and UVCLC.

Skin-core morphology ofin situ composites based on polycarbonate and a liquid crystalline polymer

The outstanding mechanical properties of an engineering liquid crystalline polymer (LCP) can be attributed to the self-reinforcement effect due to its rigid rod-like molecular structure [1-4]. High strength and high stiffness liquid crystalline polymer fibres, e.g. Kevlar and Vectran have been developed and commercialized [5, 6]. Recently there has been increasing interest in blending thermotropic liquid crystalline polymers with conventional isotropic polymers. Liquid crystalline polymer fibre reinforcement can be formed in situ in an isotropic polymer matrix via a melt blending process [7-26]. The structure and morphology of the in situ composites may be controlled by varying the processing conditions and theological history of the blends. Blends of LCPs with conventional polyesters [7, 8], nylon [9], polycarbonate [10-13], polystyrene [11, 14], polypropylene [15, 16], polysulphone [17], poly[ether imide] [18] and poly[phenylene sulphide] [19] have been studied. For extrusion-blended materials, the structure and mechanical properties were found to be closely related to the extrusion conditions, in particular the draw-down ratio. Most researchers have attempted to explain the changes in mechanical properties in terms of the morphology of the LCP phase in the blends, with the most widely used techniques to study the morphology being scanning electron microscopy (SEM) and X-ray diffraction (XRD) [7, 12]. Transmission electron microscopy (TEM) has been widely used to study the crystalline structure of liquid crystalline fibres [4, 6, 20, 21] and the morphology of multiphase polymer systems [22]. Analysis has revealed detailed information on the crystalline structure of aramid and thermotropic liquid crystalline polyester fibres and the development of skin-core morphology of such fibres [4, 21 ]. These findings were related to the properties and sample processing conditions. The work reported in this letter is concerned with the application of the TEM technique to the analysis of blends of a liquid crystalline polymer and polycarbonate. The microstructure and morphology

Thermo-electro-optic switch based on polymer dispersed liquid crystal composite

A new type of thermo-electro-optic switch based on polymer dispersed liquid crystal (PDLC) composite is reported below. The PDLC composite has been made by dispersing a dual frequency addressable liquid crystal (LC) mixture in an isotropic polymer matrix in the form of very fine droplets of micron and submicron sizes. The PDLC cell in the presence of an electric field can be made to switch from transparent to scattering state or vice-versa by varying its temperature by ±≥1 °C, respectively. Moreover, the transition temperature of the PDLC switch can be set by varying the frequency of the electric biasing field.

Ultrasonic examination of proton-transfer reactions in aqueous solutions of Glycine : Hussey, M., Edmonds, P.D., Vol 49, No 4, Part 2 (April 1971) pp 1309–1316

We consider an optimal design of composite hydrophones consisting of parallel piezoelectric PZT rods that are embedded in a porous polymer matrix. Given the material properties of the polymer and PZT ceramic, we have optimally designed the piezocomposite to maximize the hydrostatic coupling factor, hydrophone figure of merit, or electromechanical coupling factor, using the methods of homogenization theory. The optimal composite is obtained by using a two-step procedure: (i) first we find the ideal structure of the matrix material by weakening the polymer by an optimal arrangement of pores, and (ii) then we embed the PZT rods in this matrix. The design parameters are the shape, volume fraction, and spatial arrangement of the piezoceramic rods, and the structure of the matrix material. It turns out that the optimal matrix is highly anisotropic and is characterized by negative Poisson's ratios in certain directions. The optimal composites possess performance characteristics that are significantly higher than those of a piezocomposite with an isotropic polymer matrix. The results can be viewed as theoretical upper bounds on the hydrophone performance.