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Copyright of Electronic Processing of Materials / Elektronnaya Obrabotka Materialov is the property of Institute of Applied Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electronic Processing of Materials / Elektronnaya Obrabotka Materialov is the property of Institute of Applied Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper discusses a composite material from chopped thin narrow polymer tapes reinforced with carbon fibers and a polymer binder. The problem is posed to analytically determine the elastic and strength characteristics of the composite with a known minimum set of basic characteristics of the components. A methodology for sequential solving of the problem at the micro- and meso-levels is proposed. The key point in the methodology is the introduction of the “effective fiber volume factor” in the short filament and the way to calculate it using the “load-carrying factor” criterion. The following are presented: the results of calculating Young’s modulus and tensile strength of material samples from parts of tapes with fixed lengths (6, 12, 18 and 24 mm); comparison with the experimental data and evaluation of accuracy and limits of the applicability of this methodology.

Composite materials are widely used in engineering, especially in constructions working under simultaneous intensive mechanical and thermal loads. In the industry the main requirements for materials are restrictions on the elastic characteristics, such as bulk modulus and shear modulus.Composite materials consist of a base material, a so-called binder (matrix), and reinforcing inclusions. The composite matrix defines a method for the composite manufacturing and must meet a set of operational and technological requirements. The most commonly used types are a metal matrix and a polymer one, because of the relative ease of manufacture, good wettability, and chemical resistance.Reinforcing inclusions can be of different nature (boron, crystalline, etc.) and shape (spherical, lamellar, fiber). Lately, active researches have been conducted with the nanostructural elements (fullerenes, single-walled and multi-walled carbon nanotubes (SWCNTs and MWCNTs) plates, nanoclusters) used as the filler.There are various ways of modeling the elastic properties of the composites. The most common are numerical methods using a finite element method and analytical methods.In simulation of composite characteristics, in addition to the properties of its components, a reinforcing structure plays an important role.The paper considers an obtained isotropic composite with a metal matrix reinforced by the spherical nanoclusters of randomly oriented SWNTs with a reinforcement scheme similar to the cubic crystal lattice. Numerical modeling and analytical methods were used.For the numerical solution two types of periodic structure of the material were obtained: a cube with eight parts of the ball in the corners of a cube and a sphere in the center. For each of the periodic cells a representative volume is selected in which, using the kinematic and force boundary conditions, have been implemented two types of stress-strain state, namely stretching along one axis and shear. For numerical implementation was used a ANSYS software complex coupled with a specially designed software module that allows creating tensors of elastic coefficient and pliability of the composite, as well as averaging its elastic characteristics to have values of bulk and shear moduli of the material.The results of numerical simulations have been compared with the analytical estimates obtained by the self-consistent method and the dual formulation of the elasticity problem in a heterogeneous solid. It is found that in numerical implementation a choice of the composite periodic cell has a significant impact on the values of the shear modulus as opposed to the bulk modulus of elasticity. It is also shown that the numerical simulation results are between the estimates obtained using the analytical models. These results allow predicting the elastic properties of composites, reinforced by spherical inclusions, including advanced materials, i.e. nanocomposites reinforced by spherical nanoclusters of randomly oriented SWCNTs.The paper is done within the framework of implementing basic part of the Governmental task of the Ministry of Education and Science of the Russian Federation (Project 9.7784.2017/БЧ).

This paper investigated the synthesis of inorganic polymer composites for electromagnetic radiation absorption using potassium titanates. The selected polyamide 6 and potassium polytitanate materials contain TiО2, K2СО3, and KCl obtained by charge sintering. Results showed that modification of polyamide 6 with sintering products in the form of a fine powder of potassium polytitanate that contains different phases K2O × 2TiO2, K2O × 4TiO2, and K2O × 6TiO2 which increased their strength properties. With increased potassium titanates (PTT) synthesis, a gradual transition from di to potassium hexatitanates occurs K2O × 2TiO2 – K2O × 4TiO2 – K2O × 6TiO2. The optimal content of potassium polytitanate was over 20 % by mass. To fully ensure the reinforcing effect due to the filling of potassium polytitanate polyamide 6, it is necessary to use whiskers K2O × 6TiO2, which can be collected by the additional crystallization of the amorphous charge sintering product. By designing experimental-statistical mathematical models in equal regressions, mathematical optimization of inorganic polymer composites for electromagnetic radiation absorption using PTT was carried out.

In the paper, the temperature dependences of the differential thermal analysis signal, permittivity, and amplitude of the third harmonic of the (KNO3)1–х/Snx composites have been studied. It was shown that the temperature of the α → β phase transition decreased by 2 – 3 K in the potassium nitrates being parts of the composites, and the temperature of the γ → α phase transition decreased up to 360 K. This result can be explained within the framework of the Landau – Ginzburg theory, taking into account the shielding of potassium nitrate particles by tin metal particles.

The review of the works on the fabrication-technology studies, patterns of structure formation, and properties of in situ composites is presented. The main advantage of in situ (natural) composites is the thermodynamic stability of their composition and the coherence (conjugation) of the lattices of the contacting phases. All these ones provide the composite with a high level of the physical and mechanical properties. As shown, composite materials of this type are formed in the process of directed phase transformations, such as eutectic crystallization, eutectoid decomposition, etc., caused by a temperature gradient, as well as a result of diffusional changes in composition. The conditions for the growth of in situ composites are formulated. The mechanisms of growth of composite structures of the eutectic type are considered. The factors influencing on the morphology of structures of the eutectic type are indicated. The considered technological methods make it possible to obtain materials with predetermined properties, in which the size, volumetric composition, and spatial arrangement of phases are characteristic of in situ composites. The paper provides a large number of examples of in situ composites: from low-melting Bi-based alloys to refractory eutectics based on Mo and W (Bi–MnBi, Cd–Zn, Al–Al3Ni, Al–Al4La, Al–Al10CaFe2, Al–Al9FeNi, Al–Al3Zr, Al–Al3Sc, Au–Co, Si–TaSi2, Cr–HfC, Cr–ZrC, Cr–NbC, Cr–NbC, Cr–TaC, Nb–Nb5Si3, Mo–ZrC, Mo–HfC, W–TiC, W–ZrC, W–HfC, etc.). Processes and aspects of structure formation are considered. The influence of additional doping on the structure and properties of composite materials of the eutectic type of binary systems, as well as the features of the structure formation of ternary colonies in the composite are considered.

An analytical-numerical approach to solving the spatial problem of the theory of elasticity for a half-space rigidly coupled to a layer is proposed. In the half-space, parallel to its boundaries, there is an infinite circular cylindrical cavity. Both the layer and half-space are homogeneous isotropic materials, different from each other. It is necessary to investigate the stress-strain state of the elastic bodies of both the layer and half-space. On both the surface of the cavity and upper boundary of the layer, stresses are given. On the flat surface of contact between the layer and half-space, conjugation conditions arise. The solution to the spatial problem of the elasticity theory is obtained by the generalized Fourier method with regard to both the system of Lamé equations in cylindrical coordinates associated with the cavity and Cartesian coordinates associated with both the layer and half-space. The infinite systems of linear algebraic equations obtained as a result of satisfying both the boundary and conjugation conditions are solved by a reduction method. As a result, displacements and stresses are obtained at different points of both the elastic layer and elastic half-space. The fulfillment of boundary conditions was reduced to 10-4 by using the selected reduction parameter for the given geometric characteristics. An analysis of the stress-strain state of both the layer and half-space with the given physical and geometric parameters has been carried out. Graphs of stresses at the boundary between the layer and half-space, on the surface of the cavity and upper boundary of the layer, as well as on the bridge between the cavity and boundary of the half-space are presented. The indicated stress graphs show that the maximum stresses are concentrated both on the surface of the cylindrical cavity and surface of the half-space. The proposed method can be used to calculate parts and components, underground structures and communications, whose design schemes coincide with the purpose of this paper. The stress analysis presented above can be used to select geometric parameters at the design stage, and the stress graphs at the boundary between the layer and half-space, to analyze the coupling strength.

The paper shows the issue of determining the limiting load for the circular three-layer plate the middle layer of which is reinforced with four layers of fibers in the main directions. The inner contour of the plate is freely supported, and the outer one is fixed. It is shown that the plate is divided into five circular zones, in each of which various plastic states occur. Static fields of moments are determined, equations for unknown radii between plastic zones are found, as well as equations for determining the support reaction and the limiting load.

Among the desirable properties of functional materials used in various electrical and radio physical equipment and devices, dielectric characteristics, including relative permittivity (hereinafter, permittivity) are of importance. The permittivity requirements can be met when a composite with a particular combination of its matrix characteristics and inclusions [1, 2, 3] is used as a functional material. The use of metallic inclusions extends a variation range of dielectric characteristics of the composite, and thereby enhances its application. The composite structure, form of inclusions, and their volume concentration has a significant impact on the permittivity.One of the composite structure embodiments is a dispersion system when in the dispersion medium (in this case | in the composite matrix) a dispersed phase (inclusions) with highly extended interface between them [4] is distributed. There can be various forms of dispersed inclusions. Band is one of the possible forms of inclusion when its dimensions in three orthogonal directions are significantly different among themselves. For such inclusion, a tri-axial ellipsoid can be taken as an acceptable geometric model to describe its form. This model can be used, in particular, to describe the form of nanostructured elements, which recently are considered as inclusions for advanced composites for various purposes [5].With raising volume concentration of metal inclusions in the dielectric matrix composite there is an increasing probability of direct contact between the inclusions resulting in continuous conductive cluster [3, 6]. In this paper, it is assumed that metal band inclusions are covered with a sufficiently thin layer of the electrically insulating material, eliminating the possibility of direct contact and precluding consideration of the so-called percolation effect [2, 7] in the entire interval of the expectedly changing volume concentration of electrically ellipsoidal inclusions. The structural model of the composite these inclusions are replaced by the uniform ellipsoidal inclusions with equivalent anisotropic dielectric characteristics that with the ordered arrangement of the inclusions leads to anisotropy of effective dielectric characteristics of the composite as a whole.There are known various approaches [1, 8, 9, 10] to the mathematical modeling that allow us to build calculated curves to determine dielectric characteristics of the composites having inclusions of different forms. When building such models, the analogy between the formulations and problem solutions of electrostatics and steady thermal conductivity [11, 12, 13, 14] can be used. Variation approaches [15, 16, 17] to estimate effective dielectric properties of the composite allow us to obtain bilateral borders between which there are their true values, and evaluate the maximum possible error occurring in using a particular mathematical model. Such borders can be set on the basis of the dual variation formulation of the problem for a potential field in an inhomogeneous solid [18]. This formulation contains two alternative functionals (minimized and maximized), taking the same extreme values in the true problem solving.DOI: 10.7463/mathm.0515.0815604

Composites are widely used as structural or thermal protection materials; they are used as well as functional materials in a large number of different electrical devices and as dielectrics. This composite has one of the most important characteristics the relative permittivity. It depends primarily on the dielectric properties of the inclusions and the matrix as well as the shape and volume content of the inclusions.In this paper, a mathematical model of the interaction of the electrostatic fields in an isotropic plate and in the surrounding homogeneous anisotropic medium is constructed. This model describes the dielectric properties of the composite with such inclusions. A variant of the same orientation of lamellar inclusions is considered, which leads to the special case of anisotropy of the dielectric properties of the composite that has transverse isotropy towards the direction perpendicular to the inclusions. The shape of inclusions is represented as an oblate ellipsoid of revolution (spheroid). Transformation of the differential equation describing the distribution of the electric potential transversely to isotropic medium surrounding the spheroidal inclusion, to the Laplace equation with the subsequent transition from the initial spheroid to the given ellipsoid of rotation allows us to apply the self-assessment method for the determination of the dielectric properties of the composite. This method equates the result of averaging the perturbation of the electrostatic field in the inclusions and the matrix particles towards the unperturbed fields in the environment to zero.The constructed mathematical model allows us to determine the electrostatic field disturbance in the inclusions and the matrix particles towards the unperturbed field given in the environment at a distance from the inclusions and the matrix particles, much larger than their characteristic dimensions. By averaging the perturbation of the electrostatic field in all the elements of the composite structure, a system of two quadratic equations for the desired principal values of the permittivity tensor of the composite is obtained. Results of this quantitative analysis are shown in graphs and can be used to predict the dielectric characteristics of composites with identically oriented lamellar inclusions (including in the form of nanostructured elements).DOI: 10.7463/mathm.0115.0776021

Composites are increasingly used for application in engineering as structural, thermal protection and functional materials, including dielectrics, because of a wide variety of properties. The relative dielectric constant and the dielectric loss tangent are basic functional characteristics of a composite used as a dielectric. The quantitative level of these characteristics is mainly affected by the properties of the composite matrix and inclusions as well as their shape and volume concentration. Metallic inclusions in a dielectric, which serves as a function of the composite matrix, expand electrical properties of the composite in particular increase its dielectric constant and dielectric loss tangent and thereby greatly expand its application field. Dielectric losses are defined by the imaginary component of the complex value of the relative dielectric constant of the dielectric. At a relatively low vibration frequency of electromagnetic field affecting the dielectric, this value is proportional to the electrical conductivity of the dielectric and inversely proportional to the frequency. In order to predict the expected value of the electric conductivity of the dielectric with metallic inclusions, a mathematical model that properly describes the structure of the composite and the electrical interaction of the matrix and inclusions is required.In the paper, a mathematical model of the electrical interaction of the representative element of the composite structure and a homogeneous isotropic medium with electrical conductivity, which is desired characteristics of the composite, is constructed. Globular shape of the metallic inclusions as an average statistical form of dispersed inclusions with a comparable size in all directions is adopted. The inclusion is covered with a globular layer of electrical insulation to avoid percolation with increasing volume concentration of inclusions. Outer globular layer of representative structure of composite elements consists of the dielectric material matrix.Quantitative analysis of two-sided estimates of possible values of the electrical conductivity of the composite, which are constructed by using dual variational electrokinetics problem statement for a heterogeneous solid body, showed that for real dielectric matrix material combinations and metallic inclusions in case when their electrical conductivity can differ by more than 10 orders of magnitude, these estimates can vary widely the specified characteristics of a composite. Therefore, to obtain the estimated effective dependence, a solution to the electrokinetics problem for representative element of the composite structure based on the assumption about ideal conductivity of metallic inclusions is found. It is shown that this dependence reflects properly the influence of the properties of the structural elements of a composite on its electrical conductivity.DOI: 10.7463/mathm.0315.0793596

Composites are inhomogeneous materials (heterogeneous solid body, which fall into the matrix and inclusions. The matrix in a composite is a binder between the inclusions. The properties of the inclusions mainly determine the application of composites. Selection of the characteristics of the matrix and inclusions enables us to meet the requirements for materials to be used in various fields of technology. Composites are widely used as structural or thermal protection material and as functional materials in various electrical devices, including dielectrics. One of the most important characteristics of the composite dielectric is the relative permittivity. The latter is primarily determined by the dielectric properties of the matrix and inclusions, as well as the shape and volume concentration of inclusions.For a composite with dispersed inclusions we are able to construct adequate mathematical models which enable us to predict sufficiently reliably the dependence of its dielectric constant on these defining parameters. In this paper, among the various approaches to the construction of such models we emphasize a variational approach which allows us not only to determine this dependence, but also obtain guaranteed bilateral boundaries of the area of possible values of the dielectric constant of the composite used to estimate the highest accuracy of calculated values.The representative element of the composite structure with inclusions of spherical shape modeling the form of dispersed inclusions with dimensions close to all directions is considered. For the representative element we obtained the electrostatic potential distribution that is permissible for the minimized functional. The latter is the part of the variational form of a mathematical model which describes the dielectric properties of the considered composite. From the equality of the values of this functional on the received permissible distribution in a representative element of the composite structure and on the distribution in the equal-element of homogeneous medium with the desired dielectric constant of the composite we determined the dependence of this value on the dielectric characteristics of the matrix and inclusions and on the volume concentration of inclusions.Quantitative analysis of the obtained dependence in a wide range of defining parameters showed that all the results of the calculations are located in the area of possible values. This area is defined by constructed bilateral estimates. This confirms the appropriate use of the variational approach and the possibility of its application for the prediction of the dielectric characteristics of composites with dispersed inclusions.DOI: 10.7463/mathm.0215.0769483

Among the desirable properties of functional materials used in various electrical and radio physical equipment and devices, dielectric characteristics, including relative permittivity (hereinafter, permittivity) are of importance. The permittivity requirements can be met when a composite with a particular combination of its matrix characteristics and inclusions [1, 2, 3] is used as a functional material. The use of metallic inclusions extends a variation range of dielectric characteristics of the composite, and thereby enhances its application. The composite structure, form of inclusions, and their volume concentration has a significant impact on the permittivity.One of the composite structure embodiments is a dispersion system when in the dispersion medium (in this case | in the composite matrix) a dispersed phase (inclusions) with highly extended interface between them [4] is distributed. There can be various forms of dispersed inclusions. Band is one of the possible forms of inclusion when its dimensions in three orthogonal directions are significantly different among themselves. For such inclusion, a tri-axial ellipsoid can be taken as an acceptable geometric model to describe its form. This model can be used, in particular, to describe the form of nanostructured elements, which recently are considered as inclusions for advanced composites for various purposes [5].With raising volume concentration of metal inclusions in the dielectric matrix composite there is an increasing probability of direct contact between the inclusions resulting in continuous conductive cluster [3, 6]. In this paper, it is assumed that metal band inclusions are covered with a sufficiently thin layer of the electrically insulating material, eliminating the possibility of direct contact and precluding consideration of the so-called percolation effect [2, 7] in the entire interval of the expectedly changing volume concentration of electrically ellipsoidal inclusions. The structural model of the composite these inclusions are replaced by the uniform ellipsoidal inclusions with equivalent anisotropic dielectric characteristics that with the ordered arrangement of the inclusions leads to anisotropy of effective dielectric characteristics of the composite as a whole.There are known various approaches [1, 8, 9, 10] to the mathematical modeling that allow us to build calculated curves to determine dielectric characteristics of the composites having inclusions of different forms. When building such models, the analogy between the formulations and problem solutions of electrostatics and steady thermal conductivity [11, 12, 13, 14] can be used. Variation approaches [15, 16, 17] to estimate effective dielectric properties of the composite allow us to obtain bilateral borders between which there are their true values, and evaluate the maximum possible error occurring in using a particular mathematical model. Such borders can be set on the basis of the dual variation formulation of the problem for a potential field in an inhomogeneous solid [18]. This formulation contains two alternative functionals (minimized and maximized), taking the same extreme values in the true problem solving.

Composites are widely used as structural or thermal protection materials; they are used as well as functional materials in a large number of different electrical devices and as dielectrics. This composite has one of the most important characteristics the relative permittivity. It depends primarily on the dielectric properties of the inclusions and the matrix as well as the shape and volume content of the inclusions.In this paper, a mathematical model of the interaction of the electrostatic fields in an isotropic plate and in the surrounding homogeneous anisotropic medium is constructed. This model describes the dielectric properties of the composite with such inclusions. A variant of the same orientation of lamellar inclusions is considered, which leads to the special case of anisotropy of the dielectric properties of the composite that has transverse isotropy towards the direction perpendicular to the inclusions. The shape of inclusions is represented as an oblate ellipsoid of revolution (spheroid). Transformation of the differential equation describing the distribution of the electric potential transversely to isotropic medium surrounding the spheroidal inclusion, to the Laplace equation with the subsequent transition from the initial spheroid to the given ellipsoid of rotation allows us to apply the self-assessment method for the determination of the dielectric properties of the composite. This method equates the result of averaging the perturbation of the electrostatic field in the inclusions and the matrix particles towards the unperturbed fields in the environment to zero.The constructed mathematical model allows us to determine the electrostatic field disturbance in the inclusions and the matrix particles towards the unperturbed field given in the environment at a distance from the inclusions and the matrix particles, much larger than their characteristic dimensions. By averaging the perturbation of the electrostatic field in all the elements of the composite structure, a system of two quadratic equations for the desired principal values of the permittivity tensor of the composite is obtained. Results of this quantitative analysis are shown in graphs and can be used to predict the dielectric characteristics of composites with identically oriented lamellar inclusions (including in the form of nanostructured elements).

Composites are increasingly used for application in engineering as structural, thermal protection and functional materials, including dielectrics, because of a wide variety of properties. The relative dielectric constant and the dielectric loss tangent are basic functional characteristics of a composite used as a dielectric. The quantitative level of these characteristics is mainly affected by the properties of the composite matrix and inclusions as well as their shape and volume concentration. Metallic inclusions in a dielectric, which serves as a function of the composite matrix, expand electrical properties of the composite in particular increase its dielectric constant and dielectric loss tangent and thereby greatly expand its application field. Dielectric losses are defined by the imaginary component of the complex value of the relative dielectric constant of the dielectric. At a relatively low vibration frequency of electromagnetic field affecting the dielectric, this value is proportional to the electrical conductivity of the dielectric and inversely proportional to the frequency. In order to predict the expected value of the electric conductivity of the dielectric with metallic inclusions, a mathematical model that properly describes the structure of the composite and the electrical interaction of the matrix and inclusions is required.In the paper, a mathematical model of the electrical interaction of the representative element of the composite structure and a homogeneous isotropic medium with electrical conductivity, which is desired characteristics of the composite, is constructed. Globular shape of the metallic inclusions as an average statistical form of dispersed inclusions with a comparable size in all directions is adopted. The inclusion is covered with a globular layer of electrical insulation to avoid percolation with increasing volume concentration of inclusions. Outer globular layer of representative structure of composite elements consists of the dielectric material matrix.Quantitative analysis of two-sided estimates of possible values of the electrical conductivity of the composite, which are constructed by using dual variational electrokinetics problem statement for a heterogeneous solid body, showed that for real dielectric matrix material combinations and metallic inclusions in case when their electrical conductivity can differ by more than 10 orders of magnitude, these estimates can vary widely the specified characteristics of a composite. Therefore, to obtain the estimated effective dependence, a solution to the electrokinetics problem for representative element of the composite structure based on the assumption about ideal conductivity of metallic inclusions is found. It is shown that this dependence reflects properly the influence of the properties of the structural elements of a composite on its electrical conductivity.

The process of heat conduction can be modeled via random motion of particles of heat energy, although these particles do not physically exist: they are considered as special formal objects. The speed of diffusion of heat particles in each material is proportional to its temperature conductivity coefficient. This mathematical model underlying the method of obtaining the effective heat conductivity coefficient of a composite material described in the previous paper \Heat conductivity of composite materials with included balls of zero heat conductivity" now is being modified in order to deal with materials with various nonzero heat conductivity and capacity coefficients. Namely, when a particle passes from one material to another one, having smaller heat conductivity, it is reflected from the frontier with a certain probability.As a criterion of heat conductivity, we consider the probability that a heat particle starting on one surface of a composite layer, goes to its other surface in a time shorter than T. For a homogeneous material, this probability is calculated theoretically.For a layer of a composite, we perform a multiple computational experiment modeling heat conduction, and for the desired probability we find the confidence interval, wherefrom we obtain the confidence interval for the effective temperature conductivity coefficient, and, finally, calculate the effective heat conductivity coefficient.We have considered inclusions of materials with heat conductivity and volume heat capacity coefficients differing from those of the matrix in 3 times up or down. Ball inclusions of equal size were situated in a cubic order or chaotically. The ratio of the ball radius to the size of cubes was 0.2, 0.3, or 0.4.In series of 4300 randomly moving particles, in all cases considered, the difference between the effective heat conductivity coefficients and those calculated by other methods does not exceed a statistical error.The developed method makes it possible to obtain effective heat conductivity coefficients for composites with inclusions of any size and shape; it can be applied also in a case of inclusions from several materials. The results obtained are reliable and only the computer capability restricts their exactness.

Composites are inhomogeneous materials (heterogeneous solid body, which fall into the matrix and inclusions. The matrix in a composite is a binder between the inclusions. The properties of the inclusions mainly determine the application of composites. Selection of the characteristics of the matrix and inclusions enables us to meet the requirements for materials to be used in various fields of technology. Composites are widely used as structural or thermal protection material and as functional materials in various electrical devices, including dielectrics. One of the most important characteristics of the composite dielectric is the relative permittivity. The latter is primarily determined by the dielectric properties of the matrix and inclusions, as well as the shape and volume concentration of inclusions.For a composite with dispersed inclusions we are able to construct adequate mathematical models which enable us to predict sufficiently reliably the dependence of its dielectric constant on these defining parameters. In this paper, among the various approaches to the construction of such models we emphasize a variational approach which allows us not only to determine this dependence, but also obtain guaranteed bilateral boundaries of the area of possible values of the dielectric constant of the composite used to estimate the highest accuracy of calculated values.The representative element of the composite structure with inclusions of spherical shape modeling the form of dispersed inclusions with dimensions close to all directions is considered. For the representative element we obtained the electrostatic potential distribution that is permissible for the minimized functional. The latter is the part of the variational form of a mathematical model which describes the dielectric properties of the considered composite. From the equality of the values of this functional on the received permissible distribution in a representative element of the composite structure and on the distribution in the equal-element of homogeneous medium with the desired dielectric constant of the composite we determined the dependence of this value on the dielectric characteristics of the matrix and inclusions and on the volume concentration of inclusions.Quantitative analysis of the obtained dependence in a wide range of defining parameters showed that all the results of the calculations are located in the area of possible values. This area is defined by constructed bilateral estimates. This confirms the appropriate use of the variational approach and the possibility of its application for the prediction of the dielectric characteristics of composites with dispersed inclusions.

The paper presents the results of experimental studies of thermal conductivity and microwave absorption in aluminum nitride based composites with different percentages of silicium carbide and molybdenum. It is shown that the optimal composition of the studied materials is the composite with 46% of silicium carbide and 4% of molybdenum. This composition reveals high UHF-energy absorption level of 42 dB/cm in the frequency range of 9.5—10.5 GHz and high thermal conductivity of 65 W/(m*K).

Scope composites as structural materials sensing mechanical stresses are largely determined by a complex of their elastic properties. Described in the article of review papers devoted to the elastic properties of the composite, it follows that the problem of theoretical evaluation of these characteristics, remains relevant. When considering composites reinforced with spherical inclusions, most famous works of the composite matrix and the inclusion is considered to be isotropic. However, for use as inclusions of metal particles and nanostructured elements often need to consider the anisotropy of the elastic characteristics.In the article for a composite with anisotropic spherical inclusions built two types of estimates of values of the bulk modulus and shear modulus . As background information used elastic properties of the matrix and the inclusions and their content by volume in the composite.The first type is classified as two-sided estimates of desired values that are based on the dual variational formulation of the linear elasticity problem of an inhomogeneous solid body containing alternative functionals (Lagrange and Castigliano). These functionals on the true distribution of strains and stresses in an inhomogeneous body reach the same meaning extremes (minimum and maximum respectively). On the convergence of the distribution of the Lagrange functional application allows you to get an upper bound of desired values, and the use of functional Castigliano - their lower bound.The second type of assessment is built by self-consistency, this method allows for the interaction of a single particle on or matrix composite with a homogeneous isotropic medium having measured the elastic moduli. Averaging over the volume of the composite disturbances arising strains and stresses in the inclusions and matrix particles makes it possible to obtain the calculated dependences for the bulk modulus and shear modulus of the composite. Comparison of these calculations for these dependences with relevant bilateral estimates not only allows you to set the degree of reliability of the results, but also to quantify their possible error.

Samples of the «polyethylene — VO2» composite have been obtained using technologies for manufacturing self-healing polyswitch fuses. The volume fraction of vanadium dioxide in the samples ranged from 0,25 to 0,6. It is shown that the electrical conductivity of the composite is of percolation character. The paper presents research results of the microstructure, the resistance temperature dependence and current-voltage characteristics of polymer composite samples, as well as the impact of the VO2 content on the samples.

The paper deals with computing technique of effective dielectric permittivity of crystobalite formed in glass-ceramic body by means of measured dielectric permittivity of glass-ceramic composit. Dependence of the calculated parameter from the time of crystallization is found.