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Porous plastics are used in various fields of industry, including radio- and electrotechnical fields. They are characterized by good heat- and sound isolating, dielectric and mechanical properties as well as by resistance to effect of various external factors during operation. The problem of estimation of effective permittivity of foam-polymer materials with a large volume fraction of pores, in particular, polyepoxide foam materials, has been considered. Two methods for solving it, both based on the matrix have been proposed. In the first method the matrix is considered as a polyepoxide binder, and the cavities filled with gas are taken as inclusions. In the second method the polyepoxide walls, separating cavities, are taken as inclusions, and gas filling cavities is considered as a matrix. To obtain the formulas for calculation, both methods use a generalized singular approximation of the theory of random fields. Based on the obtained expressions, the model calculations of the effective permittivity of a macroscopically isotropic foam material with a polymer binder based on E-20 and the cavities filled with freon, depending on the apparent density of the material, have been made. The calculations in the generalized singular approximations have been carried out for two of its variants: when the matrix was considered as a comparison medium; and, also by the self-consistent method. In the calculations using the second method two variants of the shape of the cells of the material have been considered: a weakly leaked or heavily leaked polyhedron. The calculated dependences obtained by all me-thods have shown the qualitative compliance with the experimental data.

A method is proposed for predicting the effective thermal conductivity of a matrix composite with several types of spherical inclusions, in the case of contact thermal resistance at the matrix–inclusion boundary. The method is based on generalized effective-field approximation for a inhomogeneous medium containing inclusions that have an outer shell. As an example, calculations are presented for a matrix tribocomposite with two types of inclusions.

Theoretical model has been developed for predicting the average stress values during melting of water frozen in silicon-based mesoporous structures in the temperature range 233...273 K, caused by the difference in the thermal expansion coeffi cients of the heterogeneity elements in the materials studied. Numerical calculations were carried out using and dependences of the average stress tensor components on the volumetric water content in the mesoporous silicon matrix were investigated.

A method is proposed for predicting the effective thermal conductivity of a matrix composite with several types of spherical inclusions with contact thermal resistance at the boundary of the matrix and inclusions. The method is based on a generalized effective-field approximation for an inhomogeneous medium with inclusions with a shell. Model calculations were performed for a matrix tribocomposite with two types of inclusions. Keywords: effective thermal conductivity, contact thermal resistance, composite material, matrix, inclusion with a shell, Maxwell—Garnett approximation, generalized effective-field approximation. alekc_sap@mail.ru

By means of a generalized effective-field approximation, formulas are derived for the effective thermal conductivity of a three-component tribocomposite based on a phenylone matrix with spherical strengthening inclusions (alumoborosilicate glass) and inhomogeneous antifrictional inclusions (spherical capsules of glycerin in a Kapton® shell). The thermal conductivity is investigated as a function of the concentrations of inclusions and the ratio of the internal and external radii of the antifrictional inclusions.

This study is devoted to the confinement effects on freezing and melting in electrochemical systems containing nanomaterial electrodes and liquid electrolytes. The melting of nanoparticles formed upon freezing of liquids confined in pores of disordered nanostructured n-type silicon has been studied by low-temperature differential scanning calorimetry. Experimental results obtained for deionized water, an aqueous solution of potassium sulfate, and n-decane are presented. A model is proposed for predicting the melting point of nanoparticles formed during freezing of liquids inside the pores of a disordered nanostructured material. The model is based on the classical thermodynamic concept of the phase transition temperature dependence on the particle size. It takes into account the issues arising when a liquid is dispersed in a matrix of another material: the effect of mechanical stress resulted from the difference in the thermal linear expansion coefficients at a temperature gradient, the effect of the volumetric liquid content in the matrix, the presence of a nonfreezing liquid layer inside the pores, and the effect of wettability of the matrix with the liquid. Model calculations for water and n-decane confined in nanostructured silicon matrix have been carried out considering the volumetric liquid content. The results obtained have been compared with the differential scanning calorimetry data.

In the generalized singular approximation the expression for a tensor $\mathbf{k}^{\ast }$ of effective thermal conductivity of a multicomponent matrix composite is received. Each component is considered consisting of isotropic ellipsoidal inclusions with orientations distributed under some probabilistic law. The shape of the inclusions of a given type (relating to the given component) is considered identical.On the basis of the received expression the method is developed for calculation of a tensor $\mathbf{k}^{\ast }$ of the three-component textured matrix tribocomposite with epoxy ED-20 system as a matrix, inclusions from a polytetrafluoroethylene of spherical shape as an antifrictional component and glass fibers as the reinforcing component. It is considered that glass fibers, have small dispersion in orientations around some axis - a texture axis, their volume fraction changes in the range from 0,4 to 0,7. The method uses fine tuning of parameter $k^{(c)}$ of the comparison medium depending on a volume fraction of glass fibers and a ratio between thermal conductivities of inclusions and of matrix. This tuning dependence is received by comparison of results of model and finite-differences calculations for a two-component matrix composite with glass fibers without dispersion of their orientations. The method is applied to a research of influence of size of dispersion in orientations of glass fibers to tensor $\mathbf{k}^{\ast }$ components. Dependences of principal components of tensor of the effective thermal conductivity of this tribocomposite on a volume fraction of the glass reinforcing inclusions are given at various sizes of dispersion in their orientations. It is shown that increase in dispersion in orientations of glass fibers leads to reduction of longitudinal component and to growth of transverse component of tensor $\mathbf{k}^{\ast }$ with respect to the texture axis. It is also shown that values of the principal components of a tensor of effective thermal conductivity are less than average on volume basis value of a thermal conductivity.

The paper presents model calculations on which to predict volume-average external stress under changes of local internal stress in matrix composites with non-isometric inclusions. It is assumed that the rise of local stress owes to different coefficients of linear thermal expansion of non-isometric inclusions and matrix. The inclusions are taken as ellipsoids of rotation (disks, short fibers) and their principal semiaxes as oriented either along three mutually perpendicular directions x, y, and z of a rectangular coordinate system, only along x and y, or only along x. The average stress in the heterogeneous material and its local stress within an individual inclusion are related through a stress concentration operator (fourth rank tensor) for which an explicit expression is derived in a generalized singular approximation of random field theory. The relations obtained for external stress take into account thermoelastic characteristics of the two components as well as inclusion concentrations and orientations in the matrix. The calculation is applied to estimate the average stress along three axes in a composite consisting of an ED-20 epoxy binder and non-isometric copper inclusions.

A method for predicting the local elastic characteristics of multicomponent matrix-assisted tribocomposites with spherical microcapsules filled with a liquid lubricant is proposed. These characteristics are defined by the operators (tensors) of the stress and strain concentration. This method is based on a generalized singular approximation of the theory of random fields and allows taking into consideration the inherent size of microcapsules (the ratio of the shell thickness to the radius of the liquid filler) and the volume fraction of the tribocomposite components. The local elastic characteristics are numerically modelled for the composites based on phenylon with disperse inclusions of alkali-free glass and microcapsules, which are spherical kapton shells filled with glycerin. The dependences of the local elastic properties of the tribocomposites on the inherent size of the microcapsules at fixed volume fractions of the heterogeneity elements are studied.

The article suggests the technology of modifying a polymer matrix by microencapsulation, i. e. the introduction of microparticles (lubricants with nano-additives in polymer shells) into nanocomposites matrix, to form multilevel structures on the tribounit surface. Besides, it suggests the method of predicting the operational elastic properties of multicomponent matrix composites with microcapsules, filled with a liquid substance. The method is based on the generalized singular approximation of the theory of random fields and allows, taking into account the geometric dimensions of the inclusions in the shell. It contains the results of numerical modelling of the effective elastic characteristics (Young’s modulus and Poisson’s ratio) of composites, based on phenylone with dispersed inclusions (microcapsules), which are glycerin-filled spherical shells of the kapton. The paper investigates the effect of the geometric dimensions of microcapsules and the volumetric content of components on the operational elastic properties of tribocomposites. The developed antifriction nanomaterials with microcapsules are able to create an oriented lubricating coating on the friction surfaces, apply lubrication to a certain friction area and carry out the lubrication portion wise precisely in the necessary contact zone of the bodies.

On the basis of a generalized singular approximation, formulas are derived for the effective thermal conductivity of a three-component tribocomposites with reinforcing spheroidal inclusions. The dependence of the thermal conductivity on the volume fraction and aspect ratio of the ellipsoidal inclusions is investigated.

An approach developed on the basis of a model of a composite with heterogeneous inclusions—the effective-field approximation—is proposed. With the help of this approximation, an expression is obtained for the tensor of effective dielectric characteristics of a heterogeneous medium consisting of inclusions representing a core inside a coating, the outer and inner boundaries of which are ellipsoids. The proposed approach has a large degree of generality and can be used both for multicomponent composites and for polycrystals. It was shown that this approach gives the same result as the generalized singular approximation in the case of the uncoated inclusions.

The limiting strength of antifrictional polymer composites in uniaxial compression is investigated as a function of their components, by numerical modeling.

The strain energy in nanocomposites based on porous anodic aluminum oxide and filamentary nanoparticles of Cu, Ag, and Au is simulated numerically. The results allow us to estimate the contribution from mechanical stresses produced upon heating, due to differences between the thermal coefficients of the linear expansion of elements of heterogeneity upon a change in the melting point of spatially confined metallic filamentary nanoparticles. The dependence of the energy of deformation on the structural parameter associated with the concentrations of Cu, Ag, and Au fibers in the considered nanocomposite systems is studied. It is found that at temperatures close to 1000°C, the contribution from mechanical stresses to the change in melting point, quantitatively expressed by the studied energy characteristic, is negligible in comparison to the contribution from the surface.

[For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version)].The research of V. I. Kolesnikov and A. P. Sychev was carried out thanks to the grant of the Russian Science Foundation (project No. 14-29-00116) at Rostov State Transport University. ABSTRACT The problem of predicting the operational elastic properties of composites based on binders with a high content of epoxy groups (the grade of EPAF and its modification), chaotically reinforced with short polyimide (or glass) fibers with antifriction disperse additives of polytetrafluoroethylene was solved. Numerical model calculations of the effective elastic characteristics (Young’s modulus and Poisson’s ratio) of these tribocomposites were made taking into account changes in the concentrations of their components. Keywords: transport engineering, modeling, tribocomposite, inclusion, epoxy binder, effective elastic moduli.

The problem of numerical simulation is solved for operators (tensors) of the stress and strain concentrations, which are related material-average stresses and strains with their local values in epoxyphenolic composites reinforced randomly by short polyimide fibers with antifrictional dispersed additives of polytetrafluoroethylene. Simulation is based on the generalized singular approximation of random field theory. The dependences of mentioned operators on the percentage of isotropic components are investigated. It is shown that an increase in the antifrictional additive concentration with a fixed fiber concentration does not result in a substantial decrease in the local elastic characteristics of the composite.

Bulk strain energy density was numerically simulated for epoxy-phenol-based composites randomly reinforced with short polyimide fibers, with antifriction dispersed polytetrafluoroethylene (PTFE) additives. A mathematical model was constructed using the notion of a stress concentration operator (fourth-rank tensor) that relates volume averaged, or external, stresses within a heterogeneous material with their local values within an individual heterogeneity. The simulation was based on a generalized singular approximation of random field theory used to solve a stochastic differential equation of equilibrium of an elastic medium. This approximation yields an explicit expression for stress concentration in a composite material. The explicit expression allows one to analyze the distribution of bulk strain energy density depending on the composition, structure, volume and mass fraction of heterogeneities, and on the type and value of applied load. We studied how the considered energy characteristic depends on the type of external mechanical loading and concentration of isotropic components in the model composites. It is shown that with the increasing concentration of polyimide fibers at a fixed concentration of PTFE inclusions, the bulk strain energy density values of all components decrease and approach each other independently of the type of external loading. The form of these dependences is nonlinear. A change in the mass fraction of dispersed PTFE inclusions in the model composites exerts little effect on local energy values of all components under any of the considered applied external loads.

A method of prediction of distributions of local electric fields in composite media based on analysis of the tensor operators of the concentration of intensity and induction is proposed. Both general expressions and the relations for calculating these operators are obtained in various approximations. The analytical expressions are presented for the operators of the concentration of electric fields in various types of inhomogeneous structures obtained in the generalized singular approximation.

The elastic properties of composites (the Young’s modulus, Poisson’s ratio, Lame constant, and shear elastic modulus) are determined in model calculations, when the variation in concentration of the components is taken into account.

The limiting strength in the compression of composites based on an epoxy-resin matrix with disperse inclusions (graphite, E-glass, copper, and iron) is simulated on the basis of the generalized singular approximation of random-field theory, using the stress-concentration operator and data regarding the strength of the epoxy matrix.

The problems of calculating the effective dielectric characteristics of polycrystalline materials are considered taking into account the frequency dependence of the characteristics of individual components. The effective characteristics of ceramics such as lead zirconate-titanate with titanium and zirconium oxide, metal lead, and water inclusions are calculated in the Maxwell-Garnett and Bruggeman approximations. The dependences of the effective dielectric characteristics on the inclusion concentration and applied electromagnetic-field frequency are obtained.

The problem of determining the bulk density of the energy of deformation in composites with threadlike metal nanocrystals in a matrix of anodic aluminum oxide is solved with allowance for the difference between the thermal coefficients of the linear extension of elements of heterogeneity. Model calculations are performed for nanocomposites with tin, zinc, and indium nanocrystals.

Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman’s approximation), the Maxwell-Garnett approximation, Wiener’s bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.

We have assessed the average stress induced by the thermal expansion mismatch between the components of composites consisting of metallic nanowires and an anodic aluminum oxide matrix and performed model calculations for composites containing tin, zinc, and indium nanocrystals.

The energy of the elastic field in unidirectional composites based on high-epoxy resins is calculated. The influence of the composition and concentration of isotropic components and the type of external mechanical loading on that elastic energy is considered.

Filling dielectric porous matrices, particularly anodic aluminum oxide, with metal confers a promising solution for nanocomposite creation. In this regard, the problem of estimating and predicting the physical and mechanical properties of such materials is of prime importance. The present work focuses on the numerical modeling of the effective and ultimate stress-strain (under compression) characteristics of nanocomposites based on anodic aluminum oxide with unidirectional filamentary pores filled with different metals (In, Sn, and Zn). The dependences of the tensor components of the effective elastic moduli, coefficients of elastic anisotropy (in different directions), and compression strength (along the nanowires) on the structure parameters and the concentration of nanowires are investigated.

The arrays of metallic nanowires are considered as promising precursors for 1D semiconductor nano-structures after appropriate treatment at temperatures close to the melting point. Therefore the melting behaviour of the metallic structures in oxide templates is a key parameter for the subsequent conversion process. The present paper focuses on understanding of the effect of mechanical stress generated during heating on the melting point of the metal nanowires deposited into the pores of anodic alumina. Extremely high local compressive stress appears due to the difference in the thermal coefficients of the oxide template and nanowires inside the pores. The effect of the composite structural parameter that may be related to the concentration of nanowires on the melting temperature has been investigated. A numerical model predicting the melting point has been developed for composites with indium, tin, and zinc nanowires. The simulation results obtained using the suggested model were compared with the experimental data.