V. B. Yakovlev

Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation

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.

Predicting the Limiting Strength of Nontextured Matrix Composites

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.

Bulk strain energy density in randomly reinforced polymer composites with antifriction dispersed additives

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 analysis of distributions of local electric fields in composites

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.

Effect of Thermoelastic Characteristics of Components, Shape of Non-Isometric Inclusions, and Their Orientation on Average Stresses in Matrix Structures

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 generalized effective-field approximation for an inhomogeneous medium with coated inclusions

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.

Predicting the elastic properties of randomly reinforced polymer composites with antifrictional additives

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.

Concentration effect of antifrictional additives on local elastic characteristics of randomly reinforced polymer composites

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.

Effect of bottom-electrode morphology on the dielectric characteristics of the metal-ferroelectric-metal planar structure

The effect of the morphology of metal-ferroelectric-metal interfaces on their electrical properties is studied. The effect of buffer layers and methods for depositing electrodes on ferroelectric-film morphology are experimentally studied. A theoretical analysis of the dielectric properties is performed based on the experimental data for heterostructures; however, final estimation is carried out using mathematical modeling methods.

Strain energy density in fiber composites based on high-epoxy binders

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.