Based on the results of the experimental investigations of the samples made of stainless steels SS304, 12X18H9 and 12X18H10T subject to a hard (controlled deformations) and soft (controlled stresses) cyclic loadings under uniaxial tension-compression and normal temperature we carried out a comparative analysis of the adequacy of the currently used variants of the plasticity theories which belong to flow theories with a combined hardening. The loads that include the sequences of cyclic and monotonic loads as wells as placing and ratcheting of the plastic hysteresis loop are considered. The loads are applied until fracture, i.e. the emergence of macrocracks with a length of 1 mm. Within the scope of our analysis we have considered the following variants of theories including the models of Korotkih, Bondar and Chaboche. For each model, a set of material functions is given on basis of which the calculations of the kinetics of the stress-strain state of the cyclic loading processes are made. By comparing the results of the calculations and experiments, it has been shown that the description of the cyclic loop placing and ratcheting processes is possible only within the Bondar and Chaboche models with a certain advantage of the modified Bondar model, which enables an adequate description of the nonstationary cyclic loading and nonlinear damage accumulation. It is shown that the modified Bondar model - including the third type of microvoltage (Ono-Wang) and kinetic equations of damage accumulation - provides the most adequate (in comparison with other models) description of the kinetics of the stress-strain state and fracture under nonstationary nonsymmetric cyclic loading processes. It can be recommended for practical computations of the kinetics of the stress-strain state and the design life affected by an arbitrary load action.

We framed a precise solution of the nonsymmetrical boundary value problem of the elasticity theory for a cylindrical vessel with liquid placed in the thermal field. The thermoelastic problem is unlinked, i.e. at first we solve the thermal conductivity equation, and then the linear problem of the elasticity theory for a circular cylinder in displacements. It should be noted that until the present time there were no precise solutions of nonsymmetrical problems of the elasticity theory in the cylindrical coordinate system with a consideration of the thermal field. It is explained by the complexity of the system of resolvent equations, such as high order, variable coefficients. The authors of the article managed to form integrable combinations of resolvent equations in this work, at first by taking no account and then considering the thermal fields. For this purpose an additional equation related to a volumetric deformation was introduced into the system of resolvent equations instead of the relator connecting the volumetric deformation with the movement of the cylinder points. When we took into account the heat conduction equation, we managed to gain the equation which had been obtained earlier without the consideration of the thermal elements. As a result, the problem was brought to a successive solution of each equation separately. Since the additional equation was obtained by the derivation of the rest of the equations, the order of the resolvent equations system became higher which resulted in «excess» constants of the integration. The authors proved that the use of the replaced correlation between the volumetric deformation and displacements as an additional condition eliminated this disadvantage. We formed a precise solution of the boundary value problem for the cylindrical vessel with liquid upon the condition of the linear dependence of temperature and displacements of the cylinder along its axis. The numerical example was considered where the temperature of the external side area of the cylinder is changed in the circumferential direction.

The concentration of the field takes place on the structural defects of the material, if it is affected by the electromagnetic field. In particular, it initiates electrical, thermal and mechanical processes in the vicinity of micro-defects (cracks, pores, inclusions, etc.). The transformation and interaction of defects are investigated in the article, e.g. the flat intergranular micro-cracks with linear dimensions of the order of 10 microns. These processes occur in the material when the metal samples are treated with a high-energy pulsed electromagnetic field which induces a short pulse of a high density electrical current in the material. The study uses the numerical coupled model related to the impact of the high-energy electromagnetic field on the pre-damaged thermal elastoplastic material with defects. This model considers the metal’s melting and evaporation, as well as the dependence of its physical and mechanical properties on temperature. The system of equations is solved numerically using the finite elements method on adaptive lattices using the alternative method of Euler-Lagrange. The simulation shows that the treatment by the short pulse of current results in the welding of the crack and healing of the micro-defects. The healing occurs due to a simultaneous reduction of length, ejection of the molten metal into the cracks and closing of micro-crack edges. It leads to the fact that the edges of the crack start to contact the jet stream of the molten material, and, finally, the stream becomes completely jammed by the crack’s edges. Meanwhile the volume of the micro-cracks starts to decrease in time. In this paper, the material healing and damage parameters are introduced for the macroscopic description of the healing process. The parameter of healing is determined as a relation of the micro-crack’s change of volume to the initial micro-crack’s volume at a time when the material is affected by the electromagnetic field. The damage (porosity) is understood as a ratio of the micro-crack’s volume at a time to the volume of the representative element. The healing of micro-cracks increases the material’s healing parameter and reduces its damage. The paper studies the changes in the material’s healing and damage parameters depending on time under the action of the current pulse. The issues of selecting the preferred regions of integration in modeling the considered processes are researched. It is investigated how the distance between the micro-cracks and their mutual arrangement influence the healing and damage over time. The simulation of the considered processes in the entire investigated range of distances between the defects (or, for any initial damage equivalently) have shown that the dependences of the healing and damage on the time will not be different, no matter if we calculate these dependences in the regions of integration consisting of one or several representative elements. The arrangement of micro-cracks relative to each other and the distance between them do not affect the dependences of the healing and damage on the time under the current pulse. These changes are affected by the value of the initial damage only. The dependences of healing and damage on time will be practically the same for all different mutual arrangements of micro-cracks provided that the initial damages are equal for these different mutual arrangements of defects. Based on the simulation results, the approximate piecewise-linear dependences of healing and damage on time and the initial damage are obtained. It is clear that until a certain moment all the micro-cracks in the material (regardless of the initial damage) are not healed or damaged when they are affected by the current. After this moment, the process of micro-cracks’ healing starts. Meanwhile, under the action of the current, the material’s damage decreases over time at a constant rate (independent of the initial damage), while the healing increases over time at a rate inversely proportional to the initial damage of the material.

Linear thermoelasticity is studied of a plane regular truss formed by four families of straight homogeneous rods. Rods of two of them are mutually orthogonal and form rectangular cells that are repeated in two perpendicular directions. The other two families combine differently oriented diagonal rods of the cells. All the rods are only in tension-compression and their elastic lines belong to the same plane. Adjacent rods are rigidly connected together in the truss nodes, i.e. the points of intersection of the elastic lines of mutually orthogonal rods. The regularity of the truss implies the invariance of the thermoelastic and geometrical parameters of the rods within the same family. External actions on the truss belong to its plane and generally include the external nodal forces, the linear axial forces of the rods and their non-uniform heating. The rigorous linear thermoelasticity of the truss is constructed by the gluing method. According to this method, the truss was split into rods and nodes, i.e. the elements of the truss. The given external actions were applied to the isolated elements as well as the forces of interaction with their neighbors. Then the analytical study of thermoelastic rods with geometric conditions of the conjugation of the adjacent elements and the analysis of the equilibrium of the nodes were carried out. The theory was formulated in terms of nodal displacements and total elongations and internal initial forces of the rods. All these variables are the functions of two integer arguments used for numbering of the elements of the truss. The complete closed system of equations of the truss thermoelasticity is represented by geometric and physical relationships, the equilibrium equations of the nodes and the compatibility equations of the total elongations of the rods. Alternative formulations of the discrete boundary-value problems are presented with their help. An application of the theory is illustrated by the exact analytical solution of the problem of thermoelastic deformation of the truss without internal nodes.

The paper deals with studying the distribution of the scattered (dissipating) mechanical energy transferred to the pavement cover when it is used by road transport. For the numerical simulation of the energy transfer process we improved the analytical model of the dynamic stress-strain state of the multilayered half-space by introducing the moving coordinate system. The energy distribution was studied for three road structures with different strengths. For each structure we obtained the amplitude-time characteristics of stress and strain on the surface of the coating layers, on the base and subgrade soil which have been used to build the dynamic hysteresis loops. We analyzed the areas of the dynamic hysteresis loops on the surface of the coating layers as well as the base and subgrade soil, which made it possible to reveal the qualitative and quantitative dependences of the density distribution of energy dissipation in the pavement layers. It is found that when the solidity of the road structure increases, the energy density which is dissipated on its surface decreases. The rate of the energy attenuation of wave fields in road structures which has been generated by the impact of the design load vary significantly depending both on the solidity of the pavement and various types of its structural layers. In this case the greatest difference is determined by the material properties which are used as the base layer (reinforced, unreinforced). Based on the studies, a new approach of evaluating the design service life of nonrigid road structures in terms of the energy transferred on its surface during its entire service life has been proposed.

Highly-filled polymer composites are widely used in critical structures in aerospace and other industries. Such structures have to endure complex harmonic loadings. Thus it is important to develop methods of experimental studies and determine deformation properties of highly-filled polymer materials, as well as computational methods for structures working in extreme conditions. The aim of this research is to develop methods of conducting the dynamic experiment, determine viscoelastic parameters of highly-filled polymer composites under stationary two-frequency loadings and find the mathematical model to calculate the stress-strain state of viscoelastic aerospace structures. Linear and nonlinear integral representations of stress and strain for mechanical behavior description of the viscoelastic materials are presented. The general description of a method to mathematically model the nonlinear viscoelastic behavior was accomplished by Volterra using an earlier representation developed by Frechet (Volterra-Frechet integral series). By using the Volterra-Frechet integral series we presented the nonlinear mathematical model based on complex parameters to describe the viscoelastic material behavior under stationary two-frequency loadings (under various values of frequencies and amplitudes). This mathematical model was analyzed and compared to an earlier model with some assumptions in linear dependencies of viscoelastic parameters on strain amplitudes and without hysteresis loop distortions (harmonics distortions) under deformation. We suggest using polynomials to describe the dependencies of viscoelastic parameters on frequency and temperature by using the time-temperature superposition. The two-frequency (dual-frequency) experiments to determine these polynomials are conducted. After the experimental data has been processed, the dependencies of the viscoelastic parameters on frequency and temperature are determined. These results allow developing an optimal experimental design, determining mathematical model constants and assessing the influence of the viscoelastic parameters on the description accuracy of the material behavior under complex harmonic loadings.