This paper presents the solutions for the plane-strain extrusion of porous material. We consider the problem of a stationary plastic flow through a wedge shaped die. We neglect friction between the die and the deformed material since it is rather a negative effect and should be avoided in manufacturing. The elliptic Green type yield condition and its piecewise-linear approximation are adopted for this problem. In the last case, we obtain analytical solution that links extrusion pressure and area reduction to the initial and final density of the porous material. For elliptic Green yield condition the problem reduced to nonlinear ODE that integrated numerically. The results are compared with known solution for Gurson model. The extrusion pressure predicted by the piecewise-linear model is lower than what obtained by the elliptic Green model. In turn, the pressure predicted by elliptic Green model is lower than the pressure obtained in the frame of Gurson model. At low values of area reduction, all three models predict approximately the same extrusion pressure. With a small initial porosity of the material, the Gurson model gives results that are close to the elliptic Green model, and with a large initial porosity, to the piecewise-linear Green model.

In the present article we consider a novel approach to analyze the processes and kinetics of transformation of magnesium to hydride. Here approach consists to take into account the contributions of mechanics factors such as the work of external forces, the energy of elastic deformation and the energy required to form a unit volume nucleate of new phase. Request for a stable state of either a mechanical system or thermodynamic conditions governing a phase transformation, is to determine a minimum value to the total energy of the system. Analyzing the stability conditions needed when forming a metal hydride nucleus at constant temperature and pressure needs to consider the following: - the volumetric effects at the phase transformation, - the ratio of elastic moduli of metal to hydride phase, - the work spent at the formation of a unit volume of hydride. Under these considerations, it was shown that the most energetically favorable is forming an ellipsoidal hydride nucleus. Moreover, the larger difference in semi-axes, the more stable ellipsoid nucleus. Then, calculations of the stress-strain level states on both sides of the metal/hydride interface have been carried out. It was shown that the near-boundary range during the phase transformation is the place where accumulate inhomogeneous and intense stresses, which can contribute to two parallel processes. Firstly, increase of hydrogen concentration could appear in the distorted area. Secondly, a local accumulation of incoherent boundaries in between the two phases will develop stresses exceeding by more twice the shear yield stress. The presence of these compression zones could give rise new defects such as dislocations, micro-cracks. Consequently this should lead to decrease in magnitude of the powder of material.

This article suggests a method for the solution of the plane problem of the theory of elasticity on the bending of an articulated fixed multilayered panel with a circular axis based on the polynomial approximation of displacements through the thickness of the panel. In contrast to the known solutions of this problem, in this case the coefficients of the approximating polynomials are calculated from the equilibrium conditions and equality of displacements and transverse stresses at the transition across the layer interface and solution of differential equations of equilibrium at several points through the thickness of the layers. Finally, the problem is reduced to the solution of a system of linear equations with respect to the coefficients of approximating polynomials. The validity of the method is confirmed by comparing the results of calculations obtained on its basis and the results obtained with the help of the reference finite element model. The problem is solved in two stages. At the first stage, for a single-layer panel, we investigate the dependence of the polynomial degree on the ratio of the average panel radius to its thickness and the ratio of the transverse shear modulus to the modulus of longitudinal elasticity, which characterize the nonlinearity of displacements. At the second stage, on the example of a three-layered panel, we consider the application of the proposed method for the calculation of multilayered panels. In such case, the results obtained at the first stage are used in selecting the initial degree of polynomials approximating displacements through the thickness of layers. The method proposed in this article makes it possible to obtain an analytical solution without introducing simplifying hypotheses about the nature of displacement of layers and their elastic characteristics in a wide range of variation in geometric dimensions and elastic characteristics of panel layers. This method can be used both for verification of numerical models and for carrying out strength calculations of multilayer panels.

Application of vibration impacts for purposeful influence on such processes as drop formation, melt bath formation and crystallization of welding bead allows to control heat and mass transfer in liquid, crystallization process and shape of bead in technological processes of welding. Impact of vibration influences on nature of motion of liquid in the drop, which is reflected in the change of value of surface tension coefficient, is considered in the article. The mathematical model of the liquid flow considering surface tension force in formalism of smoothed particles hydrodynamics method is offered. This method allows direct consideration of the vibration effect by introducing additional boundary conditions. Verification of developed mathematical model is conducted in comparison with in-situ experiments, in which dependence of surface tension coefficient value on amplitude of speed of vibration influences was determined. To determine surface tension coefficient two methods were implemented: pending drop method and stalagmometric method. The implemented model satisfactorily describes the effect of decreasing surface tension coefficient for water. A series of numerical experiments for determining the effect of vibration influences on the value of surface tension coefficient for 12X18H10T steel grade was carried out. It was found that at vibration with speed amplitude equal to 2.0 m/s the decrease of surface tension coefficient value by 30 % is observed. Decrease in surface tension coefficient should facilitate the realization of continuous flowing of metal from the wire, which may positively influence the formation of metal during wire surfacing. Thus, the proposed mathematical model can clearly simulate the effect of vibration effects on the value of the surface tension coefficient and will allow the effect of vibration effects in additive manufacturing to be investigated in the future.

A generalized approach to statistical processing of the results is proposed fatigue parameters of static strength using methods of mathematical statistics and conventional statistics using the following probabilistic parameters: the mean square deviation, the initial moment, the central moment of dispersion and the coefficient of variation of the distribution series of physical and mechanical characteristics of the part material. Further, the analysis of fatigue strength research at the initial stage is carried out according to statistical information processing, graphical design of a number of stress distributions, statistical stress analysis, a graphical approach is applied in the form of a histogram of a number of distributions, a polygon of frequencies, a polygon of accumulated frequencies, the selection of theoretical stress distribution laws with their empirical confirmation is compared with a more rigorous assessment of the conformity of the distribution laws, which is performed using special consent criteria, for example, the Pearson criterion, a parallel verification of the correctness of the chosen approach using classical dependences of the resistance of materials is proposed. the total error is estimated in the form of a methodological error and a direct discrepancy between the theoretical and experimental values of stresses and temperatures of the physico-mechanical process according to experimental and theoretical normal and tangential stresses arising during the operation of the part as a result of the application of external force factors, a temperature-time superposition is used, in the form of a function of the predicted durability of the fluctuating kinetic theory of strength, in which the temperature, as a linear function, it can be replaced by any energy or force criterion, in particular: specific energy, relative deformation, normal or tangential stresses. The proposed approach requires substantial experimental study on a basic batch of the same type of samples and coordination according to schematized diagrams of the limiting amplitudes of Goodman, Sorensen - Kinasoshvili, Kogaev, subject to the conditions of safe operation of parts in the field of low-cycle fatigue. The proposed probabilistic model of statistical processing of fatigue strength can be recommended for solving applied problems of the theories of mechanics of materials, elasticity, plasticity and creep, resistance of materials, structural mechanics

It is well known that the performance properties of products made of metals and alloys are determined mainly by the meso- and microstructure of the latter. The structure of materials is formed and undergoes significant changes in the processes of manufacturing parts and structures using thermomechanical processing methods. A very important parameter that determines the physical and mechanical characteristics of materials is the grain structure (size, shape, relative positions of grains and inclusions of various phases). In recent decades, in this regard, special attention has been paid to the processes of severe plastic deformation (SPD), which make it possible to obtain a submicro- and nanocrystalline grain structure, which provides a significant increase in the performance properties of products made of metals and alloys. The development of SPD technologies in modern conditions is unthinkable without mathematical modeling of the processes under consideration; the most important component in the development of such a "toolkit" are constitutive relations (or, more broadly, constitutive models). In connection with the foregoing, the latter should be able to describe the evolutionary structure at various scale levels. Until now, the practice of developers of materials processing technologies has been dominated by the use of macrophenomenological models based on classical continuum theories of plasticity, viscoplasticity, and creep. From the second half of the 20th century to the present, various improvements to the constitutive models of the above class have been proposed, in which additional parameters and kinetic equations are introduced for them, describing certain characteristics of the structure of materials. As a rule, such models make it possible to obtain an adequate picture of the changing structure, however, for specific materials and methods of thermomechanical treatment. At the same time, such models, unfortunately, do not have the necessary universality; when changing the material or processing method, they have to be significantly “customized” to specific conditions, up to a complete change in the relationships included in the model. A brief review of works devoted to the creation and application of models of this class is given in the previous article by the authors. The most promising and possessing a significant degree of universality, according to the authors, are currently multilevel constitutive models based on the introduction of internal variables and physical theories of plasticity (elastoviscoplasticity). A review of works that consider various aspects of the formulation, modification, numerical implementation and application of such models is proposed in this article. The main attention is paid to models focused on the description of changes in the structure of materials due to dislocation-disclination mechanisms; a brief note is given on models that take into account thermally activated diffusion mechanisms, due to which the processes of recovery and recrystallization are realized.