# Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Металлургия

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95 лет со дня рождения В.Н. Выдрина

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A mathematical model of changes in the composition of grains during cooling a two-component melt

Drozin A.D., Naiman S.N., Kochetov N.E., Vorobyov A.V., Moiseev I.A.

Статья научная

The growth of individual grains of a solid phase during cooling liquid melt has been studied. During cooling, the compositions of the liquid and solid phases and the equilibrium conditions change. Therefore, each subsequent layer, “freezing” on the grain, will have a slightly different composition. This paper proposes a method for calculating the structure of the grain changes with increasing distance from the center. Corresponding mathematical model has been created. It is based on the following assumptions. Growing grains are considered as spherical. The temperature alignment in the system and the composition alignment in the liquid phase occur instantly. The alignment of the solid phase composition does not occur. Also, it is assumed that local equilibrium of the liquid phase with the solid phase on the grain surface is observed at any temperature. The characteristics of this local equilibrium can be found out from the corresponding equilibrium state diagram. The balance equation of phase masses and masses of their components at infinitesimal temperature decrease was made. It was assumed that the local equilibrium of the liquid phase and the infinitely thin layer of the solid phase, formed during this decrease in temperature, is observed. Taking to the limits, we have obtained a differential equation describing the investigated process. The solution of this equation has been obtained in the form of the solid phase mass as an integral function of the temperature. The grain composition depending on the distance from its center is obtained in the form of parametric functions expressing the radius of the current grain point and its composition at this point depending on the temperature. A computer program for the calculation of the mathematical model equations have been created. To use the model, it is needed to know the composition of the initial melt, the average density of the solid phase and the equations of the liquidus and solidus lines in the form of functions of concentration vs the temperature. An example of the calculation is presented.

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A mathematical model of segregation during cooling of the melt of iron with phosphorus

Drozin A.D., Kurkina E.Yu.

Статья научная

The purpose of this work is to study in detail the process of phosphorus segregation during steel solidification. A mathematical model considering a spherical melt cell with the nucleus of a solid phase in the center has been created. It has assumed that the thermal processes in this system are in accordance with the law of thermal conductivity and the mass transfer of phosphorus in the liquid and solid phases obeys the law of diffusion. In addition, it has assumed that a local equilibrium is maintained at the interface between these phases and the parameters of this equilibrium can be determined from the equilibrium phase diagram Fe-P. It has been assumed that the outer boundary of the system is cooled according to a mode that is set arbitrarily. Based on the obtained equations, a computer program has been created, that allows obtaining the temperature and the phosphorus content at any point at any time. The calculations have shown that the temperature alignment in of the system is almost instantaneous, and the concentration of phosphorus in the liquid phase has aligned quickly. However, the phosphorus concentration in the solid phase aligns much slower due to the small phosphorus diffusion coefficient in the solid phase. The principal factors determining the segregation of phosphorus are the initial concentration and the melt cooling mode. The results will help to calculate the cooling mode of the melt to produce a metal with the desired properties.

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Ab initio моделирование межфазной границы феррит/цементит

Верховых Анастасия Владимировна, Окишев Константин Юрьевич, Мирзоев Александр Аминулаевич, Мирзаев Джалал Аминулович

Статья научная

Представлены результаты первопринципного моделирования межфазной границы феррит/цементит с ориентационным соотношением Исайчева. Периодичность и близкое расположение атомов в двух решетках (феррита и цементита) для данного ориентационного соотношения свидетельствует о том, что это поверхность имеет низкую энергию формирования. Построена структурная модель данной межфазной границы. Наилучшее сопряжение решеток обеспечивается, когда на границе находится плоскость (101)ц, состоящая из атомов железа в S-позициях. Суперячейка межфазной границы содержала 64 атома: 56 атомов железа (по 28 в цементитной и ферритной частях) и 8 атомов углерода. Проведено моделирование в рамках теории функционала плотности полнопотенциальным методом линеаризованных присоединенных плоских волн с учетом обобщенного градиентного приближения в программном пакете WIEN2k. Определены оптимальные параметры моделирования данной системы и проведена объемная оптимизация структуры. Рассчитана энергия формирования межфазной границы феррит/цементит, которая оказалась равна 0,594 Дж/м2, что хорошо согласуется как с теоретическими, так и с экспериментальными данными. Наблюдается хорошая корреляция между значениями магнитного момента и межплоскостным расстоянием для атомов железа на межфазной границе. С уменьшением расстояния магнитный момент на атомах железа уменьшается.

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Ab initio моделирование энергии растворения азота в ГЦК-решётке железа

Ридный Ярослав Максимович, Мирзоев Александр Аминулаевич, Мирзаев Джалал Аминулович

Статья научная

В программном пакете WIEN2k проведено ab initio моделирование равновесной структуры и свойств раствора внедрения азота в ГЦК-железе. Вычислена энергия растворения атома азота в немагнитном (НМ) и антиферромагнитном двухслойном (АФМД) состояниях ГЦК-железа.

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Ab initio-моделирование комплексов водород-вакансия (VHN) в ОЦК-железе

Урсаева Анастасия Владимировна, Мирзоев Александр Аминулаевич, Рузанова Галина Евгеньевна

Статья научная

Представлены результаты ab initio-моделирования взаимодействия вакансии в ОЦК-железе с одним и несколькими (до четырёх) атомами водорода. Рассчитаны равновесные положения атомов водорода, плотности состояний, определены энергии взаимодействия.

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By hydrogen reduction from a-FeOOH hydroxide compound under isothermal conditions

Tien Hiep Nguyen, Nguyen Van Minh, Tang Viet Phuong, Tang Xuan Duong, Le Hong Quan

Статья научная

In this work, the process of obtaining magnetite nanopowder Fe3O4 by hydrogen reduction from α-FeOOH hydroxide compound under isothermal conditions was studied. The α-FeOOH nanopowder was prepared in advance by chemical precipitation from aqueous solutions of iron nitrate Fe(NO3)3 (10 wt. %) and alkali NaOH (10 wt. %) at room temperature, pH = 11, under the condition of continuous stirring. The hydrogen reduction process of α-FeOOH powder under isothermal conditions was carried out in a tube furnace in the temperature range from 310 to 375 °С. The study of the crystal structure and phase composition of the powder samples was performed by XRD phase analysis. The specific surface area S of the samples was measured using BET method by low-temperature nitrogen adsorption. The average particle size D of powders was calculated using the data of measuring the specific surface area S. The size and morphology characteristics of the particles were investigated by scanning and transmission electron microscopy method. The calculation of the kinetic parameters of the process of obtaining the Fe3O4 nanopowder under isothermal conditions was carried out using the Gray-Weddington model and the Arrhenius equation. It was found that the reduction process of the α-FeOOH nanopowder begins to accelerate strongly in the temperature range from 340 to 375 °С. The reduction rate constant at 375 °С is about 2 times that of the reduction at 310 °С. The value of the activation energy for the process of obtaining Fe3O4 nanopowder under isothermal conditions was ~ 36 kJ/mol, which indicates a mixed mode of limiting the kinetics of the process. It has been shown that the time-temperature regime of the reduction of the α-FeOOH hydroxide compound with holding at 340 °С for 3 h makes it possible to obtain a nanosized magnetite powder Fe3O4 with high purity at an increased rate of the process. The obtained Fe3O4 nanoparticles have a crystalline structure and generally have a polygonal or irregular shape, the size of which ranges from 30-80 nm with an average value of 65 nm, each of them being connected to several neighboring particles by isthmuses.

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Computer modeling of hot isostatic pressing process of porous blank

Barkov L.A., Cheskidov P.A., Samodurova M.N., Latfulina Yu.S.

Статья научная

Existing mathematical models for the process of HIP porous blanks are based on the solution of approximately differential equations of the equilibrium of quasi-continuous medium. The continual approach is used for computer modeling of the compressible body HIP process. Partial differential equations of motion for a quasi-continuous packing medium and physical equations for a viscous-plastic isotropic porous material subjected to work hardening are taken as the basis for the mathematical model by means of these simultaneous equations. Besides the equations of motion and the rheological equation, the equation of continuity deformation and the equation of heat flow are used. Numerical calculations for additional packing of a high-speed steel powder billet preliminary pressed in the hydrostat are performed. Numerical calculation of the problem for hardening the cylindrical high-speed steel billet with a mild steel shell is done using Lagrange’s method by means of the difference scheme of continuous calculation of the Wilkins’ type. Computer modeling allows to control the process of hardening and changing the form of a porous body during the HIP process.

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Consolidation model of powder magnetic materials

Barkov L.A., Samodurova M.N., Latfulina Yu.S.

Статья научная

Known models of deformation processes of powder materials in a die compaction are based on a decision of partial differential equilibrium equations. This paper presents the mathematical model of the die powder compaction process which is based on the decision of partial differential equations of motion. The equations for an elastic-plastic isotropic powder hardening material are used as rheological ones. A quasi-continuous powder medium has an irreversible volumetric and shear deformation. Numerical calculations of the die compaction are fulfilled for ferrite, Sm-Co, Nd-Fe-B magnets using Lagrange’s method by means of the difference scheme of continuous calculation of Wilkins’ type. Boundary conditions are assigned by a friction low on lateral surfaces of the die. Pressed articles have the form of rings.

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High velocity compaction of carbon compositions

Samodurova M.N., Barkov L.A., Latfulina Yu.S.

Статья научная

High velocity compaction of metal, ceramic and other powders have no widespread industrial application at the present time. Carrying out a large number of experiments with processes of high velocity compaction with powders of non-ferrous, ferrous metals, ceramics and polymers - showed that formation with speeds of the ram tester more than 1-2 m/s, causes the following adverse effects: pressing of gases and vapors of the liquids containing in initial powders and destruction of the specimens. In Chelyabinsk there are several large-scale enterprises (“Electrode Plant”, “Electrometallurgical Integraыted Plant”, Plant “Grafitoplast”, branch of “Doncarb Graphite”, “Uglegraphite”, “Carbon Material Plant” and others), which produce a brand range of products from carbon compositions. Scientists from Resource Centre of Special Metallurgy of South Ural State University (RCSM of SUSU) carried out the theoretic, technologic and experimental investigations for these enterprises. This article is devoted to the analysis of the experimental studies on devices of the Swedish company HY-DROPULSOR and the American company Instron. Foreign researchers established values of devices striker pin kinetic energy at which density of specimens comes nearly to theoretical, but, unfortunately, without indication of powder compositions, kind of specimens pressing and also strikers and specimens masses, their density at various values of speed and mass of strikers. Therefore the aim of the article is studying processes of High Velocity Compaction providing different indications of powder compositions containing graphite and optimized strikers and specimens masses, strikers speed.

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Investigation of the process of martensite tetrahedral distortion formation by molecular dynamics

Chirkov P.V., Mirzoev A.A., Mirzaev D.A.

Статья научная

Formation of tetragonal martensite in Fe-C system was studied. Parameters of thermodynamic ordering theory are calculated using energy minimization and molecular dynamic simulations with EAM potentials. It was found that carbon atoms in tetragonal martensite form plane-shaped groups.

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New method of crystal material heterogeneity examination

Barkov L.A., Samodurova M.N., Ekk E.V., Latfulina Yu.S.

Статья научная

A principally new method of phase heterogeneity examination based on diffractometric analysis of interference maximum integral intensity of X-ray beam reflections from microvolumes of different sizes in irradiated samples of crystal materials has been developed. Also, some quantitative relationships have been experimentally tested and theoretically justified, namely the dependence of X-ray line integral intensity on the structure of incident radiation, the size of beam projection on the surface of a sample and other survey parameters. Newly developed diffractometric survey of interference line profiles allows to reach an effective averaging in texture heterogeneities that is important for high accuracy and reliable determination of quantitative values of integral intensity. Basing on the above quantitative dependences, necessary relationships have been established to find the values of relative differences between concentrations. New method is advantageous in phase heterogeneity and crystal material porosity analysis as well as in the analysis of the efficiency of blending in multi-phase powder mixtures.

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On the problem of modeling temperature fields in bodies with variable boundaries

Panferov S.V., Panferov V.I.

Статья научная

Introduction. When melting, solidifying and oxidizing a metal, the problem arises of calculating the temperature field in areas with time-varying boundaries. Usually, to solve the heat equation in such cases, the method of catching the boundary into a node of a spatial grid is used, which necessitates the use of a variable time step in calculations, in addition, the number of spatial nodes will also be variable. All this leads to a change in the amount of computational work. However, in many cases the method of grids with moving nodes may be more preferable, in this case there is no need to change the number of spatial nodes and the time step. Purpose of the study. Develop an algorithm for approximating the convective boundary condition for grids with moving nodes. Materials and methods. The analysis and generalization of literature data on the problem is carried out. It has been established that the direct replacement of derivatives in the boundary condition by finite differences leads to a large error in calculating the surface temperature and, as a result, the entire temperature field of the body. When using a grid with a constant spatial step for a finite-difference approximation of the boundary condition, one can use the Beck formula. There is no formula similar to the Beck formula in the literature for meshes with moving nodes, so the problem arises of determining such a formula. To solve the stated problem of approximation, the method of heat balance for an elementary cell near the surface of the body is applied. Results. An analogue of the Beck formula for grids with moving nodes is found. The obtained finite-difference formula was tested, including with the help of a computational experiment. Conclusion. The obtained formula for approximating the convective boundary condition for grids with moving nodes can be a kind of addition to the theoretical foundations of the method of grids with moving nodes used in practice for calculating temperature fields in areas with variable boundaries; its application makes it possible to increase the accuracy of calculating the temperature field of a body.

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Porous material deformability in four-roll pass rolling

Barkov L.A., Kamenshchikov Yu.I., Samodurova M.N., Latfulina Yu.S.

Краткое сообщение

Rolling in four-roll passes offers a lot of technological and ecological advantages over swaging which is presently used for working of sintered powder rods from tungsten and molybdenum. It explains the necessity of thorough experimental and theoretical investigations of such processes as plastic shaping and compacting of sintered powder materials at the zone of their deformation in rolling with four-side reduction. Authors have carried out numerous experimental investigations of compacting of powder rods in the process of their rolling in four-side passes. There exist several empirical formulae describing rod density change in the process of rolling. The present paper gives complex experimental details and justification of the proposed analytic function allowing the evaluation of powder strip density by measuring its geometric parameters. This analytic function is based on the law of constant rod mass in plastic shaping and compacting.

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Preventing cracks when casting steel slag ladles

Ivanov M.A., Shvetsov V.I.

Статья научная

The paper is dedicated to the improvement of large steel casting technology where slag ladle casting is taken as an example. The temperature measurement of the crystallization process of casting is held. The causes of the formation of cracks are reviewed. To prevent the formation of cracks the recommendations are developed to improve the casting technology.

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Properties of tungsten wire in powder metallurgical processing with ultrafine powder

Barkov L.A., Samodurova M.N., Mymrin S.A., Latfulina Yu.S.

Статья научная

The paper presents the results of the investigation of properties of the tungsten wire obtained from powders with particle sizes from 1 to 5 μm with the addition of ultrafine powders with particle sizes of less than 0.5 μm produced by the reduction of hydrogen plasma at a high temperature. Different compositions of mixtures were studied and a new optimal composition was developed. Methods of its compressing and presintering of bars were also developed. The results showed that mechanical and performance properties of the wire with a new composition have higher stability compared to the properties of the wire obtained by the standard technology. They allowed: - to lower the creep for the wire with the diameter of 1250 μm, - to achieve a stapel structure for the wire with the diameter of 650-1450 μm; - to improve the spiralability of the wire; - to increase the good-to-bad yield to 3.79 % for the wire with the diameter of 120 μm.

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Simulation of plastic deformations in metal rolling

Barkov L.A., Kamenshchikov Yu.I., Samodurova M.N., Latfulina Yu.S.

Статья научная

Mathematical simulation of plastic deformations in rolling of porous materials involves a consequent combination of the general energy relationship in plasticity and the variation inequality expressing the principle of minimum of entire deformation energy. A real deformation state in a plastic zone beneath rolls and corresponding kinematic and dynamic conditions on the contact surface are considered as a limited one for the consequent approximate deformation states and found out by the method of approximated approach. Any realization of this kind of method on personal computers requires a rational construction of a kinematic admissible velocity field in the spatial domain on plastic flow. Using the ordinary propositions and assumptions it became possible to construct one of the simple spatial kinematic admissible velocity field in the plastic zone beneath rolls. On the base of a big amount of experimental data a new hypothesis and analytic function describing the density distribution along the plastic zone during the rolling process have been proposed. On the base of the consequent approach in which the general energetic relationship and the variation inequality are interrelated it has been able to find out the geometric, kinematic and dynamic characteristics of plastic deformation states in rolling of porous materials.

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X-ray study of yttrium texture using standard and extended dialing pole densities

Stepanenko A.V.

Статья научная

Various methods of experimental study of the texture of polycrystalline metals and alloys are considered. The texture formed upon plastic deformation or upon recrystallization annealing leads to anisotropy of the physical and mechanical properties of metallic materials. For express calculations of the values of anisotropic physical properties of polycrystals, methods based on the use of integral characteristics of textures are preferred. An X-ray method for calculating orientation factors for textured metals with a hexagonal close-packed structure is discussed. Calculation of the orientational factor of texture Δi assumes averaging over the representative volume of the polycrystalline sample under study. The basis for calculating the orientational factors of a textured polycrystal is the reverse pole figure. In the standard method for calculating the reverse pole figure of hcp metals, 17 crystallographic orientations are used. Yttrium texture analysis can be performed using an extended set of pole densities on the reverse pole figure. A method for calculating the reverse pole figure for hcp metals is proposed, which takes into account 24 crystallographic orientations. The data of X-ray diffraction studies of polycrystalline yttrium after deformation by cold rolling with a degree of deformation = 45% are discussed. On the basis of the obtained X-ray data, the reverse pole figures of deformed yttrium were constructed using the standard method and using an extended set of pole densities. The orientation factor of the texture Δi of the deformed yttrium polycrystal was determined. A comparative calculation of the resistivity ρi of textured yttrium has been performed using two experimental procedures. The extended set of pole densities on the reverse pole figure is most convenient when studying samples in which a sharp deformation texture is formed. The proposed technique accurately describes the dynamics of texture formation, describes more precisely the features of the pole density distribution on the reverse pole figure, and allows one to determine the anisotropic physical properties of materials.

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Абразивная и ударно-абразивная износостойкость твёрдых наплавленных покрытий

Нефедьев Сергей Павлович, Дма Роман Рафаэлевич, Котенко Дмитрий Александрович

Статья научная

Многие механизмы машин горного и металлургического оборудования, испытывающие абразивное изнашивание при эксплуатации, преждевременно выходят из строя. Износ их рабочих поверхностей вызывает необходимость в проведении восстановления, что приводит к удорожанию механизмов. Поэтому разработка материалов и технологий, значительно повышающих износостойкость таких деталей без их значительного удорожания, является важной задачей. Наиболее перспективным является применение плазменно-порошковой наплавки на изнашивающиеся поверхности деталей. Для этих целей разработан и изготовлен специальный наплавочный порошок, представляющий собой высокоуглеродистый сплав эвтектического состава. Благодаря оптимально подобранному легированию наплавленные покрытия обладают высокими значениями твёрдости, абразивной и ударно-абразивной износостойкости. Также повышение износостойкости при наплавке предлагаемого порошка связано с измельчением структуры и ориентированием направления ее роста по направлениям приложения усилий.

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