The grain structure of metals changes significantly during severe plastic deformation (SPD), and ... more The grain structure of metals changes significantly during severe plastic deformation (SPD), and grain refinement is the main process associated with SPD at low homologous temperatures. Products made of ultrafine-grained materials exhibit improved performance characteristics and are of considerable industrial interest, which generates a need for the creation of comprehensive grain refinement models. This paper considers the integration of the ETMB (Y. Estrin, L.S. Toth, A. Molinari, Y. Brechet) model, which describes the evolution of an average cell size during deformation into the two-level statistical crystal plasticity constitutive model (CM) of FCC polycrystals. The original relations of the ETMB model and some of its modifications known from the literature were analyzed to obtain an accurate, physically admissible description of the grain refinement process. The characteristics of the grain substructure determined with the framework of the advanced ETMB model were taken into ac...
This paper considers the influence of subgrain coalescence at initial high-angle boundaries on th... more This paper considers the influence of subgrain coalescence at initial high-angle boundaries on the initiation and growth of recrystallization nuclei (subgrains) under thermomechanical treatment. With certain processing regimes, adjacent subgrains in polycrystalline materials can be assembled into clusters during coalescence. Subgrain clusters at high-angle boundaries are the preferred potential nuclei of recrystallization. Coalescence is one of the dynamic recovery mechanisms, a competing process to recrystallization. When intensive coalescence develops on both sides of the grain boundary, recrystallization slows down or even stops. The problem formulated is solved using a multilevel modeling apparatus with internal variables. Application of the statistical multilevel model modified to take into account the local interaction between crystallites makes it possible to explicitly describe dynamic recrystallization and recovery. The results of modeling the behavior of a copper sample ar...
The study of grain and defect structure evolution in materials subjected to thermomechanical proc... more The study of grain and defect structure evolution in materials subjected to thermomechanical processing is still an urgent problem because the state of a structure substantially determines the physical and mechanical macro properties of polycrystals and polycrystalline products. Significant changes in the structure of polycrystalline materials are associated with the process of dynamic recrystallization (DRX). To investigate DRX, an extended statistical model of inelastic deformation with internal variables is proposed, which takes into consideration contact interactions between neighboring grains. We constructed a geometric image of the grain structure by applying a Laguerre polyhedron in order to describe such interactions in the statistical framework. During the recrystallization simulation, this image is being reconstructed as new recrystallized grains emerge. This leads to the problem of establishing correspondence between an initial grain structure and a reconstructed structur...
Grain boundary sliding is an important deformation mechanism, and therefore its description is es... more Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which takes into account intragranular dislocation sliding, crystallite lattice rotation and grain boundary sliding. A key advantage of our model over the classical Taylor-type models is that it also includes a consideration of grain boundaries and possible changes in their mutual arrangement. The constitutive relations are defined in rate form and in current configuration, which makes it possible to use additive contributions of intragranular sliding and grain boundary sliding to the strain rate at the macrolevel. In describing grain boundary sliding, displacements along the grain boundaries are conside...
Co-rotation derivatives and the determining relations in the theory of large plastic deformations
On the constitutive Ilyushin’s theory relations for the case of large deformations. I
ABSTRACT
Flow in antroduodenal pzart of digestive tract: Mathematical model and some results
Mathematical Biology and Bioinformatics
ABSTRACT
Simulation of the process of pump rods recovery
Hydraulic Engineering Software VII
The irregular loading of waste water treatment systems is determined by the non-uniformity of dwe... more The irregular loading of waste water treatment systems is determined by the non-uniformity of dwelling and industrial sewers. Only industrial sewers can be controlled to regulate the total amount of waste waters received in the treatment system. To carry out such regulation it is necessary to take into account the enterprises' locations, pipe parameters and sewer system configurations. The computer model of the uniaxial liquid flow is based on a system of non-linear equations in partial derivatives with corresponding initial and boundary conditions. To solve this problem the finite - difference method is applied here. Two approaches are compared: the linearized system of the nonlinear equations and Newton's method. Areas of stability and convergence of both numerical solutions are estimated. The problem of modelling the dynamics of a liquid flow in a system of pipelines is also formulated. The objective function is determined as the remainder between the highest and lowest w...
Residual Thermal Stresses and Warping of Hot-Rolled Asymmetrical Sections
The development of technological methods for processing and manufacturing of functional (with a p... more The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying internal variables that give an effective characterization of the material structure at different structural scale levels. High temperature plastic deformation is accompanied by these processes, which leads to a significant rearrangement of the meso- and microstructure of the material. The most substantial contribution to changing the properties of polycrystals is made by the evolution of grain and defect structures at the expense of dynamic recrystallization, which significantly depends on dynamic recovery. In this paper, we consider the problem of the coalescence of subgrains undergoing rotation during inelastic hot deformation. This process is called subg...
This work is devoted to a problem of creation of a multiphase flow model in an antroduodenum that... more This work is devoted to a problem of creation of a multiphase flow model in an antroduodenum that includes the lower part of the stomach and the upper part of the small intestine (duodenum). The mathematical model is developed for the next purposes: description of the process of digestion in normal physiological state and with functional disorders, prediction of the flow characteristics in distinct conditions. The antroduodenum is considered as a complex form canal with moving boundaries. The mathematical statement of the problem includes mass and momentum conservation equations for phases and components as well as initial and boundary conditions with peristaltic movement. To describe secretion and absorption processes we use mass sources/sinks in a layer adjacent to the tract wall. Using computational simulation we got the digestion processes characteristics in dynamic: pH of the medium, components and phases velocities and fractions. In some scenarios with secretory and motor diso...
The products made by the forming of polycrystalline metals and alloys, which are in high demand i... more The products made by the forming of polycrystalline metals and alloys, which are in high demand in modern industries, have pronounced inhomogeneous distribution of grain orientations. The presence of specific orientation modes in such materials, i.e., crystallographic texture, is responsible for anisotropy of their physical and mechanical properties, e.g., elasticity. A type of anisotropy is usually unknown a priori, and possible ways of its determination is of considerable interest both from theoretical and practical viewpoints. In this work, emphasis is placed on the identification of elasticity classes of polycrystalline materials. By the newly introduced concept of "elasticity class" the union of congruent tensor subspaces of a special form is understood. In particular, it makes it possible to consider the so-called symmetry classification, which is widely spread in solid mechanics. The problem of identification of linear elasticity class for anisotropic material with elastic moduli given in an arbitrary orthonormal basis is formulated. To solve this problem, a general procedure based on constructing the hierarchy of approximations of elasticity tensor in different classes is formulated. This approach is then applied to analyze changes in the elastic symmetry of a representative volume element of polycrystalline copper during numerical experiments on severe plastic deformation. The microstructure evolution is described using a two-level crystal elasto-visco-plasticity model. The well-defined structures, which are indicative of the existence of essentially inhomogeneous distribution of crystallite orientations, were obtained in each experiment. However, the texture obtained in the quasi-axial upsetting experiment demonstrates the absence of significant macroscopic elastic anisotropy. Using the identification framework, it has been shown that the elasticity tensor corresponding to the resultant microstructure proves to be almost isotropic.
Рассматривается задача исследования теплового состояния шумотеплоизолирующего кожуха (КШТ), в кот... more Рассматривается задача исследования теплового состояния шумотеплоизолирующего кожуха (КШТ), в котором располагается газотурбинная установка (ГТУ). Отмечается, что при исследовании теплового состояния стенок КШТ важную роль играет учет теплопередачи за счет радиационного излучения нагретых элементов конструкции. Предложена математическая модель, позволяющая рассчитывать скорости течения воздуха внутри КШТ, а также температуру воздуха и материала, из которого изготовлены стенки КШТ, с учетом радиационного теплообмена. Разработан параллельный алгоритм для решения задачи газовой динамики на вычислительном кластере. Решена задача оптимизации разбиения расчетной области при распараллеливании расчетов. Проведены расчеты для КШТ одного из существующих газоперекачивающих агрегатов. Из полученных результатов следует, что при решении задачи твердотельной теплопроводности для стенок КШТ необходимо учитывать лучистый теплообмен. Отмечается удовлетворительное соответствие расчетных и экспериментально измеренных величин температуры характерных точек внешней поверхности стенок КШТ.
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