PNRPU Mechanics Bulletin最新文献

{"title":"ABOUT THE YIELD PLATEAU UNDER SIGN-VARIABLE LOADING","authors":"B. Rychkov, I. Goncharova, P. M. Rezin","doi":"10.15593/perm.mech/2021.3.13","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.13","url":null,"abstract":"During tension of samples of low-carbon steels and some other plastic materials, the sharp yield point and the yield plateau are fixed on the deformation diagram. In this case, Chernov-Luders bands appear on the surface of the sample in the local section, which then propagate along the tension axis. The physical nature of the sharp yield point is established: the drop in the load after reaching the (upper) yield limit occurs as a result of dislocations being an extraction out of the cloud of the embedded atoms and vacancies (Cottrell's cloud). At the occurrence of the sharp yield point , the plastic strain is limited to a small area. When the sample deformation increases, the plasticity zone (the yield plateau is marked on the diagram at this time) expands, and the stress-strain state in this zone becomes almost homogeneous, if we do not consider its boundary with the elastic region. At the end of the yield plateau, the entire sample experiences a uniform plastic deformation, excluding its ends (galtels). From this point on, the strain diagram shows the of material hardening; presumably, this hardening occurred from the very beginning, but was hidden under the yield plateau. This is evidenced by the resulting strain-induced anisotropy. After unloading the sample, when the plastic strain front (in the form of Chernov-Luders bands) has not yet passed through the entire sample, and the Bauschinger's effect is observed with the subsequent change in the stress sign. The fact that after the occurrence of the sharp yield point , the plastic strain is not localized in a certain volume, similar to what occurs during the neck formation, but spreads along the sample, serves as proof of the material hardening due to plastic deformation immediately after the load falls. Therefore, if the plastically deformable part of the sample did not have a hardening of the material due to the plastic strain growth, it would not be able to spread to the elastic part of the sample. This paper presents the experimental data of the sign-variable torsion of the thin-walled tubular samples of steel 45 in the annealed state. The deformation atdiagram of the occurrence and development of the yield plateau in distinct sections along the length of the test sample is obtained. The material hardening diagram hidden under the yield plateau is reconstructed using the well-known Masing's principle.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48878953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algorithm for topology optimization of a structure made of anisotropic material with consideration of the reinforcement orientation parameters","authors":"","doi":"10.15593/perm.mech/2021.3.17","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.17","url":null,"abstract":"Advanced design methods offer not only a number of methods of modeling structures but also quite profound optimization approaches. The topology optimization is one of such advantageous methods. There are several implementations of this type of structural analysis, but the most common option is to deal with the material density as a generalized parameter. The development of 3D printing technologies increases the interest in algorithms of this type. However, it mostly refers to printing with metal or plastic, which implies the material isotropy. Advances in continuous fiber printing systems and automatic placement machines using composite tapes make it possible for engineers to control not only a material’s position, but also to choose the local orientation of reinforcing elements. Such systems require optimization algorithms taking into account additional parameters characterizing the material anisotropy. In this case the traditional problem of the topology optimization should first be modified for the model of an orthotropic material with restrictions on the value of the angle of rotation of the reinforcement lines along the print path. In this paper, an idea of such a topology optimization algorithm is proposed, which is implemented using the Abaqus finite element modeling facilities, and examples of solving typical problems are considered.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46621392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anti-icing indicator polymer coating with built-in fiber-optic PEL-sensor for indication, location and de-icing of aerodynamic surfaces","authors":"A. A. Pan’kov, P. Pisarev","doi":"10.15593/perm.mech/2021.4.11","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.11","url":null,"abstract":"A mathematical model was developed and a numerical modal analysis of the anti-icing mode of operation of the new indicator polymer coating with an integrated optical fiber piezoelectroluminescent (PEL) sensor for icing indication, location and self-cleaning from icing of aerodynamic surfaces was given. The fiber optic PEL-sensor is located in the plane of the coating. Receiver-analyzer of informative integral intensities of light signals is installed at output from optical fiber of sensor. Alternating voltage generator is connected to outputs of two control electrodes of sensor. The anti-icing function of the polymer coating is carried out automatically by thermo-mechanical actuation of the PEL-sensor on the appeared ice layer (on the ice crust of the coating) and only in those local areas of the coating where the thickness of the attached ice layer has reached a given critical value. Quality of cleaning from icing of surface of anti-icing coating is controlled by algorithms of digital processing of informative light signals at output from optical fiber of PEL-sensor. As a result, improved efficiency and control of de-icing on aerodynamic surfaces is achieved, especially for extended surfaces. The energy efficiency of the anti-icing polymer coating is increased due to the locality and self-control of the icing process. The modal analysis was carried out in an ANSYS finite element analysis package based on a numerical solution of the electrical-elasticity boundary value problem of stationary electromechanical oscillations of the representative cell of the anti-icing indicator polymer coating in the absence and presence of an ice layer of different thickness. Results of calculation of natural frequencies and forms of oscillations of representative cell of anti-icing coating, amplitude-frequency characteristics of mechanical stresses at coating/ice boundary for different values of thickness of attached ice layer for case of action of harmonic \"force\" in form of control electric voltage on electrodes of built-in PEL-sensor are presented.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":"42 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41300918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigation of the stress-strain state of a hollow cylinder with a coating based on the gradient model of thermoelasticity","authors":"","doi":"10.15593/perm.mech/2021.4.07","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.07","url":null,"abstract":"The study of the stress-strain state of a thermoelastic hollow cylinder with a homogeneous coating is carried out taking into account the scale effects. Aifantis' one-parameter gradient model is used to account for scale effects. Equilibrium equations and boundary conditions for a composite hollow thermoelastic cylinder are obtained on the basis of the Lagrange variational principle. In comparison with the classical formulation of the problem, additional boundary conditions and conjugation conditions are set for moment stresses and displacement gradients. The dimensionlessness of the task of thermoelasticity has been carried out. Solving the problem of uncoupled thermoelasticity begins with finding the radial temperature distribution of a layered cylinder on the basis of solving the problem of heat conduction in the classical formulation. The solution of the problem in displacements is presented as a sum of solutions in the classical formulation of the problem and additional boundary layer terms found on the basis of the asymptotic properties of the modified Bessel functions. Simplified analytical expressions are obtained for finding radial displacements, radial and circumferential Cauchy stresses, nonzero components of the tensor of moment and total stresses. On specific examples, calculations of the radial distribution of displacements and stresses of a composite cylinder in the case of both mechanical and thermal loading are carried out. The limits of applicability of the asymptotic solution of the problem are investigated. The difference between the radial distribution of displacements and stresses found on the basis of solutions to the problem in the classical formulation and in the gradient formulation is shown. It was found that the Cauchy radial stresses experience a jump at the boundary of the cylinder and the coating, which is explained by the continuity of radial displacements and their first derivatives. The components of the moment stress tensor either take on peak values or experience a jump at the interface. The moment stresses are proportional to the square of the gradient parameter, at small values of which they have values that are much less than the values of the total stresses. With an increase in the dimensionless scale parameter, the values of radial displacements and total circumferential stresses decrease, but moment stresses increase.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47679524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The potential of using SWCNTs, MWCNTs and CNFs capable of increasing the composite material dimensional and technological stability as modifiers of a polymer matrix","authors":"","doi":"10.15593/perm.mech/2021.4.10","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.10","url":null,"abstract":"In this study, the effect of carbon nanofibers (CNN), single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) on the warpage expected value and warpage dispersion of a plate made of a fibrous composite material are investigated. Laminates with fiber disorientation were considered as asymmetric and the model proposed by Dano and Hyer was used to evaluate the warpage. The results obtained confirm that the addition of carbon nanoparticles as a modifier to the polymer matrix of a fibrous composite material can increase the dimensional stability (the mathematical expectation of the standard deviation) and the technological stability of the reinforcement scheme (the variance of the standard deviation of the composite plate). Modeling of the warpage of plate, taking into account the possible disorientation of the fiber, showed a decrease in the warpage dispersion by 12.6 and 26.6 % with the modification of the SWNTs and MWCNTs, respectively. The coefficient of thermal extension (CTE) of a nanostructured polymer matrix with various fillers were experimentally determined. It was found that carbon nanomodifiers are more effective as compensators for the thermal expansion of the polymer matrix in composite laminates reinforced with carbon fibers than the polymer matrix without macrofibers. The addition of 0.05 % SWCNTs, 1 % MWCNTs to the epoxy resin reduces the CTE by 9.7 and 15.4 %, respectively. At the same time, the addition of a similar amount of nanoparticles to the epoxy matrix of the fiber composite reduces the CTE in the transverse direction by 15.56 and 35.8 %, respectively. On the basis of the obtained results, the dependences of the transverse CTE of the polymer composite material, the mathematical expectation of the standard deviation, and the variance of the standard deviation of the composite plate form accuracy on the concentration of the modifier were constructed. According to the obtained data, it can be concluded that in order to reduce the mathematical expectation and the variance of the warping of the composite material, there is an effective concentration, the increase of which is impractical, despite the further decrease in the transversal CTE.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45175444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frequency characteristics of built-in fiber-optic PEL-sensor to diagnose complex harmonic deformations within the polymer composite structure","authors":"A. A. Pan’kov, P. Pisarev","doi":"10.15593/perm.mech/2021.3.10","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.10","url":null,"abstract":"Fundamentals of operation of an optical fiber piezoelectroluminescent (PEL) sensor inside a polymer composite structure at its cyclic loading are considered. The optical fiber PEL-sensor is considered as part of the composite/sensor electromechanical system taking into account the presence of anisotropy, piezoactivity and Maxwell-Wagner relaxation of the electric fields of the sensor elements. The purpose of the optical fiber PEL-sensor is to diagnose the inhomogeneous complex volumetric deformed state of a long cylindrical area (a neighborhood along the built-in linear sensor) inside a cyclically loaded composite structure. A numerical model has been developed to solve the 3D related boundary value problem of electric elasticity for a representative fragment of the system composite/sensor in the ANSYS package. The numerical modeling of deformation and electric harmonic fields inside the representative fragment was carried out; in particular, distributions of amplitudes of these fields in elements of the structure of the optical fiber PEL sensor were found. The resonant modes are revealed, and the analysis is given of regularities of frequency dependences for the real and imaginary parts of controlling and informative transfer coefficients of the built-in fiber-optic PEL-sensor in the composite/sensor system. Additionally, graphs of frequency dependencies of tangents of mechanical loss angles for various cases of deformation of the composite/sensor system are given. Damping of the composite/sensor system is carried out as a result of the conversion of some part of the mechanical energy (transmitted from the composite to the sensor during their joint deformation) into Joule heat by the fiber-optic PEL sensor with a subsequent dispersion. The latter is caused by the direct piezoelectric effect and Maxwell-Wagner relaxation of electric fields in the sensor elements. The frequency range of deformation of the composite/sensor system is set, in which the passive vibration damping mode is most effectively implemented. It is numerically confirmed that for the extreme high-frequency case of deformation of the composite/sensor system, relaxation processes are not implemented and, as a result, solutions for the controlling and informative transfer coefficients of the PEL-sensor practically coincide with previously obtained numerical solutions that did not take into account the electrical conductivity of the sensor structure elements.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48448044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigation of the features of crystallization of granules of high-strength aluminum alloys of the Al-Zn-Mg-Cu system at ultra-high cooling rates","authors":"M. Zharov","doi":"10.15593/perm.mech/2021.4.08","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.08","url":null,"abstract":"The article presents the results of studies of the process of obtaining granular materials from high-strength aluminum alloys of the Al - Zn - Mg - Cu system by centrifugation of the melt with ultra-high cooling rates of granules. The concept of a «steam jacket» is introduced, namely, a steam layer that occurs between the granule body and the cooling liquid, which prevents the intensity of heat removal and is an obstacle to increasing the crystallization rate due to the lower thermal conductivity of water vapor. It is established that the formation of a vapor layer always occurs due to the heating of the cooling liquid in contact with the melt drop to boiling temperatures and the transition of the cooler from the liquid phase to steam. The technology of increasing the rate of crystallization of granules due to the constant removal of the vapor layer is proposed. The removal (knocking down) of the vapor shell that occurs around the drop occurs due to the high speed of the drop movement in the cooling medium. Fundamentally important in the industrial implementation of this technology is not so much the design of the device for obtaining pellets by centrifugation of the melt, namely, the high required rotation speed of the spraying crucible of the device under consideration. The results of experimental data are presented to determine the necessary rotation speed of the perforated cup, which ensures the creation of a sufficient initial velocity of the drop movement, leading to a constant churning of the «steam jacket». It is determined that an increase in the rates of heat removal from the crystallized granules and, as a result, an increase in the crystallization rate leads to an increase in the strength characteristics of granular aluminum alloys of the Al-Zn-Mg-Cu system. In particular, in the production of pressed semi-finished products from alloys of the Al-Zn-Mg-Cu system, such as B95, B96c. the increase in the strength characteristics of the material of the press products is up to 15 % compared to the same granular materials obtained by traditional methods with industrial crystallization rates of melt droplets. It is established that this method, based on the removal of the vapor layer around the formed granule, is the only possible one for further increasing the cooling rate and, as a result, the crystallization rate. Reducing the size of granules to the size of powders leads to serious technological problems in the further consolidation of granules and, in fact, is a dead end branch of the further development of granulation methods.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49315806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Numerical simulation of composite sandwich cylindrical shells reinforced with circular frames under local loadings","authors":"","doi":"10.15593/perm.mech/2021.3.15","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.15","url":null,"abstract":"The paper considers a woven fabric (based on fiberglass) composite structure in the form of a foam core sandwich cylindrical shell reinforced with circular frames, under the action of local loads applied to the frames. A technique is described for obtaining a numerical solution (with the confirmed reliability) to the problem of the stress-strain state of this type of structure using two alternative computational models, one of which is based on the numerical integration method, and the other one is based on the finite element method. The first model is developed by adopting a scheme, in which the frames are considered as short cylindrical shells obeying the single normal hypothesis. The foam core sandwich sections connected to them are considered within the framework of the zig-zag theory of soft core sandwich shells based on the assumption of incompressibility of the core along thickness. In this case, the corresponding calculation problem is formulated in the form of systems of algebraic and differential (in partial derivatives) equations for each of the shell sections being considered, which are supplemented by kinematic and force conditions at their joints, as well as boundary conditions at the left and right ends of the structure. The problem solving for each harmonic number is reduced to solving a set of boundary value problems for systems of 8 and 12 linear ordinary differential equations of the first order, related by conditions at the specified joints and using the procedure for expanding the parameters of the stress-strain state and applied loads into Fourier series in the circumferential direction. The solution algorithm is constructed using the numerical integration procedure in the orthogonal sweep version combined with the displacement method procedure (to satisfy the conditions at the joints). The declared finite element model is built within the ABAQUS software package using S4 shell elements (for composite layers) and C3D20 volume elements (for frames and core). The formed model, when setting deliberately overestimated values of the corresponding elastic modules, can implement a situation close to fulfilling the set of hypotheses adopted when constructing the first model. Having fixed in such a situation the consistency of the calculation results on the basis of the alternative computational models constructed in this way and thereby confirming the reliability of the obtained numerical solution, we carry out the transition to the calculation using the real values of the mentioned modules and the analysis of their influence on the stress-strain state of the investigated sandwich shell. The presented example of the calculation of a composite sandwich cylindrical structure, one of the frames of which is under the action of two local axial loads, demonstrates the possibilities of the adopted modeling method.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41523769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison of foam models from regular and irregular arrays of Gibson-Ashby open-cells","authors":"","doi":"10.15593/perm.mech/2021.3.07","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.07","url":null,"abstract":"The paper studies effective elastic properties of foam or cellular materials modeled by a set of Gibson-Ashby open cells with regular or irregular structures. Currently, there are many papers that present results of studying cellular materials using theoretical, numerical and experimental methods. However, these papers consider either regular lattices, or a single cell, or representative volume models based not on the Gibson-Ashby models. In this paper, in addition to the regular lattice, irregular structures were numerically studied. A mathematical formulation of the homogenization problem based on the energy equivalence of a foam-like material and on a homogeneous comparison medium is described. Formulations of six boundary value problems are presented. The solutions of these problems allow us to determine a complete set of effective stiffness modules for foams with different types of physical and geometric anisotropies. All stages of the numerical study were implemented in the ANSYS finite element package. Two algorithms for forming solid-state and finite-element models of irregular Gibson-Ashby lattices with small and large porosity are described in detail. As an example, numerical calculations are carried out for polycarbonate foams. The values of the effective elastic modules for regular and irregular lattices and for the Gibson-Ashby analytical model are compared. The results of numerical experiments showed that the Gibson-Ashby model describes the behavior of highly porous materials quite well (for porosity more than 75%), but this model gives a less satisfactory prediction in case of lower porosity. It is noted that for a large number of cells, regular and irregular lattices statistically give similar results for effective modules. However, for individual structures of irregular lattices, especially with strongly differing cells in individual directions, the effective moduli can have significantly different values, and the effective homogeneous medium can have pronounced anisotropic properties. These effects are due to geometric anisotropy and stress concentration in long connecting beams and at the joints of beams of various sizes in highly irregular Gibson-Ashby lattices. Examples of such lattices are given. We analyze the scatter of value for relative modules, which characterizes the anisotropy of such structures.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44449557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DETERMINATION OF THE STRESS STATE AND THE FORCE OF DEFORMATION OF BALL-SHAPED BILLETS IN A CLOSED MATRIX","authors":"Z. Ashkeyev, V. Andreyachshenko, M. Abishkenov, Z. Bukanov","doi":"10.15593/perm.mech/2021.4.01","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.01","url":null,"abstract":"At the present stage of development of science and technology, the problem of improving the quality of metal products by integrating methods of severe plastic deformation into existing technological processes is urgent. Intense plastic deformation makes it possible to obtain nanostructured metallic materials with improved quality and an attractive set of properties due to the saturation of the metal with nanoscale defects. Spherical billets with two ends along the edges are a common form of metal products. For the manufacture of such metal products, the effect of mutual influence of all-round compression and ECAP pressing in a device for the implementation of equal-channel angular pressing in a closed matrix was used. The purpose of this study is to develop a theoretical approach to determining the stress state and deformation force of spherical blanks in a closed matrix. To achieve this goal, an integrated approach was used to determine the stress state and deformation force by the method of slip lines and computer simulation in the Deform-3D software package. Analysis of the results of the stress state of the workpieces obtained by the slip line method showed that a uniform stress state is formed with a predominance of the maximum compressive stresses. The combination of the latter with angular metal extrusion into the lateral channels of the matrix predicts the production of workpieces with sub-ultrafine-grained and/or nanostructure. By the method of joint solution of differential equations of equilibrium and plasticity conditions, as well as computer modeling, the deforming force of the blanks at the final stage of deformation, when the metal flows out into the lateral channels of the matrix, is determined. The analysis of the obtained results shows that the value of the deformation force obtained by the two methods is comparable with a difference of up to 2 %, which confirms the correctness of the obtained values.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44378627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}