PNRPU Mechanics Bulletin最新文献

{"title":"Energy conditions for the formation of magnesium hydride","authors":"В.Н. Аптуков, Н.Е. Скрябина, Д. Фрушар, Valery N. Aptukov, N. Skryabina, D. Fruchart","doi":"10.15593/perm.mech/2022.2.03","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.03","url":null,"abstract":"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.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42557081","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":"Evolution of the grain structure of metals and alloys under intense plastic deformation: multilevel models","authors":"П.В. Трусов, Т.В. Останина, А.И. Швейкин, P. Trusov, Tatyana V. Ostanina –, T. V. Ostanina, A. Shveykin","doi":"10.15593/perm.mech/2022.2.11","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.11","url":null,"abstract":"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 t","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42672501","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":"MODELING OF CREEP PROCESSES OF SINGLE-CRYSTAL ALLOYS WITH TAKING INTO ACCOUNT OF RAFTING","authors":"","doi":"10.15593/perm.mech/2022.4.11","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.11","url":null,"abstract":"The research is devoted to the development and verification of a two-level micromechani-cally motivated model of viscoelastic deformation of two-phase nickel-based single-crystal al-loys, predicting behavior under high thermomechanical loading with taking into account the presence of γ and γ' phases. The model is relevant for computations of the stress-strain state of cooled single crystal blades of gas turbine units. The formulation of the constitutive equations for each of the phases considered the anisot-ropy of elastic and viscous properties, the presence of octahedral slip systems, the features of the cubic system, and the presence of viscous properties both below and above the yield stress. Model parameters for γ and γ' phases were identified based on known creep curves for each phase. The effective properties of a single-crystal alloy, considering the presence of γ and γ' phas-es, were determined both based on finite element homogenization for a representative volume and using the simplest rheological (structural) models of the material, considering the series and parallel connection of phases. Based on multivariant computational experiments and analytical estimates, the dependences of the viscoelastic properties of nickel-based single-crystal alloys on the volume fraction of the γ' phase are determined. Phenomenological creep models that take into account the change in the volume fraction and the morphology of γ' inclusions have been proposed. The simulation results using the proposed two-level microstructural model of the material demonstrate a good agreement with the experimental data for the ZhS32 single-crystal heat-resistant alloy.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43800123","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":"Solution of the plane problem of the theory of elasticity on bending of an articulated fixed multilayer panel with a circular axis","authors":"S. A. Bukaty, N. Osadchy","doi":"10.15593/perm.mech/2022.2.05","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.05","url":null,"abstract":"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.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45992436","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":"Composite materials in aircraft engine blades","authors":"","doi":"10.15593/perm.mech/2021.4.02","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.02","url":null,"abstract":"","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":"42415746","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":"Multilevel model of polycrystals: application to assessing the effect of texture and grains misorientation on the critical deformation of the dynamic recrystallization initiation","authors":"N. Kondratev, P. Trusov, A. Podsedertsev","doi":"10.15593/perm.mech/2021.4.09","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.09","url":null,"abstract":"The current state of materials constitutive models and the computer technology development make it possible to numerically implement complex multilevel models that allow describing the material structure evolution. In this regard, it is possible to formulate optimal control problem for metal forming processes in order to create the required performance characteristics of finished products and their ingots. To solve this problem in this study, the effective multilevel modeling approach is used to describe the thermomechanical treatment of polycrystalline materials. The model is based on this approach with the introduction of internal variables, in which the carriers and physical mechanisms of the processes of hot intense plastic deformation are explicitly considered. At deformation temperatures order of 0.5 homologous and above, recrystallization process have a special effect on the formation and change of the grain and defect material structure. The paper considers the problem of determining the critical deformation of dynamic recrystallization initiation, that depending on the material texture and the mutual misorientation of neighboring grains. Numerical experiments of the multilevel model are used to simulate two stages of inelastic deformation for this purpose. At the first stage, cold inelastic deformation by simple shear and compression is considered, that leading to the formation of a corresponding texture. At the second stage, uniaxial hot tension deformation is considered. The initial distribution of crystallographic grain orientation is assumed to be uniform. Two variants of the grains mutual misorientation with the prescribed increased and decreased values of the average misorientation angles are considered. The recrystallization process is not explicitly modeled. The current model is intended to assess the recrystallization critical deformation. It is shown that the mutual misorientation of grains, rather than texture, has the most influence on the critical deformation. An increase in the angle of grains mutual misorientation contributes to an earlier start of the dynamic recrystallization process. The formation of a deformation texture leads to a decrease in the angle of mutual misorientation, and, accordingly, to a decrease in dynamic recrystallization intensity. Despite this, with an increase of deformation, the driving force of recrystallization (the average value of the difference of stored energy between neighbor grains) is increases, which leads to the implementation of dynamic recrystallization.","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":"43696724","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":"Analysis of stress fields at the crack tip and fracture resistance parameters under conditions of gradient plasticity","authors":"Р Хамидуллин, Д Федотова, Вестник Пнипу, Механика","doi":"10.15593/perm.mech/2021.4.13","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.4.13","url":null,"abstract":"This paper presents a numerical analysis based on previously obtained experimental data on crack growth for P2M and 34X steels, aluminum 7050 and titanium alloy Ti-6Al-4V compact samples (CTS) with a one-sided lateral incision, within the framework of the conventional theory of strain gradient plasticity (CMSG), based on the Taylor dislocation model. In this study, the initial points of the curved crack trajectory were considered for two classical states: plane strain and plane stress with normal separation and pure shear. The constitutional equations of material behavior for CMSGP theories were introduced into the finite element computational complex and new fields of stress-strain state parameters for the conditions of strain gradient plasticity were obtained. The results of FE calculations show a significant increase in the magnitude of the true stress fields at the crack tip, taking into account the plastic deformation gradients and the internal characteristic length of the material. The numerical results also show that the singularity in the crack tip region is different for the model of gradient plasticity of deformations and depends on the mode I/II. An important conclusion regarding the numerical results regarding the parameters of the material's fracture resistance is that the new plastic stress intensity coefficients for gradient plasticity differ for plane strain and plane stress, and also show significant sensitivity to the plastic properties of the material and to the scale parameter of the intrinsic material length, which is attractive from the point of view of practical application and further fundamental research.","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":"41674081","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":"STRESS STATE AND CONDITIONS FOR CRACK INITIATION IN THE ADHESION LAYER OF THE COMPOSITE","authors":"V. E. Bogacheva, V. Glagolev, L. V. Glagolev, A. Markin","doi":"10.15593/perm.mech/2021.3.03","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.03","url":null,"abstract":"The paper deals with the elastic deformation of a composite consisting of plates connected with an adhesive layer on the basis of the interaction layer concept. The layer thickness is taken as a linear parameter. Under loading by the normal separation in the case of plane deformation, the triaxial stress state of the adhesive layer is taken into account. From the general variational setting, by using the hypothesis of flat sections, the problem is formulated in a differential form. Within the framework of a simplified formulation, an analytical solution is found that agrees with the numerical solution obtained by the finite element method. It is shown that Poisson's ratio of the adhesive layer significantly affects its stress state, in which there is a coincidence of the two principal stresses. For weakly compressible adhesion layers, a stress state close to hydrostatic tension is realized. In order to analyze the stress state of the adhesion layer, which is singular at extremely small values of the linear parameter, it is proposed to use the energy product (EP), local stresses (LS) and local deformations (LD). EP is determined as the product of the specific free energy of the layer and the linear parameter, and LS (LD) is determined as the product of stresses (deformations) and the square root of the linear parameter. It is shown that these characteristics are not singular with respect to small layer thicknesses and do not depend on the linear parameter. It was found that the value to which the EP converges at a fixed external load and the linear parameter tends to zero does not depend on the mechanical properties of the adhesive, and the LS (LD) values depend on the properties of the adhesive. At the critical load of crack initiation in the adhesive, the LD in the direction of the separation is significantly (by several orders of magnitude) higher than the LD in the orthogonal direction. In this case, the LS and LD of separation make the main contribution to the formation of the EP. A method is proposed for determining the critical value of the EP corresponding to crack initiation in the adhesive based on the use of the maximum external load from the experimental R-curves.","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":"45691899","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":"Finite Element Model Updating Method of Dynamic Systems","authors":"","doi":"10.15593/perm.mech/2021.3.08","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.08","url":null,"abstract":"The finite element model updating method of dynamical systems based on results of modal tests is proposed. The purpose of updating is to change eigenspectrum. The method alters a stiffness matrix by adding an updating finite element model created on the nodes of the intial one with respect to the existing links between the linear degrees of freedom. The stiffnesses of the updating elements are utilized as the updating parameters to be defined. The objective function equals to the least square weighted sum of residuals between the target, which were determined experimentally, and current values of modal stiffnesses. The iterative solution process is carried out. At each iteration step the conjugate gradient method is applied to solve the unconstrained minimization problem. The modeshapes, which were calculated as the result of solving the generalized eigenvalue problem at the previous iteration step, are employed to calculate the current modal stiffnesses. The method does not have a limit to a size of matrices and keeps their sparsity and symmetry. It provides the model updating of selected regions of a structure and step-by-step model updating of predefined groups of eigenfrequencies. Moreover, geometrical features of a structure, such as the presence of the symmetry planes and structurally identical elements, may be taken into account. The method is implemented into a program and verified by the example of the free dynamically-scaled model of Tu-204. In order to perform the ground vibration testing, the model was suspended with a low-rigidity flexible support. The finite element model made of solid elements has been updated on the basis of the six experimentally determined sets of eigenfrequencies. The target frequencies from each set have been achieved with a high level of accuracy.","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":"44622558","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":"Elastic diffusion vibrations of an isotropic Kirchhoff-Love plate under an unsteady distributed transverse load","authors":"Gu Yu, A. Zemskov, D. Tarlakovskii","doi":"10.15593/perm.mech/2021.3.05","DOIUrl":"https://doi.org/10.15593/perm.mech/2021.3.05","url":null,"abstract":"We investigated an unsteady elastic diffusion vibration of a simply supported rectangular isotropic Kirchhoff-Love plate. The plate is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in a multicomponent continuum is used for the mathematical problem formulation. The model is taking into account the diffusion fluxes relaxation. The transverse vibration equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d'Alembert variational principle. The initial-boundary value problem of a freely supported isotropic rectangular plate bending is formulated on the basis of the obtained equations. The plate is under the action of elastic diffusion perturbations distributed over the surface. The problem solution of an unsteady elastic diffusion plate vibration is sought in an integral form. The surface Green's functions are the kernels of the integral representations. To find the Green's functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green's functions in the image domain are represented in the form of rational functions and depend on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The surface Green's function analytical expressions are obtained. As a calculation example, we considered a freely supported elastodiffusive plate under the action of suddenly applied unsteady bending moments distributed over the plate surface. By using a three-component continuum, a numerical study of interactions between unsteady mechanical and diffusion fieldsis done for an isotropic plate. The influence of relaxation effects on the kinetics of mass transfer is investigated. The solution is presented in the analytical form, as well as in the graphs of the displacement fields and concentration increments on time and coordinates. At the end of the publication, the main conclusions are given about the fields coupling effect and the relaxation of diffusion fluxes on the stress-strain state and mass transfer in the plate.","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":"43674913","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}