Pub Date : 2019-12-16DOI: 10.32326/1814-9146-2019-81-4-429-442
E. V. Petrakov, H. L. Pour, E. Drobny
The damping efficiency is considered for a console beam described by a linear viscosity Bernoulli-Euler model. The article presents the methods of damping transverse vibrations implemented by a dynamic damper from a piezoelectric layer distributed symmetrically along the axis of symmetry of the beam. Piezoelectric layers with a triangular and rectangular shape of electrode plates are considered, which affects the nature of mechanical stresses upon application of electrical voltage. The electrode plates are thin layers made of nickel or silver several microns thick and located normal to the polarization axis, that is, along the length of the piezoceramic plate. The control of the piezoelectric layers is realized by changing the potential difference between the electrode plates, while the piezoelectric material uncoated by the electrode plate on both sides is useless to use as an active material. Mathematical models of the effect of piezoelectric elements on the cantilever beam are derived from the Hamilton principle. The Pareto-efficiency of quenching by piezoelectric plates with different electrode shapes is evaluated relative to two criteria: the level of control voltage and the maximum deflection of the beam. To compare the results with the best variant of vibration damping, in this formulation, the result of vibration damping for a beam with piezoelectric layer applied along the entire length is given. The damping efficiency was confirmed in an applied and particular example by means of vibrograms. The synthesis of Pareto-optimal controls is based on the Germeier convolution, and the search for optimal feedback is based on the application of the theory of linear matrix inequalities and effective algorithms for solving them.
{"title":"ACTIVE DAMPING OF TRANSVERSE VIBRATIONS OF CONSOLE BEAM BY PIEZOELECTRIC LAYER WITH DIFFERENT ELECTRODE SHAPES OF DAMAGED MEDIA","authors":"E. V. Petrakov, H. L. Pour, E. Drobny","doi":"10.32326/1814-9146-2019-81-4-429-442","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-429-442","url":null,"abstract":"The damping efficiency is considered for a console beam described by a linear viscosity Bernoulli-Euler model. The article presents the methods of damping transverse vibrations implemented by a dynamic damper from a piezoelectric layer distributed symmetrically along the axis of symmetry of the beam. Piezoelectric layers with a triangular and rectangular shape of electrode plates are considered, which affects the nature of mechanical stresses upon application of electrical voltage. The electrode plates are thin layers made of nickel or silver several microns thick and located normal to the polarization axis, that is, along the length of the piezoceramic plate. The control of the piezoelectric layers is realized by changing the potential difference between the electrode plates, while the piezoelectric material uncoated by the electrode plate on both sides is useless to use as an active material. Mathematical models of the effect of piezoelectric elements on the cantilever beam are derived from the Hamilton principle. The Pareto-efficiency of quenching by piezoelectric plates with different electrode shapes is evaluated relative to two criteria: the level of control voltage and the maximum deflection of the beam. To compare the results with the best variant of vibration damping, in this formulation, the result of vibration damping for a beam with piezoelectric layer applied along the entire length is given. The damping efficiency was confirmed in an applied and particular example by means of vibrograms. The synthesis of Pareto-optimal controls is based on the Germeier convolution, and the search for optimal feedback is based on the application of the theory of linear matrix inequalities and effective algorithms for solving them.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124807982","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}
Pub Date : 2019-12-16DOI: 10.32326/1814-9146-2019-81-4-416-428
A. Ipatov, F. dell’Isola, I. Giorgio, I. Rahali, S. Eugster, A. Zaikin
In present paper wave propagation poroviscoelastic solids is studied. Study of wave propagation in saturated porous media is an important issue of engineering sciences. The poroelasticity theory was developed and nowadays is an important to engineering applications. Also research is dedicated to modeling of a slow compressional wave in poroviscoelastic media by means of boundary-element method. Poroviscoelastic formulation is based on Biot's model of fully saturated poroelastic media with a correspondence principal usage. Standard linear solid model is employed in order to describe viscoelastic behavior of the skeleton in porous medium. The boundary-value problem of the three-dimensional dynamic poroviscoelasticity is written in terms of Laplace transforms. Direct approach of the boundary integral equation method is employed. The boundary-element approach is based on the mixed boundary-element discretization of surface with generalized quadrangular elements. Subsequent application of collocation method leads to the system of linear equations, and then to the solution in Laplace domain. Numerical inversion of Laplace transform is used to obtain time-domain solution. The problem of the load acting on a poroelastic prismatic solid is solved by means of developed software based on boundary element approach. An influence of permeability of porous material on dynamic responses is studied. Slow wave phenomena appearance is demonstrated. Viscosity parameter influence on dynamic responses of displacements and pore pressure is studied.
{"title":"DYNAMICS OF POROVISCOELASTIC PRISMATIC SOLID FOR VARIOUS VALUES OF MATERIAL PERMEABILITY","authors":"A. Ipatov, F. dell’Isola, I. Giorgio, I. Rahali, S. Eugster, A. Zaikin","doi":"10.32326/1814-9146-2019-81-4-416-428","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-416-428","url":null,"abstract":"In present paper wave propagation poroviscoelastic solids is studied. Study of wave propagation in saturated porous media is an important issue of engineering sciences. The poroelasticity theory was developed and nowadays is an important to engineering applications. Also research is dedicated to modeling of a slow compressional wave in poroviscoelastic media by means of boundary-element method. Poroviscoelastic formulation is based on Biot's model of fully saturated poroelastic media with a correspondence principal usage. Standard linear solid model is employed in order to describe viscoelastic behavior of the skeleton in porous medium. The boundary-value problem of the three-dimensional dynamic poroviscoelasticity is written in terms of Laplace transforms. Direct approach of the boundary integral equation method is employed. The boundary-element approach is based on the mixed boundary-element discretization of surface with generalized quadrangular elements. Subsequent application of collocation method leads to the system of linear equations, and then to the solution in Laplace domain. Numerical inversion of Laplace transform is used to obtain time-domain solution. The problem of the load acting on a poroelastic prismatic solid is solved by means of developed software based on boundary element approach. An influence of permeability of porous material on dynamic responses is studied. Slow wave phenomena appearance is demonstrated. Viscosity parameter influence on dynamic responses of displacements and pore pressure is studied.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122974122","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}
Pub Date : 2019-12-16DOI: 10.32326/1814-9146-2019-81-4-501-512
I. A. Z. Eremeeva, D. Scerrato, C. Cardillo, A. Tran
Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.
{"title":"A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS","authors":"I. A. Z. Eremeeva, D. Scerrato, C. Cardillo, A. Tran","doi":"10.32326/1814-9146-2019-81-4-501-512","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-501-512","url":null,"abstract":"Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129216103","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}
Pub Date : 2019-12-16DOI: 10.32326/1814-9146-2019-81-4-443-448
V. Balandin, L. Meyer, S. Abdel-Malek
The study of the laws of contact interaction of hard and deformable impactors with frozen soils is of great scientific and applied value. In solving such problems, numerical methods are widely used. For numerically modeling the behavior of frozen soil under dynamic loading, it is necessary to use models of soil media that adequately describe their behavior at various negative temperatures, humidities and strain rates. To identify the parameters of these models, experimental studies are required for determining dynamic properties of soils at low temperatures. The paper presents the results of experimental studies of dynamic deformation of samples of frozen sand with humidities of 10% and 18%. Compression experiments were conducted using a stand implementing the Kolsky method. Deformation curves of frozen sand at a temperature of -18 °С were obtained under uniaxial stress conditions at various strain rates in the range of 400-2500 s-1. Diagrams of strength of frozen sand under uniaxial compression as a function of strain rate are constructed. The diagrams are linear for samples of different humidity in the studied range of strain rates. Maximum stresses in frozen water-saturated sand are higher than those in frozen sand of 10% humidity. With increasing strain rate, compressive strength of water-saturated sand grows faster than that of sand with a moisture content of 10%: at a strain rate of about 500 s-1, the stresses in frozen water-saturated sand, at which the samples fail, are 1.5 times higher than those in the frozen sand with a moisture content of 10%, and at a strain rate of 2500 s-1 they are 3 times as high.
{"title":"DYNAMIC TESTS OF FROZEN SAND SOILS","authors":"V. Balandin, L. Meyer, S. Abdel-Malek","doi":"10.32326/1814-9146-2019-81-4-443-448","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-443-448","url":null,"abstract":"The study of the laws of contact interaction of hard and deformable impactors with frozen soils is of great scientific and applied value. In solving such problems, numerical methods are widely used. For numerically modeling the behavior of frozen soil under dynamic loading, it is necessary to use models of soil media that adequately describe their behavior at various negative temperatures, humidities and strain rates. To identify the parameters of these models, experimental studies are required for determining dynamic properties of soils at low temperatures.\u0000\u0000The paper presents the results of experimental studies of dynamic deformation of samples of frozen sand with humidities of 10% and 18%. Compression experiments were conducted using a stand implementing the Kolsky method. Deformation curves of frozen sand at a temperature of -18 °С were obtained under uniaxial stress conditions at various strain rates in the range of 400-2500 s-1. Diagrams of strength of frozen sand under uniaxial compression as a function of strain rate are constructed. The diagrams are linear for samples of different humidity in the studied range of strain rates. Maximum stresses in frozen water-saturated sand are higher than those in frozen sand of 10% humidity. With increasing strain rate, compressive strength of water-saturated sand grows faster than that of sand with a moisture content of 10%: at a strain rate of about 500 s-1, the stresses in frozen water-saturated sand, at which the samples fail, are 1.5 times higher than those in the frozen sand with a moisture content of 10%, and at a strain rate of 2500 s-1 they are 3 times as high.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133870245","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}
Pub Date : 2019-09-16DOI: 10.32326/1814-9146-2019-81-3-369-380
A. Vatulyan, Y. Zubkov
In the framework of the model of coupled electroelasticity of inhomogeneous bodies, the problem of steady-state oscillations of a thin piezodisc with inhomogeneous properties is considered, in particular, in the presence of radial polarization. The necessary simplifications are made within the framework of traditional hypotheses, the formulated boundary-value problem is reduced to a canonical system of first-order differential equations with respect to dimensionless components of radial displacement and radial stress with corresponding boundary conditions. The direct problem of oscillations of an inhomogeneous disk is solved numerically based on the shooting method by numerically analyzing auxiliary Cauchy problems. The analysis of the amplitude-frequency characteristics and resonance frequencies depending on various laws of variation of the inhomogeneous properties of the piezodisc is performed, which in the presented model are characterized by two functions, one of which characterizes the change in the elastic modulus, the second changes in the piezomodule. The inverse problem is formulated in the first statement, in which the laws of variation of the piezodisc heterogeneity (two functions) are restored from the values of the functions characterizing the radial displacement and stress, known in a finite set of points. The results of computational experiments on solving the inverse problem in the first formulation are presented, various aspects of reconstruction are discussed. The second formulation of the inverse problem is formulated to determine the piezoelectric characteristics of the disk, where a function that describes the laws of change in the elastic characteristics of the disk and the amplitude-frequency characteristic is considered known. To solve the inverse problem, in this formulation, the Fredholm integral equation of the first kind with a smooth kernel is formulated. The results of numerical experiments on solving the Fredholm integral equation of the first kind using the Tikhonov regularizing method are presented, various aspects of reconstruction are discussed.
{"title":"ON THE VIBRATIONS OF INHOMOGENEOUS PIEZO DISC","authors":"A. Vatulyan, Y. Zubkov","doi":"10.32326/1814-9146-2019-81-3-369-380","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-3-369-380","url":null,"abstract":"In the framework of the model of coupled electroelasticity of inhomogeneous bodies, the problem of steady-state oscillations of a thin piezodisc with inhomogeneous properties is considered, in particular, in the presence of radial polarization. The necessary simplifications are made within the framework of traditional hypotheses, the formulated boundary-value problem is reduced to a canonical system of first-order differential equations with respect to dimensionless components of radial displacement and radial stress with corresponding boundary conditions. The direct problem of oscillations of an inhomogeneous disk is solved numerically based on the shooting method by numerically analyzing auxiliary Cauchy problems. The analysis of the amplitude-frequency characteristics and resonance frequencies depending on various laws of variation of the inhomogeneous properties of the piezodisc is performed, which in the presented model are characterized by two functions, one of which characterizes the change in the elastic modulus, the second changes in the piezomodule. The inverse problem is formulated in the first statement, in which the laws of variation of the piezodisc heterogeneity (two functions) are restored from the values of the functions characterizing the radial displacement and stress, known in a finite set of points. The results of computational experiments on solving the inverse problem in the first formulation are presented, various aspects of reconstruction are discussed. The second formulation of the inverse problem is formulated to determine the piezoelectric characteristics of the disk, where a function that describes the laws of change in the elastic characteristics of the disk and the amplitude-frequency characteristic is considered known. To solve the inverse problem, in this formulation, the Fredholm integral equation of the first kind with a smooth kernel is formulated. The results of numerical experiments on solving the Fredholm integral equation of the first kind using the Tikhonov regularizing method are presented, various aspects of reconstruction are discussed.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131311551","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}
Pub Date : 2019-09-16DOI: 10.32326/1814-9146-2019-81-3-271-291
A. Khokhlov
We study analytically the Boltzmann - Volterra linear constitutive equation for isotropic non-aging viscoelastic media in order to elucidate its capabilities to provide a qualitative simulation of rheological phenomena related to different types of evolution of triaxial strain state and of the lateral contraction ratio (the Poisson ratio) observed in uni-axial tests of viscoelastic materials under tension or compression at constant stress rate. In particular, we consider such effects as increasing, decreasing or non-monotone dependences of lateral strain and Poisson's ratio on time, sign changes and negativity of Poisson's ratio (auxeticity effect) and its stabilization at large times. The viscoelasticity equation implies that the hydrostatic and deviatoric parts of stress and strain tensors don't depend on each other. It is governed by two material functions of a positive real argument (that is shear and bulk creep compliances). Assuming both creep compliances are arbitrary positive, differentiable, increasing and convex up functions on time semi-axis, we analyze general expressions for the Poisson ratio and strain triaxiality ratio (which is equal to volumetric strain divided by deviatoric strain) generated by the viscoelasticity relation under uni-axial tension or compression. We investigate qualitative properties and peculiarities of their evolution in time and their dependences on material functions characteristics. We obtain the universal accurate two-sided bound for the Poisson ratio range and criteria for the Poisson ratio increase or decrease and for extrema existence. We derive necessary and sufficient restrictions on shear and bulk creep compliances providing sign changes of the Poisson ratio and negative values of Poisson's ratio on some interval of time. The properties of the Poisson ratio under tension at constant stress rates found in the study we compare to properties the Poisson ratio evolution under constant stress (in virtual creep tests) and illustrate them using popular classical and fractal models with shear and bulk creep functions each one controlled by three parameters. The analysis carried out let us to conclude that the linear viscoelasticity theory (supplied with common creep functions which are non-exotic from any point of view) is able to simulate qualitatively the main effects associated with different types of the Poisson ratio evolution under tension or compression at constant stress rate except for dependence of Poisson's ratio on stress rate. It is proved that the linear theory can reproduce increasing, decreasing or non-monotone and convex up or down dependences of lateral strain and Poisson's ratio on time and it can provide existence of minimum, maximum or inflection points and sign changes from minus to plus and vice versa and asymptotic stabilization at large times.
{"title":"NON-MONOTONICITY, SIGN CHANGES AND OTHER FEATURES OF POISSON'S RATIO EVOLUTION FOR ISOTROPIC LINEAR VISCOELASTIC MATERIALS UNDER TENSION AT CONSTANT STRESS RATES","authors":"A. Khokhlov","doi":"10.32326/1814-9146-2019-81-3-271-291","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-3-271-291","url":null,"abstract":"We study analytically the Boltzmann - Volterra linear constitutive equation for isotropic non-aging viscoelastic media in order to elucidate its capabilities to provide a qualitative simulation of rheological phenomena related to different types of evolution of triaxial strain state and of the lateral contraction ratio (the Poisson ratio) observed in uni-axial tests of viscoelastic materials under tension or compression at constant stress rate. In particular, we consider such effects as increasing, decreasing or non-monotone dependences of lateral strain and Poisson's ratio on time, sign changes and negativity of Poisson's ratio (auxeticity effect) and its stabilization at large times. The viscoelasticity equation implies that the hydrostatic and deviatoric parts of stress and strain tensors don't depend on each other. It is governed by two material functions of a positive real argument (that is shear and bulk creep compliances).\u0000\u0000Assuming both creep compliances are arbitrary positive, differentiable, increasing and convex up functions on time semi-axis, we analyze general expressions for the Poisson ratio and strain triaxiality ratio (which is equal to volumetric strain divided by deviatoric strain) generated by the viscoelasticity relation under uni-axial tension or compression. We investigate qualitative properties and peculiarities of their evolution in time and their dependences on material functions characteristics. We obtain the universal accurate two-sided bound for the Poisson ratio range and criteria for the Poisson ratio increase or decrease and for extrema existence. We derive necessary and sufficient restrictions on shear and bulk creep compliances providing sign changes of the Poisson ratio and negative values of Poisson's ratio on some interval of time. The properties of the Poisson ratio under tension at constant stress rates found in the study we compare to properties the Poisson ratio evolution under constant stress (in virtual creep tests) and illustrate them using popular classical and fractal models with shear and bulk creep functions each one controlled by three parameters.\u0000\u0000The analysis carried out let us to conclude that the linear viscoelasticity theory (supplied with common creep functions which are non-exotic from any point of view) is able to simulate qualitatively the main effects associated with different types of the Poisson ratio evolution under tension or compression at constant stress rate except for dependence of Poisson's ratio on stress rate. It is proved that the linear theory can reproduce increasing, decreasing or non-monotone and convex up or down dependences of lateral strain and Poisson's ratio on time and it can provide existence of minimum, maximum or inflection points and sign changes from minus to plus and vice versa and asymptotic stabilization at large times.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123315070","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}
Pub Date : 2019-09-16DOI: 10.32326/1814-9146-2019-81-3-345-358
A. Antipov, V. A. Gorokhov, V. V. Egunov, D. Kazakov, S. Kapustin, Yu. A. Churilov
The technique of numerical research on the basis of FEM processes of deformation and damage accumulation in the structural elements of heat-resistant alloys under conditions of high-temperature creep taking into account the influence of neutron irradiation is developed. The description of the mechanical behavior of the material is carried out within the framework of the previously developed general model of the damaged material and the creep model for non-irradiated heat-resistant alloys, supplemented by taking into account the effect of irradiation on the creep rate and the appearance of brittle fracture in a given range of temperature variation and irradiation intensity. The defining relations of the creep model of the irradiated material were obtained by modifying the creep model of the non-irradiated material: a material function was introduced, taking into account the effect of the flux of neutrons on the rate of thermal creep deformation; a material function was introduced that takes into account the effect of the neutron flux on the creep surface radius; A material function was introduced, which takes into account the effect of the neutron flux on the ultimate value of the dissipation energy at full power. To simulate the processes of brittle fracture during creep under neutron irradiation conditions, it is assumed that the destructive values of effective normal stresses are a function of temperature, flux of neutrons and the current value of accumulated creep. The material functions of the model were obtained from the results of basic experiments conducted at the Research Institute of Mechanics for the heat-resistant alloy without irradiation under consideration and the available experimental data on the study of the creep of this alloy during its irradiation. Based on the proposed model, a numerical method for solving problems of high-temperature creep of structures made of heat-resistant alloys under neutron irradiation was developed and implemented within the UPAKS computing complex. To verify and illustrate the capabilities of the developed methodological and software tools, a number of problems of modeling the processes of high-temperature creep and destruction of structural elements made of the high-temperature alloy under consideration are solved.
{"title":"NUMERICAL SIMULATION OF HIGH-TEMPERATURE CREEP OF ELEMENTS OF HEAT-RESISTANT ALLOYS STRUCTURES TAKING INTO ACCOUNT NEUTRON IRRADIATION EFFECTS","authors":"A. Antipov, V. A. Gorokhov, V. V. Egunov, D. Kazakov, S. Kapustin, Yu. A. Churilov","doi":"10.32326/1814-9146-2019-81-3-345-358","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-3-345-358","url":null,"abstract":"The technique of numerical research on the basis of FEM processes of deformation and damage accumulation in the structural elements of heat-resistant alloys under conditions of high-temperature creep taking into account the influence of neutron irradiation is developed. The description of the mechanical behavior of the material is carried out within the framework of the previously developed general model of the damaged material and the creep model for non-irradiated heat-resistant alloys, supplemented by taking into account the effect of irradiation on the creep rate and the appearance of brittle fracture in a given range of temperature variation and irradiation intensity. The defining relations of the creep model of the irradiated material were obtained by modifying the creep model of the non-irradiated material: a material function was introduced, taking into account the effect of the flux of neutrons on the rate of thermal creep deformation; a material function was introduced that takes into account the effect of the neutron flux on the creep surface radius; A material function was introduced, which takes into account the effect of the neutron flux on the ultimate value of the dissipation energy at full power. To simulate the processes of brittle fracture during creep under neutron irradiation conditions, it is assumed that the destructive values of effective normal stresses are a function of temperature, flux of neutrons and the current value of accumulated creep. The material functions of the model were obtained from the results of basic experiments conducted at the Research Institute of Mechanics for the heat-resistant alloy without irradiation under consideration and the available experimental data on the study of the creep of this alloy during its irradiation. Based on the proposed model, a numerical method for solving problems of high-temperature creep of structures made of heat-resistant alloys under neutron irradiation was developed and implemented within the UPAKS computing complex. To verify and illustrate the capabilities of the developed methodological and software tools, a number of problems of modeling the processes of high-temperature creep and destruction of structural elements made of the high-temperature alloy under consideration are solved.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130443333","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}
Pub Date : 2019-09-16DOI: 10.32326/1814-9146-2019-81-3-333-344
A. M. Antonov, V. Erofeev
We consider a simplified (reduced) dynamic model of a Cosserat medium, which occupies an intermediate position between the classical dynamic theory of elasticity and the proper Cosserat medium model, which has asymmetry in the stress tensor and the presence of moment stresses. In contrast to the latter, in the simplified model, three of the six elastic constants are zero and, as a result, there is no moment stress tensor. In the two-dimensional formulation for the model of a reduced medium, the problem of the propagation of an elastic surface wave along the half-space boundary was solved. The solution of the equations was described as the sum of the scalar and vector potentials, and only one component of the vector potential is nonzero. It is shown that such a wave, in contrast to the classical surface Rayleigh wave, has a dispersion. In the plane “phase velocity-frequency” for such waves there are two dispersion branches: the lower (acoustic) and upper (optical). With increasing frequency, the phase velocity of the wave related to the lower dispersion branch decreases. The phase velocity of the wave related to the upper dispersion branch increases with increasing frequency. The phase velocity of the surface wave in the entire frequency range exceeds the phase velocity of the bulk shear wave. The stresses and displacements arising in the zone of propagation of the surface wave are calculated.
{"title":"DISTRIBUTION OF THE RAYLEIGH WAVE ALONG THE BORDER OF THE HALF-SPACE, DESCRIBED BY THE SIMPLIFIED MODEL OF THE COSSERAT","authors":"A. M. Antonov, V. Erofeev","doi":"10.32326/1814-9146-2019-81-3-333-344","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-3-333-344","url":null,"abstract":"We consider a simplified (reduced) dynamic model of a Cosserat medium, which occupies an intermediate position between the classical dynamic theory of elasticity and the proper Cosserat medium model, which has asymmetry in the stress tensor and the presence of moment stresses. In contrast to the latter, in the simplified model, three of the six elastic constants are zero and, as a result, there is no moment stress tensor.\u0000\u0000In the two-dimensional formulation for the model of a reduced medium, the problem of the propagation of an elastic surface wave along the half-space boundary was solved. The solution of the equations was described as the sum of the scalar and vector potentials, and only one component of the vector potential is nonzero.\u0000\u0000It is shown that such a wave, in contrast to the classical surface Rayleigh wave, has a dispersion. In the plane “phase velocity-frequency” for such waves there are two dispersion branches: the lower (acoustic) and upper (optical). With increasing frequency, the phase velocity of the wave related to the lower dispersion branch decreases. The phase velocity of the wave related to the upper dispersion branch increases with increasing frequency. The phase velocity of the surface wave in the entire frequency range exceeds the phase velocity of the bulk shear wave.\u0000\u0000The stresses and displacements arising in the zone of propagation of the surface wave are calculated.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126051258","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}
Pub Date : 2019-06-16DOI: 10.32326/1814-9146-2019-81-2-177-190
V. Kotov
A one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in an infinite elastoplastic medium is considered. The problem has a first-kind self-similar solution. Elastoplastic deformation of the soil is described based on Hooke's law and the Mohr-Coulomb yield criterion. An analytical solution of the problem in the elastic region contacting with the plastic yield region has been obtained. To determine stress and velocity fields in the plastic region, a known algorithm, based on the shooting method, of analyzing a boundary-value problem for a system of two first-order ordinary differential equations, including the fourth-order Runge - Kutta method, has been realized. An effective algorithm of numerically analyzing an expanding cavity problem, earlier proposed in the works by М. Forrestal et al., makes it possible to solve the problem accurately enough for practical applications. A formula for determining the critical pressure - the minimal pressure required for the nucleation, accounting for internal pressure of a cavity in the framework of the Mohr - Coulomb yield criterion, has been derived, which is a generalization of the earlier published solution for an elastic ideally plastic medium with Tresca's criterion. The obtained critical value was compared with a numerical solution in a full formulation at the cavity expansion velocities close to zero in a wide range of variation of the parameters of the Mohr - Coulomb yield criterion. It is shown that the inaccuracy of the approximation of the proposed formula does not exceed 6% for the variation of the internal friction coefficient all over the admissible range, and for the initial value of the yield strength increasing by three orders of magnitude.
{"title":"MAPPROXIMATING STRESSES IN THE VICINITY OF A CAVITY EXPANDING AT A CONSTANT VELOCITY IN A MEDIUM WITH THE MOHR - COULOMB PLASTICITY CONDITION","authors":"V. Kotov","doi":"10.32326/1814-9146-2019-81-2-177-190","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-2-177-190","url":null,"abstract":"A one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in an infinite elastoplastic medium is considered. The problem has a first-kind self-similar solution. Elastoplastic deformation of the soil is described based on Hooke's law and the Mohr-Coulomb yield criterion. An analytical solution of the problem in the elastic region contacting with the plastic yield region has been obtained. To determine stress and velocity fields in the plastic region, a known algorithm, based on the shooting method, of analyzing a boundary-value problem for a system of two first-order ordinary differential equations, including the fourth-order Runge - Kutta method, has been realized. An effective algorithm of numerically analyzing an expanding cavity problem, earlier proposed in the works by М. Forrestal et al., makes it possible to solve the problem accurately enough for practical applications.\u0000A formula for determining the critical pressure - the minimal pressure required for the nucleation, accounting for internal pressure of a cavity in the framework of the Mohr - Coulomb yield criterion, has been derived, which is a generalization of the earlier published solution for an elastic ideally plastic medium with Tresca's criterion. The obtained critical value was compared with a numerical solution in a full formulation at the cavity expansion velocities close to zero in a wide range of variation of the parameters of the Mohr - Coulomb yield criterion. It is shown that the inaccuracy of the approximation of the proposed formula does not exceed 6% for the variation of the internal friction coefficient all over the admissible range, and for the initial value of the yield strength increasing by three orders of magnitude.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123116177","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}
Pub Date : 2019-06-16DOI: 10.32326/1814-9146-2019-81-2-212-221
S. Kirikov, V. Perevezentsev
A new method of calculation of elastic stress fields from internal interfaces (intergranular and interphase boundaries) of plastically deformed polycrystals is proposed. As elementary sources of stress fields, rectangular boundary segments containing uniformly distributed segments of dislocation families accumulating on these segments during plastic deformation are considered. It is shown that the elastic stresses field from a segment with arbitrary geometry of plastic flow and segment orientation can be represented as a superposition of fields from four families of continually distributed dislocation segments with tangential and normal components of the Burgers vector. Analytical expressions for the elastic stress tensor components from each of the four families are obtained. In the limiting case, when the length of dislocation segments tends to infinity, the resulting expressions for the components of the elastic stress field transform known expressions for rotational and shear mesodefects. If dislocation segments have a normal burgers vector, then the stress field is equivalent to the stress field from the biaxial dipole of wedge disclinations. In the case of tangential components of the burgers vector, the field is equivalent to the stress field of the planar mesodefect. As an example of the method application, the calculation of internal stress fields in the plastically deformed crystal containing uniformly distributed cubic particles of the second phase is given. It is shown that the intensity of internal stresses at a given value of strain increases with increasing volume fraction of particles. It is found that for a given volume fraction of the second phase, the internal stresses does not depend on their size.
{"title":"ABOUT THE CALCULATION OF INTERNAL STRESSES FROM MESODEFECTS ACCUMULATING AT THE BOUNDARIES DURING PLASTIC DEFORMATION OF SOLIDS","authors":"S. Kirikov, V. Perevezentsev","doi":"10.32326/1814-9146-2019-81-2-212-221","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-2-212-221","url":null,"abstract":"A new method of calculation of elastic stress fields from internal interfaces (intergranular and interphase boundaries) of plastically deformed polycrystals is proposed. As elementary sources of stress fields, rectangular boundary segments containing uniformly distributed segments of dislocation families accumulating on these segments during plastic deformation are considered. It is shown that the elastic stresses field from a segment with arbitrary geometry of plastic flow and segment orientation can be represented as a superposition of fields from four families of continually distributed dislocation segments with tangential and normal components of the Burgers vector. Analytical expressions for the elastic stress tensor components from each of the four families are obtained. In the limiting case, when the length of dislocation segments tends to infinity, the resulting expressions for the components of the elastic stress field transform known expressions for rotational and shear mesodefects. If dislocation segments have a normal burgers vector, then the stress field is equivalent to the stress field from the biaxial dipole of wedge disclinations. In the case of tangential components of the burgers vector, the field is equivalent to the stress field of the planar mesodefect. As an example of the method application, the calculation of internal stress fields in the plastically deformed crystal containing uniformly distributed cubic particles of the second phase is given. It is shown that the intensity of internal stresses at a given value of strain increases with increasing volume fraction of particles. It is found that for a given volume fraction of the second phase, the internal stresses does not depend on their size.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127981663","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}
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