Pub Date : 1900-01-01DOI: 10.32326/1814-9146-2021-83-3-285-293
Yu. V. Svirina, S. Kirikov, V. Perevezentsev
Plastic deformation of polycrystalline solids is accompanied by the appearance of linear rotational-type mesodefects at grain boundary ledges and triple junction of grains, such as starin induced junction disclinations. Junction disclinations generate long-range spatially inhomogeneous fields of elastic stresses, which significantly influence on the structure formation, strain hardening and fracture of materials. In present work a comparative analysis of the contributions of junction disclinations of different sign and strength to the plastic flow stress of a polycrystal is performed. The results of calculationsshow, that when a pile-up of lattice dislocations passes through the elastic field of disclinations, general regularities are observed.Regardless of the sign of disclination, it has a retarding effect on the plastic shear. The equilibrium distributions of the linear density and the density of the Burgers vector of dislocations pile-upretarded by the elastic field of disclination are calculated.It is shown that the largest number of dislocations is concentrated not in the pile-up head, as in classical dislocation pile-upsstoped near impenetrable barriers, but in its central part. The dependences of the critical stress of the passage of the head dislocation of the pile-up through the force barrier of disclination are calculated depending on the strength and sign of disclination, the number of dislocations in the pile-up, and the distance between the disclination and the slip plane of lattice dislocations.It is shown that the change in the sign of disclination significantly influences on the form of the equilibrium distribution of dislocations along the length of the pile-up, but practically does not affect the value of the critical shear stress. It is shown that for a fixed number of dislocations in the pile-up, the critical shear stress increases with the distance between the slip plane and disclination. Thus, when plastic deformation is localized, the greatest strengthening effect from the elastic field of junction disclination is achieved not near the boundary, but far from it.
{"title":"INVESTIGATION OF THE INFLUENCE OF JUNCTION DISCLINATIONS ON PLASTIC FLOW STRESS OF POLYCRYSTALS","authors":"Yu. V. Svirina, S. Kirikov, V. Perevezentsev","doi":"10.32326/1814-9146-2021-83-3-285-293","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-3-285-293","url":null,"abstract":"Plastic deformation of polycrystalline solids is accompanied by the appearance of linear rotational-type mesodefects at grain boundary ledges and triple junction of grains, such as starin induced junction disclinations. Junction disclinations generate long-range spatially inhomogeneous fields of elastic stresses, which significantly influence on the structure formation, strain hardening and fracture of materials. In present work a comparative analysis of the contributions of junction disclinations of different sign and strength to the plastic flow stress of a polycrystal is performed. The results of calculationsshow, that when a pile-up of lattice dislocations passes through the elastic field of disclinations, general regularities are observed.Regardless of the sign of disclination, it has a retarding effect on the plastic shear. The equilibrium distributions of the linear density and the density of the Burgers vector of dislocations pile-upretarded by the elastic field of disclination are calculated.It is shown that the largest number of dislocations is concentrated not in the pile-up head, as in classical dislocation pile-upsstoped near impenetrable barriers, but in its central part. The dependences of the critical stress of the passage of the head dislocation of the pile-up through the force barrier of disclination are calculated depending on the strength and sign of disclination, the number of dislocations in the pile-up, and the distance between the disclination and the slip plane of lattice dislocations.It is shown that the change in the sign of disclination significantly influences on the form of the equilibrium distribution of dislocations along the length of the pile-up, but practically does not affect the value of the critical shear stress. It is shown that for a fixed number of dislocations in the pile-up, the critical shear stress increases with the distance between the slip plane and disclination. Thus, when plastic deformation is localized, the greatest strengthening effect from the elastic field of junction disclination is achieved not near the boundary, but far from it.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133835426","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 : 1900-01-01DOI: 10.32326/1814-9146-2021-83-2-227-234
I. Peshkhoev
The problem of the asymptotic solution of a modified system of nonlinear Karman equilibrium equations for a longitudinally compressed elongated elastic rectangular plate with internal stresses lying on an elastic base is considered. Internal stresses can be caused by continuously distributed edge dislocations and wedge disclinations, or other sources. The compressive pressure is applied parallel to the long sides of the plate to the two short edges. The boundary conditions are considered: the long edges of the plate are free from loads, and the short edges are freely pinched or movably hinged. A small parameter is introduced, equal to the ratio of the short side of the plate to the long side. The solution of the system – the compressive load, the deflection function, and the stress function – is sought in the form of series expansions over a small parameter. The system of Karman equations with dimensionless variables is reduced to an infinite system of boundary value problems for ordinary differential equations with respect to the coefficients of asymptotic expansions for the critical load, deflection, and stress function. In this case, to meet the boundary conditions, the boundary layer functions are additionally introduced, which are concentrated near the fixed edges and disappear when moving away from them. Boundary value problems for determining the functions of the boundary layer are constructed. It is shown that the main terms of the small parameter expansions for the critical load and deflection are determined from the equilibrium equation of a compressed beam on an elastic base with the boundary conditions of free pinching or movable hinge support of the ends. In this case, the main term of the expansion into a series of the stress function has a fourth order of smallness in the parameter of the relative width of the plate.
{"title":"ASYMPTOTICS OF CRITICAL LOADS OF A COMPRESSED NARROW ELASTIC PLATE WITH INTERNAL STRESSES","authors":"I. Peshkhoev","doi":"10.32326/1814-9146-2021-83-2-227-234","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-2-227-234","url":null,"abstract":"The problem of the asymptotic solution of a modified system of nonlinear Karman equilibrium equations for a longitudinally compressed elongated elastic rectangular plate with internal stresses lying on an elastic base is considered. Internal stresses can be caused by continuously distributed edge dislocations and wedge disclinations, or other sources. The compressive pressure is applied parallel to the long sides of the plate to the two short edges. The boundary conditions are considered: the long edges of the plate are free from loads, and the short edges are freely pinched or movably hinged. A small parameter is introduced, equal to the ratio of the short side of the plate to the long side. The solution of the system – the compressive load, the deflection function, and the stress function – is sought in the form of series expansions over a small parameter. The system of Karman equations with dimensionless variables is reduced to an infinite system of boundary value problems for ordinary differential equations with respect to the coefficients of asymptotic expansions for the critical load, deflection, and stress function. In this case, to meet the boundary conditions, the boundary layer functions are additionally introduced, which are concentrated near the fixed edges and disappear when moving away from them. Boundary value problems for determining the functions of the boundary layer are constructed. It is shown that the main terms of the small parameter expansions for the critical load and deflection are determined from the equilibrium equation of a compressed beam on an elastic base with the boundary conditions of free pinching or movable hinge support of the ends. In this case, the main term of the expansion into a series of the stress function has a fourth order of smallness in the parameter of the relative width of the plate.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115789575","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 : 1900-01-01DOI: 10.32326/1814-9146-2019-81-1-53-62
V. Krysko, I. Papkova, I. E. Kutepov, A. Krysko
An attempt is made to clear vibrations of a beam resting on a viscoelastic support from noise effects. It is assumed that Bernoulli-Euler hypothesis holds. Effects of white, red, pink, purple and blue noise are considered. Noise is accounted for as a component of an alternating distributed load. Equations of motion of the beam areobtained as partial derivatives from Hamilton-Ostrogradski principle. Partial derivative equations are reduced to a Cauchy problem, using a second-order accuracy finite difference method, which is solved by Runge-Kutta-type methods. To clear vibrations of the beam from noise, the main component method was applied. This method was used to process the solutions of linear partial differential equations describing vibrations of rectangular beams resting on a viscoelastic support. Solutions of the equations were represented in the form of a 2D data array corresponding to deflections in the nodes of the beam at different times. The quality of clearing was assessed by comparing the Fourier power spectra obtained in the absence of noise effects with those that had noise effects, and after clearing. Problems for beams simply supported at both ends, fully fixed at both ends, simply supported at one end and fully fixed at the other one are considered. It was possible to clear the signals from four types of noise: white, pink, blue and purple.
{"title":"VIBRATIONS OF A BEAM IN A FIELD OF COLOR NOISE","authors":"V. Krysko, I. Papkova, I. E. Kutepov, A. Krysko","doi":"10.32326/1814-9146-2019-81-1-53-62","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-1-53-62","url":null,"abstract":"An attempt is made to clear vibrations of a beam resting on a viscoelastic support from noise effects. It is assumed that Bernoulli-Euler hypothesis holds. Effects of white, red, pink, purple and blue noise are considered. Noise is accounted for as a component of an alternating distributed load. Equations of motion of the beam areobtained as partial derivatives from Hamilton-Ostrogradski principle. Partial derivative equations are reduced to a Cauchy problem, using a second-order accuracy finite difference method, which is solved by Runge-Kutta-type methods.\u0000To clear vibrations of the beam from noise, the main component method was applied. This method was used to process the solutions of linear partial differential equations describing vibrations of rectangular beams resting on a viscoelastic support.\u0000Solutions of the equations were represented in the form of a 2D data array corresponding to deflections in the nodes of the beam at different times. The quality of clearing was assessed by comparing the Fourier power spectra obtained in the absence of noise effects with those that had noise effects, and after clearing. Problems for beams simply supported at both ends, fully fixed at both ends, simply supported at one end and fully fixed at the other one are considered. It was possible to clear the signals from four types of noise: white, pink, blue and purple.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125795414","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 : 1900-01-01DOI: 10.32326/1814-9146-2021-83-2-220-226
N. Zemlyakova, S. Rogachev
In this work, experimental methods were used to study the refinement of the structure of commercially pure copper (grade M 1) after double cold (at room temperature) plastic deformation by drawing and subsequent severe plastic deformation by equal channel angular pressing. The paper presents the results of measuring the structural components obtained on thin sections and foils cut from the cross-section of samples with a diameter of 20 mm after four and eight passes through the press channel with a 90° rotation after each pass (route Bc). A transmission electron microscope was used to study the structure. To compare changes in the microstructure at the mesolevel (less than we used the data obtained earlier in the study of copper samples using a scanning electron microscope. It is shown that after 4 passes and 8 passes, the deformation bands are formed – fragments (from in length), which alternate with transition bands – fragments with a dislocation structure. After 8 passes, the average size of the fragment was about 300 nm. As a result of crossing the shear bands in eight passes, diamond-shaped zones 1.5´1.5 mm was formed, in which fragmented deformation bands with less dislocation was surrounded by transition dislocation bands and fragments with dislocations. At the macro level, the copper structure obtained after 4 passes can have anisotropy of mechanical properties. The numerical characteristics of the structural components of copper after severe cold plastic deformation presented in the article make it possible to understand the structure refinement scheme at the mesoscale.
在这项工作中，采用实验方法研究了商业纯铜(m1级)经过两次冷(室温)拉伸和随后的等道角压剧烈塑性变形后的组织细化。本文介绍了在直径为20mm的样品的横截面上切割的薄片和箔片上经过4次和8次压道，每次压道后旋转90°(路线Bc)后测量结构部件的结果。用透射电镜对其结构进行了研究。为了比较微观结构在中观水平上的变化(小于我们使用扫描电子显微镜研究铜样品时获得的数据)。结果表明:在经过4道次和8道次后，形成了变形带——从长度上看与过渡带交替的碎片——具有位错结构的碎片。经过8次后，片段的平均尺寸约为300 nm。通过8道次剪切带的穿越，形成1.5 mm ~ 1.5 mm的菱形区域，其中位错较少的破碎变形带被过渡位错带和位错碎片所包围。宏观上看，经过4道次后得到的铜组织具有力学性能的各向异性。文中提出的铜在剧烈冷塑性变形后的结构组分的数值特征，使得在中尺度上理解结构细化方案成为可能。
{"title":"SHAPE AND DIMENSIONS OF FRAGMENTED BANDS AFTER COLD DRAWING AND INTENSE PLASTIC DEFORMATION OF THE COPPER","authors":"N. Zemlyakova, S. Rogachev","doi":"10.32326/1814-9146-2021-83-2-220-226","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-2-220-226","url":null,"abstract":"In this work, experimental methods were used to study the refinement of the structure of commercially pure copper (grade M 1) after double cold (at room temperature) plastic deformation by drawing and subsequent severe plastic deformation by equal channel angular pressing. The paper presents the results of measuring the structural components obtained on thin sections and foils cut from the cross-section of samples with a diameter of 20 mm after four and eight passes through the press channel with a 90° rotation after each pass (route Bc). A transmission electron microscope was used to study the structure. To compare changes in the microstructure at the mesolevel (less than we used the data obtained earlier in the study of copper samples using a scanning electron microscope. It is shown that after 4 passes and 8 passes, the deformation bands are formed – fragments (from in length), which alternate with transition bands – fragments with a dislocation structure. After 8 passes, the average size of the fragment was about 300 nm. As a result of crossing the shear bands in eight passes, diamond-shaped zones 1.5´1.5 mm was formed, in which fragmented deformation bands with less dislocation was surrounded by transition dislocation bands and fragments with dislocations. At the macro level, the copper structure obtained after 4 passes can have anisotropy of mechanical properties. The numerical characteristics of the structural components of copper after severe cold plastic deformation presented in the article make it possible to understand the structure refinement scheme at the mesoscale.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127295219","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 : 1900-01-01DOI: 10.32326/1814-9146-2019-81-4-512-518
V. V. Eremeev
In the framework of three-dimensional nonlinear elasticity we consider linear instability of a composite plate made of functionally graded material and having initial stresses. The plae consists of two layers which were obtained as a result of flattening of an annual sector of an elastic cylinder. This deformation results in appearance of internal stresses. Thus, the plate becomes initially stressed. The initial stresses depend on the thickness coordinate, so we get inhomogeneous stress field. We have two types of inhomogeneities, the first is the inhomogeneity of the initial stresses whereas the second is the material inhomogeneity.We use the incompressible neo-Hookean material model as a constitutive relation. Despite of relatively simple form this model describes properly severe deformations of some rubber-like materials. For incompressible materials the flattening constitutes one of the so-called universal deformations, that is such deformation which is independent on the choice of constitutive relation. The material inhomogeneity is described through a dependence of the shear modulus on the thickness coordinate. Such inhomogeneity could be related to the manufacturing of the material or to further treatment. The stability was analysed using the linearization approach. We superimpose infinitesimal deformations on the finite initial one. The linearized boundary-value problem was derived and its nontrivial solutions were obtained. The solution was obtained in series of trigonometric functions. This helps to automatically satisfy a part of boundary conditions. We consider the influence of the inhomogeneity and initial stresses. We show that the initial stresses may significantly change critical deformations. For example, the loss of stability is possible due to initial stresses only.
{"title":"ON THE LOSS OF STABILITY OF A TWO-LAYERED PLATE MADE OF A FUNCTIONAL-GRADIENT MATERIAL WITH A NON-UNIFORM FIELD OF PRE-STRESSES","authors":"V. V. Eremeev","doi":"10.32326/1814-9146-2019-81-4-512-518","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-512-518","url":null,"abstract":"In the framework of three-dimensional nonlinear elasticity we consider linear instability of a composite plate made of functionally graded material and having initial stresses. The plae consists of two layers which were obtained as a result of flattening of an annual sector of an elastic cylinder. This deformation results in appearance of internal stresses. Thus, the plate becomes initially stressed. The initial stresses depend on the thickness coordinate, so we get inhomogeneous stress field. We have two types of inhomogeneities, the first is the inhomogeneity of the initial stresses whereas the second is the material inhomogeneity.We use the incompressible neo-Hookean material model as a constitutive relation. Despite of relatively simple form this model describes properly severe deformations of some rubber-like materials. For incompressible materials the flattening constitutes one of the so-called universal deformations, that is such deformation which is independent on the choice of constitutive relation. The material inhomogeneity is described through a dependence of the shear modulus on the thickness coordinate. Such inhomogeneity could be related to the manufacturing of the material or to further treatment. The stability was analysed using the linearization approach. We superimpose infinitesimal deformations on the finite initial one. The linearized boundary-value problem was derived and its nontrivial solutions were obtained. The solution was obtained in series of trigonometric functions. This helps to automatically satisfy a part of boundary conditions. We consider the influence of the inhomogeneity and initial stresses. We show that the initial stresses may significantly change critical deformations. For example, the loss of stability is possible due to initial stresses only.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128968249","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 : 1900-01-01DOI: 10.32326/1814-9146-2019-81-3-292-304
V. Kotov, D. B. Timofeev
An analytical solution of the one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a space occupied by a plastic medium has been obtained. Impact compressibility of the medium is described using linear Hugoniot's adiabat. Plastic deformation obeys the Mohr - Coulomb yield criterion with constraints on the value of maximum tangential stresses according to Tresca's criterion. In the assumption of rigid-plastic deformation (the elastic precursor being neglected), incompressibility behind the shockwave front and the equality of the propagation velocities of the fronts of the plastic wave and the plane shockwave defined by linear Hugoniot's adiabat, a boundary-value problem for a system of two first-order ordinary differential equations for the dimensionless velocity and stress depending on the self-similar variable is formulated. A closed-form solution of this problem has been obtained in the form of a stationary running wave - a plastic shockwave propagating in an unperturbed half-space. This solution is a generalization of the earlier obtained analytical solution for a medium with the Mohr - Coulomb plasticity condition. The effect of constraining the limiting value of maximal tangential stresses on the distribution of dimensionless stresses behind the shockwave front has been examined. Formulas for determining the range of cavity expansion velocities, within which a simple solution for a medium with Tresca's plasticity condition is applicable, have been derived. The obtained solution can be used for evaluating resistance to high-velocity penetration of rigid strikers into low-strength soil media.
{"title":"ANALYZING THE SPHERICAL CAVITY EXPANSION PROBLEM IN A MEDIUM WITH MOHR − COULOMB − TRESCA'S PLASTICITY CONDITION","authors":"V. Kotov, D. B. Timofeev","doi":"10.32326/1814-9146-2019-81-3-292-304","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-3-292-304","url":null,"abstract":"An analytical solution of the one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a space occupied by a plastic medium has been obtained. Impact compressibility of the medium is described using linear Hugoniot's adiabat. Plastic deformation obeys the Mohr - Coulomb yield criterion with constraints on the value of maximum tangential stresses according to Tresca's criterion. In the assumption of rigid-plastic deformation (the elastic precursor being neglected), incompressibility behind the shockwave front and the equality of the propagation velocities of the fronts of the plastic wave and the plane shockwave defined by linear Hugoniot's adiabat, a boundary-value problem for a system of two first-order ordinary differential equations for the dimensionless velocity and stress depending on the self-similar variable is formulated. A closed-form solution of this problem has been obtained in the form of a stationary running wave - a plastic shockwave propagating in an unperturbed half-space. This solution is a generalization of the earlier obtained analytical solution for a medium with the Mohr - Coulomb plasticity condition.\u0000\u0000The effect of constraining the limiting value of maximal tangential stresses on the distribution of dimensionless stresses behind the shockwave front has been examined. Formulas for determining the range of cavity expansion velocities, within which a simple solution for a medium with Tresca's plasticity condition is applicable, have been derived. The obtained solution can be used for evaluating resistance to high-velocity penetration of rigid strikers into low-strength soil media.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123353534","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 : 1900-01-01DOI: 10.32326/1814-9146-2021-83-2-151-159
E. Korovaytseva
Results of hyperelastic soft shells nonlinear axisymmetric dynamic deforming problems solution algorithm testing are represented in the work. Equations of motion are given in vector-matrix form. For the nonlinear initial-boundary value problem solution an algorithm which lies in reduction of the system of partial differential equations of motion to the system of ordinary differential equations with the help of lines method is developed. At this finite-difference approximation of partial time derivatives is used. The system of ordinary differential equations obtained as a result of this approximation is solved using parameter differentiation method at each time step. The algorithm testing results are represented for the case of pressure uniformly distributed along the meridian of the shell and linearly increasing in time. Three types of elastic potential characterizing shell material are considered: Neo-hookean, Mooney – Rivlin and Yeoh. Features of numerical realization of the algorithm used are pointed out. These features are connected both with the properties of soft shells deforming equations system and with the features of the algorithm itself. The results are compared with analytical solution of the problem considered. Solution behavior at critical pressure value is investigated. Formulations and conclusions given in analytical studies of the problem are clarified. Applicability of the used algorithm to solution of the problems of soft shells dynamic deforming in the range of displacements several times greater than initial dimensions of the shell and deformations much greater than unity is shown. The numerical solution of the initial boundary value problem of nonstationary dynamic deformation of the soft shell is obtained without assumptions about the limitation of displacements and deformations. The results of the calculations are in good agreement with the results of analytical studies of the test problem.
{"title":"INVESTIGATION OF HYPERELASTIC SOFT SHELLS NONSTATIONARY DYNAMICS PROBLEMS SOLUTION FEATURES","authors":"E. Korovaytseva","doi":"10.32326/1814-9146-2021-83-2-151-159","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-2-151-159","url":null,"abstract":"Results of hyperelastic soft shells nonlinear axisymmetric dynamic deforming problems solution algorithm testing are represented in the work. Equations of motion are given in vector-matrix form. For the nonlinear initial-boundary value problem solution an algorithm which lies in reduction of the system of partial differential equations of motion to the system of ordinary differential equations with the help of lines method is developed. At this finite-difference approximation of partial time derivatives is used. The system of ordinary differential equations obtained as a result of this approximation is solved using parameter differentiation method at each time step. The algorithm testing results are represented for the case of pressure uniformly distributed along the meridian of the shell and linearly increasing in time. Three types of elastic potential characterizing shell material are considered: Neo-hookean, Mooney – Rivlin and Yeoh. Features of numerical realization of the algorithm used are pointed out. These features are connected both with the properties of soft shells deforming equations system and with the features of the algorithm itself. The results are compared with analytical solution of the problem considered. Solution behavior at critical pressure value is investigated. Formulations and conclusions given in analytical studies of the problem are clarified. Applicability of the used algorithm to solution of the problems of soft shells dynamic deforming in the range of displacements several times greater than initial dimensions of the shell and deformations much greater than unity is shown.\u0000\u0000The numerical solution of the initial boundary value problem of nonstationary dynamic deformation of the soft shell is obtained without assumptions about the limitation of displacements and deformations. The results of the calculations are in good agreement with the results of analytical studies of the test problem.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121401128","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 : 1900-01-01DOI: 10.32326/1814-9146-2021-83-2-235-244
S. Kirikov, A. Pupynin, Yu. V. Svirina
The work is devoted to the study of the structure of the elastic stress field in the area of junctions of grain boundaries containing strain-induced rotational-shear mesodefects. The jumps in plastic distortion of grains when passing through grain boundaries create additional misorientations on them, the mismatch of which at the junctions of grains leads to the appearance of linear mesodefects of the rotational type – junction disclinations. Planar mesodefects of the shear type appear on the flat sections of the boundaries, which are plastic shears uniformly distributed along the boundaries. These mesodefects create spatially inhomogeneous elastic stress fields near the junctions and ledges of the grains. They increase during plastic deformation and, at sufficiently large value of strain, initiate the formation of a fragmented material structure. Rotational-shear mesodefects are also the cause of the nucleation and accumulation of microcracks at the stage of viscous fracture of polycrystalline solids. In this work, asymptotic formulas are obtained that make it possible to analyze the distribution and anisotropy of the internal stress field in the vicinity of the grain junction from rotational-shear mesodefects. It was found that the components of the stress field weakly depend (logarithmically) on the length of the grain boundaries formatting junction of the grains. It is shown that the screening disclination of the dipole leads to the appearance of an angular dependence of the diagonal components of the elastic stress tensor in the vicinity of the junctions and its contribution to the elastic field of the disclinations dipole is about 10–15%. The obtained asymptotic expressions can be used to study the kinetics of a dislocation ensemble and to analyze the conditions for the nucleation of microcracks in the vicinity of joints and ledges of grains.
{"title":"ANALYSIS OF LOCAL FIELDS OF ELASTIC STRESS GENERATED BY ROTATIONAL-SHEAR MESODEFECTS NEAR THE JUNCTIONS OF GRAINS","authors":"S. Kirikov, A. Pupynin, Yu. V. Svirina","doi":"10.32326/1814-9146-2021-83-2-235-244","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-2-235-244","url":null,"abstract":"The work is devoted to the study of the structure of the elastic stress field in the area of junctions of grain boundaries containing strain-induced rotational-shear mesodefects. The jumps in plastic distortion of grains when passing through grain boundaries create additional misorientations on them, the mismatch of which at the junctions of grains leads to the appearance of linear mesodefects of the rotational type – junction disclinations. Planar mesodefects of the shear type appear on the flat sections of the boundaries, which are plastic shears uniformly distributed along the boundaries. These mesodefects create spatially inhomogeneous elastic stress fields near the junctions and ledges of the grains. They increase during plastic deformation and, at sufficiently large value of strain, initiate the formation of a fragmented material structure. Rotational-shear mesodefects are also the cause of the nucleation and accumulation of microcracks at the stage of viscous fracture of polycrystalline solids.\u0000\u0000In this work, asymptotic formulas are obtained that make it possible to analyze the distribution and anisotropy of the internal stress field in the vicinity of the grain junction from rotational-shear mesodefects. It was found that the components of the stress field weakly depend (logarithmically) on the length of the grain boundaries formatting junction of the grains. It is shown that the screening disclination of the dipole leads to the appearance of an angular dependence of the diagonal components of the elastic stress tensor in the vicinity of the junctions and its contribution to the elastic field of the disclinations dipole is about 10–15%. The obtained asymptotic expressions can be used to study the kinetics of a dislocation ensemble and to analyze the conditions for the nucleation of microcracks in the vicinity of joints and ledges of grains.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126599815","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 : 1900-01-01DOI: 10.32326/1814-9146-2021-83-3-344-353
V. Erofeev, A. V. Ilyahinskii, E. Motova, V. Rodyushkin, A. V. Shekoyan
In the work with the use of nondestructive control methods, the issues of determining acceptable durability or safe resource are considered. It is shown that the design monitoring procedure can be presented as follows: determines the original state zero zone, where the material of the product was subjected to low operational loads; further, with the use of nondestructive control methods, the acoustic parameter is measured (without disassembling the product)., such as the speed of elastic acoustic waves, nonlinear acoustic parameter, difference of velocities with twofrequency sensing, etc.; acoustic scanning of the product's metal is performed, in areas where there have been significant loads, signoff voltages, leading to an intensive accumulation of damage (the destruction of metal leading to cracks); defined zone “N” where the metal state parameter, for which the value is taken, characterizing the difference of the acoustic parameter (the speed of elastic waves, nonlinear acoustic parameter, the difference in velocity in twofrequency sensing) relative to the same parameter in the zone of zero exceeds the established level. The regularities established in the work linking the presence of plastic deformation with the difference in the delays (velocity) of elastic Rayleigh waves at different sounding frequencies at a fixed base between the emitter and the receiver of elastic waves, as well as the behavior of a nonlinear acoustic parameter during the safe resource time, suggest the possibility of using the observd fact as a principle for controlling the limiting state of the material due to plastic deformations on industrial structures. Based on the proposed approach, an engineering methodology for determining the technical condition of the material of the structures of production facilities is proposed, which allows to establish three stages of operation: the reliable operation mode; the controlled operation mode and the critical operation mode.
{"title":"ON THE ACOUSTIC PARAMETERS OF METAL CONSTRUCTIONWHEN DAMAGE IS ACCUMULATED","authors":"V. Erofeev, A. V. Ilyahinskii, E. Motova, V. Rodyushkin, A. V. Shekoyan","doi":"10.32326/1814-9146-2021-83-3-344-353","DOIUrl":"https://doi.org/10.32326/1814-9146-2021-83-3-344-353","url":null,"abstract":"In the work with the use of nondestructive control methods, the issues of determining acceptable durability or safe resource are considered. It is shown that the design monitoring procedure can be presented as follows: determines the original state zero zone, where the material of the product was subjected to low operational loads; further, with the use of nondestructive control methods, the acoustic parameter is measured (without disassembling the product)., such as the speed of elastic acoustic waves, nonlinear acoustic parameter, difference of velocities with twofrequency sensing, etc.; acoustic scanning of the product's metal is performed, in areas where there have been significant loads, signoff voltages, leading to an intensive accumulation of damage (the destruction of metal leading to cracks); defined zone “N” where the metal state parameter, for which the value is taken, characterizing the difference of the acoustic parameter (the speed of elastic waves, nonlinear acoustic parameter, the difference in velocity in twofrequency sensing) relative to the same parameter in the zone of zero exceeds the established level. The regularities established in the work linking the presence of plastic deformation with the difference in the delays (velocity) of elastic Rayleigh waves at different sounding frequencies at a fixed base between the emitter and the receiver of elastic waves, as well as the behavior of a nonlinear acoustic parameter during the safe resource time, suggest the possibility of using the observd fact as a principle for controlling the limiting state of the material due to plastic deformations on industrial structures. Based on the proposed approach, an engineering methodology for determining the technical condition of the material of the structures of production facilities is proposed, which allows to establish three stages of operation: the reliable operation mode; the controlled operation mode and the critical operation mode.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125464662","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 : 1900-01-01DOI: 10.32326/1814-9146-2019-81-4-474-487
A. Demareva
Large changes of a lead spherical shell enclosed in an aluminum spacesuit under the action of an overload pulse are considered. The defining system of equations is formulated in Lagrange variables in a two-dimensional (axisymmetric) formulation. Strain and stress rates are determined in the local coordinate system. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with isotropic hardening are used as state equations. The contact interaction of the shell and the spacesuit is modeled by non-penetration conditions taking into account friction. The numerical solution of the problem under given boundary and initial conditions is based on the finite element method moment scheme and the explicit time integration “cross” type scheme. 4-node isoparametric finite elements with bilinear form functions are used to discretize the defining system of equations for spatial variables. To suppress the numerical solution high-frequency oscillations, the procedure of nodal displacements rates conservative smoothing is used. As shown by the results of numerical research spherical shell in the process of intensive dynamic loading undergoes large deformation and rotation angles as a rigid whole. The calculation results reliability is confirmed by a good correspondence to the experimental data. The influence of conservative smoothing procedure and moment components of deformations and stresses on the solution accuracy is analyzed. It is shown that without conservative smoothing procedure using, the shape of the spherical shell buckling obtained in the calculation does not correspond to the experimental data. Neglect of the moment components of strains and stresses leads to the development of instability of the “hourglass” type.
{"title":"ANALYSIS OF THE CONSERVATIVE SMOOTHING EFFECT ON THE ACCURACY OF DYNAMIC ELASTIC-PLASTIC SPHERICAL SHELLS BUCKLING NUMERICAL SIMULATION","authors":"A. Demareva","doi":"10.32326/1814-9146-2019-81-4-474-487","DOIUrl":"https://doi.org/10.32326/1814-9146-2019-81-4-474-487","url":null,"abstract":"Large changes of a lead spherical shell enclosed in an aluminum spacesuit under the action of an overload pulse are considered. The defining system of equations is formulated in Lagrange variables in a two-dimensional (axisymmetric) formulation. Strain and stress rates are determined in the local coordinate system. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with isotropic hardening are used as state equations. The contact interaction of the shell and the spacesuit is modeled by non-penetration conditions taking into account friction. The numerical solution of the problem under given boundary and initial conditions is based on the finite element method moment scheme and the explicit time integration “cross” type scheme. 4-node isoparametric finite elements with bilinear form functions are used to discretize the defining system of equations for spatial variables. To suppress the numerical solution high-frequency oscillations, the procedure of nodal displacements rates conservative smoothing is used. As shown by the results of numerical research spherical shell in the process of intensive dynamic loading undergoes large deformation and rotation angles as a rigid whole. The calculation results reliability is confirmed by a good correspondence to the experimental data. The influence of conservative smoothing procedure and moment components of deformations and stresses on the solution accuracy is analyzed. It is shown that without conservative smoothing procedure using, the shape of the spherical shell buckling obtained in the calculation does not correspond to the experimental data. Neglect of the moment components of strains and stresses leads to the development of instability of the “hourglass” type.","PeriodicalId":340995,"journal":{"name":"Problems of strenght and plasticity","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127711745","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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