Deformation Diagrams Research Articles

Research of physicomechanical and design characteristics of vibrated, centrifuged and vibro-centrifuged concretes

Introduction. Currently, the obtaining of lightweight concrete and reinforced concrete products and structures with the improved structure and characteristics is a challenge. This can be achieved through centrifugation or in a more advanced way — vibro-centrifugation. At the same time, the influence of centrifugal and centripetal forces of inertia in these types of technologies causes differences in the cross-section properties of concrete products and structures. To reflect this in the calculations, it is required to experimentally and analytically investigate the qualitative and quantitative patterns of such differences in the characteristics of concretes obtained through different technologies. Materials and Methods. The study used the cross-section averaged characteristics of concrete — “integral characteristics of concrete”. The applicable raw materials included portland cement 500, crushed stone fraction 5-20, medium sand. Nine control samples of annular cross-section obtained through vibrating, centrifuging, and vibro- centrifugation were manufactured and tested. The essence of the technique was that each manufactured experimental control sample was used in several types of tests in-parallel. From the total annular section of each sample, three conditional quadrants were distinguished, from which standard samples of small size were cut out. Subsequently, they were tested for axial compression, tension, and flexural tension. The following test equipment was used: electronically controlled mechanical press IPS-10 — for compression testing of prisms, and the breaking machine R-10 — for testing samples for axial tension. Strain sensors and dial indicators were used to measure concrete deformations. Oscilloscopes were also used to obtain the deformative and strength properties of concrete, including full deformation diagrams with descending branches. Results. We have analyzed the calculation results of the integral design characteristics of the concretes obtained through vibration, centrifugation and vibro-centrifugation. It is established that due to the influence of centrifugal and centripetal forces of inertia under centrifugation and vibration centrifugation, the characteristics of concrete in cross-section become different. In some cases, these differences can be very significant. We have developed and tested the following: a new method for evaluating the dependence of the integral (cross–section averaged) design characteristics of concrete (density, cubic and prismatic axial compressive strength); ultimate deformations under axial compression; axial tensile and flexural tensile strength; ultimate deformations under axial tension; elasticity modulus; diagram of “stress ϭb– strain εb” under compression; diagram of “stress ϭbt–strain εbt” under tension on the manufacturing technology (vibrating, centrifuging, vibration centrifugation). Discussion and Conclusions. Based on the results of the research, conclusions are formulated on the positive effect of the proposed technology of joint vibrating and centrifuging. It consists in improving the integral design characteristics and structure of concrete from vibrating to centrifuging and from centrifuging to vibro-centrifuging.

Reaction synthesis of gradient coatings by annealing of three-layer Ti–Ni–Ti nanolaminate magnetron sputtered on the TiNi substrate

In this work, Ti-Ni-Ti nanolaminate was deposited on a TiNi substrate by magnetron sputtering. Subsequent synthesis in Ar at temperatures of 500, 700 and 900 °C was carried out. To investigate the effect of the reaction synthesis temperature for obtaining a dense thin intermetallic biofunctional coating, a comparative analysis of the morphology, structure, phase composition, mechanical properties and wettability of the coatings was carried out. It was found that crystallization processes have a different impact on the amorphous Ti and Ni layers depending on temperature. In all cases, multilayer gradient crystalline coatings were formed that bound to the substrate by the diffusion zone. The reaction synthesis temperatures of 500 and 700 °C are insufficient for reaction completion and complete transformation; therefore, the obtained thin loose layers are unstable under stresses caused by the substrate. Reaction synthesis in Ti – Ni – Ti nanolaminate at 900 °С formed a dense two-layer gradient coating 2 µm thick, which reliably protects the matrix from further diffusion of interstitial impurities and segregation of Ni atoms onto the surface. An analysis of the nano-indentation deformation diagrams showed that the coatings do not prevent the viscoelastic deformation of the TiNi substrate.

Evaluation of the brittleness and viscosity of metals upon tensile testing

The indicators of the brittleness and viscosity of metals calculated from their mechanical properties are considered with allowance for the stress state proceeding from the results of tensile testing of cylindrical smooth and notched samples of perlite 16KhSN, martensitic-aging (maraging) 03Kh11N10M2T, and austenitic 10Kh11N23T3MR steels. Tests were carried out on a UEM-10TM tensile strength testing machine, deformation diagrams developed on a scale of ~50:1 at a deformation rate of 5 mm/min. The sample size before and after testing were measured using a micrometer and an ISA-2 comparator with an accuracy of ±10–3 mm. Pendulum impact bending tests were carried out on a MK15 with the same cylindrical notched samples used to plot the plasticity and viscosity diagrams depending on the Bridgman stress state stiffness index. The new indicators of the brittleness λ = εk/η and viscosity η = (Sk/σb) – 1 (where εk = ln(1/(1 – ψk)) is the true limit plasticity) are proposed proceeding from the testing data. The special feature of the brittleness index λ is growth of the index with increase in the metal strength, e.g., due to pre-deformation or strengthening heat treatment procedures. However, a decrease in the groove radius on the samples, i.e., an increase in the Bridgman stress state stiffness, has almost no effect on the brittleness value λ, but is accompanied by a correlation decrease in the values of the viscosity indices η and the ultimate ductility εk of steels. The curves of the temperature dependences of the mechanical properties of steels 16KhSN and 03Kh11N10M2T show that anomalies in the brittleness indices λ observed at elevated test temperatures can be attributed to the structural transformations like increase in the grain size of 16KhSN steel or in the amount of the residual austenite in 03Kh11N10M2T steel due to reverse martensitic transformation. In this case, the temperature dependences of the viscosity η and brittleness λindicators change in the opposite way.

Deformation Dependences of the Power and Environmental Resistance of Reinforced Concrete Structures Under Accidental Actions

The problem of determining the parameters of the stress-strain state of reinforced concrete bending elements with the simultaneous manifestation of force loading and environmental impact under static-dynamic loading conditions is considered. Dependences of the deformation model were constructed using the integral modulus of deformations by V M Bondarenko. The parameters of the diagrams of the static-dynamic deformation of the section of corroded concrete under the action of a static and short-term dynamic load are determined on the basis of a rheological two-element model of concrete deformation of the theory of plasticity by G A Genieva. At the same time, the hypothesis was accepted that the relationship between stresses and strains in corrosion damaged concrete under its short-term loading is affinity-like to similar dependencies of undamaged concrete, and the ultimate deformations of concrete under static and static-dynamic loading modes are equal to each other. A methodology and an algorithm for the computational analysis of the strength and environmental resistance of reinforced concrete structures at all stages of static-dynamic deformation are proposed.

ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ РАВНОВЕСИЯ ИДЕАЛЬНО УПРУГОПЛАСТИЧЕСКОЙ СПЛОШНОЙ СРЕДЫ ДЛЯ ПЛОСКОЙ ОДНОМЕРНОЙ ДЕФОРМАЦИИ ПРИ АППРОКСИМАЦИИ ЗАМЫКАЮЩИХ УРАВНЕНИЙ БИКВАДРАТ ИЧНЫМИ ФУНКЦИЯМИ

The present article considers the construction of differential equations of equilibrium of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of one-dimensional plane deformation, when the diagrams of volumetric and shear deformation are approximated by biquadratic functions. The construction of physical dependencies is based on calculating the secant moduli of volumetric and shear deformation. When approximating the graphs of the volumetric and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volumetric expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volumetric and shear deformation, the secant shear modulus is a fractional (rational) function of the shear strain intensity; the secant modulus of volumetric expansion-compression is a fractional (rational) function of the first invariant of the strain tensor. Based on the assumption of independence, generally speaking, from each other of the volumetric and shear deformation diagrams, five main cases of physical dependences are considered, depending on the relative position of the break points of the graphs of the diagrams volumetric and shear deformation. On the basis of received physical equations, differential equations of equilibrium in displacements for continuous medium are derived under conditions of plane one-dimensional deformation. Differential equations of equilibrium in displacements constructed in the present article can be applied in determining stress and strain state of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of plane one-dimensional deformation, closing equations of physical relations for which, based on experimental data, are approximated by biquadratic functions.

ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ РАВНОВЕСИЯ ИДЕАЛЬНО УПРУГОПЛАСТИЧЕСКОЙ СПЛОШНОЙ СРЕДЫ ДЛЯ ПЛОСКОЙ ДЕФОРМАЦИИ В ЦИЛИНДРИЧЕСКИХ КООРДИНАТАХ ПРИ БИЛИНЕЙНОЙ АППРОКСИМАЦИИ ЗАМЫКАЮЩИХ УРАВНЕНИЙ

Abstract. The article considers the construction of differential equations of equilibrium in displacements for plane deformation of elastic perfectly plastic regarding shear deformations continuous medium and nonlinearly elastic continuous medium with respect to volumetric deformations with bilinear approximation of the closing equations, both regarding and regardless geometrical nonlinearity in a cylindrical coordinate system. Nonlinear diagrams of volumetric and shear deformation are approximated by bilinear functions. Proceeding from the assumption of independence, generally speaking, of volume and shear deformation from each other, five main cases of physical dependencies are considered, depending on the relative position of the break points of bilinear diagrams of volume and shear deformation. The construction of bilinear physical dependencies is based on the calculation of the secant moduli of volumetric and shear deformation. In this case, in the first section of the diagrams, the secant modulus of both volumetric and shear deformation is constant, while in the second section of the diagrams, the secant modulus of volumetric deformation is a function of volumetric deformation, and the secant shear modulus is a function of the intensity of shear deformations. Substituting the corresponding bilinear physical relations into the differential equations of equilibrium of a continuous medium, written both regardless and regarding geometrical nonlinearity, the resolving differential equations of equilibrium in displacements for plane deformation in a cylindrical coordinate system are received. The received differential equations of equilibrium in displacements in cylindrical coordinates can be applied in determining the stress-strain state of elastic perfectly plastic with respect to shear deformations continuous medium and nonlinearly elastic with respect to volumetric deformations continuous medium under conditions of plane deformation, both regarding and regardless geometrical nonlinearity, physical relations for which are approximated by bilinear functions.

ИЗМЕНЕНИЕ НЕСУЩЕЙ СПОСОБНОСТИ КОРРОЗИОННО- ПОВРЕЖДЕННЫХ ПЛИТ ПЕРЕКРЫТИЯ В ЗАВИСИМОСТИ ОТ ГЛУБИНЫ ПОВРЕЖДЕНИЯ БЕТОНА РАСТЯНУТОЙ ЗОНЫ

In this work, the influence of the depth of tensile concrete deterioration on the load-bearing strength and deflections of precast reinforced concrete slabs were determined experimentally. The momenta determination and measurement of deflections was carried out by loading the structure stepwise. Analysis of the results of the study indicated the following: as the plates are damaged, with the increase in the height of tensile concrete deterioration, the stress diagram gets gradually filled in the compressive sectional area and its height decreases, which can lead to the destruction of the structure. At the same time, the shear and bending moment diagram of sectional deformation gets curved. As the slab deflections increase, its load-bearing strength decreases.

Determining stresses in the metallic structure of an overhead crane when using running wheels of the new design

This paper proposes a method to experimentally study the stressed state of the metallic structure of an overhead crane when using running wheels of different designs. The study employed a functioning electric, supporting, double-girder overhead crane with a capacity of 5 tons and a run of 22.5 m. Strain gauges assembled in a semi-bridge circuit and connected to the analog-digital converter Zetlab210 (Russia) were used to determine the girder deformations at the time of hoisting and moving cargoes of different masses. The cargo was lifted and displaced under the same conditions, on the regular wheels of a cargo trolley and the wheels with an elastic rubber insert. The girder deformation diagrams were constructed. The subsequent recalculation produced the stressed state's dependences at each point of cargo movement when using both regular wheels and the wheels with an elastic rubber insert. Also established were the dependences and the duration of oscillations that occur over the cycle of cargo lifting and moving. The experimental study cycle included cargo lifting in the far-left position by a trolley, moving the cargo to the far-right position, and returning the trolley with the cargo to its original position.
 It should be noted that the application of a new, modernized design of the running wheels of a cargo trolley with an elastic rubber insert effectively dampen the oscillations in the metallic structure of the crane.
 The experimental study's results helped establish an 18 % reduction in stresses in the girder of the overhead crane, as well as a decrease in peak vibrations, by 20 seconds, at the same cycles of cargo hoisting and moving. In addition, using wheels with an elastic rubber insert reduces the period of oscillation damping at the end of the cycle of cargo movement, by at least 30 %.

ФІЗИЧНІ ПЕРЕДУМОВИ МОДЕЛЮВАННЯ ГАЗОВОЇ ПРОНИКНОСТІ ПІДРОБЛЕНОГО ВУГЛЕПОРОДНОГО МАСИВУ

Purpose. Justification of the gas collectors formation physical model on the basis of research of conformity of permeability of rock mass to the full diagram of rock sample deformation. Methodology consists in sequential analysis of the stages of the complete deformation diagram of the rock specimen under “hard” loading, comparing them with the stages of formation of the high stress zone in front of the lava bottom and statistical analysis of laboratory test results. Results. Based on the rock’s deformation properties analysis and their comparison with the rock sample full deformation diagram, the physical model of formation of gas reservoirs during the development of gas-saturated coal seam is substantiated. Within the solved problem framework, four stages of the complete deformation process are analyzed, namely: elastic, at the limit of strength, out-of-bounds stage and equivoluminal flow zone. The gas collector boundaries, which are the characteristic points of the rock sample deformation diagram in specified deformations mode (the limit of elastic strength and the limit of final strength) are determined. It is proved that the structural and textural features of the coal mass in connection with the course of gas-dynamic processes are manifested in the change in the pores and cracks volume contained in it, which together make the filtration space. Knowledge regarding the transfer of the permeability changes established regularities and free methane accumulation zones formation to the real rock mass, if the process of its forgery is considered as a consistent change of geomechanical states of rocks, is obtained. Scientific novelty lies in the first substantiated possibility of modeling the stress state before the longwall face by equivalent stages of the rock sample destruction in the given deformations mode. Gradual comparative analysis of the internal mechanism of rock samples deformation along the complete deformation diagram allowed establishing causal relationships between geomechanical and gas-dynamic processes in coal mass, and qualitatively characterizing general trends in permeability and volumetric expansion in changes of these samples. Practical value of the work lies in the justification of the principle of construction of a digital geomechanical model for the detection of man-made gas collectors in a mined coal mass.

Обгрунтування застосування неліній-ної моделі в’язкопружності типу моделі Работнова в задачах повзучості

The relationship between the components of the strain tensor, stress tensor and time is given by the defining equations of the hereditary type, which are written based on the hypothesis of proportionality of the deviators. Thin-walled tubular low-pressure polyethylene elements are considered as the object of research. The scope of the model is substantiated based on the hypothesis of the existence of a single diagram of instantaneous deformation and a single diagram of long-term deformation. The invariance of the tensile and torsion diagrams with respect to the stress state is checked. The region of nonlinear elastic deformation is determined. The defining equations of the model contain a set of functions and coefficients determined from the basic experiments. A method for determining the parameters of heredity kernels of nonlinear viscoelastic materials under complex stress state has been developed. The nonlinearity of viscoelastic properties is given by equations of the Rabotnov's model type. The method is based on the relations between the creep kernels obtained under conditions of complex stress state and the creep kernels under one-dimensional stress state. The method is tested experimentally on the problems of calculating creep deformations under combined loading of thin-walled tubular elements made of low-pressure polyethylene.

Thermomechanical analysis of nitinol memory alloy behavior

Shape memory alloys are functional materials characterized by the effect of shape memory and superelasticity. Due to these properties, they are widely used, particularly, in bioengineering, aeronautics, robotics and civil engineering. The temperatures of phase transformations and the influence of external temperature and strain rate on the functional and mechanical characteristics of Ni55.75Ti44.15 shape memory alloy are investigated in this paper. The temperature of alloy phase transformations is obtained by differential scanning calorimetry (DSC) in the temperature range from -70°C to 70°C. Diagrams of differential scanning calorimeters at different heating and cooling rates of Ni55.75Ti44.15 alloy is constructed and analyzed. Samples for mechanical tests are made of round rod 8 mm in diameter. The samples working area is 12.5 mm in length and 4 mm in diameter. Mechanical tests are carried out at temperatures close to the maximum value of the completion temperature of martensitic-austenitic transformation Af = 14.7°C. Diagrams of deformation under uniaxial tension are constructed and stresses of phase transformations, Young's modulus and relative elongations of transformation areas at different loading speeds and exterior temperatures are determined. Using Clausius-Clapeyron formula, it is shown that with simultaneous changes in temperature and strain rate, the stresses of phase transformations are largely due to changes in temperature rather than load rates. The coefficients of Clausius-Clapeyron equation for superelastic Ni55.75Ti44.15 alloy with shape memory, which are consistent with those known in the literature, are determined.

Influence of the loading system stiffness on the jerky flow in Al-Mg alloy at inelastic and postcritical deformation stages

The work is devoted to studying the issues of experimental studies of the behavior of materials under conditions of inhomogeneous discontinuous flow at the stages of plastic and supercritical deformation (deformation softening). Obtaining reliable experimental data on the indicated stages of inelastic deformation of materials is important for understanding the physical processes occurring in materials during deformation and ultimately leading to fracture. The results of tests are presented, confirming the influence of the rigidity of the loading system in relation to the working part of the sample on the processes of intermittent plastic deformation. The tests were carried out on samples of Al-Mg alloy. The loading rigidity was varied using a rig with variable rigidity. Registration of displacement and deformation fields on the surface of the working part of the samples was carried out by a non-contact video system Vic-3D Correlated Solutions based on the digital image correlation (DIC) technique. The use of this system makes it possible to measure both deformation at the macro level and the distribution of its components in the working part of the specimen under conditions of inhomogeneous discontinuous deformation. As a result of tensile tests, deformation diagrams were obtained for Al-Mg alloy samples tested at different values ​​of the rigidity of the loading system: 120 MN/m (nominal value), 50 MN/m, 18 MN/m, and 5 MN/m. All the diagrams show discontinuous plastic deformation (the Portevin-Le Chatelier effect). A decrease in the rigidity of loading with respect to the working part of the specimen led to a change in the type of discontinuous yield and an increase in the magnitude of the stress drop at each tooth of the diagram. The indicated effects of inhomogeneous plastic deformation are observed both at the stage of strain hardening and at the stage of postcritical deformation.

ВЕРИФИКАЦИЯ ЗАВИСИМОСТЕЙ, АППРОКСИМИРУЮЩИХ ДИАГРАММЫ ДЕФОРМИРОВАНИЯ БЕТОНОВ ЦЕМЕНТНОГО И ПОЛИМЕРНОГО МЕТОДОМ НОРМИРУЕМЫХ ПОКАЗАТЕЛЕЙ

The article verifies some approximating power-law and hyperbolic dependences between stresses σ and deformations ε for experimental deformation diagrams of cement concrete and polymer concrete. When analyzing the state and residual life of reinforced concrete structures, one has to solve the problem of determining the relationship between stresses and deformations in various design sections of structures. The traditional approach, based on the selection of the approximating function "σ – ε" from the numerical values of the deformation diagram obtained by testing samples (cubes, prisms, cylinders), is practically impossible. Therefore, an alternative approach is proposed based on the selection of an approximating function according to standardized indicators: ultimate strength (σ_bu); modulus of elasticity (E_b0); ultimate deformation (ε_bu). The numerical values of the normalized indicators can be determined at a given point by analyzing the results of indentation of the indenter into the material of structures. As approximating ones, consider the power functions that are most preferable for materials with a fractal structure. Various boundary conditions are considered for determining the constant coefficients α and β according to the system of normalized indicators. The graphs of changes in tangent modules are analyzed.

Моделювання деформацій циклічної повзучості нелінійно-в’язкопружних матеріалів за допомогою функції Хевісайда

The problem of calculating the deformations of the cyclic creep of nonlinear viscoelastic materials is considered, which is given in the form of cyclic alternations of loads and unloadings of equal amplitude over rectangular cycles, where the duration of loading and unloading half-cyclescoincide. The program of loading is realized in the form of sequence of elementary loadings set by means of unit functions of Heaviside. A nonlinear creep model with a time-independent nonlinearity of Yu. Rabotnov's model is used to describe the deformation process. The fractional-exponential function is used as the nucleus of heredity. The paper develops a nonlinear viscosity model with time-independent nonlinearity due to the use of instantaneous deformation diagrams as isochronous for zero time and smoothing cubic splines, as approximations of nonlinear instantaneous deformation diagrams that define the nonlinearity of the model. The concept of a single isochronous deformation diagram for the studied material is experimentally substantiated. A system of solution equations of nonlinear creep under cyclic loading is formulated. The problem of calculating the deformations of stationary and cyclic creep for nylon fibers FM 10001 is solved and experimentally tested.

Щодо розрахунку деформацій зсуву в призматичних стержнях із полімерних матеріалів за умов розтягу з крученням

The process of creep of prismatic rods made of linear-viscoelastic polymeric materials under combined loading is considered. Defining equations that determine the relationship between strains, stresses and time are given in the form of a superposition of shear and bulk strain. The object of study is prismatic bars made of fiberglass ST-1. The area of linearity of the model is substantiated on the basis of the hypothesis of the existence of the creep function, which is built on the yield curves, a single diagram of long-term deformation and the statistical value of the quantile of statistics. The region of linear-elastic deformation is recognized based on the fulfillment of the condition of existence of a single creep function. The defining equations of the model contain a set of functions and coefficients determined from the basic experiments. On the basis of the relations between the kernels of the one-dimensional stress state, the parameters of the kernels under the condition of a complex stress state are determined. The linearity of viscoelastic properties is given by the Boltzmann-Voltaire equations. The fractional-exponential kernels of heredity are chosen as the kernels of heredity. The obtained values of the core parameters are used to calculate the creep deformations of prismatic bars made of ST-1 fiberglass under conditions of simultaneous tensile tension.

Уточненный расчет сталежелезобетонных комплексных балок по предельным состояниям

The paper considers the issues of calculating complex steel-reinforced concrete beams by the limit states on the basis of the nonlinear diagram of concrete deformation ε-σ. Sargin`s formula normalized in Eurocodes and Russian norms is taken as a reference diagram. A comparison is made with the calculation for the formation of an ideal plastic hinge. There are pointed out significant discrepancies (up to 11%) in some calculation cases. The possibility of using the proposed formulas for calculating conventional reinforced concrete beams of complicated cross-section is indicated.

Laboratory experimental study of contact interaction between cut shells and resilient bodies

The study presented herein describes promising designs of shell vibration isolators. The feature of the proposed designs is the cut thin-walled shell usage as the main bearing link. These resilient elements have high load capacity and, on the other hand, can provide the desired level of damping. From the point of view of mechanics, shell resilient elements are considered as the deformable systems with dry friction. When simulating these systems, structurally nonlinear non-conservative mixed contact issues of cut shell – resilient body frictional interaction arise. In order to take into account all essential options of the aforementioned issues and specify shell resilient element peculiarities of behavior under operational loads, the authors used the method of laboratory experiments for research. We considered two different contact systems. The first one is a cylindrical shell cut along its generatrix, which contacts a deformable filler. The second system is a cylindrical shell with several incomplete slots interacting with the elastic filler. The stress state and radial displacements of the shells, pliability of the resilient elements, and energy dissipation in the contact systems were time-tracked. As a result, we obtained relations for monitored options of the contact bodies and deformation diagrams for different physical-mechanical and geometrical options of the systems It was found that for a fixed cycle asymmetry coefficient with an increase in the friction coefficient between the shell and the filler, the amount of energy dissipated per cycle gradually decreases. The idea of optimizing shell vibration protection devices according to the criterion of maximum absorption of energy from external influences by determining the required tribological properties of contacting pairs is declared.

Расчет несущей способности внецентренно сжатых трубобетонных элементов с учетом нелинейных диаграмм материалов

The article provides an example of practical calculation of eccentrically compressed steel tube confined concrete using a nonlinear deformation model taking into account the standard deformation diagrams of materials. The calculation was performed on the example of a test specimen made of concrete filled steel tube (steel tube confined concrete) using the method of sequential approximation based on iterative procedures. The nonlinear method is aimed at making deformation assessment of the element bearing capacity by searching for the calculated deformation at particular points of the normal section at its maximum curvature and comparison with the standard admissible values. The task of iterative calculations is assessing the value of the maximum curvature of eccentrically compressed steel tube confined concrete which is under the action of a longitudinal compressive force. The basic calculation formulas are given. Comparison with the results of numerical and analytical calculations has shown a good convergence.

Numerical Modeling of Large Deformations for Porous Metals and Identification of Carcass Deformation Diagrams

The static compression of porous aluminum specimens, with free vertical surfaces fixed in a cylindrical holder, was investigated both theoretically and experimentally. Calculation were performed using the principle of 3D similarity of the stress-strain state in structural elements of constructions. Such an approach allows one to take into account the nonuniform distribution of stresses and strains caused by pores and to vary the small number of structural elements (representative volumes) in calculations, while retaining the porosity index and the characteristic dimensions of construction. Based on the calculation-experimental method, properties of the carcass material were identified using the results of compression tests of the porous specimens. The numerical results obtained are compared with experimental data, and they testify to the effectiveness of the principle of 3D similarity for this class of problems.

The method for determining the parameters of the diagrams of a truncated-wedge destruction of cylindrical samples of rocks

Purpose. Development of an analytical method for calculating the parameters of complete diagrams longitudinal tension deformation for the truncated-wedge shape of destruction of cylindrical rock samples to control the stress-strain state of the rock mass and effective destruction of these materials during disintegration. Methodology. Analytically, by developing a mathematical model of the fracture process of cylindrical rock samples with their truncated-wedge form of crack development, an algorithm is created for calculating the full deformation diagram from the acting tension using the experimental values of four indicators of material properties the shear resistance limit, internal and external friction coefficients and elastic modulus. The method is based on the improved Coulomb strength criterion, supplemented by the parameters of contact friction and allowing one, using the theory of slip lines, to calculate the limiting state of the material at the tip of cracks developing from the edges of the sample of the correct geometry, taking into account the release of part of the material from the load and compliance with Hookes law deformation of the sample bearing area and the specific force on it. Findings. The method of mathematical modeling makes it possible to determine the ultimate strength and residual strength of cylindrical rock samples using four property indicators that can be experimentally established by simple methods. Originality. For the first time, analytical modeling of the process of destruction of cylindrical rock samples with their truncated-wedge form of destruction was carried out, taking into account the internal contact friction depending on the properties of the rock material and external contact friction. Practical value. The proposed method of mathematical modeling and the calculation algorithm make it possible to determine the limit and residual strength of rock samples using four property indicators, which can be established experimentally by simple methods under laboratory conditions of enterprises of the mining and metallurgical complex. The calculation results can be quickly used to control the state of the rock mass and effective destruction upon disintegration.