Processes Of Elastoplastic Deformation Research Articles

Rock bolt and frame support of mine workings with a compound cross-section: Collective refuge chambers for mine workers

Purpose is to study the influence of mining and geological conditions on the time-dependent stability of the collective refuge chamber for mine workers with the adjacent mine workings and develop support schemes for different conditions of construction of such mine workings. Methods. Numerical modelling methods of the connected processes of elastoplastic deformation of gas-bearing rocks and gas filtration within the area disturbed during mining operations were used to study stability of mine workings with a compound cross-section, i.e. the collective refuge chambers and its adjacent extraction gallery. The model was based on fundamental principles of solid mechanics and filtration theory. The problem was solved using a finite element method. Findings. A classification of the conditions for locating collective refuge chambers for mine workers according to the relative strength of the enclosing rocks was developed. Support schemes for the chamber and its adjacent mine working were elaborated. The schemes include basic support and provide for its strengthening with rock bolts located in the roof of the mine working and chamber, or in their walls. The compliance of these support schemes with the developed classification of location conditions was determined. A numerical study of the time-dependent stability of the chamber and its adjacent mine working, while applying the recommended support scheme, was performed. It is shown that the strengthening of rock bolting schemes reduces the multicomponent stress field and the area of the zone of inelastic deformations, forms a rock-bolt overlap in the roof of the mine workings and chambers, which helps increase their stability under the complicated mining and geological conditions. Originality. Dependence of the changes within the area of a zone of inelastic deformations around the chamber with its adjacent mine working on the relative strength of the enclosing rocks was identified; time-dependent changes within the area of the zone of inelastic deformations, when using different support types, were specified. Practical implications. Support schemes for collective rescue chambers for mine workers in terms of different construction conditions were developed along with the procedure of their selection for specific mining and geological conditions. The results of the study provide theoretical substantiation and scientific guidelines for the selection of supports for collective refuge chambers adjacent to the mine working.

Twist design of lattice structure fabricated by powder bed fusion to adjust the energy absorption behavior

Additive manufactured lattice structures offer great potential for impact resistance applications. They exhibit excellent energy absorption characteristics during the elasto-plastic deformation process, providing protection to internal devices. However, the mechanical response of lattice structures undergoes substantial variations during the deformation process, thereby imposing limitations on their energy absorption behavior. This study introduces a novel twist design to modify the energy absorption behavior of rectangular and hollow cylindrical lattice structures. Powder bed fusion was used to fabricate the twisted lattice structures. The study employed a combination of compressive simulations and experimental investigations to systematically explore the impact of the twist angle on the peak crushing force, energy absorption, and crash load efficiency of the structures. Adjusting the twist angle results in a reduction of the peak crushing force and a transition towards a stable loading profile during the deformation process. Moreover, the crash load efficiency is also reduced. The twist design concept presented in this paper provides insight into designing and optimizing lattice structures for energy absorption applications.

Memory surfaces separating the processes of monotonous and cyclic loads

The processes of elastoplastic deformation of structural materials can consist of a sequence of monotonous and cyclic loading regimes, in which peculiar effects and features arise. Mathematical modeling of such processes, as well as resource assessment and forecasting, is a very difficult task. In addition, the analysis of transient processes from cyclic to monotonous and from monotonous to cyclic shows the need to separate these processes. Based on the analysis of the results of experimental studies of samples of stainless steel 12Х18Н10T under a rigid (controlled deformation) deformation process, which is a sequence of monotonic and cyclic loading modes, under conditions of uniaxial tension-compression at normal temperature, the features and differences in the processes of monotonic and cyclic loading are revealed. To describe these features and separate the processes of monotonic and cyclic loading modes in the theories of plastic flow with combined hardening, various variants of memory surfaces are introduced. An analysis of the results of experimental studies of stainless steel showed that in the space of the plastic strain tensor, the size of the memory surface is determined by the range of plastic strains, and the position of the center is determined by the values of average plastic strains under cyclic loading. Various variants of the memory surface are considered, their capabilities and disadvantages are identified, and the most adequate variant of the memory surface is determined. To confirm the operability of this version of the memory surface, together with the equations of the Bondar plasticity model, the calculated and experimental results were compared and a reliable agreement was obtained between these results both in terms of the kinetics of the stress-strain state and in terms of the number of cycles to failure.

Modeling of the elastoplastic deformation process of single crystal superalloys

The aim of the research is the development and verification of a micromechanically motivated model of elastoplastic deformation of two-phase single-crystal nickel-based alloys, predicting behavior under high-temperature thermomechanical actionswith taking into account the presence of γ and γ' phases. The model is relevant for computations of the stress-strain state of cooled single crystal blades of gas turbine units. The constitutive equations for each of the phases took into account the anisotropy of elastic and plastic properties, the presence of octahedral slip systems, features of the cubic system, and various hardening mechanisms, including kinematic, isotropic and latent ones. The identification of the elastic and plastic constants of the material for the γ and γ 'phases was carried out on the basis of the known stress-strain curves for each phase. The determination of the effective properties and deformation diagrams of a two-phase single-crystal alloy, taking into account the presence of γ-γ'phases, was carried out both on the basis of finite element homogenization for the representative volume element, and using the simplest rheological (structural) models of the material, considering serial and parallel connection of phases. The dependences of the elastoplastic properties of two-phase single-crystal nickel-based alloys on the volume fraction of the γ'phase are determined by computational experiments and analytical estimates. In order to determine the optimal strategy for solving the class of problems under consideration, multivariant computational experiments were carried out for various types of boundary conditions of the homogenization problem, the number of periodicity cells, forms of inclusion of the γ'phase, volume fractions of the γ' phase, types of hardening, variants of rheological models and appropriate recommendations were given. The simulation results using the proposed two-level microstructural model of the material demonstrate a good agreement with the experimental data for the single-crystal superalloy CMSX-4.

The deformation model of the DCB-sample with elastoplastic properties

The loading of a strip with a crack-like defect according to mode I is considered. In contrast to the classical representation of a crack in the form of a mathematical section, the proposed model defines a crack as a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer (IL). It is important that the stress-strain state of the layer at a finite value of the linear parameter does not introduce a singularity into the crack model. The process of elastoplastic deformation with a constant layer length is considered. We obtained a simplified analytical solution to the problem of deformation of two elastic bodies connected by a thin layer with elastoplastic properties. The dependence of the displacement and stress fields on the length and thickness of the interaction layer has been found. It is shown that, under the classical plasticity condition, the range of variation of the external load leading to a purely elastic behavior is possible only for a finite layer thickness. As the layer thickness tends to zero, as in the Dugdale model, the plasticity region is formed at an arbitrarily small external load. For small layer thicknesses, a local plasticity criterion is proposed, by using which it is possible to distinguish the intervals of the external load variations associated with elastic and plastic deformations. The local plasticity condition, determined by the critical value of the energy product, makes it possible to reflect the stage of elastic deformation at an arbitrarily small finite thickness of the interaction layer. An asymptotic dependence of the external load on the IL thickness and the reduced length of the plastic zone is obtained. At the same time, the separation of the external load into elastic and plastic components is preserved. From the analysis of the experimental data, an estimate of the elastic limit of the energy product for the AV138 adhesive was obtained.

Physical nature of metal fatigue at low temperatures

Mechanisms of fatigue failure of metals at low temperatures are considered. It is shown that, in this case, a feature of fatigue fracture is the processes of elastoplastic cyclic deformation, which are realized with an increased yield point and an increase in the thermal conductivity of metals. Localization of deformations and sliding of dislocations are preserved in thin surface layers along planes quite definite for a given material. Keywords: low temperature, yield point, hardness, fatigue properties, failure mechanism. uru.40@mail.ru

РОЗРАХУНОК НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ПЛАКУЮЧОГО ШАРУ ПРИ ПЛАКУВАННІ (ЗВАРЮВАННІ) ВИБУХОМ

Purpose. Development of a mathematical model of the process of elastoplastic deformation of the cladding layer of a layered workpiece during welding (cladding) by explosion with the formation of the objective function of optimal deformation and establishing a relationship between the parameters of welding (cladding) by explosion and the shear bond strength of the layers and the wear resistance of the cladding layer. Methodology. The solution to the problem of elastoplastic deformation is carried out using the equations of the flow theory and the nodal calculation scheme. The required deformation values are determined at the nodal mass points of the computational grid. At each moment of time, the positions of the nodes of the cladding workpiece, thrown under loading by a traveling pressure wave, are de-termined. Deformations and their intensity are determined by the position of the nodes. The task of determining the re-quired parameters of explosion welding (cladding) is reduced to the task of mathematical programming. The objective function is minimized on a family of curves, the arguments of which are the explosion welding (cladding) parameter and the welding gap. The interaction of the cladding workpiece with the pressure wave generated during the detonation of the explosive is determined by the dependences of the pressure of the detonation products, the mass velocity of the cladding workpiece and the shock wave velocity at the moment the shock wave reaches the free surface on the parame-ters of the explosion cladding (welding) with subsequent calculation of the stress-strain state of the workpieces. Accord-ing to the optimal parameters of explosion welding (cladding), a probabilistic assessment of the shear bond strength of the layers is carried out. If the strength is insufficient, the parameters are adjusted. Findings. As a result of numerical modeling, the calculation of the deformed state of the projectile is carried out. The parameters of explosion welding (cladding) are determined, at which the intensity of deformations of the cladding layer corresponds to the limit uniform ones. Based on the obtained parameters of explosion welding (cladding), the calculation of the shear strength of the layer joint was performed. Originality. For the first time, a model has been developed for the optimal deformation of the cladding layer during explosion welding (cladding) of wear-resistant compositions. The target function and the optimal process parameters have been established. A method is proposed for calculating the weighting coefficients of the objective function for multi-criteria multilevel optimization. Practical value. Recommendations for industrial application were developed and modes of explosion welding (cladding) were tested to obtain wear-resistant compositions of aluminum alloy with carbon steel.

Low Cycle Fatigue of Structural Alloys

Metallurgy, mechanical engineering, energy, agriculture, food industry, energy, electronics, rocket and space technology – this is a far from complete list of areas of the national economy in which liquid cryogenic products (cryoproducts). The production volumes of such products and the scale of their use are constantly increasing. This is due to the fact that cryogenic temperatures (below 120 K) provide unique opportunities for the implementation of such physical phenomena and processes that do not manifest themselves under normal conditions, but are used very effectively in science and technology. The solution of fundamental scientific problems and applied problems of both promising and current importance is determined by the level of development of cryogenic technology and the degree of its practical application. The continuous expansion of the scale of production of liquid cryogenic products has led in recent years to a significant increase in the volume of production of systems for their storage and transportation. These systems, as a rule, are welded shell structures in execution, they are operated in difficult conditions of temperature and force effects. The share of their production in the total output of cryogenic engineering products is very significant, and the operating conditions are the most stressful in comparison with other types of cryogenic structures. For the manufacture of cryogenic shell structures, expensive non-ferrous alloys and special steels are used, the degree of consumption of which, taking into account the sufficient material consumption of such structures and the expanding scale of their production, is constantly increasing. Therefore, one of the most urgent for cryogenic mechanical engineering at present is the problem of reducing the material consumption of shell structures and increasing their reliability and durability. It is obvious that a solution to this problem for cryogenic engineering products can be achieved by improving the methods of their strength calculations based on taking into account the specific hardening effect of low temperature on structural alloys. The phenomenon of low-cycle fatigue of metals is associated with elastoplastic deformation of their macrovolumes. The kinetics of elastoplastic deformation processes under cyclic loading depends on the loading conditions and material properties, and the nature of these processes and their intensity have a decisive influence on the features of material destruction. If the accumulation of deformation is small, then the destruction, as a rule, is of a fatigue nature; quasi-static fracture (similar in appearance to fracture during static tests for short-term strength) occurs after the realization of the ultimate plasticity of the material. The task of assessing the bearing capacity and durability under cyclic loading conditions is extremely important. Under cyclic loading, a number of specific phenomena and factors that are difficult to take into account analytically arise, which are primarily associated with the development of fatigue damage, with the need to assess the cyclic and structural instability of materials [1]. Since such studies are very laborious and expensive, the problem of minimizing such experiments is currently urgent. In this paper, we investigate the possibility of using mathematical planning methods for experimental studies at cryogenic temperatures. Experiment planning is usually understood as the procedure for choosing the volume and conditions of testing necessary and sufficient to solve the problem with the required accuracy.

Computational and experimental study of strain localization processes on the postcritical stage of deformation

The work is aimed to investigation the possibility of taking into account the processes of localization of deformations in the form of a "neck" under conditions of uniaxial tension of cylindrical samples in numerical simulation. The features of the experimental study and numerical modeling of the postcritical stage of deformation of structural steels with the localization of deformations in the form of a "neck" are considered. The formulation of a physically nonlinear boundary value problem of modeling a sample with allowance for postcritical deformation is considered using the ANSYS applied engineering analysis package. Geometric models of the studied objects are constructed, a description of the chemical composition and main mechanical characteristics of the material used is given, the parameters of discretization of the computational domain onto a finite element mesh are selected, the boundary and initial conditions are formulated, and the calculation parameters are determined. Numerical modeling of the processes of elastoplastic and postcritical deformation of a solid cylindrical sample made of 40Cr structural steel has been implemented. For each solution of the problem, the stress and strain fields are obtained, the change in the geometric shape of the sample in the process of stretching, graphs of the dependences of the conditional stresses on the elongation of the sample are plotted. The analysis of the elastoplastic behavior of a smooth cylindrical specimen and a specimen with an inherent constriction in the center of the working part is carried out. The analysis of the obtained data of numerical modeling is carried out and a comparison with experimental data is carried out, which demonstrates the possibility of modeling the processes of postcritical deformation of samples under conditions of the occurrence of localization of deformations in the form of a "neck".

Deformation of Nickel Titanium Single Crystal under Compressive Pulse

Nickel titanium single crystal is used to show the importance of the volume compressibility anisotropy in analyzing the elastoplastic deformation processes in metal single crystals with the cubic symmetry. The process of uniform bulk deformation corresponds to the process of nonuniform stress-strain state of metal single crystals of cubic symmetry for several orientations of the theoretical coordinate system relative to crystallographic directions of the main axes. The indicative surface of the volume compressibility (or its reciprocal variable of bulk modulus) has an aspherical shape and is the function of the Euler angles. This is shown for the first time based on the solution of the model problem, viz. determination of the stress-strain state of a spherical body made of nickel titanium single crystal during the transmission of a compressive pulse through the tested material. In general case of orientation of the theoretical coordinate system relative to main crystallographic axes, a spherical body made of nickel titanium single crystal undergoes deformation due to the compressive load and acquires the shape of a two-axial ellipsoid.

Экспериментальное и теоретическое исследование процессов сложного упругопластического деформирования материалов по некоторым многозвенным траекториям

Представлена верификация математической модели теории процессов путем сравнения численных расчетов с экспериментальными данными при сложном упругопластическом деформирования стали 45 по некоторым многозвенным ломаным траекториям. The verification of the mathematical model of the theory of processes by comparing numerical calculations with experimental data for complex elastoplastic deformation of steel 45 along some multi-link broken paths is presented.

The effect of replacing non-analytic trajectories with break points on smooth paths to the complexity of deformation and loading processes of materials

This article is devoted to an experimental study of the effect of rounding off corner points of two-link strain trajectories on complex loading processes during elastoplastic deformation of materials. Replacing corner points in their vicinity with local sections of circles allows a nonanalytic trajectory to be replaced with a smooth trajectory. Experimental studies were performed on thin-walled tubular specimens of the low-carbon steel St3 on an SN-EVM automated testing system. The loading programs for tubular specimens were set in the Ilyushin's deviatoric strain space. The rounding of the corner point of a two-link strain trajectory with an angle of 90° between the branches by arcs of circles with curvatures of 200, 400, as well as the rounding of the corner point of a two-link strain trajectory with an angle of 135° between the branches by arcs with curvatures of 400, 800 are considered. The experimental data characterizing the vector and scalar properties of the material are presented. The experimental data show that the effect of complex loading on the relationship between stresses and strains in a curved section is not immediately apparent. In the curved section, the magnitude of the stress vector modulus first increases, and then decreases with the formation of stress dives. The minimum point of the stress dive is located on the next straight branch of the strain trajectory. In the curvilinear section, the angle of delay increases, and in the next straight branch it decreases, and with the increase of the strain it tends to be zero. The rate of decrease of the angle of delay depends little on the differences in the geometry of the previous history of strain trajectory. In the second straight branch, the experimental results for a smooth and original two-link strain trajectories become little distinguishable from each other. Thus, replacing the original non-analytical strain trajectory to a smooth trajectory affects the complexity of the process of deformation and loading of the materials only in the vicinity of the corner point. This circumstance can be taken into account when numerically modeling the processes of elastoplastic deformation of materials and integrating the defining relations, replacing nonanalytic trajectories with smooth ones. This can be taken into account in the numerical calculation of elastic-plastic deformation and integration of constitutive relations, replacing non-analytical strain trajectories by smooth ones.

On the Main Hypotheses of the General Mathematical Theory of Plasticity and the Limits of Their Applicability

The article discusses and analyzes the issues of applicability and the limits of applicability of some of the main hypotheses of the general mathematical theory of plasticity. In the theory of elastoplastic deformation processes, this is the postulate of the isotropy of initially isotropic bodies, in which the invariance of orthogonal transformations of the process images is established when a relationship between stresses and deformations is established. In the theory of flow, this is a hypothesis about the decomposition of total deformations into elastic and plastic deformations and the influence on its relationship between stresses and deformations under complex loading.

Elastoplastic Deformation of a Ni3Al-Based Single Crystal Depending on Crystallographic Direction

The results of a numerical study in a three-dimensional formulation of the processes of elastoplastic deformation of a cubic single crystal based on the Ni3 Al intermetallic (VZHM8) under impact loading are presented. Impact loading is carried out in the [001] direction. The development of deformation processes is studied in the [100] and [010] or [011] and [011] directions. In the former case, the crystallographic directions of the single crystal coincide with the axes of the computational coordinate system and the elastic constants in these directions are the same. In the latter case, only one axis coincides with the [100] crystallographic direction, the other two are rotated by an angle of 45°. It is shown that a change in the elastic constants of a single crystal in new directions results in a change in the volume compressibility in all three directions. This is a consequence of the generalized Hooke's law. In the mathematical model used in this work to describe elastoplastic deformation, it is assumed that the volume compressibility of the single crystal is constant in the region of elastic and plastic deformations. It is shown for the first time that with the above rotation of the coordinate axes in a cubic single crystal, a change in elastoplastic deformations in the direction of the axis of impact loading is observed.

Elastoplastic deformation processes in materials with cubic symmetry of properties

Some results of studies of the processes of elastoplastic deformation in a material with a cubic symmetry of elastic and plastic properties are presented. Cases of shock loading of a cylinder from a single crystal alloy on a rigid target (Taylor test) along three different directions ([111], [001] and [011]) are considered. These directions are characterized by the fact that along them propagation of longitudinal and transverse waves with different speeds is possible. Using the example of solving the Taylor test problem, it is shown that the differences in elastic properties along the [011] directions in cubic crystals determine elastoplastic deformations.

Experimental and numerical study of the subsurface deformation and residual stress during the roller burnishing process

Abstract Roller burnishing process is being extensively used to enhance the fatigue life of the aircraft engine components by introducing compressive residual stress and work hardening. The temperature rise during the burnishing process could be neglected due to the low friction rolling contact between the roller and workpiece, thus simplifying it an elastoplastic deformation process. In this paper, the digital image correlation technique was adopted to obtain the subsurface deformation field during the roller burnishing process. A 3D finite element model was built up to simulate the burnishing process. The predicted surface integrity parameters including subsurface deformation and residual stress are compared with the experimental measurements.

Особенности процессов деформирования монокристаллического никелида титана при действии импульса всестороннего сжатия

Using the example of single-crystal titanium nickelide, the importance of taking into account the volume compressibility anisotropy when calculating the processes of elastoplastic deformation in materials with cubic symmetry of elastic properties is shown. It is shown that the process of uniform volumetric deformation corresponds to the process of non-uniform stress state for materials with cubic symmetry of properties for some orientations of the calculated coordinate system relative to the directions of the main crystallographic axes. The index surface of volume compressibility (or the reciprocal of it - the compression modulus) has a non-spherical shape and is a function of Euler angles. This is shown for the first time by solving a model problem - determining the stress and strain states of a spherical body made of single-crystal titanium nickelide under the action of a comprehensive compression pulse. In the general case of orienting the calculated coordinate system relative to the directions of the main crystallographic axes, an initially spherical body of single-crystal titanium nickelide is deformed into a biaxial ellipsoid under the influence of a comprehensive compression pulse.

Process mechanism in laser peen texturing artificial joint material

Friction and wear of artificial joints seriously restrict the service life of them. Surface texturing has been recognized as an effective means to reduce friction coefficient and improve wear resistance of artificial joints. In this study, a new and promising technology named laser peen texturing (LPT) is proposed to fabricate dimple textures on artificial joints. Process applicability of LPT on artificial joint material 316 L stainless steel is studied by experiments. Experimental results show that LPT is capable of fabricating dimple arrays on 316 L stainless steel and has good controllability and repeatability. Fundamental process mechanism of LPT is explored by numerical simulation. A 2D axisymmetric and semi-infinite finite element analysis (FEA) model has been developed and validated to predict the stress distribution and deformation process of the biomedical metal. The simulated dimple profiles are well consistent with the measured ones. Stress analysis shows obvious residual compressive stress after LPT. The maximum residual compressive stress and the thickness of the residual compressive stress zone are sensitive to LPT processing parameters. The local dynamic elasto-plastic deformation process of the material is discussed based on the deformation analysis at different time.

Equations of state in materials beyond the assumption of isotropy of volume compressibility

The process of elastoplastic deformation is considered for materials whose symmetry of elastic properties is modeled by means of five or more independent elastic constants. In the simulation of shock loading of a zinc single crystal characterized by a transversal isotropy of elastic and plastic properties, it was assumed that there is no volume isotropy of compressibility. Different equations of state are applied in a three-dimensional arrangement in the condition of plastic deformation in the direction of each axis. They reflect the relationship of hydrostatic stress to the degree of compression of the material. It is shown that the application of various equations of state changes the propagation velocity of volume waves and introduces a change in the wave pattern of deformation in anisotropic materials.

Physical and Constructive (Limiting) Criterions of Gear Wheels Wear

We suggest using a generalized model of friction - the model of elastic-plastic deformation of the body element, which is located on the surface of the friction pairs. This model is based on our new engineering approach to the problem of friction-triboergodynamics. Friction is examined as transformative and dissipative process. Structural-energetic interpretation of friction as a process of elasto-plastic deformation and fracture contact volumes is proposed. The model of Hertzian (heavy-loaded) friction contact evolution is considered. The least wear particle principle is formulated. It is mechanical (nano) quantum. Mechanical quantum represents the least structural form of solid material body in conditions of friction. It is dynamic oscillator of dissipative friction structure and it can be examined as the elementary nanostructure of metal’s solid body. At friction in state of most complete evolution of elementary tribosystem (tribocontact) all mechanical quanta (subtribosystems) with the exception of one, elasticity and reversibly transform energy of outer impact (mechanic movement). In these terms only one mechanical quantum is the lost – standard of wear. From this position we can consider the physical criterion of wear and the constructive (limiting) criterion of gear teeth and other practical examples of tribosystems efficiency with new tribology notion – mechanical (nano) quantum.