Elastic-plastic Body Research Articles

Linear Contact Load Law of an Elastic–Perfectly Plastic Half-Space vs. Sphere under Low Velocity Impact

The impact of contact between two elastic–plastic bodies is highly complex, with no established theoretical contact model currently available. This study investigates the problem of an elastic–plastic sphere impacting an elastic–plastic half-space at low speed and low energy using the finite element method (FEM). Existing linear contact loading laws exhibit significant discrepancies as they fail to consider the impact of elasticity and yield strength on the elastic–plastic sphere. To address this limitation, a novel linear contact loading law is proposed in this research, which utilizes the concept of equivalent contact stiffness rather than the conventional linear contact stiffness. The theoretical expressions of this new linear contact loading law are derived through FEM simulations of 150 sphere and half-space impact cases. The segmental linear characteristics of the equivalent contact stiffness are identified and fitted to establish the segmental expressions of the equivalent contact stiffness. The new linear contact loading law is dependent on various factors, including the yield strain of the half-space, the ratio of elastic moduli between the half-space and sphere, and the ratio of yield strengths between the half-space and sphere. The accuracy of the proposed linear contact loading law is validated through extensive Finite Element Method simulations, which involve an elastic–plastic half-space being struck by elastic–plastic spheres with varying impact energies, sizes, and material combinations.

Investigation of transportation infrastructure elements on the example of spherical bridge bearing

Transportation infrastructure consists mainly of critical elements. They are subjected to a large set of requirements for strength, rigidity, reliability. The article considered deformation behavior of spherical bridge bearing at different introduction depth parameters of sliding layer. The influence of contact surface treatment on the character of contact parameters distribution is studied. Earlier the polymers and composites behavior was viewed as an elastic-plastic material. However, for predicting their life-cycle it is necessary to consider them as viscoelastic. The article compared the parameters obtained by modeling elastic-plastic and viscoelastic materials behavior. The influence of sliding layer thickness on the deformation structure behavior was also discussed. It is revealed that sliding layer modeling as an elastic-plastic body is sufficient for numerical calculations on determination of strength characteristics. However, it is necessary to consider the sliding layer as a viscoelastic/viscous-elasticplastic material to design the life cycle of the structure taking into account rheology, thermomechanics and cyclic loads in different directions.

Effect of different friction coefficient models on numerical simulation of inertia friction welding of 2219 Al alloy to 304 stainless steel

In inertia friction welding (IFW) of Al alloy to steel, the friction coefficient of interface influences the friction heat production and determines the accuracy of the numerical simulation of welding process. A fully coupled three-dimensional model was established to simulate the IFW process of 2219 Al alloy to 304 stainless steel. By taking different simplifications in the influencing factors (i.e., temperature, sliding velocity, and pressure) of friction coefficient, three types of friction coefficient models were established and utilized in the simulation of IFW process. The strain compensated Arrhenius and Johnson-Cook models were employed to describe the deformation behavior of Al alloy and steel, respectively. Both Al alloy and steel were assumed to be the elastic-plastic body, and the friction stress was calculated by the Coulomb friction model. The friction interface temperature, angular velocity attenuation, axial shortening distance, and joint appearance were measured to verify and compare the accuracy of the established models. The temperature and stress evolutions during the IFW process were also analyzed. With the smallest error in validation, the friction coefficient model, which was a function of temperature, sliding rate, and pressure, showed the best accuracy in describing the friction behavior. By considering the effect of pressure, a more accurate shear stress at the center region of the interface was calculated with a lower value. It means that the friction resistance at the region was lower, promoting the flow of internal Al alloy and the formation of curly-shape flash.

Propagation of a Transverse Wave through the Interface of Elastic-Plastic Bodies with Dislocations

Propagation of a Transverse Wave through the Interface of Elastic-Plastic Bodies with Dislocations

Application of the Godunov scheme to solve three-dimensional problems of high-speed interactions of elastic-plastic bodies

Развивается 3D методика моделирования в эйлеровых переменных высокоскоростного ударно-волнового взаимодействия твердых деформируемых тел при больших перемещениях и деформациях. Численная методика основана на применении модифицированной схемы Годунова повышенной точности и эйлерово-лагранжевых многосеточных алгоритмов. Используется решение упругой задачи распада разрыва для пространственного напряженно-деформированного состояния, зависящее от времени и обеспечивающее второй порядок аппроксимации по времени и пространству в области гладких решений. Применяется три вида расчетных сеток для каждого взаимодействующего тела с явным лагранжевым выделением подвижных свободных и контактных поверхностей. Первый тип - лагранжевая поверхностная сетка в виде непрерывного набора треугольников, которая применяется как для задания начальной геометрии твердого тела, так и для его сопровождения в процессе расчета, и два вида объемных трехмерных сеток: базовая декартова фиксированная сетка для каждого тела и вспомогательные подвижные локальные эйлерово-лагранжевы сетки, связанные с каждым треугольником поверхностной сетки. Приводятся результаты тестирования методики и моделирования процессов высокоскоростного ударного взаимодействия тел и глубокого проникания деформируемых ударников в упругопластические преграды.

Theoretical Study of a Design Method for Underexcavation in Building Rectification

For buildings with shallow foundations embedded in natural soil sediments, the underexcavation method is often used to correct building inclination. Relying on engineering experience and close field monitoring, rectification has been conducted successfully. However, theoretical studies are relatively scarce, resulting in an inadequately informed rectification design and procedure. Assuming the soil is an ideal elastic-plastic body, a simplified analysis was adopted to study the issue theoretically. First, the redistribution of the base contact pressure after building inclination was deduced. Second, according to the force balance between the total contact pressure of the base and the total stress on the horizontal plane at the excavation hole, the limit hole spacing at the critical state of building back tilt was obtained, which was also the preferable hole spacing for soil strip collapse. Third, because the amount of anticipated forced settlement at a certain section of soil excavation is equal to the volume of soil hole collapse, an accurate formula for the hole diameter was obtained. Combined with engineering experience, suggestions for the design procedure were proposed. Finally, two case histories were introduced to verify the correctness and practicability of the theoretical formula for hole spacing and diameter. These two key parameters provide a strong theoretical basis for building rectification in future engineering practice.

Closure to “Contact Unloading Behaviors of Elastic-Power-Law Strain Hardening Material Considering Indenter Elasticity Effect” (Chen, C., Wang, Q., Wang, H., Ding, H., Hu, W., Xie, W., Weng, P., Jiang, L., and Yin, X., 2022, ASME J. Tribol., 144(12), p. 121501)

First of all, thanks to Professor Itzhak Green for the interest in our research paper and providing some comments. The main comments by Professor Green focus on the definitions of some mechanical parameters at initial yield. We have read them in detail and will make explanations in the following: The first parameter is the initial yield indentation δY (Eq. (3) in our paper).In fact, the Poisson’s ratio υ of most common metals is about in the range of 0.28–0.35, such as aluminum (υ = 0.33), bronze (υ = 0.34), stainless steel (υ = 0.3), tungsten (υ = 0.28), iron (υ = 0.3), magnesium (υ = 0.35), etc. After calculation, in this range, the maximum error of δY between the formula suggested by Johnson [1] and the formula suggested by Green [2] is only 6.8% and for the certain Poisson’s ratio υ = 0.3, the error is 4.2%. It illustrates that, in this range, the effect of Poisson’s ratio on δY is limited. It also should be emphasized that, for all contact simulations in our paper, the Poisson’s ratio of elastic-plastic materials is a constant value of 0.3 (as clearly stated in Sec. 2.2). Selecting p0=ϑYσY,ϑY=1.1, which is also selected by Stronge [3] when υ = 0.3, is reasonable, because it is a simpler formula with a good accuracy for common metals.The second parameter is the initial yield stress σY (Eq. (6) in our paper).The authors should state that, in our paper, Ref. [40] in Sec. 2 clearly reported the same form of σY with Eq. (6). In our paper, the research objects are elastic sphere and elastic-plastic half-space. To ensure the purely elastic deformations of the spheres, the ratio of the sphere yield stress to the half-space yield stress should be larger than 2.5 as suggested by Tabor [4], and 2.0 as suggested by Larsson and Olsson [5]. For all contact cases in our paper, the ratio of the sphere yield stress to the half-space yield stress is larger than 3.5. It is obviously that the initial plastic deformation occurs in the elastic-plastic half-space and there is no plastic deformation in sphere during contact. As for the comment by Professor Green, the controversy in Eq. (6) is for the condition that when the yield stresses of the two contact bodies are relatively close and plastic deformation will occur in both contact bodies. It is related to the contact between to two elastic-plastic bodies, which is more complex problem and not involved in our paper. To the author’s knowledge, the contact between the two elastic-plastic bodies has not been fully understood yet. So, when the yield stress of the elastic sphere is much larger than that of the elastic-plastic half-space, Eq. (6) is reasonable.The third parameter is the usage of ratios such as E*/σY.This comment is related to the selection of σY and the effect of Poisson’s ratio on initial yield. The authors would like to reiterate two facts in our paper: (1) the effect of Poisson’s ratio on δY is limited to most common metals and for all contact cases, Poisson’s ratio of elastic-plastic materials is a constant value of 0.3; (2) the research objects are elastic sphere and elastic-plastic half-space, and the yield stress of the elastic sphere is much larger than that of the elastic-plastic half-space. Based on these two facts, the usage of ratios such as E*/σY in our paper is reasonable.Professor Green's comments inspired the authors to research in detail the effect of Poisson’s ratio on contact unloading behaviors and the contact unloading between two elastic-plastic bodies. If there is any problem, please do not hesitate to contact us.There are no conflicts of interest.The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Methodology for testing pipeline steels for resistance to grooving corrosion

The methodology for testing pipeline steels is suggested on the assumption that for the destruction of pipes in field oil pipelines by the mechanism of grooving corrosion the simultaneous fulfillment of such conditions as the occurrence of scratches on the lower generatrix of the pipe, eventually growing into a channel in the form of a groove, emulsion enrichment with oxygen, presence of pipe wall metal in a stressed state, presence of chlorine-ion in the oil-water emulsion is required. Tests are suggested to be carried out in 3 % aqueous solution of NaCl with continuous aeration by air on bent plates 150×15×3 mm, made of the analyzed steel, the middle part of which is under the action of residual stresses σres, close to the level of maximum equivalent stresses σeqv in the wall of the oil pipeline, with the presence of a cut on this part on the inner side of the plate as an initiator of additional mechanical stresses. Using the value of the modulus of normal elasticity of the analyzed steel, the degree of residual strain of the elastic-plastic body from this material, corresponding to the value σres ≈ σeqv is calculated, based on which the plates are bent to the required deflection angle, after which the cut is applied to them. After keeping the plates in the corrosive medium for each of them the increase in depth of the cut as a result of corrosion of the walls by the corrosive medium is analyzed, from which the rate of steel K by the mechanism of grooving corrosion is calculated taking into account the duration of tests. Corrosion rate values for two pipe steel grades determined by the suggested procedure are given. The comparison of K values obtained leads to the conclusion about the higher resistance to grooving corrosion of 09G2S steel.

Regularities of Structure Formation in 30 mm Rods of Thermoelectric Material during Hot Extrusion.

In this study, Ingots of (Bi, Sb)2Te3 thermoelectric material with p-type conductivity have been obtained by hot extrusion. The main regularities of hot extrusion of 30 mm rods have been analyzed with the aid of a mathematical simulation on the basis of the joint use of elastic-plastic body approximations. The phase composition, texture and microstructure of the (Bi, Sb)2Te3 solid solutions have been studied using X-ray diffraction and scanning electron microscopy. The thermoelectric properties have been studied using the Harman method. We show that extrusion through a 30 mm diameter die produces a homogeneous strain. The extruded specimens exhibit a fine-grained structure and a clear axial texture in which the cleavage planes are parallel to the extrusion axis. The quantity of defects in the grains of the (Bi, Sb)2Te3 thermoelectric material decreases with an increase in the extrusion rate. An increase in the extrusion temperature leads to a decrease in the Seebeck coefficient and an increase in the electrical conductivity. The specimens extruded at 450 °C and a 0.5 mm/min extrusion rate have the highest thermoelectric figure of merit (Z = 3.2 × 10−3 K−1).

Simulation of nonstationary hydrogen diffusion processes near the crack tip in a field of inhomogeneous mechanical stresses

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed.

Driving force on line fracture process zone and fracture parameters suitable for elastic–plastic materials

The driving force on the line, zero height, fracture process zone (FPZ) is investigated in this paper. First, basic laws for crack propagation based on the configurational force approach are derived in the framework of traditional continuum mechanics. The driving force on steady line FPZ is a direct consequence of these derivations. Fracture parameters suitable for growing cracks in elastic–plastic materials such as near tip integrals based on the incremental theory of plasticity, the energy-, displacement-, and strain-type parameters are consistent with the driving force on steady line FPZ. Therefore, the steady line FPZ has provided a unified framework encompassing the fracture parameters of stable crack growth in elastic–plastic bodies. Besides, the driving force on non-steady line FPZ is also derived, which consists of the driving force related to the self-expansion of FPZ and the driving force corresponding to the translation of FPZ. Before the crack initiation, the work of separation in the cohesive zone model (CZM) is associated with the self-expansion driving force. During the steady-state crack growth, the work of separation is equal to the translation driving force. Since the translation driving force is independent of the self-expansion driving force, the cohesive parameters at the crack initiation can differ from those during the steady-state phase.

Influence of a Liquid Film Covering a Solid on Liquid Jet Impact Against Its Surface

The impact of a cylindrical liquid jet with a hemispherical tip on an elastic-plastic body uniformly covered in the impact domain by a liquid film has been studied, depending on the thickness of the film. The jet is directed orthogonally to the body surface, which is plane. The liquid in the jet and the film is water; the material of the body is Monel 400. The radius of the jet is $$R$$ , its velocity is $$V=300$$ m/s. The film thickness $$d$$ is varied in the range $$0-0.2R$$ . The action of the jet is considered until it becomes nearly stationary. A similar configuration can occur during the collapse of cavitation bubbles nearby a solid. The dynamics of the liquid (in the jet and the film) and the surrounding gas is calculated by the CIP-CUP method without explicit interface tracking using dynamically adaptive Soroban grids. The body is modeled by an ideal elastic-plastic semi-space, in which the deformations are considered to be small; the plasticity effect is realized according to the Mises condition. The dynamics of the body is calculated by a UNO-modification of the Godunov method of the second order of accuracy. Some features of the body surface loading and the corresponding response of the body (the deformation of its surface, the changes in its stress state) resulting from varying the liquid film thickness have been revealed. It is shown, in particular, that the body surface pressure profiles, initially very different for various $$d$$ , after the time moment $$t\approx R/V$$ become approximately the same (with a small exception at the periphery) and closely correspond to the profile arising under the stationary action of a similar jet of incompressible liquid. The jet impact results in the formation of a very shallow pit on the body surface (with a depth of about $$10^{-3}R$$ ). At $$d=0$$ , the depth of the pit in its center is approximately two times greater than at $$d=0.2R$$ .

Fracture toughness correction due to the in- and out-of-plane constraints

This work generalizes O'Dowd’s and Shih’s formula for the stress field in front of a crack in an elastic–plastic body in a plane strain situation for a three-dimensional case. The Guo Wanlin formula was used for this purpose. This formula extends the solution of Hutchinson, Rice and Rosengren from a plane strain case to a three-dimensional case. The second term in this generalized formula, the Q parameter, becomes a function of the Tz parameter introduced by Guo to characterize the stress triaxiality. This parameter is now computed numerically using an assumption of large strains and experimentally recorded and calibrated constitutive equations. The parameter Q calculated in such a way was used to estimate the fracture toughness taking into account both in- and out-of-plane constraint measures.

Assessing surface fatigue crack growth in railway wheelset axle

Purpose: The aim of the proposed research is to create a calculation model of surface fatigue crack growth at the axle of railway wheelset working under operational loads. Design/methodology/approach: The energy approach of the fracture mechanics was used to formulate the calculation model of fatigue crack propagation at the wheelset axle surface. The method of least squares was used to determine the investigated material mechanical constants that the kinetic equations of the calculation model contain. The system of differential equations of crack growth kinetics was solved numerically using the Runge-Kutta method. Findings: On the basis of the energy approach of the fracture mechanics the calculation model of fatigue macrocrack growth in three-dimensional elastic-plastic body in case of a mixed-mode I+II+III macromechanism of fracture has been built. On the basis of the created calculation model, the kinetics of the growth of fatigue cracks was investigated both in the middle part of the wheelset axle and in the axle journal. Research limitations/implications: The results obtained on laboratory specimens should be tested during a real railway wheelset axle investigation. Practical implications: The created calculation model can be used in practice to formulate method of residual lifetime estimation of railway wheelset axle. Originality/value: It was shown, that surface crack kinetics depends not only on the crack initial area but also significantly depends on the crack edge geometry and comparatively small crack-like defects at the wheelset axle surface can reach critical sizes in comparatively short run. It has been found that mechanical shear stresses caused by the weight of the loaded railway wagon in the cross section of the wheelset axle journal can significantly accelerate the growth of the transverse fatigue crack at the axle surface, reducing the period of crack subcritical growth by about 20%.

RESULTS OF RESEARCH OF PROCESSES OF EXTRACTION OF CUT WITH IMPLEMENTATION OF ULTRASOUND OSCILLATIONS ON THE INSTRUMENT

The possibility of improving the quality of rubber due to the directional action of various types of ultrasonic vibrations, with the aim of forming the maximum compressive residual stresses, will ultimately improve the performance of the rize joint under variable loads. The process of rizenization using forced ultrasonic vibrations has been investigated. When compiling a mathematical model of the process of extrusion of rubber with the imposition of ultrasonic vibrations on the tool, it was assumed that the phenomenon of surface hardening has little effect on the magnitude of the contact pressure and the friction force during plastic deformation. This assumption allows us to simplify the mathematical model by not taking into account this factor. New methods of calculating the contact pressure and specific frictional force during rubber extrusion with the imposition of axial, radial and torsional vibrations are proposed. The description of the deformation processes with the superposition of ultrasonic vibrations was carried out on the basis of the rheological model of deformation of an ideal elastic-plastic body. The work developed nonlinear mathematical models for the study of plastic deformation processes, consisting of equations of tool displacement and equations taking into account the elastic-plate properties of the processed material. This structure of the mathematical model most fully reflects the processes occurring during thread rolling with the imposition of ultrasonic vibrations. As a result of the research, it has been established that the use of forced ultrasonic vibrations during machining with a tool will significantly increase the productivity, tool durability and quality of the processed surface, especially when processing with special physical and mechanical properties. In the study of the contact interaction of the tool with the part with the imposition of ultrasonic vibrations in the axial and radial directions, as well as in the imposition of torsional vibrations, it was found that the use of axial vibrations is on average 50 % more effective.

MODELING THE PROCESS OF CONTACT INTERACTION OF A TOOL WITH A PART WITH A SUPPLEMENT OF AXIAL ULTRASONIC OSCILLATIONS

The process of ultrasonic extrusion of rubber with superposition of ultrasonic vibrations is investigated and modeled. Based on the rheological model of deformation of an ideal elastic-plastic body, dependences have been developed for calculating contact pressures and specific friction. When conducting this study in order to simplify the mathematical model, the assumption was made that the phenomenon of surface hardening has little effect on the magnitude of the contact pressure and the friction force during plastic deformation. This mathematical model describes the complex movement of a tool (rotational and oscillatory movement of a tap). The system of obtained dependences, which describes the influence of the amplitude of oscillations, the direction of oscillations, the strain rate, and the mechanical properties of the processed material on the value of the contact pressure, allows one to calculate the parameters of the plastic deformation process with the application of ultrasound. Thanks to this description, it is possible to obtain the value of contact pressure and friction forces for each section of the load diagram. When analyzing the results, it was found that with an increase in the amplitude of the oscillations, the contact time of the tool with the machined surface decreases, therefore, the contact pressure, the specific friction of axial and torsional vibrations during the period, respectively, decrease within the limits of the studied factors. The obtained dependence for determining the diameter of the hole when extruding the rubber with superposition of axial vibrations, taking into account the elastic properties of the workpiece material. These dependences make it possible to determine the diameter of the hole and the tolerance for its manufacture, depending on the size and design of the tap, the size of the rubber, the mechanical properties of the workpiece material, processing conditions and the magnitude of ultrasonic vibrations. The advantage of this study is a detailed analysis of the contact interaction of the tool with the part and taking into account the mechanical properties of the processed material, which allows you to select processing modes and ensure maximum performance.

Calculation of Waves in an Elastic-Plastic Body Based on ENO Modifications of the Godunov Method

The efficiency of two ENO modifications of the Godunov method for calculation axisymmetric problems of the dynamics of elastic-plastic bodies, namely a UNO scheme of the second-order of accuracy and a TVD scheme of the second order of accuracy outside the solution extremes where it decreases to the first order, has been numerically studied. The efficiency of the modifications is estimated by comparing the results of calculation of a number of problems on the propagation of spherical and cylindrical waves in a body with the results of reference solutions and the Godunov method. The exact and numerical solutions are used as reference solutions, the latter are obtained on fine grids. It is shown that for all the problems considered, the solutions by the TVD and UNO schemes are much closer to the reference ones than those by the Godunov method. The TVD and UNO schemes are characteristic of significantly less smearing of sharp wave fronts and a more accurate resolution of extrema. At the same time, the wave profiles and the extrema are reproduced by the UNO scheme somewhat better than by the TVD scheme.

Use of Magnetic Anisotropy Method for Assessing Residual Stresses in Metal Structures

A series of experiments on measuring of difference between the main mechanical stresses (DPMS) was carried out using a mechanical stress scanner based on the magnetoanisotropic method. The magnitude of the DPMS is fixed when a magnetic field is induced on a carbon steel plate under uniaxial tension. A direct proportional relationship is shown between the magnitude of the DPMS signal recorded by the scanner and the magnitude of tensile stresses in the plate in the region of elastic deformation of steel. Measurement of the DPMS signal in the central part of similar plates previously subjected to elastic-plastic bending showed that positive values of the signal are fixed in the surface layers of the metal on the inside of the plate, which corresponds to tensile residual stresses, while the negative ones concentrate at the external surface, which corresponds to compressive stresses. A transverse incision on a curved plate from the inside leads to a decrease in the value of the signal of the DPMS, which indicates a decrease in the level of residual stresses in the metal. The values of the DPMS signal in the central part of the curved plate, recalculated using the established calibration dependence on the value of the residual stresses, were compared with the values of the stresses established by calculation, based on the Henki’s theorem on the unloading of an elastic-plastic body. A satisfactory convergence was obtained between the experimental and calculated data.

Unloading behavior of low velocity impact between elastic and elastic–plastic bodies

In this paper, the unloading behavior is investigated by finite element (FE) analysis for low-velocity frictionless impact between elastic sphere and elastic-perfectly plastic half-space. The material property and impact velocity are varied to cover the elastic-plastic and fully plastic unloading regimes by 301 FE simulations. Based on the FE results, the yield strain is a crucial material property to characterize the unloading law, and spherical residual cavity and Hertzian-type unloading assumptions are validated. By introducing a scalar factor to revise Stronge's geometric similarity, a new unloading model is presented to fast and accurate precut the unloading behavior. The unloading model is validated numerically, experimentally and compared with other unloading models. Its applications combining with loading models are also validated experimentally.

Destruction Features of Impactors Made of a Porous Alloy Based on Tungsten with Reinforcing Filler When Interacting with Armored Obstacles

In this study, we perform calculations and experimental studies of the destruction of composite impactors from a porous tungsten–nickel–iron–cobalt alloy with 10 wt % tungsten titanium carbide at high-speed impact with steel barriers. In ballistic tests over a wide range of velocities, there is a significant excess of the penetration depth of these impactors into steel barriers compared to the mass-dimensional analog of a tungsten–nickel–iron alloy with 90% tungsten content. Based on the analysis of crater morphology and the structure of impactor fragments after introduction into the obstacle, we assume that the impactor is “self-sharpened” by localizing plastic deformation, which reduces the effective interaction area and increases the penetration depth. To describe the destruction, we modified the mathematical model of a porous ideal elastic-plastic body with a complex structure with the possibility of considering the adiabatic shear mechanism during interaction between the impactor and the obstacle.