scholarly journals APPLICATION OF CURRENT LINES IN DETERMINING KINEMATIC CHARACTERISTICS IN STATIONARY PROCESSES OF PLASTIC FLOW OF METAL

2021 ◽  
pp. 92-98
Author(s):  
Roman Sivak ◽  
Iryna Нunko ◽  
Roman Zalizniak
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Plastic Flow ◽  
Strain State ◽  
Stationary Processes ◽  
Strain Rate Tensor ◽  
Stress Strain ◽  
Stress Strain State ◽  
Kinematic Characteristics ◽  
Current Lines

Methods of theoretical solution of problems in the processing of metals by pressure are insufficiently developed for practical use in the development and implementation of new technologies and improvement of existing ones. To meet the stringent requirements for the accuracy of determining the stress-strain state, it is necessary to have reliable information about the evolution of the development of the plastic deformation process at each point of the metal from the very beginning of the deformation. This will allow to obtain with high accuracy the important characteristics of the technological heredity of the products that they acquire as a result of their plastic processing. The first and important step in the calculations of the stress-strain state is to obtain the kinematic characteristics of the plastic flow of metal in the form of analytical dependences, which will formulate the patterns of deformation in the technological processes of metal forming. The article considers the possibility of applying the method of current functions to determine the components of the strain rate tensor in established stationary processes of plastic deformation. It is assumed that in the case of axisymmetric plastic deformation of a metal in a channel with curvilinear boundaries, the kinematics of the process is similar to a plane flow. In obtaining the equations, the differential equation of current lines taking into account the incompressibility condition was used to determine the components of the strain rate tensor. To explain the physical meaning of the current functions, two infinitely close current lines were considered in the flow plane, and an expression was obtained for the flow through a finite transverse current tube. In the absence of radial velocity components at the boundaries, constraints are obtained that are imposed on derivatives of current functions at these boundaries. The developed method of calculating the kinematic characteristics of plastic deformation for established axisymmetric stationary processes will simplify the mathematical processing of the obtained results and increase the reliability of the determination of the stress-strain state.

scholarly journals Stress strain state of elastic plate with elliptical cut-out

2020 ◽  
pp. 3-8
Author(s):  
E.E. Deryugin ◽  
Keyword(s):  
Plastic Deformation ◽  
Stress Concentration ◽  
Driving Force ◽  
Strain State ◽  
Mechanical State ◽  
Concentration Coefficient ◽  
Stress Strain ◽  
Crack Driving Force ◽  
Stress Strain State ◽  
Stress Concentration Coefficient

The article considers a crack in the form of a narrow cut with a certain cfn at the cut out in an unbounded plate. The characteristics of the mechanical state of this system under uniaxial loading are determined: the stress concentration coefficient, the crack-driving force, and the energy of a solid with a crack. The elastic energy expenditure during crack propagation is determined. The general regularities of the mechanical state of a solid with a crack, not necessary having the form of an ellipse, are revealed. An important parameter of a crack is the curvature at the tip. It is shown that the Griffiths crack does not actually have a singularity at the tip. The stress strain state of the plate with an elliptical crack is identical to the same of the plate with a focus of homogeneous plastic deformation.

Effect of Stress-Strain State during Combined Deformation on Microstructure Evolution of High Carbon Steel Wire

2016 ◽  
Vol 870 ◽  
pp. 460-465 ◽  
Author(s):  
Alexandr Gulin ◽  
Marina Polyakova ◽  
Eduard Golubchik
Keyword(s):  
Plastic Deformation ◽  
Carbon Steel ◽  
Cross Section ◽  
Strain State ◽  
Steel Wire ◽  
High Carbon Steel ◽  
Grain Structure ◽  
Basic Operation ◽  
Stress Strain ◽  
Stress Strain State

It is shown that new methods of severe plastic deformation design require combining different methods of plastic deformation. As for carbon steel wire, using drawing as a basic operation is obvious. The combination of drawing with bending and twisting was estimated by the stress-strain uniformity complex. It allows choosing the deformation processing conditions which ensure the uniform stress-strain state in each point of the carbon steel wire cross section. Based on such combination, a new method for manufacturing of semi-products with ultra fine grain structure by drawing with torsion was developed. The combination of wire drawing in two consecutively arranged dies with simultaneous bending and torsion allows achieving complex stress-strain state of the processed metal and ensure the share stresses. Metallographic investigation shows that such scheme of combined plastic deformation provides the uniformity of metal microstructure in its cross section.

scholarly journals Assessment of stress-strain state in cylindrical parts after transverse running with flat plates

2017 ◽  
Vol 2 (5) ◽  
pp. 38-43 ◽  
Author(s):  
Семен Зайдес ◽  
Semen Zaides ◽  
Дак Фам ◽  
Dac Pham
Keyword(s):  
Plastic Deformation ◽  
Strain State ◽  
Surface Plastic Deformation ◽  
Surface Plastic ◽  
Flat Plates ◽  
Stress Strain ◽  
Program Complex ◽  
Vertical Loading ◽  
Stress Strain State ◽  
Cylindrical Parts

For the deformation strengthening of parts like axles, pins, and bushes there is offered a method of surface plastic deformation based on blank rolling with flat plates. The method allows machining parts which do not have center holes. At transverse running a blank bending affected by transverse loading forces is excluded. With the aid of ANSYS program complex there is considered a change of a stress-strain state in cylindrical parts at transverse running. There are defined plastic and elastic cylinder deformations after loading. The distribution of residual stresses along cylinder section in the plane of vertical loading is obtained. The stress state of samples run with flat plates on equivalent stress is assessed. An efficient value of running at transverse running used as a basic parameter of surface plastic deformation is defined.

scholarly journals Numerical Study of Stress-Strain State of Workpiece in Contact Problem of Surface Mandrel Drilling

2021 ◽  
Vol 20 (3) ◽  
pp. 259-267
Author(s):  
N. S. Sivtsev ◽  
V. V. Tarasov
Keyword(s):  
Plastic Deformation ◽  
Friction Coefficient ◽  
Contact Interaction ◽  
Computational Experiment ◽  
Strain State ◽  
Numerical Study ◽  
Surface Plastic Deformation ◽  
Surface Plastic ◽  
Stress Strain ◽  
Stress Strain State

In recent years, the economic factor has played an increasingly important role in the selection of technologies for manufacturing machine parts with specified values of normalized parameters of geometric accuracy and quality of working surfaces. As applied to surface plastic deformation processes, this is noticeably manifested in the search for effective friction control methods in the “tool – workpiece” pair, which ultimately determines the distribution pattern and the magnitude of stresses and strains in the workpiece and the tool. It is not possible to obtain a rigorous analytical solution to the problem of establishing a connection between surface conditions, friction, and the stress-strain state of the contacted bodies. In this regard, the construction of mathematical models comes to the fore, the solution of which is possible by numerical methods. The paper presents the results of a numerical study (computational experiment) of a finite-element model of workpiece deformation under various conditions of contact interaction and friction by one of the methods of surface plastic deformation – surface mandrel drilling. The friction coefficient has been chosen as the criterion for assessing the conditions of contact interaction and friction. It is shown that a change in the friction coefficient in the process of surface mandrel has no noticeable effect on the formation of a stress field in the deformable workpiece both in the axial, and in the radial and circumferential directions. At the same time, with an increase in the value of the friction coefficient in the “tool – workpiece” pair and with the associated increase in the force of mechanical resistance to deformation of the workpiece, their growth is observed. A computational experiment has confirmed the presence of non-contact deformations of the workpiece and tool during surface mandrel drilling, as well as  as a decrease in the value of residual deformations in the workpiece with a decrease in the coefficient of friction. Balance assessment of contact surface displacements in the workpiece (the inner surface of the hole to be machined) and the tool (mandrel) has shown that the deformations of the tool in the elastic region can lead to a significant decrease in the real tightness of surface mandrel drilling.

scholarly journals Stress-Strain State of Steam Turbine Lock Joint Under Plastic Deformation

2020 ◽  
Vol 23 (4) ◽  
pp. 28-37
Author(s):  
Ihor A. Palkov ◽  
◽  
Mykola H. Shulzhenko ◽  
Keyword(s):  
Plastic Deformation ◽  
Strain State ◽  
Contact Stresses ◽  
Rotor Blades ◽  
Bilinear Approximation ◽  
Stress Strain ◽  
Deformation Curves ◽  
Stress Strain State ◽  
Pressure Cylinder ◽  
Lock Joint

The stress-strain state problem for the lock joint of the rotor blades of the first stage of the medium-pressure cylinder under plastic deformation is solved. When solving the problem, the theory of elastic-plastic deformations is used. The problem is solved using two different approaches to specifying plastic deformation curves. The applicability of using a simpler bilinear approximation instead of the classical multilinear one is estimated. Based on the example of solving this problem, the time required to perform the calculation with the use of the bilinear and multilinear approximations is shown. Comparison of the results obtained in the form of the distribution of plastic deformations, equivalent stresses, and contact stresses over support pads made it possible to assess the difference when the two types of approximation are used. The obtained result error value when using the bilinear approximation made it possible to draw conclusions about the applicability of this approach to the processing of plastic deformation curves for solving problems of this kind. The problem is solved using the finite element method. To objectively assess the effect of plastic deformation on the redistribution of loads in the lock joint, a finite element model is used, obtained when solving the problem of the thermally stressed state of the rotor blade lock joint. The distribution of contact stresses in the lock joint is shown. The results are compared with those obtained earlier when solving the problem of thermoelasticity. Significant differences in the level of contact stresses are noted. Results of the computational assessment of the stress-strain state of the lock joint of the rotor blades of the first stage of the medium-pressure cylinder of a steam turbine are presented, which allow characterizing the degree of relaxation and redistribution of stresses in the structure in comparison with the results obtained earlier when solving the problem of thermoelasticity. Conclusions are made about the economic viability of using the calculation methods presented.

Derivation of Stress, Strain, Temperature, Strain-Rate Relation for Plastic Deformation

1947 ◽  
Vol 14 (3) ◽  
pp. A229-A230
Author(s):  
J. D. Lubahn
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Flow ◽  
Stress Strain ◽  
Rate Relation ◽  
Temperature Strain

Abstract This paper carries out the derivation and correction of an equation previously presented by J. H. Hollomon and the author, relating to stress for plastic flow (σ), plastic strain (ϵ), strain rate (ϵ.), and temperature (T).

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