Plastic Diagram Research Articles

Determination of Limiting Deformations at Testing Cylindrical Samples for Tension

This paper proposes a method for calculating limiting deformations under conditions of localized deformation during tensile testing. The method for calculating limiting deformations was used to construct plasticity diagrams under conditions of strain localization under uniaxial tension.
 The plasticity diagram is one of the material functions that forms the technological map of the material. The plasticity diagram displays the properties of a material depending on the degree of deformation and the stress state scheme.
 According to the studies carried out in this work, it was established that the critical increase in plasticity with increasing stress state indicator is explained by the influence of three factors: the strain gradient, the history of deformation and the third invariant of the stress tensor.
 The obtained dependencies make it possible to construct plasticity diagrams for materials whose destruction is preceded by localized deformation in the form of a "neck".
 This work establishes the quantitative influence of these three factors on the magnitude of the limiting deformations of a sample stretched to the point of failure.
 Application plasticity diagrams constructed using the proposed methods for cold plastic deformation processes, depending on the type of deformation path and the features of metal rheology, clarifies the value of the used plasticity resource of the metal, which allows to reduce the number of defective products for processes whose modes are calculated according to limit deformations.

О ПОСТРОЕНИИ ДИАГРАММЫ ПЛАСТИЧНОСТИ УГЛЕРОДИСТОЙ СТАЛИ РАЗЛИЧНОЙ СТРУКТУРЫ

A test for uniaxial stretching of cylindrical samples (smooth and with a recess) made of carbon steel wire rod 70, sorbitized from rolling heating and patented in lead baths, was carried out. The test results allowed us to obtain additional data for constructing diagrams of the plasticity of steel. The obtained plasticity diagrams can serve as a guide for technologists when choosing steel, its microstructure, and predict the ability to cold deformation during pressure treatment.

FEATURES OF THE CALCULATION OF THE USED PLASTICITY RESOURCE DURING COLD FORMING OF GLASS-TYPE PRODUCTS

The reverse extrusion process is widely used in the production of “Glass” type parts. Due to high technical and economic indicators and great technological possibilities, in recent years, cold plastic deformation has become widely used in machine- and instrument-building plants, in the electrical and radio engineering industry, as well as in other branches of the national economy. However, the possibility of cold plastic deformation by the extrusion method is not yet sufficiently used. The reason is that, traditionally, during the design of metal pressure processing processes, attention is paid to determining the power parameters and ensuring the geometric accuracy of the workpieces. But this does not allow us to assess the ultimate shape change and technological heredity of the finished products and make a quantitative assessment of the damage of the deformed metal. In this work, the process of forming products of the “Glass” type by reverse cold plastic deformation is investigated, in which the used plasticity resource is taken as the most important parameter responsible for the quality of the products. The method of calculation of the used resource of plasticity of “Glass” blanks in the processes of reverse cold plastic forming is clarified. When calculating the used plasticity resource, the effect of the volume of the stress state scheme is taken into account by using the limit deformation surface instead of the plasticity diagrams. The graphs of distribution of the resource of plasticity by the radius of the workpiece are obtained. From the analysis of the results it follows that the greatest intensity of accumulation of damage occurs in the areas of maximum irregularity of plastic deformation. Points of contact of the punch with the workpiece turned out to be dangerous. The use of hydrostatic support in reverse extraction allowed not only to reduce the degree of plasticity used, but also to obtain a more uniform distribution of it, therefore, to improve the quality of the obtained blanks when reverse extrusion and improve the technological heredity of the finished products. The results obtained in the work can be used to estimate the limit change in shape in similar technological processes, which are accompanied by a volumetric scheme of the stressed state.

PHENOMENOLOGICAL CRITERIA OF DESTRUCTION

The paper reviews the known deformability criteria, which have become widespread to assess the probability of failure in both monotonic and nonmonotonic plastic deformation. The most widely used methods of assessing plasticity, in which the dependence of plasticity on the stress state scheme is described by plasticity diagrams. The plasticity diagram is an experimental dependence of the ultimate deformation on the stiffness index of the stress state. In most works, this dependence is represented by a flat curve. The plasticity of metals depends on many factors, namely the nature of the metal and the thermomechanical parameters of the process. With cold plastic deformation, the main factor influencing plasticity is the stress state and the law of its change during loading. To quantify the impact of stress state on the probability of failure using failure criteria. Under the destruction is understood the appearance of macrocracks, which leads to irreparable damage to the product. A common disadvantage of the known deformation criteria, which are common to assess the probability of failure in both monotonic and nonmonotonic plastic deformation is that the subintegral functions of these criteria are based on the hypothesis that the effect of stress state on plasticity is described by the plasticity diagram and the influence of load history – flat trajectories. Due to the fact that the plasticity diagrams cover a rather narrow class of stress states, in applied theories of deformability there is no single approach to estimating the value of the used plasticity resource in the processes of metal forming. From the performed research it follows that at present there are almost very few works in which the dependence of plasticity on the history of loading is described by spatial trajectories. Therefore, the question of the destruction criteria remains open and relevant.

Hydro-mechanical behavior of two clayey soils in presence of household waste leachates

BACKGROUND AND OBJECTIVESIn landfills, containment is provided by natural or artificial clayey materials known for their low permeability and for their pollutant retention capacity. However, the properties of these media are modified by leachates, whose migration they are supposed to limit. This study aims to reconsider the criteria for choosing suitable materials to make a bottom liner through both their long term hydraulic and mechanical performances.METHODSTwo fine materials sampled in Burkina Faso (West Africa) have been characterized in order to compare their hydro-mechanical behavior in the presence of household waste leachates. The first material is classified as an inorganic clay of low to medium plasticity according to Casagrande plasticity diagram, it is mainly kaolinitic with some traces amounts of smectites. The second one is classified clayey sand of low to medium plasticity, the predominant mineral clay being kaolinite. Hydro-mechanical tests were performed on both sampled materials to judge the sealing properties of these materials, as well as the characteristics of deformation and rupture which have an important effect to ensure the durability of a bottom liner. All these tests were performed first with distilled water then with leachates as interstitial fluids in order to understand the modification of the hydro-mechanical properties of the clayey soils.FINDINGSLeachate contamination always alters hydraulic properties of the materials. However, between the two soils, the most clayey and the most impervious (soils from Nouna) undergo the deeper weathering. Indeed, hydraulic conductivity of these soils in contact with a synthetic leachate increases from 1.71x10-10 to 1.51x10-9 m/s. In contrast to soils from Boudry, these soils also undergo very significant settlements over the long term with compressibility indexes varying from 0.164 to 0.225. For both soils, the shear strength increases showing that, from this point view, the leachate work in the sense of of the bottom liner stability. For soils from Nouna, the effective cohesion increases from 3 to 21 kPa with a slight decrease of friction angle; for soils from Boudry a slight increase of cohesion is noticed while friction angle increases from 34 to 37°.CONCLUSIONThis comparative study is of practical use to environmental geotechnics professionals because it shows that the choice in designing a bottom liner must be a compromise between long term hydraulic and mechanical behaviors of soils. It is also important to know the nature of the flows to contain in order to ensure the durability of the structure.

Geotechnical soil mapping from electrical and mechanical properties: Case study of the Bafoussam urban area, west Cameroon

Preliminary work in civil engineering works often involves the investigation of soil support in order to secure or predict project safety. The objective of this work is to purpose an urban geotechnical soil map combining physical and mechanical behaviour of the soil and its electrical properties. Field work with auger corer allowed collection of samples for analysis. The results of the Atterberg limits and particle size analysis enabled classification of those soils according to HRB as silty or clayey gravels and sands (class A-2-7) and clayey soils (A-7-5). The Casagrande Plasticity Diagram classifies them as At and Lt (very plastic clays and silts) and the GTR classifies them as sandy and gravelly soils with fines (B6) and fine clay soils (A2 and A3). These classifications show that the study area is mainly covered by sandy-clay, lateritic clay and lateritic gravelly soils. The iso-resistivity maps and resistivity sections made from the results of vertical electrical soundings, allow the identification of three ranges of resistivity: a low resistivity less than 300 Ώ.m, a medium resistivity range between 300 and 500 Ώ.m and a high resistivity greater than 500 Ώ.m. These ranges of resistivity correspond to the different formation disparities that make up the subsurface. Associated penetrograms show these soils are very resistive in the cuirass subsurface zones with very compact formations with permissible stress values between 2.5 and 5.2 bars. At greater depths, these values are moderate in the clayey sands with stresses between 0.8 and 3 bars and low in the clays and lateritic soils (˂1 bar). The application of determination coefficient (R2) and Spearman correlation (rs) between permissible stress and true resistivity gives values of 0.79 and 0.74 respectively. There is a good qualitative and quantitative correlation between these two parameters in the study area. The superimposition and comparison of the different results with the geological formations enables development of a geotechnical soil map. This map enables us to understand the lithological and mechanical heterogeneity of the soils during the construction of structures in the urban perimeter of Bafoussam.

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.

TECHNOLOGICAL PASSPORT STUDY PISTON AND CONNECTING ROD BARE MATERIAL AXIAL ROTARY PISTON PUMP

A technological passport of the alloy steel material has been formed, from which a piston-connecting rod pair of an axial-rotor piston pump is made in the form of functions: flow curve, plasticity diagram, Bauschinger curve, calibration graph. Using the approximation of the neck contour by the Gaussian function at any moment of deformation of a cylindrical specimen in the supercritical region, the main parameters used in engineering calculations are related: the minimum diameter of the specimen, the current diameter of the specimen with a given coordinate, the relative (absolute) elongation and contraction with the parameters referred to the moment of rupture sample. In addition, the elongation and contraction of the sample after fracture are unambiguously associated. The approximation avoids the inconvenient and relatively expensive video filming for studying the history of deformation. It is shown that the effect of heat treatment on the mechanical properties of these steels is not the same for different stress state schemes. The tensile strengths of these steels are close as delivered. The plasticity characteristics of steel 30Kh3MFA exceed the plasticity of steel 38Kh2MYuA by 1.5 times. The flow curves of the steels under consideration have the following tendency: so the coefficient of approximation of the flow curve for 38Kh2MYuA steel in the delivery state exceeds its value in relation to steel 30Kh3MFA by 1.23 times. After heat treatment of these steels, the value of the approximation coefficient increases: for steel 38Kh2MYuA by 1.11 times, for steel 30Kh3MFA by 1.46 times. The results obtained make it possible to control the mechanics of the technological operation of rolling the piston-connecting rod pair and create a process control mechanism in order to prevent rejects during the rolling process, which manifests itself in the form of going beyond the tolerance field for the axial clearance of the piston-connecting rod pair, as well as destruction during rolling of the inner part of the piston.

Technological inheritance in metal forming

Ogorodnikov V., Arkhipova T. Technological inheritance in metal forming. Material working by pressure. 2020. № 1 (50). Р. 28-32.
 Technological heredity in metal forming processes is accompanied by hardening, the appearance of residual stresses, a deformation gradient, residual plasticity and a number of other factors that determine the operational properties of the product. The influence of most factors of technological heredity on the mechanical properties of the material of products has been studied, however, the plasticity of a pre-deformed workpiece remains insufficiently studied. For a quantitative assessment, a calculation method is proposed, with the help of which it seems possible to determine the plasticity resource of pre-deformed blanks. The developed calculation apparatus is based on a fracture model based on a tensor description of damage accumulation. It allows for the known mechanical characteristics to predict the plasticity characteristics of pre-deformed blanks at any type of stress state. The proposed method assumes the use of plasticity diagrams, which describe the change in ultimate deformation depending on the stress state indicators. Plasticity diagrams are constructed for materials tested under conditions of linear or plane stress states (tension, compression, torsion). The practical significance of the results is evidenced by the assessment of the plasticity of steeply curved elbows obtained by the method of cold plastic deformation according to a combined scheme, including deforming pulling of a pre-willed workpiece. In this case, the workpiece in the form of a pipe was subjected to plastic bending. The proposed method makes it possible to assess the residual plasticity of the finished bend. A satisfactory convergence of the calculated and experimental data has been revealed.

ДЕФОРМИРОВАНИЕ И РАЗРУШЕНИЕ ЛИПЫ И СОСНЫ ПРИ ИНТЕНСИВНЫХ ДИНАМИЧЕСКИХ ВОЗДЕЙСТВИЯХ

The paper presents the results of dynamic tests under compression of two wood species: linden and pine under loading along and across the fibers. Dynamic tests were carried out using the modified Kolsky method with the realization of multi-cycle loading of the sample during one test. As a result, strain diagrams were obtained for uniaxial stress state taking into account additional loading cycles The use of the multi-cycle loading mode made it possible to obtain a significantly greater degree of the sample deformation than with traditional single-cycle loading. To create a pulse load, a gas gun was used. According to the experimental results, dynamic deformation diagrams were obtained, as well as ultimate strength and deformation characteristics, fracture energy for linden and pine were determined depending on the cutting angle of the samples and the strain rate. A strong anisotropy of the properties of the tested materials is observed: the samples have the greatest strength when a load is applied along the fibers, and the least - across the fibers. A positive effect of the strain rate is noted. The module of the load branch is non-linear and, as a rule, is smaller than the module of the unload branch (while maintaining the integrity of the sample). The nature of the deformation and fracture of the samples strongly depends on the angle of cutting-out. At cutting angle across the fibers, the deformation diagram after reaching a certain threshold value is close to an ideally plastic diagram. At cutting angle along the fibers, the initial portion of the diagrams is close to linear, i.e. elastic deformation takes place. However, after reaching a certain value (“yield strength”), the diagram becomes nonlinear. This kind of behavior takes place in those experiments in which the destruction of the samples occurs. For both wood species, there is a significant excess of energy absorption by samples cut and tested along the fibers, compared with samples cut and tested across the fibers.

Determination of material constants for high strain rate constitutive model of high entropy alloys

The paper deals with constitutive models determination for a group of high entropy materials (coded Bl-x). The procedure includes the following steps: experimental determination of mechanical characteristics for quasi-static domain through compression tests, correction of experimental data of quasi-static tests using numerical simulation, acquisition of experimental data obtained on the Split Hopkinson Pressure Bars and their simulated interpretation. Using the processed data, the constitutive patterns of the materials under investigation are drawn. The experimental data correction for quasi-static tests performed using numerical simulation involves drawing the engineering stress/strain diagram, the transition to the plastic characteristic diagram in the hypothesis of perfectly cylindrical shape of the specimen throughout the test, simulation of the compression deformation process in the presence of friction force on the end specimen surfaces and the correction of the characteristic plastic diagram using the calculated error. Dynamic data obtained on Split Hopkinson Pressure Bar were interpreted using a methodology previously published. Experimental data under real conditions are compared with data obtained by numerical simulation on an elasto-plastic model. The viscous component of the dynamic response is the difference between the real and simulated on the elasto-plastic model responses.

Prediction of the Mechanical Properties of Metals After Cold Pressing

We propose a procedure for the evaluation of plasticity of the prestrained metal of blanks. This procedure uses the model of fracture based on the tensor description of the accumulation of defects under the conditions of cold plastic deformation. If the mechanical characteristics and plasticity diagrams are known, then this procedure makes it possible to analyze plastic properties of prestrained blanks for all kinds of the stressed state. The procedure was tested under the condition of production of strongly bent branches by method of pulling of a presewn pipe. We observed satisfactory agreement between the computed and experimental data.

Determination of Plasticity for Pre-Deformed Billet

The calculation procedure for determining the plasticity of pre-deformed metals during their processing by pressure has been developed. The calculation procedure is based on a fracture model, which in turn is based on the tensor description of damage accumulation. With known mechanical characteristics, as well as with known plasticity diagrams, the fracture model makes it possible to evaluate the plasticity of pre-deformed bend for any kind of stress state. When manufacturing steeply curved branches using the pipe extrusion method, the procedure was tested. Verification of the mathematical model has shown a high level of its adequacy, and it can be used in assessing the plasticity of pre-deformed billet.

ШТАМПОВКА ЛИСТОВИХ ЗАГОТОВОК ТА СТВОРЕННЯ БЕЗПЕЧНИХ КОНСТРУКЦІЙ

The article discusses a method of stamping sheet blanks, providing variable stiffness of the structural material of the blank. A predetermined stiffness allows to improving the passive safety parameters of structural elements of a vehicle. It is proposed to obtain a controlled technological legacy of the blank by means of electrohydropulse stamping of structural elements of a vehicle. To assess the ductility of a pre-deformed metal, the methodology was used based on the tensor description of damage accumulation under conditions of cold plastic deformation. To assess plasticity of a pre-deformed metal, a methodology was used based on the tensor description of damage accumulation under conditions of cold plastic deformation. The methodology allows for known mechanical characteristics, as well as with known plasticity diagrams, evaluate plasticity of pre-deformed blanks for any type of stress state. The technology, allowing you to create safe designs, providing as a result of road traffic accidents maximum protection for the driver and passengers. This is achieved by creating structures whose strength and stiffness are controllable and predictable. Such controllability of strength and stiffness is ensured by the technological parameters of stamping. Technology parameters create a “material memory” that provides the necessary strength and stiffness. The creation of safe structures is based on a fundamentally new model for research processes collision vehicles, namely: each specific road traffic accident is considered as a unique experimental material that is used to conduct research into the process of collision vehicles. With this approach, any road traffic accident can be considered as a comprehensive test of a vehicle for the implementation of shock loading in real conditions of a specific collision, i.e. under the conditions of his field test. Then, to determine the values of the speeds of vehicles in their collision, you can use the research model, i.e. full-scale or field test. The article proposes to use the experimental-calculation method for research the mechanical properties of sheet materials, from which the structural elements of the vehicle are made. This method makes it possible to determine the strain energy that was absorbed by the structural elements of a vehicle during a road traffic accident, by the change in the hardness of these elements after a collision.

Mechanical Characteristics of Alloys of the W–Ni–Fe System

We study the mechanical properties of TNI-type (tungsten–nickel–iron) alloy with contents of tungsten and binder equal to 89 and 11wt.%, respectively, based on nickel and iron in the ratio 7:3. For this alloy, we constructed the yield curve, the plasticity diagram, and calibration hardness–stress–strain curves. On the basis of the results of mechanical tests performed under the conditions of compression, tension, and torsion, we analyze the possibility of application of the method of cold plastic deformation to this alloy.

Diagrams: Towards a plastic-conceptual representation

This paper presents three models of diagrams. Each of one shows a different way to represent a cultural view of the world. First of them, the diagram, owns a bidimensional nature and requires a logical participation. The second one, the plastic diagram or mandala, presents the inner structure of an aspect of the reality. At the same time, the plastic diagram can be understood as a double of the reality. The third model, the hologram, does not possess inner world. This last model keeps relation with a spectral world, with a virtual world. By means of its incorporeal essence, we recognize our contemporary world, our contemporary existence.

Evaluation of metal plasticity and research on the mechanics of pressure treatment processes under complex loading

A calculating apparatus has been developed to help evaluate the stress-strain state in the plastic forming processes accompanied by a complex loading in which the Bauschinger effect can be manifested. The developed methods are based on the phenomenological approach in which a material map is devised in the form of flow curves, Bauschinger curves, a function j characterizing the hereditary influence of the loading history, plasticity diagrams, and limiting strain surfaces. To evaluate the plasticity resource used, taking into account the non-monotonicity of loading, the relations for determining the main components of the guiding strain-rate tensor were obtained, which made it possible to simplify the calculation of the components of the damage tensor. With the help of the developed calculating apparatus, the applied plasticity resource was evaluated in the process of radial extrusion with the contour sag, which allowed setting the limiting parameters of the shaping. Also, as a result of the research, an increase in the plasticity of the metal was established by selecting rational loading paths in the space of the dimensionless coordinates h, m s , and e u . For example, in the process of radial extrusion with the contour sag due to a change in the nature of the deformation, it was possible to obtain a flange diameter of 44 mm, with the initial diameter of the cylindrical workpiece being 20 mm. The results obtained are important because in most cases the processes of metal pressure treatment are accompanied by non-monotonic deformation

Crack Resistance of High-Strength Steel and Breakage of a Gas Pipeline

The available methods for identifying the type of failure of a 15–20 MPa gas pipeline used to evaluate the crack resistance of X90, X100, and Х110 high-strength steels cannot reliably predict the arrest of a main crack over the length of two or three pipes. Ductile fracture mechanics is used to determine the length of the plastic zone, the stress state, rate and degree of strain, and damage of the metal at the front of a growing macrocrack. A new fracture criterion based on plasticity diagram is proposed. The new approach to the evaluation of the crack resistance of steel reduces the growth rate of the main crack to less than the decompression rate of a gas pipeline after breakage and arrest of the main crack.

Assessment of Geotechnical Properties of Lateritic Gravels from South-Cameroon Road Network

The southern road network covers the eastern, central and southern administrative regions; its linear network of national and provincial roads is about 5 620 km. It was the subject of a survey for the identification of lateritic quarries. To this effect, 144 sites have been discovered. The collected lateritic gravels were subjected to identification analyzes (Granulometry, Atterberg Limits, densimetry, water content) and geotechnical characterization tests (Proctor Modified, CBR at 95% OPM). The obtained results show that the grain size has a great percentage of gravels (>60%) followed by sand. Stones silt and clay particles are poorly represented. The samples show a high plasticity in conformity with Casagrande’s plasticity diagram. The density values of the solid particles (γ s) are quite stable in the studied area and vary between 26 and 29 KN/m3 for a natural water content comprised between 10% and 20%. The modified proctor test gives an optimal water value (Wop %) comprised between 8% and 12%. Dry density values (γ d) varied between 18 and 30 KN/m3. The bearing capacity of the materials is good (30 < CBR < 90). These results permit the recommendation of the studied materials as foundation layers of roads for traffic classes between T1-T4.

Сравнительная оценка поврежденности металла на свободной боковой поверхности при прокатке однослойных и трехслойных полос

The paper compares the stress-strain state and damage accumulation in a steel constituting a “steel 20” single-layer strip and “12Cr18Ni10Ti – steel 20 – 12Cr18Ni10Ti” and “copper M1 – steel 20 – copper M1” three-layer strips under rolling. The areas in the middle of the free lateral surface that are the most dangerous in terms of cohesive destruction are discussed. The finite el-ement method is used to simulate the rolling process. Kolmogorov’s model of damage and the relation of peak plasticity to the stress state coefficient and the Lode coefficient are used for cal-culations. The analysis of the data shows a relationship between the configuration of the defor-mation zone and metal deformability. In particular, it is better to roll strips of steel 20 in large-diameter rolls and “copper M1 – steel 20 – copper M1” strips in small-diameter rolls. When “12Cr18Ni10Ti – steel 20 – 12Cr18Ni10Ti” strips ate rolled, the diameter of rolls has no essential effect on damage accumulation in the central layer. The proposed conclusions can be used only for the materials under study, since the mechanisms of damage accumulation for specific materials may vary depending on the peak plasticity diagram.