Stages Of Strain Hardening Research Articles

Plastic strain localization and necking in Zr-Nb alloy

Plastic strain macrolocalization at the parabolic stage of strain hardening in Zr-1 wt% Nb alloy is studied. The plastic flow is found to be unstable, which shows up as the oscillatory periodic space-time variation of the local strain distribution. The results are discussed in terms of a synergetic model of plastic flow evolution.

Use of a magnetic method for estimating the deformation stability of retained austenite in sheet high-strength economically alloyed steels used in the automotive industry

A comparative analysis of a magnetic method and X-ray diffraction analysis used for estimating the volume fraction of retained austenite in a sheet high-strength economically alloyed steel (applied in the automotive industry), which was subjected to uniaxial tension at different temperatures (+20)–(−40°C) until the onset of the strain-hardening stage, is performed. At a low austenite content (<5–8 vol %), the advantage of the magnetic method for estimating the deformation stability of austenite in these steels is shown.

Assessment of the constitutive properties from small ball punch test: experiment and modeling

An assessment of the true stress–true strain relationship has been done by means of tensile and small ball punch tests on austenitic and tempered martensitic steel at room temperature. A finite element model was developed and validated to calculate the force–deflection curve obtained from the ball punch experiment. The effects of the specimen thickness and material properties on the overall shape of the ball punch test curve are discussed. The constitutive behavior assigned to the specimen for the calculations was determined from the tensile test but we showed that assumptions have to be done to extend it to large strains as those arising during the punch tests. Using an inverse methodology, it was possible to show that a linear strain-hardening stage takes place at large strains. The potential for evaluating the evolution of the strain-hardening capacity after irradiation is outlined.

Current pattern of plastic deformation stages

A review of current concepts of strain hardening stages in metallic materials upon active deformation is presented. By now, five stages of the stress (σ) — strain (e) dependence reliably have been identified. These stages differ by the strain hardening coefficient θ = dσ/de. There are also some data on stage VI. In the paper, the role of substructural transformations in the change of strain hardening stages is discussed, the factors complicating the deformation stage pattern are analyzed, and the effect of grain size on stages of strain hardening is examined.

Analyses of behavior of stress–strain of frozen Lanzhou loess subjected to K0 consolidation

To determine the behavior of stress–strain of frozen soil in the deep alluvium, the axial loading or radial unloading triaxial shear tests were performed at temperature of −2, −5, −7 and −10 °C under the initial confining pressure of 1–5 MPa after specimens of Lanzhou loess experienced K 0 consolidation. Results indicate that both the axial loading and the radial unloading stress–strain curves can be divided into three stages: the elastic stage, the strain-hardening stage, and the yield stage (or the flow stage). The failure strength was increasing with increase of initial confining pressure and decrease of temperature. For the radial unloading triaxial test, there is no displacement at a lower negative temperature and somehow a higher initial confining pressure, even if the confining pressure is removed to zero. The ultimate deviator stress and the initial tangent modulus can be obtained from the stress–strain equation established by tested frozen soil. It is found that the initial tangent modulus determined by the axial loading tests increased linearly with an increase of the initial confining pressure but was not pronounced to temperature. Differentially, the ultimate deviator stress was linearly increasing with increase of the initial confining pressure and decreasing with increase of the temperature. The unloading triaxial test shows that the initial tangent modulus was close to a constant at a state of lower negative temperature and higher initial confining pressure, without a relation to the initial confining pressure. The ultimate deviator stress was linearly increasing with increase of the initial confining pressure, while the temperature plays a less obvious role at a condition of lower initial confining pressure. In contrast, the effect of temperature was gradually pronounced with increase of the initial confining pressure.

Dispersion of the plastic strain localization waves

The main laws of the macroscopic localization of plastic straining in a bcc alloy Fe-3% Si on the stage of linear strain hardening are considered. It is established that the strain localization exhibits a wave character and the velocity of propagation of the strain localization wave is determined. The law of dispersion of the waves of localized plastic straining is found for polycrystalline aluminum and for iron-based alloys in both single crystal and polycrystalline states.

Caractérisation de l'état de contraintes des alliages ferromagnétiques doux par mesure de leurs propriétés magnétiques : bruit Barkhausen et hystérésis magnétique

This study is in line with the issue of the non destructive evaluation of the mechani- cal state of the ferromagnetic alloys by using magnetic measurements. Both Barkhausen noise and B-H hysteresis loops were measured in situ under a loading-unloading uniaxial tensile test, for a non-oriented Fe-3%Si steel and a high-purity nickel. The different stages of the tensile deformation (perfectly elastic stage, microplastic yielding stage, the two strain-hardening stages) were clearly identified by the magnetic parameters. Furthermore, a linear relationship was found between the magnetic properties and the kinematic hardening X, representative of the long-range internal stresses state.

Magnetic behaviour versus tensile deformation mechanisms in a non-oriented Fe–(3 wt.%)Si steel

This study presents an extended in situ magnetic characterisation of a non-oriented (NO) Fe–(3 wt.%)Si steel. An appropriate experimental device was created and magnetic measurements were performed under uniaxial tensile stresses approaching and exceeding the macroscopic elastic limit σ e and in the corresponding unloaded states. Both Barkhausen noise and B–H hysteresis loops were measured. The sensitivity to stress was found to be qualitatively similar to that of polycrystalline iron. The different stages of the tensile deformation (perfectly elastic stage, microplastic yielding stage, the two strain-hardening stages) were clearly identified by the magnetic parameters. In the plastic strain domain, the coercive field H c and the inverse of the initial relative permeability 1/ μ r i linearly increase, while the maximal relative permeability μ r max and the Barkhausen noise peak height BN max linearly decrease with the applied stress σ. The remnant induction B r keeps a low and constant value. Furthermore, a linear dependence of 1/ μ r i, H c, μ r max and BN max on the kinematic hardening X was found. By using measurements on prestrained specimens under reloaded elastic stresses, an accurate identification of the effect of dislocations acting as pinning sites and of the magnetoelastic effect of long-range internal stresses was proposed.

A mechanical degradation index for rock

A unified strain-hardening and strain-softening (UHS) elastoplastic constitutive model is developed to capture the nonlinearity of intact rocks. Three new developments are incorporated into the model: (i) a unified strain-hardening and strain-softening rule, which is used to describe the nonlinearity of the stress–strain curve; (ii) the cohesion loss model, which can describe the nonlinearity of the residual strength; and (iii) normalized plastic shear strain, which is adopted as the plastic internal variable. There are 15 model parameters. All of them can be easily obtained by uniaxial compression tests and triaxial tests under different confining pressures. The proposed model has been implemented in FLAC3D and validated against five different types of rocks. The results show that the model can capture the nonlinearity of the stress–strain curve, including both the strain-hardening stage before the peak strength and the strain-softening at the post-peak stage. The model is also able to describe the effects of the confining pressure on the peak strength, residual strength and stress–strain curve. Moreover, the transition from brittle failure to ductile failure under high confining pressure can be well described.

Phenomenology of wave processes in a localized plastic flow

The motion of localized deformation sites in mono-and polycrystallites of metals and alloys is investigated experimentally at the stages of easy slip and linear strain hardening. The wave nature of localization of deformation at these stages of plastic flow is established, and the velocity of waves and their dispersion relation are determined. The scale effect and the dependence of the localized deformation wavelength on the grain size are investigated. A qualitative interpretation of the results obtained is proposed.

On the constitutive behavior of the F82H ferritic/martensitic steel

This paper focuses on the constitutive behavior of the F82H ferritic/martensitic steels internationally investigated in the frame of the fusion material development program. Tensile tests were carried out in the temperature range (80–723 K) at different strain rates. A decomposition of the flow stress into a yield stress plus a hardening stress component is proposed. The temperature, strain and strain rate dependence of the stress is discussed based on the current available data. The strain-hardening is calculated and two strain-hardening stages are identified along the deformation curves between the yield stress and the necking instability. Finally, semi-empirical constitutive relations, which are partly based on dislocation mechanics, are derived.

Reconstruction of the autowave structure upon deformation of polycrystalline aluminum

The evolution of zones of localized plastic deformation in polycrystalline aluminum was investigated. At the stage of the linear strain hardening, such zones were established to move synchronously, whereas at the stage of parabolic strengthening they are stationary. The quantitative characteristics (wavelength, propagation velocity) of deformation waves that are formed at the stage of linear strengthening were determined. A relation between the quantitative characteristics of the process of deformation localization and the grain size was found. The distribution of local deformations upon transition from one stage of plastic flow to another was investigated. A model that explains the generation of coarse-scale structures of localized plastic deformation is suggested.

Effects of Punch Test Conditions on the Mechanical Response of Polyethylene Materials

Polyethylene (PE) materials have been widely used in industrial and living fields such as natural gas pipelines, drainage pipes, sewage pipes. Punch test is an interesting tool for studying the mechanical properties of materials. However, the deformation behavior involved in punch test is complicated, it is, therefore, essential to investigate the influence of punch test conditions on the mechanical properties of PE materials. Punch tests have been carried out on PE specimens with different punching speed (0.01, 0.1, 1, 10 and 100mm/min) and different punch head diameters (4, 6, 8 and 10mm). The experimental results show that the maximum load from the load-displacement curve increases with the increase of the punch head diameter under the same punch speed. When the punch speed is slow, the force-displacement curve of PE specimens contains four typical stages, namely, elastic stage, yield stage, strain softening stage and strain hardening stage. However, the PE specimen breaks before reaching the strain hardening stage when the punch speed is fast. Similarly, the maximum load increases with the increase of punch speed when the same punch head diameters are used. Furthermore, a three-dimensional finite element (FE) model of PE specimens subjected to punch load has been established to further analyze the deformation and failure behavior. A good agreement between the simulation results and the punch test data is achieved.

Mechanoelectrochemical Behavior and Plasticity of Magnesium Alloys

The mechanical properties and mechanoelectrochemical effect (the effect of mechanical deformation on the surface electrochemical reactions) were investigated for some Mg-based alloys supposing that aluminum alloying influences them. A simple method of testing mechanoelectrochemical behavior of metals was developed. Potentiostatic polarization measurements on stressed electrode were carried out in chloride electrolyte. The correlation between the mechanoelectrochemical behavior and strain hardening stages is observed during plastic deformation. Maximum mechanoelectrochemical effect is achieved under intense strain hardening in the initial portion of this stage. The experimental observations are explained theoretically.

Strain hardening regimes and microstructural evolution during large strain compression of low stacking fault energy fcc alloys that form deformation twins

Constant true strain rate simple compression tests were conducted on annealed, polycrystalline samples of α-brass and MP35N, and the evolution of the true stress (σ)-true strain (e) response was documented. From these data, the strain hardening rate was numerically computed, normalized with shear modulus (G), and plotted against both (σ − σ 0)/G (σ0 being the initial yield strength of the alloy) and e. Such normalized plots for α-brass and MP35N were found to be almost identical to each other, and revealed four distinct stages of strain hardening: stage A, with a steadily decreasing strain hardening rate up to a true strain of about −0.08; stage B, with an almost constant strain hardening rate up to a true strain of about −0.2; stage C, with a steadily decreasing strain hardening rate up to a true strain of about −0.55; and a final stage D, again with an almost constant strain hardening rate. Optical microscopy and transmission electron microscopy (TEM) were performed on deformed samples. The results suggested that stage A corresponded to stage III strain hardening (dynamic recovery) of higher stacking fault energy (SFE) fcc metals such as copper. The onset of stage B correlated with the first observation of deformation twins in the microstructure. Further straining in stage B was found to produce clusters of parallel twins in an increasing number of grains. Stage C correlated with the development of severe inhomogeneity of deformation within most grains, and with the development of significant misorientation between the twin/matrix interface and the {111} plane in the matrix of the grain, i.e., the matrix/twin interface lost coherency with continued deformation. Stage D correlated with extensive formation of secondary twins that resulted in twin intersections in many grains. Early in stage D, some strain localization in the form of shear bands was observed. Although formation of these shear bands had no detectable effect on the macroscopic strain hardening rate, it did correlated with a marked change in texture evolution. Based on these experimental observations, we have developed and presented a physical description of the microstructural phenomena responsible for the various strain hardening stages observed in low SFE fcc alloys.

Metal surface charge change due to deformation

Deformation potential for one dislocation and dislocation pile-up in a thin surface layer was examined. It is shown that the deformation potential changes the electron work of exit, the surface charge of metal and the structure of the double electrochemical layer. The differential capacity method was used as the principal method of measuring the metal surface charge. The plastic strain increases the positive charge of the metal surface. This effect reached a maximum according to successive stages of strain hardening. The zero-charge potential of the metal surface was shifted towards negative values by the amount of the deformation potential, with the formation of an internal double layer in the metal. For example, this shift achieved the value of −0.16 V in the case of iron in 0.1 N H2SO4.

Verformter Zustand und Rekristallisationswärme tieftemperaturtordierter hochreiner Aluminiumsorten

Using aluminium samples of varying purity (99.99; 99.999; 99.9999) deformed by torsion under liquid nitrogen at 183 K, 253 K and 300 K, respectively, up to the strain hardening stages IV and V, the energy release during primary recrystallization was studied by heating up in a low temperature calorimeter. The essential results are as follows: the flow curves show four hardening regions which are typical for fcc polycrystalline metals. The curves shift to lower flow streses with increasing purity and deformation temperature

An exact elasto-plastic solution for a thick-walled spherical shell of elastic linear-hardening material with finite deformations

An exact elasto-plastic analytical solution for a finitely deformed internal-pressurized thick-walled spherical shell made of elastic linear-hardening material is derived in this paper. This solution is based on the notion of finite strains, the deformation theory of Hencky, the yield criterion of von Mises and the assumption of incompressibility. Being applicable for both the linear-elastic response and the plastic strain-hardening stages of a finitely deformed thick-walled spherical shell, the present solution can uniformly represent the whole expanding process of the shell from its initial yield at the inner surface to its full yield over the wall up to its ultimate bursting with the increase of its operating pressure. It is shown that this exact solution is of general characteristics, from which three specific solutions of practical interest can be obtained. The calculation formulae for the full-yield pressure and the bursting pressure of the finitely deformed spherical shell deduced in this paper are of value for the strength design of a strain-hardening material spherical shell. Being expressed in terms of Lagrangian variables, the explicit expressions of the solution are convenient for engineering use. The present exact solution together with the deduced formulae furnish a new analytical pattern for the elasto-plastic analysis and strength design of a finitely-deformed, internal-pressurized, thick-walled spherical shell made of strain-hardening material.

An exact elasto-plastic solution for a closed-end thick-walled cylinder of elastic linear-hardening material with large strains

An exact elasto-plastic analytical solution for a large-strained internal-pressurized thick-walled cylinder made of elastic linear-hardening material is derived in this paper. This solution is based on the notion of finite strains, the deformation theory of Hencky and the yield criterion of von Mises. Being applicable for both the linear-elastic response and the plastic strain-hardening stages of a large-strained closed-end thick-walled cylinder, the present solution can uniformly represent the whole expanding process of the cylinder from its initial yield at the inner surface to its full yield over the wall up to its ultimate bursting with an increase of its operating pressure. It is shown that this exact solution is of general characteristics, from which three specific solutions of practical interest can be obtained. The calculation formulae for the full-yield pressure and the bursting pressure of the large-strained cylinder deduced in this paper are of value for the strength design of a strain-hardening material cylinder. The present exact solution together with the deduced formulae furnish a new analytical pattern for the elasto-plastic analysis and strength design of a large-strained, internal-pressurized, closed-end, thick-walled cylinder made of strain-hardening material.

Structural and mechanical aspects of high temperature deformation of polycrystalline nickel

AbstractThe mechanisms of dynamic recrystallisation of nickel have been analysed by carrying out compression tests over a wide range of temperatures and strain rates and by examining the microstructures using optical and transmission electron microscopy. Under all deformation conditions, the true stress–true strain (σ–ɛ) curves display a typical maximum corresponding to dynamic recrystallisation, followed by a steady state flow. A correlation is shown to exist between the global strain hardening rate during high temperature straining (region of dynamic recrystallisation) and the microstructural features. Before the flow stress peak, commonly assumed to be the result of dynamic recrystallisation, two stages of strain hardening are observed, corresponding to a homogeneous (the higher hardening rate) and a heterogeneous mode of deformation, respectively. It is demonstrated that observable strain localisation takes place through the conversion of deformation bands from micro- to macrodimensions, a process whi...