Hyperbolic Sine Constitutive Equation Research Articles

Influence of Initial Microstructure on Rheology of Al-Zn-Mg-Cu Alloy during Thermal Compression

The rheological behavior of two kinds Al-Zn-Mg-Cu aluminum alloy with different extrusion ratio was studied by thermal compression in 300°C~450°C and in strain rate range of 0.01 s-1~10s-1 on Gleeble1500D simulator. The results show that: (1)the flow stress increases with deSuperscript textcreasing deformation temperature and increasing strain rate, and the initial microstructure influence the rheological behavior, the flow stress with fine grain is higher than that with coarse one except in strain rate 0.01s-1 and 0.1s-1 in 450°C owing to deformation easily with more grain boundary sliding in high temperature and low strain rate.(2)The flow stress of Al-Zn-Mg-Cu aluminum alloy during hot compression can be expressed as hyperbolic sine constitutive equation with Arrhenius parameter, the apparent steady state activation energy for hot compression with coarse grain is of 181.51kJ/mol, while that with fine grain is of 203.02kJ/mol.(3) The apparent steady state activation energy decreases with increasing temperature and strain rate, and the value of fine initial microstructure is higher than the low extrusion ratio rod commonly.

Study on Hot Deformation Behavior and Processing Maps of Cu-0.35Cr-0.15Zr Alloy

The hot deformation behavior of Cu-0.35Cr-0.15Zr (wt.%) alloy was investigated by hot compression tests using a Gleeble-1500D thermal simulator system. The tests were performed under the conditions of 700°С- 820°С temperature and 0.01-10s-1strain rate. The results show that the flow behavior of the studied alloy could be described by the hyperbolic sine constitutive equation, and an active energy of 597.53 kJ/mol was calculated. The processing maps were obtained and analyzed according to the dynamic materials model. The optimum processing parameters of hot deformation of this alloy in the range of this experiment can be attained by the maps. The hot deformation temperature was 800-820°C and the strain rate was 0.01-0.1s-1.The instability zones of flow behavior can also be recognized by the maps.

Development of constitutive relationship model of Ti600 alloy using artificial neural network

Constitutive equation which reflects the highly non-linear relationship of flow stress as function of strain, strain rate and temperature is a necessary mathematical model that describes basic information of materials deformation and finite element simulation. In this paper, based on the compression experiment data obtained from Gleeble-1500 thermal simulator, the prediction model for the constitutive relationship existed between flow stress and true strain, strain rate and deformation temperature for Ti600 alloy has been developed using back-propagation (BP) neural network method. A comparative evaluation of the traditional regression method and the trained network model was carried out. It was found that the established network model can not only predict flow stress better than the traditional hyperbolic sine constitutive relationship equation but also describe the whole deforming process for Ti600 alloy. Moreover, the ANN model provides a convenient and effective way to establish the constitutive relationship for Ti600 alloy.

Hot workability characteristics of magnesium alloy AZ80—A study using processing map

The deformation behavior of as-cast AZ80 alloy is investigated by compression test with gleeble-1500 thermal simulator. The tests are performed in the temperature range of 200–500 °C and the strain rate of 0.001–20 s −1. It is found that the flow stress behavior is described by the hyperbolic sine constitutive equation in which the average activation energy of 154.6 kJ/mol is calculated. Through the flow stresses behavior, the processing maps are calculated and analyzed according to the dynamic materials model. In the processing map the variation of the efficiency of the power dissipation is plotted as a function of temperature and strain rate. The maps exhibit a domain of dynamic recrystallization (DRX) occurring at the temperature range of 420–500 °C and in the strain rate range of 10 −3 s −1 to 10 −2 s −1 which are the optimum parameters for hot working of the alloy. The instability zones of flow behavior can also be recognized by the maps.

Effect of Dislocation Mechanisms during Extrusion of Nanostructured Aluminum Powder Alloy

Nanostructured Al-3.0Fe-0.42Cu-0.37Mn powder alloy was deformed by extrusion over a temperature range of 375 °C to 425 °C, a ram speed range of 1 to 30 mm/s, and an extrusion rate of 10:1. Flow stresses and strain rates were calculated from the experimental ram pressures and speeds. The stress–strain-rate–temperature relationship in the extrusion of the nanostructured alloy was found to be similar to that in hot-worked conventional materials. The extrusion, torsion, compression, and creep data of nanostructured and conventional materials, extending over ten orders of magnitude of strain rate and over two orders of magnitude of stress, were correlated by a hyperbolic-sine constitutive equation, because the power and exponential laws lose linearity at high and low stresses, respectively. The hyperbolic-sine equation is widely used to correlate the hot-working behavior of conventional materials. It was concluded that the hot working of nanostructured powders is a thermally activated process in which the rate-controlling mechanism is the climb of edge dislocations. Microstructural changes in the consolidated alloys as a function of the extrusion conditions were investigated. An analysis was made of the dislocation behavior in very small grains of nanostructured metal by transmission electron microscopy (TEM) and we identified a dislocation structure and the different ways it appears in 40- to 100-nm Al-alloy grains. We also discuss the thermally activated propagation of dislocations and their interactions with shear bands/grain boundaries (SBs/GBs), and dislocation loops. Microstructural features including low-angle GBs, high-angle GBs, and equilibrium GBs and subgrain boundaries were observed. Dislocation structures under a deformation condition were studied to investigate the microstructural evolutions, which revealed some unique microstructural features such as dislocation tangle zones (DTZs) and dense-dislocation walls (DDWs), and the recovery process is discussed herein.

Strain-dependent constitutive analysis of three wrought Mg-Al-Zn alloys.

The commonly used hyperbolic sine constitutive equation for metal forming at elevated temperatures, with no strain incorporated, is in principle applicable only to deformation in the steady state. However, the actual deformation processes applied to magnesium alloys are mostly in the non-steady state. In the present research, the results of hot uniaxial compression tests of three wrought magnesium alloys covering wide ranges of temperatures and strain rates were used for a strain-dependent constitutive analysis. A strain-dependent constitutive relationship for these alloys was established. It appeared that the apparent activation energy for deformation decreased with increasing the alloying content in these alloys. The constitutive parameters obtained were used to predict flow stresses at given strains and the results were in good agreement with experimental measurements.

Hot Deformation Microstructure and Mechanism of Ti53311S Titanium Alloy

Abstract The hot deformation behavior of Ti53311S titanium alloy in the temperature range of 880–1080 °C and strain rate range of 0.001-10 s −1 have been studied by hot compressive testing on a Gleeble-1500 simulator. The flow behavior was described by the hyperbolic sine constitutive equation, the activation energies in (α+ β ) region and in β region were calculated as 641 kJ/mol and 244 kJ/mol, respectively. The microstructure of Ti53311S was observed and analyzed using an optical microscope. The experimental results show that this alloy is sensitive to deformation temperature and strain rate, and the strain rate sensitivity exponent values ( m ) decreases with increasing of deformation temperature while the deformation activation energy ( Q ) increases. The leading deformation mechanism in the single phase β region is dynamic recover, while that in (α+ β ) region is grain boundary slipping and grain globularizing.

A New Integration Method Proposed for Hyperbolic Sine Constitutive Equation Used in Semi-Solid Forming

This paper describes a new integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.

Constitutive relationships for AlZnMg, AlZnMgCr, and AlZnMgZr alloys

The effects of zinc, magnesium, chromium, and zirconium on the steady-state flow stress during hot working of both as-cast and homogenized AlZnMg(Cr/Zr) alloys were determined by means of torsion testing. The equivalent strain rates varied between 0.01/s and 10/s and the temperatures ranged from 450°C to 560°C. The zinc and magnesium concentration varied from 4.5 to 7.5 wt pct and from 0.8 to 1.8 wt pct, respectively. In addition, alloys containing typically 0.15 wt pct zirconium or 0.20 wt pct chromium were investigated. Magnesium, zirconium, and chromium were found to increase the flow stress, whereas zinc had practically no effect. The flow stress in the homogenized material was in most cases higher than in the as-cast material. Fitting of the coefficients in the hyperbolic sine constitutive equation of the experimental results showed that some of the coefficients could be related to concentrations of magnesium and zinc in solid solution, whereas others might be regarded as constants. The following relationship was determined between the coefficients α andn and the magnesium and zinc concentration: α=a·[Mg] b andn=c·[Mg] d +e·[Zn]+f. The coefficientsa, b, c, d, e, andf were determined by fitting of these relationships to the experimental data. The steady-state flow stress calculated by means of the constitutive equations was in good agreement with the experimental steady-state flow stress.

Hot Workability of High Strength 6060 Alloy

The alloy with 0.4% Mg and 0.5% Si was torsion tested in the range 0.1 to 10 s-1 and 300 to 500°C with exhibition of excellent ductility. The hot strength was shown to be low compared to other 6000 series alloys and to have little tendency to dynamic precipitation. The hyperbolic sine constitutive equation was optimized with a stress multiplier of 0.03 MP a -1 .

Computer simulation of impression creep using the hyperbolic sine stress law

Impression creep of materials obeying the Eyring hyperbolic sine constitutive equation is simulated by finite element analysis using the ABAQUS program. It turns out that the impression velocity is also a hyperbolic sine function of the punching stress (the applied load divided by the contact area) and if the punching stress is divided by 3.5 to change to the tension/compression flow stress, the activation shear strain volume calculated from the impression test is the same as that obtained from the tension test. For the same punching stress, the impression velocity is proportional to the punch radius, which is also found in the computer simulation using the power law constitutive equation and by dimensional analysis for both constitutive equations. The present results support the analysis of experimental data of SnPb eutectic alloys reported previously.