Athermal Solid Solution Hardening in Tantalum

The influence of solute atoms on the athermal component of the flow stress, determined by means of dip-tests (incremental unloading), has been investigated at room temperature and slightly above in binary Ta-Re, Ta-Mo, Ta-W, Ta-Hf, Ta-Zr, and Ta-Nb alloys and in ternary Ta-W-Re, Ta-W-Mo, Ta-W-Hf, and Ta-W-Nb alloys. Binary athermal substitutional solid solution hardening in tantalum is linear up to high concentrations of solute and is dominated by the atomic size misfit parameter, in agreement with the authors’ recent model for binary athermal solid solution hardening in bcc metals at temperatures where the Peierls stress is still important. In this model, solid solution hardening is caused by interactions of solute atoms having a size misfit with polarity reversing kinks and constrictions in 〈111〉 screw dislocations. The observed solid solution hardening in the ternary alloys is well described by the authors’ phenomenological model for multicomponent solid solution hardening. L.A. GYPEN, formerly with the Departement Metaalkunde, Katholieke Universiteit Leuven, Belgium     

Predicting the liquidus temperature of complex nickel alloys

The production of steel and alloys ends with the casting of metal in a mold. In casting an alloy, its liquidus temperature must be known. This is especially important in developing a smelting technology for nickel alloys with a large number of alloying elements. In the present work, a model is developed for predicting the liquidus temperature of complex nickel alloys. The regression coefficients of the equations describing the liquidus and solidus lines of binary systems are determined on the basis of literature data regarding the phase diagrams of binary nickel systems with different elements. With increase in the set of data regarding the regression coefficients from 21 to 27 elements, a broad spectrum of complex nickel alloys may be covered. When the model based on data for binary alloys is tested for experimental liquidus temperatures of complex nickel alloys, the conclusion is that the model permits the prediction of the liquidus temperature of such alloys with sufficient precision for practical purposes (±19.8°C).     

Modeling for the structure evolution of alloys of the Al-Cu-Mg system during natural ageing

Natural ageing in alloys of the Al-Cu and Al-Cu-Mg systems is investigated and modeled. To determine the kinetic parameters, a method for measuring the electrical resistance is applied as the basic method. With the use of the Avrami equation in the differential form, a model for the structure evolution (changes in the volume fraction of the Guinier-Preston zones (GPZs) and the depletion of the solid solution) and the change in the yield strength for the alloys during natural ageing is constructed. In the case of the Al-Cu-Mg ternary system, two types of zones are present (the GPZ and the Guinier-Preston-Bagaryatskii zone (GPBZ)). In this case, the dissociation of the oversaturated solid solution at room temperature is described by a set of differential equations. The accuracy of the constructed model of the dependence of the yield strength on the alloy composition and the natural ageing time is 6%, which is within the error of experimental determination for this parameter.     

Microstructural evolution and transformation pathways in the near monotectic Zn rich ZnBi alloys during rapid solidification

The possible pathways for microstructural development under nonequilibrium condition by the rapid solidification of alloys containing liquid miscibility gap have been studied using ZnBi binary alloys as a model system. The primary aim is to explore the possibility of the intermediate formation of a thermodynamically unstable solid solution as a precursor phase which can spontaneously decompose to yield nanodispersions. It is shown that the information of crystallographic shape of the nanosized dispersions obtained by transmission electron microscopy and the derived point groups can be utilised to arrive at a definite conclusion of this possibility. Our results establish the formation of such a solid solution owing to the kinetic process of nonequilibrium trapping in spite of a very strong clustering tendency. The latter leads to the spontaneous decomposition of the solid solution during quenching to yield nanodispersions.     

Modeling the evolution of the structure and properties of alloys for an Al-Zn-Mg system in ageing

An investigation into and modeling of artificial ageing in alloys of an Al-Zn-Mg system are carried out. To determine the kinetic parameters of the dissociation of a supersaturated solid solution, methods of transmission electron microscopy, a measurement of electric resistance at heightened temperature, and differential scanning calorimetry are used. To describe the evolution of the structure in ageing, the Avrami equation and the ageing time dependence of the particle size are applied. A comparison between the computational and experimental values of particle sizes showed the sufficiently high accuracy of the model. Based on this, the yield strength for alloys of the system under consideration in the aged state was computed. The computational error was 11%, which is comparable with the error of the experimental determination of the yield strength.     

Temperature and compositional dependencies of normal spectral emissivities at 632.8 nm for solid Cu-Ni alloys—Ellipsometric measurements and formulation of empirical prediction equation

Normal spectral emissivities of solid Cu-Ni alloys were determined using an ellipsometer combined with an electric furnace for a wavelength of 632.8 nm in the temperature ranges between 800 K and the respective solidus temperatures. The emissivities of the alloys had slightly positive temperature coefficients and seemed to be on quadratic functions of the atomic fraction of nickel. Thermal radiation of transition metals in the visible and near-infrared regions is generally considered to stem from the excitation-relaxation processes of free electrons and inner shell electrons, i.e., electrons at the d-like levels in the Cu-Ni system. Thus, the contribution from the former to the emissivities has been calculated on the basis of the free-electron model with damping. The difference between measured and calculated values corresponds to the contribution from inner shell electrons, which has been found to depend strongly upon neither temperature nor chemical composition in the range of the nickel atomic fraction, X _Ni>0.2. On the basis of these findings, an empirical prediction equation for the emissivity at 632.8 nm for solid Cu-Ni alloys has been proposed: this equation applies at temperatures higher than 800 K in the range of X _Ni>0.2 and can predict emissivity with an uncertainty less than 13 pct.     

Strengthening mechanisms in solid solution aluminum alloys

A number of commercial and high-purity non-heat-treatable aluminum alloys are investigated in this work. It is found that both magnesium and manganese in solid solution give a nearly linear concentration dependence of the strength at a given strain for commercial alloys. This deviates from high-purity AlMg binary alloys, where a parabolic concentration dependence is found. Mn in solid solution is found to give a considerably higher strengthening effect per atom than Mg, both in terms of yield stress and initial work hardening rate. This strengthening effect is stronger comparing commercial grades to high-purity alloys. This enhanced strengthening is believed to be a synergy or clustering effect caused by interaction between Mn atoms and trace elements, probably silicon, in solid solution.     

Sub-zero Temperature Dependence of Tensile Response of Friction Stir Welded Al-Cu-Li (AA2198) Alloy

Mechanical properties at ambient and cryogenic temperatures of Al-Cu-Li alloy are required for design and fabrication of liquid hydrogen and liquid oxygen tanks of satellite launch vehicles. In the present work, bead-on-sheet, friction stir welding was carried out with three different rotation speeds. The yield and strain hardening behaviors of the welds were evaluated in temperature range of 20 K to 298 K. Both yield stress and strain hardening ability in the specimen increased with decrease in testing temperature. The dependence of yield stress on temperature was modeled on the basis of thermally activated dislocation mobility, while that of strain hardening was modeled on the temperature dependence of dynamic recovery rate parameter. The recovery parameter followed an Arrhenius-type relationship with temperature. The model parameters determined from the experimental data were further used to simulate the stress–strain curves at different sub-zero temperatures for the friction stir welds.

     

The effect of microstructure and composition on the properties of vapour quenched AlCr alloys—II. Tensile properties

The effect of chromium and iron additions and of annealing and working on the microstructure and tensile properties of vapour quenched AlCr and AlCrFe alloys has been determined. Tensile strengths of the worked AlCrFe alloys were in the range 568–831 MPa. Chromium in solid solution or iron present as iron-rich precipitates increased the yield stress by 44.7 MPa/at.%Cr and 333 MPa/at.%Fe respectively. The contributions to the yield strength of AlCr alloys were solid solution 40% and dislocation density/cell size 60% and to the yield strength of AlCrFe alloys were solid solution 25%, iron-rich precipitates 42% and dislocation density/cell size 33%. Vapour quenching may allow the more efficient use of alloying elements in the strengthening of Al-alloys and greater flexibility in obtaining the desired combination of solute concentration, particle volume fraction and particle size.     

The determination of the surface tensions of liquid iron,nickel and iron-nickel alloys using the electromagnetic oscillating droplet technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid pure iron, nickel and iron-nickel alloys as a function of the temperature. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser. The theoretical background of this method and the experimental set-up were described, and the influence of magnetic field strength was also discussed. The experimental results were compared with those of other investigators and interpreted using theoretical models (Butler's equation, subregular and perfect solution model for the surface phase).     

Copper-scandium system: Thermodynamic properties of intermetallics and liquid alloys

Thermodynamic simulation of the binary Cu-Sc system is performed for a wide temperature range using experimental data on the thermodynamic properties of solid Cu-Sc alloys. The results obtained are used to estimate the thermodynamic functions of mixing and the activities of the components and to determine the composition of melts using an ideal solution model for interaction products. The calculated enthalpies of mixing at 1873 K agree adequately with the experimental data obtained by calorimetry.     

Effect of precipitates on plastic anisotropy for polycrystalline aluminum alloys

The effects of crystallographic texture and precipitate distribution on macroscopic anisotropy in aluminum alloys were investigated. In order to simultaneously consider the effects of crystallographic texture and precipitate distribution on macroscopic anisotropy, predictions of plastic properties were carried out using an anisotropic yield function based on the material texture and a combined isotropic-kinematic hardening rule. The input to the model was a single stress-strain curve, the crystallographic texture, and the precipitate volume fraction, shape, and habit planes. It was shown that the kinematic hardening rule, which expresses a translation of the yield surface in stress space, was a function of all the parameters describing the precipitate distribution. The model was applied to the case of an extruded and recrystallized binary Al-3 wt pct Cu alloy deformed in uniaxial compression in different directions. Excellent agreement was observed between the experimental and predicted yield stress anisotropy and the specimen cross section shape anisotropy. Gaussian distributions of grain orientations around ideal texture components typical of aluminum alloys were generated using computer simulations. These textures were combined with the isotropic-kinematic hardening rule determined for the Al-3 wt pct Cu binary alloy to theoretically assess the influence of precipitates on the r-value (the width-to-thickness plastic strain ratio in uniaxial tension) and yield stress anisotropy for aluminum sheets. It was shown that, for these textures, the precipitate distribution had the effect of reducing plastic anisotropy, in agreement with the trends generally observed in practice.     

The temperature independent plateau stress of solid solution crystals

A calculation of the plateau stress in solid solution crystals is presented assuming an arbitrarily oriented dislocation loop of lengthL, that moves under an applied stress. At high concentrations of solute atoms the dislocation segment does not interact with an individual solute atom but instead with all the solute atoms along the dislocation segment within a certain radius. The macroscopic flow stress is assumed to be determined by the maximum force that is encountered when a dislocation is moved over a distance equal to the distance between the position at zero stress and the critical position of an activated Frank-Read source. If the dislocation segment is assumed to be large compared to atomic distances, the interaction with groups of atoms will lead to an athermal process and therefore can explain the origin of the temperature independent flow stress in solid solution crystals. From this model the flow stress can be calculated with the help of statistical methods similar to those used in calculations of the movement of Bloch walls in magnetic materials. Besides the proper temperature dependence of the plateau stress the above model yields a dependence of the plateau stress upon the square root of the solute concentration, a result that is in good agreement with the measurements on silver, gold, and copperbased alloys. A linear relation between the solid solution hardening parameter dT/d√c and the strength of the solute atoms is obtained which is confirmed by the experimental results on copper-based alloys.     

Steady state creep in two Ni-Al alloys

Creep of two Ni-AI alloys containing 4.8 and 7.0 wt pct Al was studied in the temperature range 873 to 1073 K and stress range 30 to 400 MPa. The former alloy represents the solid solution of aluminum in nickel, the latter a solid solution strengthened by NI3AI particles. As to its creep behavior the solid solution alloy belongs to the Class n of solid solu-tions,i.e. the creep controlling mechanism is the same as in pure nickel. From the analy-sis of an effective stress dependence of steady state creep rate it follows that the mo-tion of jogged screw dislocations can be considered as the most probable creep control-ling mechanism. The apparent activation energy of creep in the two phase alloy increases with tempera-ture. This effect is caused by changes in the volume fraction of second phase particles and by the onset of climb around particles at high temperatures. At lower temperatures particles are cut by dislocation pairs.     

Thermodynamic properties of solid alloys of chromium with nickel and iron

The thermodynamic properties of chromium have been determined in the Ni-Cr and Fe-Cr binary systems and in the Fe-corner of the Fe-Ni-Cr system. These properties are based on experimental measurements using solid oxide electrolyte cells of the type: Cr, Cr₂O₃ I ThO₂-Y₂O₃Cr (alloy), Cr₂O₃. In the Ni-Cr system, between 900 and 1300°, the activity of chromium exhibits negative deviation from ideality up to about 25 at. pct chromium. For alloys higher in chromium content, the activity of chromium exhibits positive deviation from ideality. In the Fe-Cr system, between 900 and 1200°, and 0 and 63 at. pct Cr, the chromium activity when referred to solid pure chromium exhibits positive deviation from ideality in both the γ and α phases, approaching ideality with increasing temperature. The nickel and iron activities in these two respective binary systems were calculated by a Gibbs-Duhem integration. The activity of chromium, referred to solid pure chromium, was measured between 900 and 1200° in solid Fe-Ni-Cr alloys with chromium concentrations of 9, 20, and 30 at. pct and Ni concentrations of 8, 18, and 30 at. pct. Additions of nickel to Fe-Cr alloys in the above concentration range are found to increase the chromium activity. The effect of nickel in increasing the chromium activity is greater at both greater chromium contents and lower temperatures. Formerly Graduate Student at The University of Michigan, is Staff Associate, Gulf Energy and Environmental Systems, LaJolla, California. This paper is based on a portion of a thesis submitted by F. N. MAZANDARANY in partial fulfillment of the requirements for the degree Doctor of Philosophy at The University of Michigan.     

Growth kinetics of dispersed thoria in Ni and Ni-Cr alloys

The growth rates of dispersed thoria particles in nickel have been measured as a function of time at 1350°C in gases of two separate oxygen partialpressures. Samples were prepared for electron microscopic study after these treatments for particle size distribution measurements. The diffusion coefficient and solubility of thorium in nickel placed in contact with thoria were also determined under the same conditions. The results of the measurements then provide the necessary information for the elucidation of the kinetics of Ostwald ripening in the ThO₂-Ni system. A linear relationship was found between the cube of the mean radius of the dispersed particles and the time at temperature. Substitution of the experimental results into the Lifshitz-Wagner equation for particle growth under diffusion control yielded values of the ThO₂-Ni solid-solid interfacial energy, which are in good agreement with what is expected by comparison with the corresponding solid oxide-liquid metal interface. Further studies were made of the coarsening of thoria in 20 pct Cr-Ni alloys. It was found that the enhanced rate of particle growth could be accounted for by the increased value of the diffusion coefficient of thorium in the alloy over the value in pure nickel.     

Yield behavior of commercial Al-Si alloys in the semisolid state

Systematic experimental work and modeling efforts have been conducted to characterize the yield behavior of commercial aluminum alloys in the semisolid state. In this study, extensive compression experiments were performed to measure the yield stress of semisolid aluminum slurries at high solid fractions (0.5 to 1.0), and a cone penetration method was employed to measure yield stress at low solid fractions (<0.5). A functional relationship between yield stress and temperature/solid fraction has been established for these alloys. The effect of the processing route on the resultant yield stress of the material in the semisolid state was studied by evaluating commercial A356 billets manufactured via magnetohydrodynamic stirring, grain refining, and UBE’s new rheocasting (NRC) processes, respectively. Detailed microstructure observations and image analyses reveal that the difference in yield-stress values among the alloys evaluated is intricately related to the semisolid structure. At a given solid fraction, the yield stress of semisolid slurries depends on microstructural indices (i.e., entrapped-liquid content, shape factor of the alpha phase, and the alpha particle size). In addition, numerical simulation results indicate that the finite yield stress of semisolid metals plays a significant role in determining the flow pattern during die filling. Depending on processing conditions, five distinct filling patterns (shell, disk, mound, bubble, and transition) have been identified and confirmed through experimental observations. Recent simulations demonstrate that the finite yield stress is also responsible for flow instabilities encountered in commercial forming operations, such as “toothpaste behavior.” Specifically, most flow instabilities can be avoided by properly controlling processing parameters and the initial semisolid microstructure. A stability map that provides a control guide for semisolid processing has been developed and is presented.     

Critical Driving Forces for Formation of Bainite

An empirical equation for predicting bainite start temperatures of steels was recently derived by starting from binary Fe-C alloys and continuing with ternary Fe-C-M alloys. This result is now illustrated with a family of B_S lines in a T,C diagram for a series of constant Mn contents. The critical driving force for the formation of ferrite is calculated for diffusionless or diffusional processes, and these quantities are used as dependent variables with carbon content or temperature as independent variables. Negative critical driving forces are predicted for a diffusionless process in binary Fe-C alloys, showing that this process cannot apply to the formation of bainite. The critical driving force for a diffusional process increases strongly with decreasing temperature and increasing carbon content. Mn and Ni, contrary to Cr, Mo and Si, have remarkably small effects on this critical driving force. The results are discussed by imagining that the magnitude of the critical driving force is governed by the height of an energy barrier that must be surmounted during growth. It is modeled as completely determined by the alloy composition. It is represented with an equation evaluated by fitting to the recent empirical equation and describing the carbon dependence of the barrier.