Characterization and modeling of the high temperature flow behavior of aluminum alloy 2024

Isothermal flow curves were determined for aluminum alloy 2024-0 at temperatures of 145 to 482 °C and at constant true-strain rates of 10^-3 to 12.5 s^-1 using compression tests of cylindrical specimens. The average pressure was corrected for friction and for deformation heating to determine the flow stress. At 250 °C and above, the isothermal flow curves usually exhibited a peak followed by flow softening. At 145 °C the flow curves exhibited strain hardening. For 250 °C≦ T<= 482 °C, 10^-3 s^-1 ≦ ≦ 12.5 s^-1, and ε ≦ 0.6 the flow behavior was represented by the constitutive equation σ =K (T, ε) where logK andm are simple functions of temperature and strain. The as-deformed microstructures generally supported the idea that flow softening in Al 2024-0 is caused by dynamic recovery. At the higher temperatures and strain rates, however, fine recrystallized grains were observed in local areas near second phase particles and at as-annealed grain boundaries. At 482 °C, there was evidence of re-dissolution of the CuMgAl₂ precipitate. Formerly Visiting Associate Professor, Wright State University, Dayton, OH 45435 Formerly a Mechanical Systems Engineering Student at Wright State University Formerly a Materials Engineering Student at Wright State University Formerly Director, Metallurgy Program, National Science Foundation, Washington, DC     

Shear ligament phenomena in Fe3Al intermetallics and micromechanics of shear ligament toughening

The environment-assisted cracking behavior of a Fe₃Al intermetallic in an air moisture environment was studied. At room temperature, tensile ductility was found to be increased with strain rate, from 10.1 pct at 1×10⁻⁶ s⁻¹ to 14.3 pct at 2 × 10⁻³ s⁻¹. When tensile tests were done in heat-treated mineral oil on specimens that have been heated in the oil for 4 hours at 200°C, ductility was found to be recovered. These results suggest the existence of hydrogen embrittlement. Shear ligaments, which are ligament-like structures connected between microcracks, were observed on the tensile specimens. They undergo ductile fracture by shearing and enhance fracture toughness. This toughness enhancement (represented byJ _l ) was estimated by a micromechanical model. The values of the unknown parameters, which are the average ligament length , the area fractionV _l , and the work-to-fractureτ ₁ γ ₁, were obtained from scanning electron microscopy (SEM) observation. The total fracture toughnessK _c andJ _l were reduced toward a slower strain rate. The experimental fracture toughness,K _Q , was found to be increased with strain rate, from 35 MPa at 2.54×10⁻⁵ mm·s⁻¹ to 47 MPa at 2.54×10⁻² mm·s⁻¹. The fact that strain rate has a similar effect onK _Q andK _c verifies the importance of shear ligament in determining fracture toughness of the alloy. With the presence of hydrogen, length and work-to-fracture of the shear ligament were reduced. The toughening effect caused by shear ligament was reduced, and the alloy would behave in a brittle manner.     

Structural superplasticity at higher strain rates of hypereutectoid Fe-5.5Al-1Sn-1Cr-1.3C steel

A fine-grained ultra-high-carbon steel—UHC steel—containing 1.35 wt pct carbon, 5.5 wt pct aluminum, 1 wt pct tin, and 1 wt pct chromium exhibits fine-structure superplasticity in the temperature regime between 775 °C and 900 °C at higher strain rates up to 10⁻² s⁻¹. Thermomechanical processing was performed in order to achieve a fine-grained equiaxed microstructure consisting of κ-carbides of about 0.7 to 2.5 μm in size finely distributed within the ferritic Fe(Al, Sn, Cr) solid solution matrix with a linear intercept grain size of 3 to 5 μm. Superplasticity occurred in the strain rate regime of 10⁻⁴<- ≤10⁻² s⁻¹ with m values of 0.5 to 0.6 (stress exponent n=1.6 to 2). Tensile elongations of more than 900 pct were recorded. From thermal activation analysis, activation energies of Q=230 to 243 kJ/mole were determined, which clearly reveal a contribution of the alloying elements Al and Sn to the lattice diffusion of iron. The governing deformation mechanism is grain boundary sliding accommodated by dislocation climb controlled by lattice diffusion sustained by chemical diffusion. At very high strain rates of ≳2 · 10⁻² s⁻¹, the strain-rate-sensitivity exponent decreases to about 0.2≤m≤0.27, which indicates class II solid solution behavior of this material.     

Effect of initial microstructure on plastic flow and dynamic globularization during hot working of Ti-6Al-4V

Plastic flow behavior and globularization kinetics during subtransus hot working were determined for Ti-6Al-4V with three different transformed beta microstructures. These conditions consisted of fine lamellar colonies, a mixture of coarse colonies and acicular alpha, and acicular alpha. Isothermal hot compression tests were performed on cylindrical samples at subtransus temperatures and strain rates typical of ingot breakdown (i.e., T∼815 °C to 955 °C, ∼0.1 s⁻¹). For all three material conditions, true stress-true strain curves exhibited a peak stress followed by noticeable flow softening; the values of peak stress and flow softening rate showed little dependence on starting microstructure. On the other hand, the kinetics of dynamic globularization varied noticeably with microstructure. By and large, the globularization rate under a given set of deformation conditions was most rapid for the fine acicular microstructure and least rapid for the mixed coarse-colony/acicular structure. At temperatures close to the beta transus, however, the difference in globularization rates for the three microstructures was less, an effect attributed to the rapid (continuous) coarsening of the laths in the acicular microstructure during preheating prior to hot working. The absence of a correlation between the globularization kinetics and the observed flow softening at low strains suggested platelet/lath bending and kinking as the primary deformation mechanism that controls the shape of the flow curves.     

Free energy of formation of Mo2C and the thermodynamic properties of carbon in solid molybdenum

The activity of C in the two-phase region Mo+Mo₂C has been obtained from the C content of iron rods equilibrated with metal+carbide powder mixtures. From this activity data the free energy of formation of α-Mo₂C has been determined as ΔG _f ^o (α-Mo₂C) (1270 to 1573 K)=−47,530−9.46T±920 J/mol. This is in good agreement with the expression obtained from gas-equilibration studies by Gleiser and Chipman, ΔG _f ^o (α-Mo₂C) (1200 to 1340 K)=−48,770−7.57 J/mol, but both our and Gleiser and Chipman's values are about 10 pct lower than those of Pankratz, Weller and King calculated from ΔH _f,298 ^o andC _p vs T data. With the aid of available data for the solid solubility of C in Mo, the thermodynamic properties of C in the terminal solid solution have been calculated as J/mol, J/mol and , the excess entropy ofC in the solid solution assumingC is in the octahedral interstices =43.4±8.2 J/deg.-mol.     

A constitutive description for aluminum-0.1 pct magnesium alloy under hot working conditions

The constitutive behavior of an aluminum 0.1 wt pct Mg alloy deformed in the temperature range of 573 to 823 K at strain rates between 0.001 and 100 s⁻¹ is analyzed on the basis of the concept of the mechanical threshold stress (MTS), , taking into consideration the contributions from the different strengthening mechanisms that could be present in this alloy, , which include one component that arises from the interaction between dislocations and solute atoms, , and another contribution from the interaction between mobile and forest dislocations, . The evolution of is described in terms of a generalized form of an exponential-saturation equation, whereas the characterization of the ratio, s _i ( , T), between the flow stress at any strain rate and temperature, and the two components is carried out by means of the phenomenological model advanced by Kocks and co-workers. It is shown that the experimental values of the flow stress as well as the work-hardening rate can be accurately described following this approach and that the maximum difference between the experimental and calculated values of such a parameter is less than ±4 MPa. The analysis conducted from continuous stress-strain curves determined at constant temperature and strain rate indicates that the relaxation strain in the generalized form of the Sah et al. relationship displays a significant strain rate dependence. The inclusion of such a dependence into the analysis by means of a simple parametric relationship leads to an improvement in the accuracy of the prediction of the model.     

Modeling creep and fatigue of copper alloys

This article reviews expressions to quantify the thermal creep and fatigue lifetime for four copper alloys: Cu-Ag-P, Cu-Cr-Zr, Cu-Ni-Be, and Cu-Al₂O₃. These property models are needed to simulate the mechanical behavior of structures with copper components, which are subjected to high heat-flux and fatigue loading conditions, such as molds for the continuous casting of steel and the first wall in a fusion reactor. Then, measurements of four-point bending fatigue tests were conducted on two-layered specimens of copper alloy and stainless steel, and thermal ratchetting behavior was observed at 250 °C. The test specimens were modeled with a two-dimensional elastic-plastic-creep finite-element model using the ABAQUS software. To match the measurements, a primary thermal-creep law was developed for Cu-0.28 pct Al₂O₃ for stress levels up to 500 MPa and strain rates from 10⁻⁸ to 10⁻² s⁻¹. Specifically, (s⁻¹)=1.43×10¹⁰ exp (−197,000/8.31 T(K)) (σ(MPa))^2.5 (t(s))^−0.9.     

Interdiffusion in the carbides of the Nb-C system

Interdiffusion coefficients in Nb₂C and NbC_1−x were measured using bulk diffusion couples in the temperature range from 1400 °C to 1700 °C. Marker experiments were used to show that carbon is the only component undergoing significant diffusion in both carbides. Carbon concentrations were measured by difference using electron probe microanalysis, and interdiffusion coefficients were taken from Boltzmann-Matano analyses of the resulting concentration profiles. This analysis clearly showed that, in NbC_1−x, interdiffusion coefficient varies with carbon concentration, and is expressed by

Assessment of service induced microstructural damage and its rejuvenation in turbine blades

Correlations between service induced microstructural degradation and creep properties in investment cast IN738LC turbine blades are discussed. Microstructural degradation in the form of γ’ coarsen-ing, MC carbide degeneration, formation of continuous networks of grain boundary M₂₃C₆ carbides, and the disappearance of serrated grain boundaries are considered in some detail. Their influence on primary (t _p ,ε _p ), secondary (t _s , ε _s ,ε _m ) and tertiary (t_t, ε_t) creep behavior is analyzed through rela-tionships of the form:

The high temperature creep and fracture behavior of 70-30 alpha-brass

Constant stress creep tests have been carried out over a range of stresses at 324°, 413°, 503°, and 550°C. In all cases, over almost the entire creep curve, the time dependence of the true creep strain, ∈, can be described accurately as where ∈₀ is the instantaneous strain on loading, ∈_T the transient creep strain,m a parameter relating to the rate of exhaustion of transient creep, the steady creep rate, ∈_L andP are tertiary creep parameters, andt _t is the time to the onset of tertiary creep. A number of relationships exist between the transient and tertiary parameters in this equation and the steady creep rate, which suggests that the same basic deformation process operates throughout almost the entire creep life. Transient creep ends after a time,t _s, such thatmt _s is a constant (≃4). Similarly, the duration of tertiary creep (t _f – t_t), wheret _f is the time to fracture, depends on the parameter,p, asp (t_f − t_t) is a constant (≃4.5). The time to fracture is found to be related to the parametersm andp asmt _s +pt _f − t_s) =constant (−12) independent of stress and temperature. Formerly Research Student, University College     

Stress-state dependence of cavitation and flow behavior in superplastic aluminum alloys

A detailed and quantitative investigation of the stress-state dependence of superplastic cavitation in fine-grained aluminum alloys has been carried out to develop clear evidentiary support to build future models. Several stress states, such as uniaxial tension, plane-strain tension, plane-strain compression, shear, and equibiaxial tension have been examined. Tests were carried out to large strain in an interrupted manner under a constant effective strain rate ( _e ) in the range of 10⁻⁴ to 10⁻² s⁻¹. Measurements of volume fraction, population density, and size distribution of cavities, made by image analysis via optical microscopy, show continuous emergence of new cavities as well as growth of cavities during superplastic straining. The total cavity volume fraction (V) increases exponentially with strain. The cavity growth rate, represented by η (equal to d ln V/dε _e ), as well as the cavity population evolution rate with strain (dN _c /dε _e , where N _c is the cavity number/unit area) are found to increase with normalized mean hydrostatic tensile stress (σ _m / σ _e ). An empirical equation for the biaxial forming limit in terms of the principal surface strains (ε ₁ and ε ₂) has been defined for a fixed cavity volume, as given by ε ₁=a V ^b − α ε ₂, where a and b are constants determined from ε ₁ values for plane strain (ε ₂=0). The value of b is found to be 0.2 to 0.3, and α is 0.4 to 1.0.     

Large strain mechanical behavior of 1018 cold-rolled steel over a wide range of strain rates

The large-strain constitutive behavior of cold-rolled 1018 steel has been characterized at strain rates ranging from to 5 × 10⁴ s⁻¹ using a newly developed shear compression specimen (SCS). The SCS technique allows for a seamless characterization of the constitutive behavior of materials over a large range of strain rates. The comparison of results with those obtained by cylindrical specimens shows an excellent correlation up to strain rates of 10⁴ s⁻¹. The study also shows a marked strain rate sensitivity of the steel at rates exceeding 100 s⁻¹. With increasing strain rate, the apparent average strain hardening of the material decreases and becomes negative at rates exceeding 5000 s⁻¹. This observation corroborates recent results obtained in torsion tests, while the strain softening was not clearly observed during dynamic compression of cylindrical specimens. A possible evolution scheme for shear localization is discussed, based on the detailed characterization of deformed microstructures. The Johnson-Cook constitutive model has been modified to represent the experimental data over a wide range of strain rates as well as to include heat-transfer effects, and model parameters have been determined for 1018 cold-rolled steel.     

C-Ni and Al-C-Ni phase diagrams and thermodynamic properties of C in the alloys from 1550 °C to 2300 °C

The C-Ni and Al-C-Ni phase diagrams were determined by chemical analysis of alloys saturated with carbon within sealed graphite crucibles. The solubility of carbon in nickel over the temperature range 1550 °C to 2300 °C is given by log (at. pct C)=2.0376−1874.68/T, where T is temperature in kelvin. Isothermal sections for the ternary system were determined at intervals of 150 °C over the range of temperatures investigated. The univariant points on the 1700 °C, 1850 °C, and 2000 °C isotherms were determined by metallographic examination of rapidly cooled alloys to be about 67.2Al-1.1C-31.7Ni, 70.3Al-2.3C-27.4Ni, and 82.5Al-7.0C-10.5Ni, respectively, where all concentrations are in atomic percent. Graphite, Al₄C₃ (decomposition temperature 2156 °C), and AlNi (decomposition temperature 1638 °C) were the only solid phases observed within the temperature range investigated. The excess partial Gibbs energy for dissolved C, , in liquid Al-C-Ni solutions in equilibrium with C, as calculated from the experimental solubilities and thermodynamic data on Al-Ni, is

Interdiffusion in Co-Mn alloys

Interdiffusion coefficient in cobalt-manganese alloys has been determined by Matano's method in the temperature range between 1133 and 1423 K on (pure Co)-(Co-30.28 at. pct Mn alloy) and (pure Co)-(Co-51.76 at. pct Mn alloy) couples. This, ∼D, has been found to increase with the increase of manganese content. However, the activation energy (∼Q) and frequency factor ( ₀) show a maximum at about 10 at. pct Mn. The concentration dependence of and has been discussed taking into account the thermodynamic properties of the alloy. The difference in between the ferro- and paramagnetic phases in Co-5 at. pct Mn alloy has been found to be 24 kJ/mol, which is larger, than that for the diffusion of Mn⁵⁴ in this alloy. Further it has been found that the Kirkendall marker moves toward manganese-rich side, showing that manganese atoms diffuse faster than cobalt atoms. From the marker shift, the intrinsic diffusion coefficients,D _Co andD _Mn, at 33 at. pct Mn have been determined as follows:D _Co=0.22×10⁻⁴ exp(−263 kJ mol⁻¹/RT) m²/s, andD _Mn=0.98×10⁻⁴ exp(−229 kJ mol⁻¹/RT) m²/s.     

A planar simple shear test and flow behavior in a superplastic Al-Mg alloy

Superplasticity is generally studied by performing tensile and gas-pressure-bulge tests. In formed parts, however, a variety of strain states, including in-plane shear, are encountered. The understanding of the mechanical response in shear is helpful in the study of superplastic metal forming. In this study, a device for a planar simple shear test was designed and used to perform tests on a superplastic Al-Mg alloy sheet at the elevated temperatures of 500 °C (773K) and 550 °C (823K). In such a test, the incremental rotation of the principal strain axes and specimen-end effects during deformation can complicate the determination of true mechanical response. The possible approximations regarding the strain state in the specimen gage have been investigated. The σ _e -ε _e curves developed based on a simple-shear assumption show a lower flow stress than that under uniaxial tension, and strain hardening is related to dynamic grain growth. The rate of strain hardening at a fixed _e level is essentially the same for both uniaxial tension and shear, but the difference in the effective stress between uniaxial tension and shear depends upon strain rate and temperature. This study marks the first known attempt to characterize large strain response for superplastic metals under conditions of simple shear.     

Grain-growth-inhibiting effects of primary inclusion particles of ZrO2 and MgO in Fe-10 mass pct Ni alloy

Grain-growth inhibition in an Fe-10 mass pct Ni alloy, which was continuously cooled from a melt, was studied at 1673 K in the presence of primary deoxidation products of ZrO₂ or MgO particles. The mean grain size and grain-size distribution in a cross section were measured as a function of holding time for up to 240 minutes. The grain growth was strongly inhibited by the inclusion particles and was influenced by the dissolved Zr. In the Zr deoxidation, the number of particles per unit area (N _A) ranged from 80 to 650 mm⁻², the ZrO₂ particle size ( ) varied from 1.1 to 1.6 μm, and the dissolved Zr level was below 1800 mass ppm. In the Mg deoxidation, the particle-number density was 90 to 270 mm⁻², the MgO particle size was 1.1 to 1.7 μm, and the dissolved Mg level was below 20 mass ppm. In a logarithmic plot of the ratio of limiting mean grain diameter ( ) to the mean particle diameter ( ) against the volume fraction of particles (f _V), both the value for a given f _V value, which ranged from 0.014 to 0.074 pct, and the slope were significantly lower than that predicted from the two-dimensional relation =(4/π) · f _V ^/−1 , i.e., Zener’s limit. This discrepancy is discussed in light of the fraction of particles at the grain boundaries measured experimentally. Normal grain growth was confirmed from the grain-size distribution observed as a function of holding time, which was best described by the log-normal distribution.     

Determination of the interdiffusion coefficients in the Fe-Ni and Fe-Ni-P Systems Below 900 °C

Analytical electron microscopy was used to measure the interdiffusion coefficients, , in the Fe-Ni and Fe-Ni-P systems between 925 and 610 °C in austenite,γ, and between 850 and 550 °C in ferrite,α. The values of binaryγ Fe-Ni follow the extrapolated high temperature values of Goldsteinet al. The values of binaryα Fe-Ni are as much as two orders of magnitude lower than previously determined tracer diffusion measurements for the ferromagnetic region between 700 and 550 °C. In both ternaryγ Fe-Ni-P and ternary ferromagneticα Fe-Ni-P, the values are increased over the equivalent binary values at the same temperature. This increase is related to the ratio of the P content in the diffusion couple to the maximum P solubility in theα orγ phase at the diffusion temperature. The increase is most likely due to the effect of the electropositive solute atom P on the vacancy formation energy of the solvent, as described by LeClaire.     

Thermodynamics of the system NaF-Alf3. part ii: The free energies of formation of cryolite (Na3AlF6) and chiolite (Na5Al3F14)

The theory of the solid-electrolyte cells is given, and it is shown that cryolite itself with Ca²⁺ in solid solution is a suitable Na⁺-ion conductor. Experimental electromotive forces for the ranges 570° to 725°C and 570° to 670°C, r − 18,960 cal with a standard deviation of ±36 cal (based on a third-law calculation). For 5NaF(s) + 3AlF₃(s) = Na₅Al₃F₁₄(s), ΔG° = −38,560 − 7.081T with a standard deviation of ±130 cal. Combination of these results with recent values for Al + 3/2 F₂ = A1F₃ and for 6NaF + Al = Na₃AlF₆ + 3Na gives ΔH°_f298(Na₃AlF₆) = −792,400 cal and ΔH°_f298(NaF) = −137,530 cal. The latter is in excellent agreement with the most recent critical assessment.     

Influence of secondary precipitates and crystallographic orientation on the strength of single crystals of a Ni-based superalloy

The effect of crystallographic orientation and aging heat treatment at 850 °C on the creep rupture strength of single crystals of a nickel-based superalloy was examined at 700 °C in detail. Initial tensile orientations were selected over a wide range on the standard stereographic triangle. The {111}〈112〉-type slip systems were found to be operative during the creep deformation. The creep behavior was found to be greatly influenced by the additional aging at 850 °C for 20 hours. It was found that the effect of the aging at 850 °C was quite different between orientations favored for the slip system and those favored for the (111) slip system and that the creep deformation mechanisms of these two slip systems were different. In the orientations favored for slip systems, in the single-aged specimens, a small mean surface-to-surface spacing due to hyperfine γ′ precipitates in the matrix channel promoted the slip and the primary creep. As a result of the additional aging at 850 °C, the hyperfine γ′ precipitates were dissolved into the matrix, and the resultant large mean surface-to-surface spacing between the cuboidal precipitates inhibited extensive shearing of the γ-γ′ structure by the slip system. As a result, the creep strengths of these orientations were increased in double-aged specimens; however, the low ductility associated with the difficulty of secondary noncoplanar slip did not enlarge rupture lifetime in the double-aged [001] specimen. In the orientations favored for the (111) slip system, creep deformation occurred by twinning shear through γ and γ′ precipitates, and a distinct effect of the aging at 850 °C was not observed. In the multiple orientation of the {111} -type slip systems, i.e., the and orientations, hyperfine precipitates improved creep strength because they prevented dislocations from gliding in the matrix channel in the single-aged specimens.     

The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensites

The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensite, , has been determined between 700 and 300 °C using electron microprobe (EMP) and scanning transmission electron microscope (STEM) techniques. Alloys of various bulk compositions (0 to 30 wt pct Ni, Fe) were homogenized in the single phase austenite (γ-fee) field and quenched to form martensite, α₂ (bcc). Appropriate alloys were tempered isothermally at 300 to 700 °C. The γ nucleated and grew in the parent α₂. The composition of the γ phase and the concentration gradients in the α₂ were measured with the EMP andJor STEM. In order to determine experimentally measured Ni concentration gradients were matched to Ni concentration gradients calculated by a simulation model. The calculated gradients were obtained by solving the appropriate form of Fick’s second law using the Crank-Nicholson numerical technique. The observed diffusivities varied with temperature. Above approximately 410 °C, while below 410°C, = (2.27 × 10⁻¹⁵) exp (− 10,600/RT) cm²/s. The effect of P is to increase the Fe-Ni diffusivities at any temperature by the factor (1 + 1.27C _p + 0.623C _p ² ) whereC _p is the amount of P (wt pct) in α₂. The discontinuous diffusion behavior of is attributable to the high dislocation density of the α₂. Above approximately 410 °C lattice diffusion is dominant while below 410 °C dislocation pipe diffusion is dominant. Formerly Research Assistant in the Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA