Effect of strain rate on the flow stress of three liquid phase sintered tungsten alloys

Stress/strain tests were carried out in compression on three liquid phase sintered tungsten alloys, with tungsten contents of 90, 95, and 97.4 wt pct, in the strain rate range 10⁻³ s⁻¹ to 10³ s⁻¹. Each alloy shows a gradual increase of flow stress with strain rate, and evidence of work softening is observed when the strain rate is of the order of 2 s⁻¹ or greater. The work softening effect is shown to result from a temperature rise due to the plastic deformation and partly masks the strain rate effect at strains greater than 0.1. The 97.4 pct tungsten alloy also shows variable behavior due to cracking associated with the presence of a brittle phase at the tungsten particle/matrix interface.     

New aspects on the superplasticity of fine-grained 7475 aluminum alloys

Thermomechanical processes were developed which give fine grain sizes of 6 and 8 μm in the 7475 Al alloy. Superplastic properties of this material were evaluated in the temperature range of 400 °C to 545 °C over the strain-rate range of 2.8 x 10^-4 to 2.8 X 10^-2 s^-1. The maximum ductility exhibited by the alloy was approximately 2000 pct, and optimum superplasticity was achieved at a strain rate of 2.8 X 10^-3 s^-1 which is higher by an order of magnitude than other 7475 Al alloys. This result is attributed to the presence of fine dispersoids which maintain the fine grain size at high homologous temperatures. The flow stress and strain-rate sensitivity strongly depend on the grain size. The superplastic 7475 Al alloy has strain-rate sensitivities of 0.67 (6 μm) and 0.5 (13 μm) and an activation energy which is similar to the one for grain boundary diffusion of aluminum. Microstructural investigation after superplastic tests revealed zones free of dispersoid particles at grain boundaries primarily normal to the tensile direction. These dispersoidfree zones (DFZs) appear even after 100 pct elongation and are occasionally as large as 5 μm across. This result demonstrates the importance of diffusional flow in superplastic deformation of the fine-grained 7475 Al alloy especially at low elongations.     

Anneal hardening and flow softening in beta zirconiumniobium alloys

The flow properties of β-Zr-Nb (Cb) alloys were investigated by means of compression testing in the strain rate range 10^-1 to 10^-5 s^-1 and from 725 to 1025°C. The flow curves obtained on Zr-Nb alloys containing 10, 15 and 20 pct Nb exhibited flow softening, and the magnitude of this effect decreased as the temperature was increased. All three alloys also exhibited anneal hardening, i.e. an increase in flow stress at 825°C with annealing time at 1000°C. Neither the flow softening, nor the anneal hardening could be associated with environmental effects, as in Zr-Mo alloys, nor could they be attributed to texture changes or to the occurrence of dynamic recrystallization. On the basis of X-ray and microprobe investigations, as well as grain size measurements, it is concluded that the anneal hardening is due to the combined effect of grain growth and the formation of solute clusters during annealing. The occurrence of flow softening is attributed to the destruction of the solute clusters by straining. Stress-strain curves were also determined for Zr-2.5 pct Nb. Unlike the high Nb alloys, these materials exhibited neither flow softening nor anneal hardening. The flow stresses were found to be highly strain rate dependent, with stress sensitivities of about 5.5 for yielding and 4.5 for steady state flow.     

Tensile strength of thermomechanically processed Cu-9Ni-6Sn alloys

The tensile properties of Cu-9Ni-6Sn alloys with different swaging amounts of 64, 77, and 95 pct, either solutionized and aged (S/A) or directly aged (D/A), were examined as a function of aging time. It was found that the aging response of Cu-9Ni-6Sn alloys varied greatly depending on the prior solution heat treatment before aging and/or different swaging amounts. The swaged S/A Cu-9Ni-6Sn alloys showed a multistage increase in tensile strength with respect to aging time, probably due to the sequential occurrence of spinodal decomposition, formation of metastable γ· precipitates, and recrystallization. The effect of different swaging amounts, ranging from 64 to 95 pct, was minimal on the aging response of S/A specimens. The prior cold working, however, appeared to favor the spinodal strengthening, comparing unswaged and swaged S/A Cu-9Ni-6Sn alloys. In 95 pct swaged D/A Cu-9Ni-6Sn alloys, the level of hardening was much less sensitive to aging time. A complex interaction between the reduction in dislocation density, the formation of equilibrium precipitates, and the reduction of Sn content in the Sn-rich segregates during an aging process is believed to be responsible for such a lean sensitivity. The increases in tensile strength of 64 and 77 pct swaged D/A Cu-9Ni-6Sn alloys were found to be much steeper than that in the 95 pct counterparts in the early and intermediate stages of aging, which is believed to be related to the relative contribution from work hardening and precipitation hardening to the strength level of D/A specimens.     

Microstructural dependence of Fe-high Mn tensile behavior

The tensile properties of Fe-high Mn (16 to 36 wt pct Mn) binary alloys were examined in detail at temperatures from 77 to 553 K. The Mn content dependence of the deformation and fracture behavior in this alloy system has been clarified by placing special emphasis on the starting microstructure and its change during deformation. In general, the intrusion of hcp epsilon martensite (ε) into austenite (γ) significantly increases the work hardening rate in these alloys by creating strong barriers to further plastic flow. Due to the resulting high work hardening rates, large amounts of e lead to high flow stresses and low ductility. Alloys of 16 to 20 wt pct Mn are of particular interest. While these alloys are thermally stable with respect to bcc α’ martensite formation, 16 to 20 wt pct Mn alloys undergo a deformation induced ε →α’ transformation. The martensitic transformation plays two contrasting roles. The stress-induced ε→ α’ transformation decreases the initial work hardening rate by reducing locally high internal stress. However, the work hardening rate increases as the accumulated α’ laths become obstacles against succeeding plastic flow. These rather complicated microstructural effects result in a stress-strain curve of anomolous shape. Since both the M_s and M_d temperatures for both the ε and α’-martensite transformations are strongly dependent on the Mn content, characteristic relationships between the tensile behavior and the Mn content of each alloy are observed.     

Effect of friction stir processing on the kinetics of superplastic deformation in an Al-Mg-Zr alloy

The effect of friction stir processing on the superplastic behavior of extruded Al-4Mg-1Zr was examined at 350 °C to 600 °C and at initial strain rates of 1×10⁻³ to 1 s⁻¹. A combination of a fine grain size of 1.5 μm and high-angle grain boundaries in the friction stir-processed (FSP) alloy led to considerably enhanced superplastic ductility, much-reduced flow stress, and a shift to a higher optimum strain rate and lower optimum temperature. The as-extruded alloy exhibited the highest superplastic ductility of 1015 pct at 580 °C and an initial strain rate of 1×10⁻²s⁻¹, whereas a maximum elongation of 1280 pct was obtained at 525 °C and an initial strain rate of 1×10⁻¹s⁻¹ for the FSP alloy. The FSP alloy exhibited enhanced superplastic deformation kinetics compared to that predicted by the constitutive relationship for superplasticity in fine-grained aluminum alloys. A possible origin for enhanced superplastic deformation kinetics in the FSP condition is proposed.     

The effect of grain boundaries on the athermal stress of tantalum and tantalum-tungsten alloys

The temperature dependence of the yield stress of polycrystalline Ta, Ta-2.47 wt pct W (Ta-2.5W), and Ta-9.80 wt pct W (Ta-10W) was measured to study the effect of grain boundaries and tungsten concentration on athermal strength components. Compression tests were performed over a temperature range from 77 to 1223 K at strain rates of 10⁻⁴ and 10⁻¹ s⁻¹. The test results show that the yield stress of Ta becomes independent of temperature above about 400 K, indicating an “athermal” regime. In contrast, the temperature dependence of yield stress was still significant for Ta-10W up to the maximum test temperature. An analysis of the test data using single-crystal data in conjunction with Taylor factors was performed to assess the effect of grain boundaries on the athermal component of flow stress at 600 K. The results indicated that the long-range athermal stress at the yield point due to grain boundaries is approximately 13 to 41 MPa for the study materials and decreases with an increase in tungsten concentration. These results are discussed with regard to constitutive modeling of flow stress.     

Alloying aluminum with magnesium for ductility at warm temperatures (25 to 250°C)

Solute additions generally increase flow stress and decrease ductility. However, in an earlier study which compared the tensile behavior of a commercial Al-4 pct Mg alloy (5182-0) relative to pure aluminum, the commercial alloy exhibited increases in both strength and ductility at elevated temperatures (<250°C). To more fully understand this unexpected behavior, a series of high purity Al-Mg alloys (0 to 6 wt pct) were tested over the same range of temperatures (25 to 250°C) and initial strain rates (10^-4 to 10^-1 s^-1) as in the earlier study. At ambient temperature the Mg solutes decreased elongation while increasing flow stress, but as the temperature was increased to 250°C the elongation increased with Mg content. This increase in ductility accompanied the linear increases in strain-rate sensitivity which occurred with increasing amounts of Mg. Stress relaxation tests indicated that Mg solutes increase the amount of dynamic recovery occurring at elevated temperatures. These results are explained on the basis of an increased amount of vacancies in the Al-Mg alloys relative to pure aluminum.     

Deformation Processing Maps for Control of Microstructure in Al-Cu-Mg Alloys Microalloyed with Sn

High-temperature deformation behaviors of Al-5.9?pct Cu-0.5?pct Mg alloy and Al-5.9?pct Cu-0.5?pct Mg alloy containing 0.06?wt pct Sn were studied by hot compression tests conducted at different temperatures and strain rates. Trace content of Sn resulted in a significant increase of flow stress at various processing conditions. Artificial neural network (ANN) modeling was carried out providing excellent prediction of flow stress at different combinations of strain, strain rate, and temperature. It was possible to predict 100 and 89?pct of the flow stress values of the respective alloys within an error less than ±10?pct. The generated flow stress data were used to develop processing maps to delineate the process domains for safe metal working. The power dissipation efficiency maps revealed a maximum efficiency of 60 and 40?pct, respectively, for the base alloy and the microalloyed material. The instability maps generated for the Sn containing alloy revealed only one instability regime. The safe processing zone of the investigated alloys primarily lies at lower regimes of strain rate, which is extended up to higher deformation temperatures, with trace addition of Sn. Optical microscopy characterized these stable regions as dynamic recrystallization (DRX), which resulted in considerable flow softening observed at a low strain rate of 0.001 s^?1. Instability was observed mainly due to shear band formation or intercrystalline cracking.     

The influence of stacking fault energy on the mechanical behavior of Cu and Cu-Al alloys: Deformation twinning, work hardening, and dynamic recovery

The role of stacking fault energy (SFE) in deformation twinning and work hardening was systematically studied in Cu (SFE ∼78 ergs/cm²) and a series of Cu-Al solid-solution alloys (0.2, 2, 4, and 6 wt pct Al with SFE ∼75, 25, 13, and 6 ergs/cm², respectively). The materials were deformed under quasi-static compression and at strain rates of ∼1000/s in a Split-Hopkinson pressure bar (SHPB). The quasi-static flow curves of annealed 0.2 and 2 wt pct Al alloys were found to be representative of solid-solution strengthening and well described by the Hall-Petch relation. The quasi-static flow curves of annealed 4 and 6 wt pct Al alloys showed additional strengthening at strains greater than 0.10. This additional strengthening was attributed to deformation twins and the presence of twins was confirmed by optical microscopy. The strengthening contribution of deformation twins was incorporated in a modified Hall-Petch equation (using intertwin spacing as the “effective” grain size), and the calculated strength was in agreement with the observed quasi-static flow stresses. While the work-hardening rate of the low SFE Cu-Al alloys was found to be independent of the strain rate, the work-hardening rate of Cu and the high SFE Cu-Al alloys (low Al content) increased with increasing strain rate. The different trends in the dependence of work-hardening rate on strain rate was attributed to the difference in the ease of cross-slip (and, hence, the ease of dynamic recovery) in Cu and Cu-Al alloys.     

An evaluation of the flow behavior during high strain rate superplasticity in an Al-Mg-Sc alloy

An Al-3 pct Mg-0.2 pct Sc alloy was fabricated by casting and subjected to equal-channel angular pressing to reduce the grain size to ∼0.2 μm. Very high tensile elongations were achieved in this alloy at temperatures over the range from 573 to 723 K, with elongations up to >2000 pct at temperatures of 673 and 723 K and strain rates at and above 10⁻² s⁻¹. By contrast, samples of the same alloy subjected to cold rolling (CR) yielded elongations to failure of <400 pct at 673 K. An analysis of the experimental data for the equal-channel angular (ECA)-pressed samples shows consistency with conventional superplasticity including an activation energy for superplastic flow which is within the range anticipated for grain boundary diffusion in pure Al and interdiffusion in Al-Mg solid solution alloys.     

Influence of precipitates on the mechanical response and substructure evolution of shock-loaded and quasi-statically deformed Al−Li−Cu alloys

The mechanical response and substructure evolution of two Al−Li−Cu alloys (Al-2.90 wt pct Li-1.00 pct Cu-0.12 pct Zr and Al-2.30 pct Li-2.85 pct Cu-0.12 pct Zr) subjected to shock-loading (strain rate έ> 10⁶ s^-1), Split-Hopkinson-Pressure-Bar compression (έ ~ 5 × 10³ s^-1), and quasi-static compression (έ ~ 1.5 × 10^-3 s^-1) were examined. The strain levels achieved in these three deformation paths were desined to be comparable,i.e., all ∼15 pct. Both alloys were either naturally or artificially aged to yield an underaged or overaged condition. Various precipitates, such as theδ' andT ₁ phase, of different sizes and volume fractions were dispersed in the matrix and at the grain boundaries. The substructure in all of the shock-loaded, Split-Hopkinson-Pressure-Bar, and quasi-static compression samples was characterized by localized slip bands and microbands with the exception of the overaged alloys. The density of dislocations and dislocation loops was higher, independent of the aging condition, in the shock-loaded specimens. Well-defined cell structures were not observed in any of the samples, independent of strain rate. The influence of precipitates, shearable or not, on the substructure development in Al−Li−Cu alloys during shock-loading was seen to be pronounced, even though the size and volume fraction of precipitates was small and low, respectively. Flow stress measurements showed that the shock-loaded samples have flow strengths 3 to 8 pct higher than the quasi-statically deformed samples. This small, but reproducible, strength increment, for alloys deformed to equivalent strains at low and high rates, indicates that the Al−Li alloys studied have a small rate sensitivity. Based upon comparison of the results of the shock-loaded and quasi-static samples, it is concluded that the fundamental deformation mechanisms and substructure evolution in all three loading paths are not drastically different, corroborating previous investigations.     

The Serrated Flow Behavior of Mg-Gd(-Mn-Sc) Alloys

The tensile deformation behavior of extruded samples of Mg-0.8 pct Gd and Mg-0.8 pct Gd-0.5 pct Mn-0.45 pct Sc (at. pct) alloys has been studied. Both alloys exhibit serrated flow when they are tensile tested at temperatures ranging from 150 °C to 300 °C and at strain rates of 1.67 × 10⁻⁴ s⁻¹ to 1.67 × 10⁻² s⁻¹, and this serrated flow behavior is significantly affected by postextrusion heat treatments. Combined with observations made by transmission electron microscopy (TEM) and three-dimensional atom probe (3DAP), the serrated flow is attributed to dynamic interactions between solute atoms and gliding dislocations. It is suggested that Gd atoms in the solid solution matrix of magnesium are mainly responsible for the serrations in the two alloys. The additions of Mn and Sc to the Mg-Gd alloy strengthen the dynamic solute-dislocation interactions and lead to a lower critical strain and larger stress drops of the serrated flow in the Mg-Gd-Mn-Sc alloy.     

Mechanical behavior of a fine-grained duplex γ-TiAl alloy

The mechanical behavior of a fine-grained duplex γ-TiAl alloy was studied in compression at strain rates ranging from 0.001 to 2000 s⁻¹ and temperatures from −196 °C to 1200 °C. The temperature dependence of the yield and flow stresses is found to depend on the strain rate. At strain rates of 0.001 and 0.1 s⁻¹, the yield stress decreases as the temperature increases, with a plateau between 600 °C and 800 °C. At strain rates of 35 and 2000 s⁻¹, the yield stress exhibits a positive temperature dependence at temperatures above 600 °C; however, postyield flow stresses exhibit a reduced temperature dependency. The work-hardening rate decreases dramatically with temperature at low and high temperatures, with a plateau occurring at intermediate temperatures for all strain rates. The workhardening-rate plateau is seen to extend to higher temperatures as the strain rate increases. The strain-rate sensitivity at strain rates of 0.1 s⁻¹ and greater is lower than 0.1, although it increases slightly with temperature. At 0.001 s⁻¹, the strain-rate sensitivity increases dramatically at high temperatures (equal to 4.5 at 1200 °C). The anomalous (positive) temperature dependence of the yield stress at high strain rates (>1 s⁻¹) and high temperatures (>600 °C) is explained via a dislocation-jog pinning mechanism. The negative temperature dependence of the yield stress at low strain rates (<1 s⁻¹) and high temperatures (>900 °C) is thought to be due to a thermally activated dislocation-jog climb process in the grain interiors and/or deformation and recovery processes at/near grain boundaries. The decreased anomalous temperature dependence of the flow stress at high strain rates and high temperatures is ascribed to dynamic recovery promoted by adiabatic heating.     

Effects of composition and microstructure on fatigue of γ/γ′-δ type eutectic alloys

Room temperature tension-tension fatigue tests were performed on two lamellar γ/γ′-δ alloys, one with 0 pct Cr and one with 6 pct Cr. The 6 pct Cr alloy was solidified at 3 cmJh while the 0 pct Cr alloy was solidified at 3 cm/h and 5.7 cm/h. Fatigue testing was done on both alloys in the as-directionally solidified condition and on the 0 pct Cr alloy after heat treatment. Increasing the growth speed of the 0 pct Cr alloy increased the fatigue life of the material at stresses above the 10⁷ cycle fatigue limit. Partial solution treating and aging of the 0 pct Cr alloy,R = 3 cm/h, increased the fatigue life relative to the as-directionally solidified material at high stresses, to the same extent as increasing the growth speed. Full solution treatment and aging of the 0 pct Cr alloy,R = 5.7 cm/ h, caused a reduction in the fatigue life relative to the as-directionally solidified material. Fatigue cracking tended to be faceted in the 6 pct Cr alloy as opposed to the more ductile failure of the 0 pct Cr alloy. Microstructural perfection, grain size and shape, interlamellar spacing, longitudinal cracking, and longitudinal and transverse ductility all are believed to have influenced the fatigue resistance of the alloys.     

The Mode of Deformation in a Cold-Swaged Multifunctional Ti-Nb-Ta-Zr-O Alloy

Multifunctional titanium alloys, termed Gum Metal?, are β-phase Ti alloys first developed in 2003. These alloys exhibit many interesting properties including, for example, low rate of work-hardening and superplasticity during cold deformation. The original report described a new plastic deformation mechanism not involving major dislocation activity to explain such deformation behavior. In the current study, a comparable Ti-36.8Nb-2.7Zr-2.0Ta-0.44O (wt pct) alloy to the original investigators was produced by powder sintering, hot forging, solution treatment, and cold swaging with the aim at investigating the microstructural development during swaging. XRD and TEM showed that the forged/solution-treated alloy was β-phase with a small amount of ω-phase. After cold swaging by up to 96 pct area reduction, TEM/HRTEM revealed the existence of dislocations, deformation twins, ω-phase, nanodisturbances, and lattice bending, with EBSD showing the grains to be highly elongated in the swaging direction, fragmented, and distorted. Most notably, swaging also generated a strong 〈110〉 fiber texture, even after moderate strains. The foregoing structural analysis provides substantial evidence that dislocations are present in the alloy after cold swaging. The major support of dislocation glide processes acting as the dominant plastic deformation mode in the swaged alloy is the strong 〈110〉 fiber texture that develops, which is a characteristic feature of all cold-drawn/swaged body centered cubic metals and alloys.     

An evaluation of the flow behavior during high strain rate superplasticity in an Al−Mg−Sc alloy

An Al-3 pct Mg-0.2 pct Sc alloy was fabricated by casting and subjected to equal-channel angular pressing to reduce the grain size to ∼0.2 μm. Very high tensile elongations were achieved in this alloy at temperatures over the range from 573 to 723 K, with elongations up to >2000 pct at temperatures of 673 and 723 K and strain rates at and above 10⁻² s⁻¹. By contrast, samples of the same alloy subjected to cold rolling (CR) yielded elongations to failure of <400 pct at 673 K. An analysis of the experimental data for the equal-channel angular (ECA)—pressed samples shows consistency with conventional superplasticity including an activation energy for superplastic flow which is within the range anticipated for grain boundary diffusion in pure Al and interdiffusion in Al−Mg solid solution alloys. MINORU NEMOTO, formerly Professor, Department of Materials Science and Engineering, Faculty of Engineering, Kyushu University.     

Coarsening of tungsten grains in liquid nickel-tungsten matrix

In sintered W-Ni alloys with 1,7, and 30 wt pct Ni the tungsten grain growth in liquid matrix at 1540°C was investigated. The observed grain size distributions and growth rate are compared with the theoretical predictions of Wagner, Lifshitz and Slyozov, Lay, and Ardell. In the 70 pct W-30 pct Ni alloy the tungsten particles settled to the bottom of the specimens immediately upon melting of the matrix, but the spherical grain shape is maintained during the initial stage of annealing. In these specimens the linear intercept distribution of the grains agrees with the prediction of the LSW (Lifshitz, Slyozov, and Wagner) theory for the reaction controlled growth mechanism. On the other hand the growth rate appears to follow the t^1/3 law predicted for the diffusion controlled mechanism. These results are consistent with Lay and Ardell's theory in which the concentration gradient around grains is inversely proportional to the average grain size in the limit of small matrix fraction. In the alloys with 1 and 7 pct Ni a meaningful comparison of the observed linear intercept distribution of the grains with theoretical predictions is difficult because of grain contact flattening due to densification. The grain growth is larger with less matrix fraction in the specimens and this result provides an evidence for the diffusion controlled grain growth during the liquid phase sintering of this alloy. Formerly a student in the Department of Materials Science at the Korea Advanced Institute of Science, Seoul, Korea. On leave at the Max-Planck-Institut für Metallforschung in Stuttgart, West Germany.     

Microstructure-composition relationships and Ms temperatures in Fe-Cr-Mn-N alloys

Microstructure-composition relationships and M_s temperatures have been determined in high purity nitrided Fe-Cr-Mn alloys, as part of a program to develop improved corrosion-abrasion resistant steels with unstable austenitic microstructures. Compositions in the range 8 to 12 pct Cr, 0 to 10 pct Mn, and 0 to 0.6 pct N were investigated by a resistivity technique to determine M_s temperatures and by X-ray diffraction and metallography to determine constitution. Hardness measurements were also made. At the low alloy end of the range, microstructures after annealing and air cooling are fully martensitic while at the high alloy end they are fully austenitic. At intermediate compositions, mixed martensite-austenite microstructures (with epsilon present as a minor phase in some cases) and unstable austenitic microstructures are obtained. The austenitic alloys contain a high density of stacking faults and the unstable austenitic alloys transform to martensite on deformation. At low N contents (up to at least 0.25 pct N) the M_s-composition relationship is linear and described by: M_s = 555 - 9(Cr - 8) - 40Mn - 450N [1] where M_s is in °C and Cr, Mn, and N are the weight percentages of these elements. At higher N contents, the M_s generally falls more rapidly with increasing nitrogen content. Nitrogen solubility at 1050 °C exceeds about 0.3 pct in all alloys and increases with increasing Cr and Mn content. In commercial purity steels, unstable austenitic microstructures are expected to be obtained in compositions around 10 to 14 pct Cr, 8 to 12 pct Mn, and 0.1 to 0.3 pct N when the total level of these elements is selected to ensure the M_s is below room temperature.     

Deformation of semi-solid Sn-15 Pct Pb alloy

The rheological behavior of semisolid Sn-15 pct Pb alloy was studied using a parallel-plate viscometer. Small nondendritic and dendritic semisolid samples of the alloy were deformed under a constant load at initial pressures up to 232 kPa (33.6 psi) and at fractions solid from 0.15 to 0.60. Strain-time data for the nondendritic material obey the non-Newtonian, two-parameter, Ostwald-de-Waele, power-law model,i.e. μ = mγ ⁿ⁻¹, where μ is viscosity γ shear rate andm andn are constants. For fractions solid above about 0.30, the following empirical equation relates viscosity, shear rate and fraction solidμ = a exp (bf_s) γ^(cf _s ^+d) 0.3 <f _s < 0.60 wheref _s is fraction solid anda, b, c, d are constants. The nondendritic alloy deformed homogeneously without cracking to very large strains (up to 80 pct). Dendritic alloys required much higher loads and cracked easily. For the nondendritic alloys the forging pressures to obtain 50 pct compression were of the order of 7 to 70 kPa (1 to 10 psi) for fractions solid under 0.55 and 172.5 to 207 kPa (25 to 30 psi) for fraction solid of about 0.60. For the dendritic alloys, the forging pressure required to achieve 10 pct compression is about 85 kPa at a fraction solid of 0.35 and increases rapidly with increasing fraction solid.