On the time exponent in isothermal grain growth

A relation between the time exponent,n, in isothermal grain growth,D=Kt ⁿ , whereD is the average grain diameter,t is the annealing time, andK is a parameter depending on material and temperature, and the driving force exponent,m, in isothermal boundary migration,V=M(δF) ^m , whereV is the boundary velocity,M is the mobility of the boundary, and δF is the driving free energy for migration, has been derived, namelym=(1/n)?1. Based on this relationship, an examination of grain growth data in the literature indicate that grain growth characteristics are consistent with the impurity-drag theory for boundary motion, but a linear dependence of rate on driving force is a rarity rather than a commonplace in grain growth.     

Characterization of recrystallization and grain growth in Ti-7.4 At. Pct Al (cph) and Ti-15.2 At. Pct Mo (bcc) alloys

Quantitative microscopy, texture and grain growth kinetic studies were made on swaged and recrystallized Ti-7.4 at. pct Al and Ti-15.2 at. pct Mo alloys. The quantitative microscopy studies indicated that the grain size distribution in both alloys is a constant for a given grain size, independent of annealing time and temperature and follows a log normal distribution. Moreover, there exists a range of grain sizes in space; the relative quantities of each size in the range varies with average grain size. Also, the grain shape factor decreases with increase in annealing time (grain size) at a constant temperature and with decrease in temperature for a constant grain size. The values of the shape factor for a given grain size and temperature were approximately the same for the two alloys. The quantitative microscopy features were essentially the same as those observed by Okazaki and Conrad for unalloyed titanium. The texture of the as-swaged Ti-7.4 at. pct Al wire specimens and the changes in this texture during grain growth were in accord with those previously reported for deformed and recrystallized titanium. The Ti-15.2 at. pct Mo alloy retained the deformation texture even after recrystallization. At ^1/3 time law was found to hold for the grain growth over most of the grain sizevs time curve. The values of the activation energy for grain boundary migration were 25.2 Kcal/mole for the Ti-7.4 at. pct Al alloy and 29 Kcal/mole for the Ti-15.2 at. pct Mo alloy. These are similar to those for diffusion of Al and Mo in titanium, indicating that the diffusion of these substitutional elements controls the rate of boundary migration in these alloys. This paper is based on a presentation made at a symposium on “Recovery, Recrystallization and Grain Growth in Materials” held at the Chicago meeting of The Metallurgical Society of AIME, October 1977, under the sponsorship of the Physical Metallurgy Committee.     

Grain boundary mobility during recrystallization of copper

Average grain boundary migration rates during recrystallization of cold-deformed copper were estimated from stereological measurements. In the same material, the instantaneous driving forces for boundary migration during recrystallization were calculated from calorimetric measurements of the release of the stored energy of cold work. The migration rate dependence on driving force was analyzed in the context of grain boundary migration rate theory, and within experimental error, a linear dependence was observed. The average mobility of grain boundaries migrating during recrystallization of cold-worked copper at 121°C was calculated to be 6.31×10⁻¹⁰ (m⁴ s⁻¹ MJ⁻¹). This result was found to be consistent with single boundary, curvature-driven grain boundary mobilities measured in copper at higher temperatures. It was also demonstrated that the average grain boundary mobility was reasonably within the expectation (order of magnitude uncertainty) of the Turnbull single process model of boundary migration with a process akin to grain boundary self-diffusivity as the rate-controlling atomic mechanism.     

Grain boundary mobility during recrystallization of copper

Average grain boundary migration rates during recrystallization of cold-deformed copper were estimated from stereological measurements. In the same material, the instantaneous driving forces for boundary migration during recrystallization were calculated from calorimetric measurements of the release of the stored energy of cold work. The migration rate dependence on driving force was analyzed in the context of grain boundary migration rate theory, and within experimental error, a linear dependence was observed. The average mobility of grain boundaries migrating during recrystallization of cold-worked copper at 121 °C was calculated to be 6.31×10⁻¹⁰ (m⁴ s⁻¹ MJ⁻¹). This result was found to be consistent with single boundary, curvature-driven grain boundary mobilities measured in copper at higher temperatures. It was also demonstrated that the average grain boundary mobility was reasonably within the expectation (order of magnitude uncertainty) of the Turnbull single process model of boundary migration with a process akin to grain boundary self-diffusivity as the rate-controlling atomic mechanism.     

Static Recrystallization Kinetics and Crystallographic Texture of Nb-Stabilized Ferritic Stainless Steel Based on Orientation Imaging Microscopy

In the present study, Nb-stabilized ferritic stainless steel was prepared with annealing (430-A) and without annealing (430-NA) annealing, and the microstructure of the resulting samples was examined. The steel was then subjected to cold rolling and isothermal annealing in order to analyze its recrystallization kinetics and texture evolution. Microstructural characterization was performed by scanning and transmission electron microscopies. Recrystallization kinetics were evaluated by measuring the microhardness of the samples, and analyzing their kernel average misorientation and grain orientation spread via electron backscatter diffraction. The Avrami exponent data revealed that one-dimensional grain growth occurred owing to the migration of high-angle grain boundaries. The mean activation energies for recrystallization for 430-NA and 430-A was found to be 365 and 419 kJ mol⁻¹, respectively. The recrystallization texture was influenced by oriented nucleation and selected growth mechanisms, as well as by the Nb carbonitride distribution and grain boundary energy. The recrystallized and growing grains with the {554}〈225〉 orientation showed a dimensional advantage over the other recrystallized components. The coincident site lattice boundaries were attributed to the progression of recrystallization since the CSL numeric fraction increased as the temperature increased. The {554}〈225〉 component was associated with the ∑19a boundary, which exerted a significant control on the selective growth during the recrystallization.

     

Abnormal grain growth in bulk Cu—The dependence on initial grain size and annealing temperature

The dependence of abnormal grain growth (AGG), also termed secondary recrystallization, on annealing temperature in the range between 600 °C and 1050 °C has been observed in pure bulk Cu specimens compressed to various levels between 5 and 75 pct. There is no grain texture after annealing. The average grain size after primary recrystallization, which represents the initial grain size for secondary recrystallization during further annealing, decreases with increasing deformation and is nearly independent of the annealing temperature, in agreement with previous observations. The incubation time for AGG decreases and the number density of abnormally large grains increases with increasing deformation (hence, a decreasing initial grain size) and increasing annealing temperature. At low temperatures, most of the grain boundaries are faceted, with some facet planes probably of singular structures corresponding to cusps in the polar plots of the grain-boundary energy vs the grain-boundary normal. With increasing temperature, the grain boundaries become defaceted and, hence, atomically rough. The observed grain-growth behavior appears to be qualitatively consistent with the movement of faceted grain boundaries by two-dimensional nucleation of boundary steps. The temperature dependence appears to be consistent with roughening of grain boundaries. Before the onset of AGG, stagnant growth of the grains occurs at low rates, probably limited by slow two-dimensional nucleation of boundary steps, and, at low deformations and low annealing temperatures, the stagnant growth persists for 100 hours. The specimens with relatively small initial grain sizes (because of high deformation) show double AGG when annealed at high temperatures.     

Recrystallization in oxide-dispersion strengthened mechanically alloyed sheet steel

Systematic annealing at temperatures between 1300 °C and 1380 °C was applied to sheets of INCOLOY MA-956, an oxide-dispersion strengthened (ODS), mechanically alloyed, iron-base steel containing (in mass percent) 20.8Cr, 5.0A1, 0.5Y₂O₃, and 0.5Ti. The billets, comprised of hot isostatically pressed (“hipped”), mechanically alloyed powder, were hot- and cold-rolled to produce a 0.5-mm-thick sheet with a strong (100)«110» deformation texture. Light and transmission electron microscopy established that recrystallization initiated by nucleation at the sheet centerline. Initial rapid growth of the centerline-nucleated grains, designated stage I, resulted in plate-shaped grains oriented parallel to the rolling plane at the sheet centerline. Subsequent growth, designated stage II, was developed by planar growth fronts through the sheet thickness at a slower rate. The final product was a very coarse grain structure, sometimes with only a single grain through the sheet thickness. The recrystallization kinetics were typified by an incubation time, a temperature dependance characterized by an activation energy of 506 kJ/mole, and a decreasing rate of boundary migration with increasing time at temperature. The microstructural evolution is discussed in terms of the influences of deformation texture, residual stress, dislocation substructure, and oxide dispersion on the recrystallization process.     

On deformation-induced continuous recrystallization in a superplastic AlLiCuMgZr alloy

The microstructural changes of a warm rolled AlLi alloy occurring during static annealing and superplastic deformation at 515°C were studied by means of transmission electron microscopy. Deformation induces a continuous recrystallization with a rapid subgrain growth and a rapid increase in boundary misorientations. The higher strain rate results in a faster subgrain growth and a finer recrystallized grain size. The increasing rate of boundary misorientations and the strain at which the average misorientation reaches about 20° increase with increasing strain rate. The increase in boundary misorientations is proportional to the subgrain growth during the whole static annealing process. Deformation results in a more rapid increase in boundary misorientation with subgrain size than static annealing. Dislocation gliding plays an important role before the formation of high angle grain boundaries during superplastic deformation. The absorption of dislocations into subgrain boundaries results in a more rapid increase in boundary misorientation during deformation. Thus, the mechanism of the deformation-induced continuous recrystallization is suggested to be the generation of dislocations in grains and the absorption of gliding dislocations into subgrain boundaries.     

Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy

The effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions.

     

Diffusion induced grain boundary migration (DIGM) and liquid film migration (LFM) in an Al-2.07 wt% Cu alloy

Diffusion induced grain boundary migration (DIGM) and liquid film migration (LFM) in an Al-2.07 wt% Cu alloy during isothermal annealing after down and up quenching from an equilibrated state at 620°C in the α + liquid phase field has been studied by light and scanning electron microscopy. Down quenching to 520, 540 and 560°C resulted in grain boundaries migrating by DIGM against their curvature from one grain into another leaving behind alloyed zones. Down quenching to 590 and 605°C resulted in liquid films migrating against their curvature from one grain into another leaving behind alloyed zones. Boundaries were also observed to migrate at these temperatures. Up quenching to 630 and 640°C resulted in liquid films migrating from one grain into another leaving behind dealloyed zones. The migration distance, s, for both boundaries and liquid films was observed to decrease monotonically with annealing time (t) and to obey a power law relationship, s = Ktⁿ, with annealing time. The exponent n falls between 0.20 and 0.25. For a given annealing time the migration rates of liquid films by LFM were about twice as fast as those of grain boundaries by DIGM. With respect to driving force for boundary and liquid film migration, the coherency strain energy developed in the grain being consumed does not seem to be great enough to drive the reactions against the curvature observed.     

Recrystallization kinetics of an austenitic high-manganese steel subjected to severe plastic deformation

The evolution of the microstructure and the properties of an austenitic high-manganese steel subjected to severe deformation by cold rolling and subsequent recrystallization annealing is investigated. Cold rolling is accompanied by mechanical structural twinning and shear banding. The microhardness and microstructural analysis of annealed samples are used to study the recrystallization kinetics of the high-manganese steel. It is shown that large plastic deformation and subsequent annealing result in rapid development of recrystallization processes and the formation of an ultrafine-grained structure. A completely recrystallized structure with an average grain size of 0.64 μm forms after 30-min annealing at a temperature of 550°C. No significant structural changes are observed when the annealing time increases to 18 h, which indicates stability of the recrystallized microstructure. The steel cold rolled to 90% and annealed at 550°C for 30 min demonstrates very high strength properties: the yield strength and the tensile strength achieve 650 and 850MPa, respectively. The dependence of the strength properties of the steel on the grain size formed after rolling and recrystallization annealing is described by the Hall–Petch relation.     

循环应变-高温退火制备Al-Cu-Li合金单晶

通过循环预拉伸应变-高温退火制备Al-Cu-Li合金单晶,同时探讨循环预拉伸应变-高温退火过程中预拉伸应变量、循环应变退火次数、应变退火温度对Al-Cu-Li合金晶粒长大的影响以及晶粒长大的过程与机制.研究结果表明,通过循环预拉伸应变退火可以使得合金晶粒异常长大,并且成功制备出厘米级别的宏观粗大晶粒,其长大机理主要为应...     

Altering the time cycle of heat treatment by preannealing prior to grain growth

Preannealing is found to alter the time cycle of grain growth in lead and lead-tin alloys by modifying the kinetics of grain boundary migration. Aging at a low temperature prior to annealing at a high temperature shows the influence of residual strains in the early stage of grain growth. A model is proposed to explain the deviation of the growth kinetics from the theoretical t^1/2 law when the samples are annealed immediately after primary recrystallization in terms of a superposition of a strain-induced and a surface tension-induced grain boundary migration. Preannealing by using multiple anneals at the same temperature enables simulation of many different alloys by changing the amount of impurities segregated at grain boundaries. In zone refined material, a good agreement between the Cahn theory and the experimental results is observed; in lead-tin alloys, grain growth kinetics are understood in terms of a superposition of the influences of the solute and of other lattice defects. Formerly, Graduate Student at Laval University. This paper is based on a presentation made at a symposium on Altering the Time Cycle of Heat Treatment, held at the Philadelphia meeting of The Metallurgical Society of AIME, October 14, 1969, under the sponsorship of the IMD Heat Treatment Committee.     

Effects of austenitizing temperature on the kinetics of the proeutectoid ferrite reaction at constant austenite grain size in an Fe-C alloy

Austenitizing an Fe-0.23 pct C alloy at 1300°C and further at 900°C prior to isothermal transformation was found to increase the growth kinetics of grain boundary ferrite allotriomorphs while decreasing their rate of nucleation. A scanning Auger microprobe was used to establish that sulfur segregates to the austenite grain boundaries and does so increasingly with decreasing austenitizing temperature. A binding free energy of sulfur to these boundaries of approximately 13 kcal/mole (54.4 kj/mole) was calculated from theMcLean adsorption isotherm. The kinetic results were explained in terms of preferential reduction of the austenite grain boundary energy decreasig nucleation kinetics, and adsorption of sulfur at α:γ boundaries increasing the carbon concentration gradient in austenite driving growth.     

The Recrystallization Behavior of an Austenitic Stainless Steel Ingot Structure Due to Hot Deformation

The kinetics of recrystallization were determined metallographically for an ingot casting of AISI type 304 stainless steel deformed over a range of strains at temperatures of 1600 to 2250°F (860 to 1232°C) at several strain rates, and annealed at temperatures of 1900 to 2250°F (1037 to 1232°C). As with recrystallization following room temperature cold work, the time for recrystallization was reduced for increasing deformation and annealing temperature and for increasing strains. Decreasing the deformation temperature resulted in a reduction of time for recrystallization at a given strain and annealing temperature. Increasing strain rate resulted in a reduction of recrystallization time for a given deformation and annealing temperature. The dependence of recrystallization time upon strain rate and deformation temperature is related to the change in deformation stress encountered for the various deformation conditions.     

The Recrystallization Behavior of Unalloyed Mg and a Mg-Al Alloy

The static recrystallization behavior of pure Mg and Mg-4Al was characterized over a range of annealing temperatures. The electron backscatter diffraction grain orientation spread technique was used to quantify the level of recrystallization at various annealing times. Recrystallization kinetics were characterized using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) relationship and it was found that two sequential annealing stages exist. Stage 1 involves heterogeneous nucleation of recrystallization in regions with a high stored energy, including twins and grain boundaries, and can be represented by an Avrami exponent of n₁ ranging from 0.35 to 0.6. During Stage 2, recrystallization occurred predominately in the interior of deformed grains with incomplete recrystallization generally observed even at annealing times in excess of two weeks. The second recrystallization stage exhibited a much lower Avrami exponent, n₂, ranging from 0.02 to 0.2. Increasing the starting grain size in the pure Mg condition led to a significant delay in recrystallization. The addition of Al had a minimal effect on the recrystallization kinetics of Mg.     

Surface recrystallization of a single crystal nickel-base superalloy

The recrystallization behavior of a single crystal nickel-base superalloy was investigated by shot peening and subsequent annealing. Two kinds of recrystallization microstructures, which are intensively dependent on the annealing temperature, are shown in the nickel-base superalloy after shot peening and subsequent annealing. Surface recrystallized grains are obtained when the superalloy is anparticles occurs. Cellular recrystallization is observed after annealing at lower temperatures. Cellular structures induced by high diffusivity of the shot-peened alloy annealed at 1050℃ accords with the Johnson-Mehl-Avrami-Kolmogorov equation. The low Avrami exponent is caused by the inhomogeneous distribution of stored energy, the decreasing of stored energy during recovery, and the strong resistance of boundary migration yb γ' particles.     

The effect of fatigue deformation on microstructural evolution in a superplastic aluminum-zinc eutectoid alloy

The microstructure of a superplastic aluminum-zinc eutectoid alloy that had been fatigue tested at 100 °C and 200 °C was examined. At 100 °C, in the aluminum-rich phase, precipitate-free zones (PFZs) formed beside (Al)/(Zn) interphase boundaries because of interphase boundary migration. Interphase boundary migration was due to phase growth, which proceeded more rapidly during fatigue deformation than during annealing. At 100 °C and 200 °C, PFZs beside (Al)/(Al) grain boundaries were asymmetrical owing to grain boundary migration. The precipitation of the equilibrium zinc-rich phase in the aluminum-rich phase proceeded more rapidly during fatigue deformation than during annealing. J. W. BOWDEN, formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto, Toronto, ON.