Modeling the kinetics of grain-boundary-nucleated recrystallization processes after cold deformation

A physical model to predict the recrystallization kinetics of single-phase polycrystalline metals, based on a single grain representation of deformed microstructure (characterized by a mean subgrain size and mean misorientation of subgrain boundaries), is presented. The model takes into account the grain geometry, the position, and the density of the nucleation sites. The selected geometry is a regular tetrakaidecahedron, combining topological features of a random Voronoi-distribution characteristic for polycrystalline material with the advantages of a single grain calculation. The model employs empirically determined relationships from existing literature to describe the deformed microstructure and, in so doing, facilitates the prediction of the recrystallization behavior when only the deformation strain and the recrystallization temperature are known. The boundary mobility and the driving force, as well as the nucleation density, are related to the true plastic strain of deformation through the microstructure. The model also describes the effects of concurrent recovery on the overall recrystallization kinetics.     

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.

     

The Kinetics of and the Microstructure Induced by the Recrystallization of Copper

The kinetics of the recrystallization of pure copper was investigated by differential scanning calorimetry (DSC). The associated microstructural change was characterized by electron backscatter diffraction imaging (EBSD), by analyzing deformed specimens before recrystallization and specimens after partial recrystallization and after completed recrystallization. The experimental results acquired by the two methods were compared with each other and discussed in the context of the available body of literature results. The observed kinetics deviate from Johnson–Mehl–Avrami–Kolmogorov (JMAK)-like behavior. The observed grain-area distribution is unusually broad and skewed toward large grains. Comparison with mesoscopic, geometric simulations showed that previously proposed (simple) models fail to correctly describe the microstructure resulting from recrystallization, although they can successfully model the recrystallization kinetics. It was concluded that the experimental results on both the kinetics and the microstructure can be reconciled employing a recrystallization model incorporating ongoing (i.e., beyond time t = 0) nucleation and accounting for the inhomogeneous nature of the deformed material.     

The thermal and metallurgical state of steel strip during hot rolling: Part III. Microstructural evolution

A mathematical model has been developed to compute the changes in the austenite grain size during rolling in a hot-strip mill. The heat-transfer model described in the first of this series of papers has been employed to calculate the temperature distribution through the thickness which serves as a basis for the microstructure model. Single-and double-hit compression tests have been conducted at temperatures of 900 °C, 850°C, 950 °C, and 875 °C on 0.34 and 0.05 pct carbon steels to determine the degree of recrystallization by metallographic evaluation of quenched samples and by measuring the magnitude of fractional softening. The Institut de Recherches de la Sidérurgie Francaise, (IRSID) Saint Germain-en-Laye, France equation has been found to yield the best characterization of the observed recrystallization kinetics. The equations representing static recrystallization kinetics, recrystallized grain size, and grain growth kinetics have been incorporated in the model. The principle of additivity has been invoked to permit application of the isothermal recrystallization data to the nonisothermal cooling conditions. The model has been validated by comparing predicted austenite grain sizes with measurements made on samples quenched after one to four passes of rolling on the CANMET pilot mill. The austenite grain size evolution during rolling of a 0.34 pct carbon steel on Stelco’s Lake Erie Works (LEW) hot-strip mill has been computed with the aid of the model. The grain size decreased from an initial value of 180μm to 35μm in the first pass due to the high reduction of 46 pct. The changes in austenite grain size in subsequent passes were found to be small in comparison because of the lower per pass reductions. It has been shown that the equation employed to represent grain growth kinetics in the interstand region has a significant influence on the computed final grain size. Altering the rolling schedule had a negligible influence on the final grain size for a given finished gage. A 200°C increase in entry temperature to the mill resulted in a 20μm increase in final grain size, which is significant. This can be attributed to increased grain growth at the higher temperature. Formerly Graduate Student, The Centre for Metallurgical Process Engineering, The University of British Columbia Metallurgical transactions a     

Dynamic Recrystallization of Hot Deformed 3Cr2NiMnMo Steel: Modeling and Numerical Simulation

Hot compression tests of 3Cr2NiMnMo steel were performed at temperatures in the range of 850 to 1100 °C and with strain rates of 10^?2s^?1 to 1s^?1. Both the constitutive equations and the hot deformation activation energy were derived from the correlativity of flow stress, strain rate and temperature. The mathematical models of the dynamic recrystallization of 3Cr2NiMnMo steel, which include the dynamic recrystallization kinetics model and the crystallization grain size model, are based on Avrami's law and the results of thermosimulation experiments. By integrating derived dynamic recrystallization models with the thermal-mechanical coupled finite element method, the microstructure evolution in hot compressive deformation was simulated. The distribution of dynamic recrystallization grains and grain sizes were determined through a comparison of the simulation results with the experimental results. The distribution of strain and dynamic recrystallization grain is also discussed. The similarity between the experimental results and the simulated results indicates that the derived dynamic recrystallization models can be applied effectively to predict and analyze the microstructure evolution in hot deformed 3Cr2NiMnMo steel.     

Modeling recrystallization kinetics in AA1050 following simulated breakdown rolling

A physical model based on the single grain approach is refined to predict the recrystallization kinetics of a single-phase alloy following hot deformation. The model involves the original and deformed grain geometry, the characteristics of the dislocation networks formed during deformation, and the average mobility of the moving interfaces. The model properly accounts for the effect of the concurrent recovery and textural components in the deformed microstructure on the recrystallization kinetics. Plane strain compression (PSC) tests on an AA1050 aluminum alloy were used to simulate the hot rolling deformation and to provide the necessary input and validation data. Using internal state variables of known magnitude and a single value for the interfacial mobility, a very good agreement between the model predictions and the experimental data were obtained.     

Computer simulation of recrystallization—III. Influence of a dispersion of fine particles

Two-dimensional Monte Carlo simulations of recrystallization have been carried out in the presence of incoherent and immobile particles for a range of different particle fractions, a range of stored energies and a range of densities of potential nuclei (embryos). For stored energies greater than a critical value (H/J > 1) the recrystallization front can readily pass the particles leading to a random density of particles on the front and a negligible influence of particles on the recrystallization kinetics. At lower stored energies the particles pin the recrystallization front leading to incomplete recrystallization. However at very low particle fractions, when the new grain has grown much larger than the matrix grains, before meeting any particles, the new grains can complete the consumption of the deformed grains giving complete “recrystallization” by a process that appears to be similar to abnormal grain growth. Particles are, as reported previously, very effective at pinning grain boundaries, both of the deformed and recrystallized grains, when boundaries migrate under essentially the driving force of boundary energy alone. Such boundaries show a density of particles that rises rapidly from the random value found at the start of the simulation. As a consequence, particles very strongly inhibit normal grain growth after recrystallization. Such growth can only occur if the as-recrystallized grain size is less than the limiting grain size seen in the absence of recrystallization. Under these circumstances a small increment of grain growth occurs until the grain boundaries once again acquire a higher than random density of particles.     

Static recrystallization mechanisms in a coarse-grained Nb-microalloyed austenite

Static recrystallization mechanisms have been studied in a coarse-grained Nb microalloyed austenite. An austenite with a coarse grain size of 800 μm, typical of thin slab casting processes, has been deformed in torsion at a temperature of 1100 °C. After deformation, the specimens have been held for different times at this high temperature and then water quenched. The microstructural changes occurring during static recrystallization were characterized by metallographic evaluation. It has been observed that new recrystallized grains nucleate preferentially on parent austenite grain boundaries and tend to form in clusters. Once all the boundaries have been consumed, intragranular nucleation is actived at late stages of recrystallization. Clustered nucleation allows impingement to take place early during the recrystallization process, favoring grain-coarsening phenomena to occur behind the recrystallization front, which is denoted by the significant reduction in the number of grains per unit volume observed during early stages of recrystallization. Static recrystallization proceeds heterogeneously, as a result of a nonuniform distribution of stored energy in the deformed material. A continuous decrease of the average migration rate of the recrystallization front is observed, which can be ascribed to the reduction of the driving force for migration as recrystallization advances.     

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.     

The effect of small deformation on abnormal grain growth in bulk Cu

The effect of small deformation below the level (about 8 pct) required for primary recrystallization on abnormal grain growth (secondary recrystallization) has been investigated in bulk polycrystalline Cu. The starting microstructure, without any texture and with a nearly uniform grain size of 168 μm, has been obtained by compressing a cylindrical Cu specimen and recrystallizing at 800 °C. The fully recrystallized specimen shows distinct abnormal grain growth (AGG) after heat treatment at 800 °C for 12 hours. Most of the grain boundaries are faceted when observed under transmission electron microscopy (TEM), and most of the faceted segments are expected to be singular. A singular grain boundary free of defects will migrate by two-dimensional nucleation of new layers, with its velocity varying nonlinearly with the driving force arising from the grain-size difference. Such a growth mechanism is analogous to the well known process for the growth of crystals with singular surfaces from liquid or vapor. The grains slightly larger than the average size will hardly grow, because the driving force for their growth is not sufficient for nucleation of new crystal layers at the boundaries. Those grains larger than a certain critical size will, however, grow at ever-increasing rates with their increasing size, because of the sufficient driving force for two-dimensional nucleation. Such a selective accelerated growth of large grains results in overall AGG behavior. The specimen deformed to 2 pct shows AGG after heat treatment for only 5 minutes at 800 °C, and after 1 hour, large impinged grains are obtained. The grain boundaries show many extrinsic dislocations even after the heat treatments. As proposed earlier by Gleiter, Balluffi, Smith, and their colleagues, the extrinsic grain-boundary dislocations increase the grain-boundary mobilities even at low driving forces, and, hence, even those grains slightly larger than the average size can rapidly grow at the early stages of the heat treatment, in agreement with the observation. In the specimens deformed to 4 to 8 pct, below the level for primary recrystallization, all grains grow steadily without producing distinct AGG. With high densities of extrinsic dislocations at the grain boundaries even after long heat treatments, all grains can readily grow, resulting in overall growth patterns resembling the normal growth. When deformed to 20 and 50 pct, primary recrystallization occurs, and the subsequent AGG behavior depends on the grain size obtained at the completion of the primary recrystallization. Similar small-deformation effects are observed with heat treatment at 600 °C.     

Interface migration during recrystallization: The role of recovery and stored energy gradients

The interface migration rate behavior during recrystallization of a deformed (111) iron single crystal is considered in detail. A spheroidal growth, site-saturated nucleation model of recrystallization is developed for iron which quantitatively takes into account the effect of concurrent recovery in the deformed regions ahead of the advancing recrystallization interfaces. The recovery kinetics model incorporated into the growth model was devised based on the experimental data of Michalak and Paxton.[10] Explanations are advanced for the nonlinear growth of grains during recrystallization of iron. Deformation-induced stored energy gradients are proposed to explain the aspects of nonlinear growth not accounted for by recovery and are introduced into the growth model also. A localized shear band deformation mechanism developed by Harataniet al.[14] is used to rationalize the presence of stored energy gradients in the deformed (111) iron single crystal.     

Interface migration during recrystallization: The role of recovery and stored energy gradients

The interface migration rate behavior during recrystallization of a deformed iron single crystal is considered in detail. A spheroidal growth, site-saturated nucleation model of recrystallization is developed for iron which quantitatively takes into account the effect of concurrent recovery in the deformed regions ahead of the advancing recrystallization interfaces. The recovery kinetics model incorporated into the growth model was devised based on the experimental data of Michalak and Paxton.[10] Explanations are advanced for the nonlinear growth of grains during recrystallization of iron. Deformation-induced stored energy gradients are proposed to explain the aspects of nonlinear growth not accounted for by recovery and are introduced into the growth model also. A localized shear band deformation mechanism developed by Harataniet al.[14] is used to rationalize the presence of stored energy gradients in the deformed iron single crystal.     

A Physical Analysis of the Stress Relaxation Kinetics of Deformed Austenite in C‐Mn Steel

The softening kinetics following hot deformation of austenite have been characterised using the stress relaxation technique. Samples were deformed in compression for a variety of temperatures, strains and strain rates. At low strains where recovery was the only softening mechanism, the stress relaxation kinetics have been analysed using a recovery model previously proposed in the literature, the main parameters being activation energy and activation volume. The activation energy for recovery was found to be 314 kJ/mol, whilst the activation volume was inversely proportional to the internal stress. At higher strains where austenite recrystallization occurred as well, the stress relaxation kinetics were modelled using the recovery model combined with a single grain model for recrystallization. Reasonable agreement was obtained between model and experiment for a variety of deformation conditions. Analysis of the model parameters and experimental data indicated that the nucleation density for recrystallization depended only on the applied strain for the range of deformation conditions imposed. In addition the mobility of recrystallizing boundaries was best explained by solute drag due to manganese atoms.     

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The effect of deformation parameters on hot deformation of superalloy 800H was studied by means of single-pass compression test. It was found that smaller initial grain size, higher deformation temperature and lower strain rate are more easily to cause dynamic recrystallization. And when dynamic recrystallization can take place during deformation, the fraction of dynamic recrystallization increases with increasing of strain. The models of dynamic recrystallization activation energy, critical strain, dynamic recrystallization kinetics, dynamic recrystallization kinematics and grain size of dynamic recrystallization for 800H were obtained through the analysis of data obtained by single-pass compression. The variation tendency for grain size simulated by Deform-2D is consistent with metallographic statistics, and the average error is 4. 5??m. Very small average error shows that the model is consistent with practical situation and can be used to predict recrystallized grain size for 800H during thermal deformation.     

Orientation imaging microscopy studies of recrystallization in interstitial-free steel

The origin of the γ fiber recrystallization texture in interstitial-free (IF) steel developed during continuous annealing has been investigated by scanning electron microscopy (SEM) and orientation imaging microscopy (OIM). Nucleation of {111∼<uvw> oriented crystals occurs in deformation banded γ grains and therefore a comprehensive study of microstructure of cold-rolled IF steel in the sections perpendicular to the rolling and transverse directions (TDs) and the rolling plane (RP) has been carried out to understand the formation, geometry, and microstructural features of recrystallization. The RP section gave abundant evidence of orientation gradients formed in γ oriented grains that had been subject to orientation splitting to give deformation bands. These orientation gradients across a single grain are around 5 to 30 deg and this orientation difference is sufficient to form nuclei with mobile interfaces during annealing and hence to create chains of γ oriented new grains in the original hot band γ grain envelopes. A grain impingement model requiring orientation pinning is then proposed to explain how these grains, contained in deformed γ grain envelopes, grow out into their neighbors to dominate the final recrystallization texture of IF steel. The α deformed grains contain only small lattice curvatures, and therefore in-grain nucleation is rare. These grains are mostly consumed by invading γ grains toward the end of the recrystallization process.     

Modeling the microstructural changes during hot tandem rolling of AA5XXX aluminum alloys: Part I. Microstructural evolution

A comprehensive mathematical model of the hot tandem rolling process for aluminum alloys has been developed. Reflecting the complex thermomechanical and microstructural changes effected in the alloys during rolling, the model incorporated heat flow, plastic deformation, kinetics of static recrystallization, final recrystallized grain size, and texture evolution. The results of this microstructural engineering study, combining computer modeling, laboratory tests, and industrial measurements, are presented in three parts. In this Part I, laboratory measurements of static recrystallization kinetics and final recrystallized grain size are described for AA5182 and AA5052 aluminum alloys and expressed quantitatively by semiempirical equations. In Part II, laboratory measurements of the texture evolution during static recrystallization are described for each of the alloys and expressed mathematically using a modified form of the Avrami equation. Finally, Part III of this article describes the development of an overall mathematical model for an industrial aluminum hot tandem rolling process which incorporates the microstructure and texture equations developed and the model validation using industrial data. The laboratory measurements for the microstructural evolution were carried out using industrially rolled material and a state-of-the-art plane strain compression tester at Alcan International. Each sample was given a single deformation and heat treated in a salt bath at 400 °C for various lengths of time to effect different levels of recrystallization in the samples. The range of hot-working conditions used for the laboratory study was chosen to represent conditions typically seen in industrial aluminum hot tandem rolling processes, i.e., deformation temperatures of 350 °C to 500 °C, strain rates of 0.5 to 100 seconds and total strains of 0.5 to 2.0. The semiempirical equations developed indicated that both the recrystallization kinetics and the final recrystallized grain size were dependent on the deformation history of the material i.e., total strain and Zener-Hollomon parameter (Z), where and time at the recrystallization temperature.     

Orientation imaging microscopy studies of recrystallization in interstitial-free steel

The origin of the γ fiber recrystallization texture in interstitial-free (IF) steel developed during continuous annealing has been investigated by scanning electron microscopy (SEM) and orientation imaging microscopy (OIM). Nucleation of {111∼<uvw> oriented crystals occurs in deformation banded γ grains and therefore a comprehensive study of microstructure of cold-rolled IF steel in the sections perpendicular to the rolling and transverse directions (TDs) and the rolling plane (RP) has been carried out to understand the formation, geometry, and microstructural features of recrystallization. The RP section gave abundant evidence of orientation gradients formed in γ oriented grains that had been subject to orientation splitting to give deformation bands. These orientation gradients across a single grain are around 5 to 30 deg and this orientation difference is sufficient to form nuclei with mobile interfaces during annealing and hence to create chains of γ oriented new grains in the original hot band γ grain envelopes. A grain impingement model requiring orientation pinning is then proposed to explain how these grains, contained in deformed γ grain envelopes, grow out into their neighbors to dominate the final recrystallization texture of IF steel. The α deformed grains contain only small lattice curvatures, and therefore in-grain nucleation is rare. These grains are mostly consumed by invading γ grains toward the end of the recrystallization process.     

Recrystallization behavior of twin roll cast low carbon steel strip

The dynamic and static recrystallization behaviors of twin roll cast low carbon steel strip were investigated with an attempt to provide guiding deformation parameters for the on line hot rolling.In order to investigate dynamic recrystallization behavior,as cast strip was reheated and soaked with austenite grain size similar to the width level of the as cast columnar structure.Tensile test was used and the deformation temperature is in the range of 900℃to 1 100℃and strain rates are 0.01 s^-1,0.1 s^-1,1 s^-1.The activation energy and stress exponent were determined as 306kJ/mol and 4.69 respectively.The ratio of critical strain to the peak strain is 0.65,and that of critical stress to the peak stress is 0.92.The dependence of the peak strain on the initial grain size and Zener - Hollomon parameters Z isε_p =9.1×10^-4×D₀^0.48Z^0.13.The kinetics of the dynamic recrystallization and recrystallized grain size was predicted using models published.The as cast coarse austenite were dramatically refined after complete dynamic recrystallization.For static recrystallization,the tensile test was carried out on Gleeble -3500 thermo - mechanical simulator.The deformation temperature is in the range of 800℃to 1 200℃with strain rate 0.01 s^-1 to 1s^-1.The pre strain is fixed at 0.04 to 0.12 and the inter-hit delay time varies from 1 s to 3 000 s.The activation energy and Avrami exponent of static recrystallization were determined as 241 kJ/mol and 0.54 respectively.A kinetics model was proposed to describe the static recrystallization kinetics.The predicted results were in good agreement with the experimental results.     

Recrystallization and grain growth in metastable beta III titanium alloy

The progress of recrystallization and subsequent grain growth has been systematically investigated in a metastable beta titanium alloy (Ti-11.5 Mo-6 Zr-4.5 Sn). Quantitative evaluation of the kinetics of these processes over a wide range of temperature, deformation, and initial grain sizes has been performed. For a given deformation, the average grain boundary velocity, decreasing with the reciprocal of annealing time, suggests the occurrences of recovery with second order kinetics concurrent with the recrystallization. The amount of deformation, varying from 20 to 80 pct cold reduction and proportional to the stored energy of deformation in the alloy, increases the average grain boundary migration rate during recrystallization by three orders of magnitude. The temperature dependence of the recrystallization rate, however, remains unaffected by the amount of deformation at 83 kcal/mole (347 kJ/mole). The isothermal grain growth kinetics follow the power law such that the time exponent of the process remains at a value of 0.35 at most annealing temperatures. The excellent agreement between the driving force exponent of recrystallization and the time exponent of grain growth based on a model which relates the driving force dependence of the rates of both processes, clearly suggests that the kinetics of these processes are controlled by a single mechanism,i.e. impurity dependent boundary migration. 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.