Modeling recystallization kinetics in a deformed iron single crystal
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The kinetics of recrystallization of a (111)[1 12] single crystal of pure iron deformed 70 pct by rolling were characterized experimentally at temperatures between 450 ~ and 600 ~ using quantitative metallography. The method of Laplace transforms was applied to the overall recrystallization kinetic behavior to separate nucleation from interface migration kinematics. A comprehensive nucleation and growth model was developed to explain all observations quantitatively. The model consisted of the following important features: (a) nucleation sites were distributed randomly; (b) nucleation was site-saturated and occurred with no practical incubation time at all annealing temperatures; (c) recrystallized grains grew three-dimensionally and were spheroidally shaped; (d) all recrystallized grains grew at approximately the same rate within experimental error; and (e) interface migration rates were not constant but decreased with time according to a/-0.38 law at all temperatures. The time dependency of the interface migration rate was rationalized in terms of deformation-induced, nonuniform distribution of stored energy. Recovery processes competing with recrystallization were evident at long annealing times at the two lowest annealing temperatures.
I.
INTRODUCTION
P R I M A R Y recrystallization refers to the thermally activated microstructural evolution process whereby a new set of comparatively strain-free grains nucleate and grow at the expense of a deformed matrix until it is consumed. The driving force for recrystallization arises from the stored energy of cold work, i.e., the excess dislocation and point defect densities introduced by cold deformation. The extent of recrystallization can be characterized by a global microstructural property, X v , the volume fraction recrystallized which can be estimated by stereological point counting procedures. The progress of isothermal recrystallization is frequently described by the empirical equation Xv = 1 - exp(-Bt")
[1]
where t is the annealing time and B and n are experimentally determined constants. Equation [1] has its roots in the work of Kolmogorov, 11] Avrami, [2] and Johnson and Mehl. [3] In reality, Eq. [1] is a special case of a more fundamental equation X v = 1 - exp(-Xv~)
[2]
in which Xv, x is the extended volume fraction recrystallized. The extended volume fraction is defined as that volume fraction that would result if no account were taken of impingement between growing recrystallized grains. In other words, new grains would be allowed to grow "through one another" and continued "phantom" nucleation in already recrystallized volumes would also be permitted. As such, Xv= can have values greater than one. A thorough discussion of XVex is given by Burke and Tumbull. I4] Equation [2] is rigorous only under the condition that the spatial distribution of nuclei be random. It is through Xv, x that geometric models of recrystallization can be introduced into a description of the microstructural evolution path. The studies of AnderR. A. VANDERMEER, Branch Consulta
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