Interface migration during recrystallization: The role of recovery and stored energy gradients
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I.
INTRODUCTION
IT is almost universally agreed that the rate of interface migration during recrystallization of pure metals is given by the product of the driving force, arising from the stored energy of cold work and the interface mobility, a parameter derived from the atomic mechanisms involved in the advance of the interface. Such a relationship can be developed by applying an absolute reaction rate formalism, as did Turnbull, m or following Machlin, (2] by invoking the thermodynamic theory of irreversible processes. The relationship may be expressed as G =MP
Ill
where G is the migration rate, M is the mobility, and P is the stored energy of deformation. The growth of a single recrystallizing grain may be described by this rate. The experimental determination of interface migration rates during recrystallization has been accomplished usually in one of two ways. The first essentially measures a local migration rate, Gl, in which the largest interceptfree length in the largest unimpinged recrystallized grain on the plane of polish is measured as a function of time. Such measurements can only be made during the early stages of recrystallization before grains impinge significantly upon one another. In most but not all of these cases, the growth is approximately linear with time; i.e., the migration rate is roughly constant. The second approach, due to Cahn and Hagel, ]31 estimates a global migration rate, (G), averaged over all the interfaces in the system. Its determination requires measurement of the global microstructural properties, X~ and Sv, the volume fraction recrystallized and the interfacial area per unit
R.A. VANDERMEER, Branch Consultant, Physical Metallurgy Branch, and B.B. RATH, Associate Director of Research, Materials Science and Component Technology Directorate, are with the Naval Research Laboratory, Washington, DC 20375-5000. Manuscript submitted September 6, 1989. METALLURGICAL TRANSACTIONS A
volume separating recrystallized grains from the unrecrystallized matrix, respectively. The working equation is (G) -
1 dXv Sv dt
[2]
where t is the annealing time. This method allows the migration rate measurements to extend over the entire range of recrystallization; i.e., 0 < Xv < 1. In most studies where the Cahn-Hagel formalism was employed, the (G) was not constant but decreased with time. An extreme example of this was reported by Speich and Fisher (4] for recrystallization of an iron-silicon alloy in which the migration rate varied inversely with annealing time. Rarely have both the local, Gl, and the interface-averaged, (G), rates been measured on the same system. Very recently, Vandermeer and Rath tS] published the results of a kinetic study of recrystallization in a deformed iron single crystal that retained, for the most part, its crystallographic orientation during deformation; e.g., visual deformation bands did not develop. Both Gt and (G) were determined in the study. Data analysis revealed that nucleation was site-saturated; that the recrystallized grains grew three-dimensionally as
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