Quantifying recrystallization nucleation and growth kinetics of cold-worked copper by microstructural analysis
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I.
INTRODUCTION
U N T I L recently, efforts at analytically representing recrystallization microstructures of metals were based primarily on the nucleation and growth approach of Kolmogorov,[1] Johnson and Mehl,t2] and Avramit3] (KJMA). The analytical descriptions of the isothermal kinetics of recrystallization based on this method can be characterized in terms of the Avrami equation: Vv= 1 - e x p ( - B . t " )
[1]
where Vv is the volume fraction recrystallized, t is the annealing time, and B and n are parametric constants. KJMA microstructural representations and Eq. [1] were formulated on simple suppositions about the nucleation rate, the growth rate, the grain shape, and the stipulation that impingement occurs uniformly within the deformed volume; i.e., the new recrystallized grains are randomly distributed throughout the volume. Frequently, the Avrami equation has fallen short of being able to describe recrystallization behavior over the full range of Vv, and the inability of Eq. [1] to describe the recrystallization kinetics of cold-worked copper adequately has been the subject of a number of recent investigations.W 81Sometimes the failure of the equation is indicated by negative deviations of the experimental data from straight line behavior at the longer times on plots of log In 1/(1 - Vv) vs log t; i.e., the Avrami equation overestimates the rate of
R.A. VANDERMEER, Branch Consultant, is with the Physical Metallurgy Branch, Naval Research Laboratory, Washington, DC 203755343. D. JUL~ JENSEN, Scientist, is with the Materials Department, Rise National Laboratory, DK-4000 Roskilde, Denmark. Manuscript submitted December 5, 1994.
METALLURGICAL AND MATERIALS TRANSACTIONS A
recrystallization in the later stages of the process. The implication of this is that the Avrami parameter, n, in Eq. [1] can no longer be regarded as a constant. Thus, for example, Hesselbarth et a/.[8] found that for reverse rolled copper reduced 91 pct and annealed in a calorimeter, n varied from a value between 3 and 4 at the start of recrystallization to a value close to 1 at the end of recrystallization. In other cases, the Avrami equation was regarded to have failed because the time exponent, n, had low values (~-2 or lower) over an extended range of Vv.[6,7,9] Such low values were difficult to reconcile if recrystallized grains grew in a roughly equiaxed manner as was generally thought. If growth is three-dimensional, a value 4 > n > 3 is to be expected,t2.3] from the KJMA approach. Therefore, the usefulness of Eq. [1] has come under considerable criticism, ta,53e~14] causing researchers to seek other modeling methodologies for recrystallization,t4,13-'5~ According to Hesselbarth and Gobel,[4] a qualitative explanation of this deviant kinetic behavior in copper seemed to "demand an inhomogeneous recrystallization process." In this same vein, Hutchinson et aL [7] concluded that "the variation in stored energy between different regions in coldworked metals has a very significant influence on the kinetics of recrystallization." Th
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