Modeling of recrystallization after inhomogeneous deformation
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I. INTRODUCTION
RECRYSTALLIZATION is a process that drastically affects the microstructure and mechanical properties of metallic materials. Although microstructural evolution during deformation and subsequent heat treatment leading to recovery and/or recrystallization has been the subject of research for the past several decades,[1a–4] a clear quantitative understanding of the effects of predeformation conditions, the microstructure of the deformed material (matrix), and annealing conditions on the kinetics of recrystallization and the resulting microstructure is still not complete, owing to the intrinsic complexity of the different governing mechanisms and their interaction. The classical recrystallization model as presented by Johnson and Mehl, Avrami, and Kolmogorov (JMAK model, in Reference 1b), proposes the relationship between the recrystallized volume fraction ƒRx and the time t as ƒRx ⫽ 1 ⫺ exp (⫺Btn)
[1]
where B is a parameter containing the nucleation and growth rates of the recrystallizing grains and n is the JMAK or Avrami exponent that depends on the geometry and nucleation conditions. The JMAK exponent has a value of n ⫽ 3 in three dimensions (3D) and n ⫽ 2 in two dimensions (2D) for site-saturated nucleation, and n ⫽ 4 in 3D and n ⫽ 3 in 2D for constant-rate nucleation. Experimentally determined values of the JMAK exponent are usually smaller than the theoretical values, especially when obtained at late stages of recrystallization.[1b,2] The discrepancy is inevitable due to the simplifying assumptions in the JMAK model,
XIAOYAN SONG, Humboldt Fellow, is with Physical Metallurgy, Institute of Materials Science, Darmstadt University of Technology, and the School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China. MARKUS RETTENMAYR and CLEMENS ¨ LLER, Senior Scientists, and HANS ECKART EXNER, Professor, MU are with Physical Metallurgy, Institute of Materials Science, Darmstadt University of Technology, 64287 Darmstadt, Germany. Manuscript submitted November 13, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
e.g., a homogeneous predeformation of the matrix, a random distribution of potential nucleation sites in the deformed matrix, and an isotropic growth of the nuclei with constant rate. In contrast to these assumptions, actual processing conditions lead to an inhomogeneous distribution of stored energy from predeformation, preferred (nonrandomly distributed) nucleation sites, and anisotropic growth of recrystallizing nuclei. In addition, there is the effect of the concurrent process of recovery. The influence of these factors varies strongly with the material and the actual processing conditions. In the JMAK model, some physical parameters governing the recrystallization process do not appear explicitly. For example, the energy stored in the material due to the predeformation is not introduced as such, but is implicitly contained in the nucleation and growth rates. If, as in the present article, an inhomogeneous predeformation is considered, it is necessar
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