New kinetic model for primary recrystallization of pure metals
- PDF / 167,955 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 86 Downloads / 309 Views
DUCTION
DURING the deformation of metals, the dislocation density of the material is increased by several orders of magnitude. This leads to a considerable additional hardness, which may impede further deformation necessary to shape the final product. Hence, an intermediate annealing treatment will be used to recrystallize the material and dramatically reduce the number of dislocations and, consequently, the raised hardness. However, the temperature and time required for the treatment are more or less determined by trial and error. Both parameters decide on costs and, e.g., in the case of continuous strip annealing, a good understanding of the kinetics of the recrystallization process would allow choosing the optimum temperature profile and strip speed. Due to its superficial resemblence with the crystallization of a melt, the process of recrystallization has always been described in a similar way. Starting from some nuclei, the material transforms by a nucleation and growth process and the grain boundaries of the final microstructure are established when advancing growth fronts impinge on each other. Details of the nucleation and growth conditions determine the kinetics and the final microstructure. The mathematical treatment of the problem goes back to Johnson and Mehl,[1] Avrami,[2] and Kolmogorov[3] (JMAK), who independently at about the same time developed an expression for the kinetics of the process under isothermal conditions.* Fundamentally important to the JMAK model *Thanks are due to Professor R.W. Cahn for pointing out to me that Evans[4] also independently worked on this problem at about the same time.
is spatial randomness of the nucleation sites. These sites are either all active from the start (site-saturated model) or become activated during the process (constant nucleation rate). Further, spherical growth based on a constant rate is assumed, which implies that the driving force for the transformation, i.e., the reduction of the energy stored in the
ERIK WOLDT, Senior Researcher, is with the Institut fu¨r Werkstoffe, Technische Universita¨t Braunschweig, D-38106 Braunschweig, Germany. Manuscript submitted January 10, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
elastic displacement fields around the dislocations, is not reduced by any other concurrent process. However, many experimental results are known that do not seem to follow a course predicted by the preceding model. For example, in some pure metals, the experimentally observed transformation slows down much more than anticipated after about 50 to 60 pct transformed fraction has been reached. This discrepancy provides a reason to have a fresh look at the model assumptions and to see if a modification of the model may correspond more closely to the transformation observed. II. BASICS OF THE JMAK MODEL In this section, the derivation of the standard JMAK model will be briefly reviewed. The first step of the model development is based on the so-called “extended volume.” At this stage, the impingement of all growing nuclei is neglected and
Data Loading...
